Version 5.68.1412

                  The Mizar Mathematical Library Catalogue
                  ========================================

             (C) Copyright 1989-2021 Association of Mizar Users



 I. Axiomatics
    ----------

1. HIDDEN
   Built-in Concepts
    by Andrzej Trybulec
   Received January 1, 1989
2. TARSKI_0
   Axioms of Tarski Grothendieck Set Theory
    by Andrzej Trybulec
   Received January 1, 1989
3. TARSKI_A
   Tarski Grothendieck Set Theory -- Tarski's Axiom A
    by Andrzej Trybulec
   Received January 1, 1989

 II. Addenda
     -------

1. AXIOMS
   Strong arithmetic of real numbers
    by Andrzej Trybulec
   Received January 1, 1989
2. STRUCT_0
   Preliminaries to Structures
    by Library Committee
   Received January 6, 1995
3. ARYTM
   Preliminaries to Arithmetic
    by Library Committee
   Received December 10, 1995
   Has been removed on February 11, 2003
4. ARYTM_3
   Arithmetic of Non Negative Rational Numbers
    by Grzegorz Bancerek
   Received March 7, 1998
5. ARYTM_2
   Non negative real numbers. Part I
    by Andrzej Trybulec
   Received March 7, 1998
6. ARYTM_1
   Non negative real numbers. Part II
    by Andrzej Trybulec
   Received March 7, 1998
7. ARYTM_0
   Introduction to Arithmetic
    by Andrzej Trybulec
   Received January 9, 2003
8. NUMBERS
   Subsets of Complex Numbers
    by Andrzej Trybulec
   Received November 7, 2003
9. BINOP_2
   Binary Operations on Numbers
    by Library Committee
   Received June 21, 2004
10.NAT_D
   Divisibility of Natural Numbers
    by Grzegorz Bancerek
   Received January 3, 2007
11.VALUED_0
   Number-valued Functions
    by Library Committee
   Received November 22, 2007
12.ALGSTR_0
   Basic Algebraic Structures
    by Library Committee
   Received December 8, 2007
13.VALUED_1
   Properties of Number-valued Functions
    by Library Committee
   Received December 18, 2007
14.SCMNORM
   Normal Computers
    by Andrzej Trybulec
   Received March 3, 2008
   Has been removed on May 20, 2010
15.PRE_POLY
   Preliminaries to Polynomials
    by Andrzej Trybulec
   Received August 7, 2009
16.NORMSP_0
   Preliminaries to Normed Spaces
    by Andrzej Trybulec
   Received March 23, 2010
17.AMI_WSTD
   Weakly Standard Ordering of Instruction Locations
    by Andrzej Trybulec , Piotr Rudnicki and Artur Korni{\l}owicz
   Received April 22, 2010
18.COMPOS_1
   Composition of Machines, Instructions and Programs
    by Andrzej Trybulec
   Received May 20, 2010
19.EXTPRO_1
   Externally Programmed Machines
    by Yatsuka Nakamura and Andrzej Trybulec
   Received June 30, 2010
20.AMISTD_5
   Relocable Instructions
    by Andrzej Trybulec
   Received November 20, 2010
21.MEMSTR_0
   Memory Structures
    by Andrzej Trybulec
   Received April 28, 2011
22.KURATO_0
   On the {K}uratowski Limit Operators, I
    by Adam Grabowski
   Extracted from KURATO_2 on May 30, 2011
23.PARTFUN4
   On the Real Valued Functions
    by Artur Korni{\l}owicz
   Extracted from PARTFUN3 on May 30, 2011
24.COMPOS_0
   Commands Structure
    by Andrzej Trybulec
   Received May 20, 2010
25.SCM_INST
   On a Mathematical Model of Programs -- Preliminaries
    by Yatsuka Nakamura and Andrzej Trybulec
   Received December 29, 1992
   Extracted from AMI_2, 2012
26.SCMFSA_I
   The Instructions for SCM+FSA Computer
    by Andrzej Trybulec , Yatsuka Nakamura and Piotr Rudnicki
   Received February 3, 1996
   Extracted from SCMFSA_1, 2012
27.SCMRINGI
   The Construction of { \bf SCM } over Ring -- Preliminaries
    by Artur Korni{\l}owicz
   Received November 29, 1998
   Extracted from SCMRING1, 2012
28.SCMPDS_I
   The Instructions for the SCMPDS Computer
    by JingChao Chen
   Received June 15, 1999
   Extracted from SCPDS_1, 2012
29.SCMFSA_M
   On the memory of SCM+FSA
    by Library Committee
   Received October 1, 2011
30.COMPOS_2
   The Elementary Macroinstructions
    by Andrzej Trybulec
   Received October 1, 2011
31.MATRIX_0
   Matrices
    by Katarzyna Jankowska
   Received June 8, 1991
   Extracted from MATRIX_1, 2012
32.SCMFSA_X
   On SCM+FSA Programs
    by Andrzej Trybulec
   Received May 19, 2013
33. TARSKI
   Tarski Grothendieck Set Theory
    by Andrzej Trybulec
   Received January 1, 1989
   Moved from Axiomatics section as now it can be proved based on TARSKI_0

III. Requirements files
     ------------------

1. BOOLE
   Boolean Properties of Sets - Requirements
    by Library Committee
   Received April 30, 2002
2. SUBSET
   Basic Properties of Subsets - Requirements
    by Library Committee
   Received February 27, 2003
3. NUMERALS
   Numerals - Requirements
    by Library Committee
   Received February 27, 2003
4. REAL
   Basic Properties of Real Numbers - Requirements
    by Library Committee
   Received February 27, 2003
5. ARITHM
   Field Properties of Complex Numbers - Requirements
    by Library Committee
   Received May 29, 2003

IV. EMM - Encyclopedia of Mathematics in Mizar
    -------------------------------------------

1. XBOOLE_0
   Boolean Properties of Sets - Definitions
    by Library Committee
   Received April 6, 2002
2. XBOOLE_1
   Boolean Properties of Sets - Theorems
    by Library Committee
   Received April 8, 2002
3. XREAL_0
   Introduction to Arithmetic of Real Numbers
    by Library Committee
   Received February 11, 2003
4. XCMPLX_0
   Complex Numbers - Basic Definitions
    by Library Committee
   Received March 7, 2003
5. XCMPLX_1
   Complex Numbers - Basic Theorems
    by Library Committee
   Received April 10, 2003
6. XREAL_1
   Real Numbers - Basic Theorems
    by Library Committee
   Received February 9, 2005
7. XXREAL_0
   Introduction to Arithmetic of Extended Real Numbers
    by Library Committee
   Received January 4, 2006
8. XBOOLEAN
   On the Arithmetic of Boolean Values
    by Library Committee
   Received November 30, 2006
9. XXREAL_1
   Basic Properties of Extended Real Numbers
    by Andrzej Trybulec, Yatsuka Nakamura, Artur Korni{\l}owicz and
      Adam Grabowski
   Received January 22, 2007
10.XXREAL_2
   Suprema and Infima of Intervals of Extended Real Numbers
    by Andrzej Trybulec
   Received June 26, 2008
11.XXREAL_3
   Basic Operations on Extended Real Numbers
    by Andrzej Trybulec
   Received September 23, 2008
12.XTUPLE_0
   Kuratowski Pairs. Tuples and Projections
    by Grzegorz Bancerek, Artur Korni\l owicz and Andrzej Trybulec
   Received December 9, 2011
13.XREGULAR
   Consequences of Regularity Axiom
    by Andrzej Trybulec
   Received January 30, 2012
14.XFAMILY
   Families of Subsets
    by Andrzej Trybulec
   Received December 13, 2012

V. MML Articles
   ------------

  1. BOOLE
     Boolean Properties of Sets
      by Zinaida Trybulec and Halina \'Swi\c{e}czkowska
     Received January 6, 1989
     Has been removed on April 10, 2002
  2. ENUMSET1
     Enumerated Sets
      by Andrzej Trybulec
     Received January 8, 1989
  3. REAL_1
     Basic Properties of Real Numbers
      by Krzysztof Hryniewiecki
     Received January 8, 1989
  4. NAT_1
     The Fundamental Properties of Natural Numbers
      by Grzegorz Bancerek
     Received January 11, 1989
  5. ZFMISC_1
     Some Basic Properties of Sets
      by Czes{\l}aw Byli\'nski
     Received February 1, 1989
  6. FUNCT_1
     Functions and Their Basic Properties
      by Czes{\l}aw Byli\'nski
     Received March 3, 1989
  7. SUBSET_1
     Properties of Subsets
      by Zinaida Trybulec
     Received March 4, 1989
  8. RELAT_1
     Relations and Their Basic Properties
      by Edmund Woronowicz
     Received March 15, 1989
  9. RELAT_2
     Properties of Binary Relations
      by Edmund Woronowicz and Anna Zalewska
     Received March 15, 1989
 10. ORDINAL1
     The Ordinal Numbers. Transfinite Induction and Defining by
     Transfinite Induction
      by Grzegorz Bancerek
     Received March 20, 1989
 11. MCART_1
     Tuples, Projections and Cartesian Products
      by Andrzej Trybulec
     Received March 30, 1989
 12. FINSEQ_1
     Segments of Natural Numbers and Finite Sequences
      by Grzegorz Bancerek and Krzysztof Hryniewiecki
     Received April 1, 1989
 13. DOMAIN_1
     Domains and Their Cartesian Products
      by Andrzej Trybulec
     Received April 3, 1989
 14. WELLORD1
     The Well Ordering Relations
      by Grzegorz Bancerek
     Received April 4, 1989
 15. ZF_LANG
     A Model of ZF Set Theory Language
      by Grzegorz Bancerek
     Received April 4, 1989
 16. SETFAM_1
     Families of Sets
      by Beata Padlewska
     Received April 5, 1989
 17. FUNCT_2
     Functions from a Set to a Set
      by Czes{\l}aw Byli\'nski
     Received April 6, 1989
 18. FINSET_1
     Finite Sets
      by Agata Darmochwa\l
     Received April 6, 1989
 19. GRFUNC_1
     Graphs of Functions
      by Czes{\l}aw Byli\'nski
     Received April 14, 1989
 20. BINOP_1
     Binary Operations
      by Czes{\l}aw Byli\'nski
     Received April 14, 1989
 21. RELSET_1
     Relations Defined on Sets
      by Edmund Woronowicz
     Received April 14, 1989
 22. FINSUB_1
     Boolean Domains
      by Andrzej Trybulec and Agata Darmochwa\l
     Received April 14, 1989
 23. ZF_MODEL
     Models and Satisfiability. Defining by Structural Induction and
     Free Variables in ZF-formulae
      by Grzegorz Bancerek
     Received April 14, 1989
 24. ZF_COLLA
     The Contraction Lemma
      by Grzegorz Bancerek
     Received April 14, 1989
 25. INCSP_1
     Axioms of Incidence
      by Wojciech A. Trybulec
     Received April 14, 1989
 26. LATTICES
     Introduction to Lattice Theory
      by Stanis{\l}aw \.Zukowski
     Received April 14, 1989
 27. PRE_TOPC
     Topological Spaces and Continuous Functions
      by Beata Padlewska and Agata Darmochwa\l
     Received April 14, 1989
 28. TOPS_1
     Subsets of Topological Spaces
      by Miros{\l}aw Wysocki and Agata Darmochwa\l
     Received April 28, 1989
 29. CONNSP_1
     Connected Spaces
      by Beata Padlewska
     Received May 6, 1989
 30. FUNCT_3
     Basic Functions and Operations on Functions
      by Czes{\l}aw Byli\'nski
     Received May 9, 1989
 31. TOPS_2
     Families of Subsets, Subspaces and Mappings in Topological Spaces
      by Agata Darmochwa{\l}
     Received June 21, 1989
 32. ABSVALUE
     Some Properties of Functions Modul and Signum
      by Jan Popio{\l}ek
     Received June 21, 1989
 33. WELLORD2
     Zermelo Theorem and Axiom of Choice. The correspondence of
     well ordering relations and ordinal numbers
      by Grzegorz Bancerek
     Received June 26, 1989
 34. SEQ_1
     Real Sequences and Basic Operations on Them
      by Jaros{\l}aw Kotowicz
     Received July 4, 1989
 35. SEQ_2
     Convergent Sequences and the Limit of Sequences
      by Jaros{\l}aw Kotowicz
     Received July 4, 1989
 36. ZFMODEL1
     Properties of ZF Models
      by Grzegorz Bancerek
     Received July 5, 1989
 37. ORDINAL2
     Sequences of Ordinal Numbers. Beginnings of Ordinal Arithmetics
      by Grzegorz Bancerek
     Received July 18, 1989
 38. RLVECT_1
     Vectors in Real Linear Space
      by Wojciech A. Trybulec
     Received July 24, 1989
 39. RLSUB_1
     Subspaces and Cosets of Subspaces in Real Linear Space
      by Wojciech A. Trybulec
     Received July 24, 1989
 40. QC_LANG1
     A First Order Language
      by Piotr Rudnicki and Andrzej Trybulec
     Received August 8, 1989
 41. ORDERS_1
     Partially Ordered Sets
      by Wojciech A. Trybulec
     Received August 30, 1989
 42. RECDEF_1
     Recursive Definitions
      by Krzysztof Hryniewiecki
     Received September 4, 1989
 43. FUNCOP_1
     Binary Operations Applied to Functions
      by Andrzej Trybulec
     Received September 4, 1989
 44. VECTSP_1
     Abelian Groups, Fields and Vector Spaces
      by Eugeniusz Kusak, Wojciech Leo\'nczuk and Micha{\l} Muzalewski
     Received November 23, 1989
 45. PARSP_1
     Parallelity Spaces
      by Eugeniusz Kusak, Wojciech Leo\'nczuk and Micha{\l} Muzalewski
     Received November 23, 1989
 46. SYMSP_1
     Construction of a bilinear antisymmetric form in symplectic vector space
      by Eugeniusz Kusak, Wojciech Leo\'nczuk and Micha{\l} Muzalewski
     Received November 23, 1989
 47. ORTSP_1
     Construction of a bilinear symmetric form in orthogonal vector space
      by Eugeniusz Kusak, Wojciech Leo\'nczuk and Micha{\l} Muzalewski
     Received November 23, 1989
 48. PARTFUN1
     Partial Functions
      by Czes{\l}aw Byli\'nski
     Received September 18, 1989
 49. SETWISEO
     Semilattice Operations on Finite Subsets
      by Andrzej Trybulec
     Received September 18, 1989
 50. CARD_1
     Cardinal Numbers
      by Grzegorz Bancerek
     Received September 19, 1989
 51. COMPTS_1
     Compact Spaces
      by Agata Darmochwa{\l}
     Received September 19, 1989
 52. ORDERS_2
     Kuratowski - Zorn Lemma
      by Wojciech A. Trybulec and Grzegorz Bancerek
     Received September 19, 1989
 53. RLSUB_2
     Operations on Subspaces in Real Linear Space
      by Wojciech A. Trybulec
     Received September 20, 1989
 54. PROB_1
     $\sigma$-Fields and Probability
      by Andrzej N\c{e}dzusiak
     Received October 16, 1989
 55. CAT_1
     Introduction to Categories and Functors
      by Czes{\l}aw Byli\'nski
     Received October 25, 1989
 56. TREES_1
     Introduction to Trees
      by Grzegorz Bancerek
     Received October 25, 1989
 57. WELLSET1
     Zermelo's Theorem
      by Bogdan Nowak and S{\l}awomir Bia{\l}ecki
     Received October 27, 1989
 58. REALSET1
     Group and Field Definitions
      by J\'ozef Bia{\l}as
     Received October 27, 1989
 59. EQREL_1
     Equivalence Relations and Classes of Abstraction
      by Konrad Raczkowski and Pawe{\l} Sadowski
     Received November 16, 1989
 60. SQUARE_1
     Some Properties of Real Numbers.
     Operations: min, max, square, and square root
      by Andrzej Trybulec and Czes{\l}aw Byli\'nski
     Received November 16, 1989
 61. QC_LANG2
     Connectives and Subformulae of the First Order Language
      by Grzegorz Bancerek
     Received November 23, 1989
 62. QC_LANG3
     Variables in Formulae of the First Order Language
      by Czes{\l}aw Byli\'nski and Grzegorz Bancerek
     Received November 23, 1989
 63. SEQM_3
     Monotone Real Sequences. Subsequences
      by Jaros{\l}aw Kotowicz
     Received November 23, 1989
 64. SEQ_4
     Convergent Real Sequences. Upper and Lower Bound of Sets of Real Numbers
      by Jaros{\l}aw Kotowicz
     Received November 23, 1989
 65. MIDSP_1
     Midpoint algebras
      by Micha{\l} Muzalewski
     Received November 26, 1989
 66. QMAX_1
     The Fundamental Logic Structure in Quantum Mechanics
      by Pawe{\l} Sadowski, Andrzej Trybulec and Konrad Raczkowski
     Received December 18, 1989
 67. FRAENKEL
     Function Domains and Fr{\ae}nkel Operator
      by Andrzej Trybulec
     Received February 7, 1990
 68. INT_1
     Integers
      by Micha{\l} J. Trybulec
     Received February 7, 1990
 69. COMPLEX1
     The Complex Numbers
      by Czes{\l}aw Byli\'nski
     Received March 1, 1990
 70. ORDINAL3
     Ordinal Arithmetics
      by Grzegorz Bancerek
     Received March 1, 1990
 71. FUNCT_4
     The Modification of a Function by a Function
     and the Iteration of the Composition of a Function
      by Czes{\l}aw Byli\'nski
     Received March 1, 1990
 72. FINSEQ_2
     Finite Sequences and Tuples of Elements of a Non-empty Sets
      by Czes{\l}aw Byli\'nski
     Received March 1, 1990
 73. FUNCT_5
     Curried and Uncurried Functions
      by Grzegorz Bancerek
     Received March 6, 1990
 74. CARD_2
     Cardinal Arithmetics
      by Grzegorz Bancerek
     Received March 6, 1990
 75. PARSP_2
     Fano-Desargues Parallelity Spaces
      by Eugeniusz Kusak and Wojciech Leo\'nczuk
     Received March 23, 1990
 76. FUNCSDOM
     Real Functions Spaces
      by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
     Received March 23, 1990
 77. CLASSES1
     Tarski's Classes and Ranks
      by Grzegorz Bancerek
     Received March 23, 1990
 78. FINSEQ_3
     Non-contiguous Substrings and One-to-one Finite Sequences
      by Wojciech A. Trybulec
     Received April 8, 1990
 79. FINSEQ_4
     Pigeon Hole Principle
      by Wojciech A. Trybulec
     Received April 8, 1990
 80. RLVECT_2
     Linear Combinations in Real Linear Space
      by Wojciech A. Trybulec
     Received April 8, 1990
 81. CARD_3
     K\"onig's Theorem
      by Grzegorz Bancerek
     Received April 10, 1990
 82. CLASSES2
     Universal Classes
      by Bogdan Nowak and Grzegorz Bancerek
     Received April 10, 1990
 83. ANALOAF
     Analytical Ordered Affine Spaces
      by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
     Received April 11, 1990
 84. METRIC_1
     Metric Spaces
      by Stanis{\l}awa Kanas, Adam Lecko and Mariusz Startek
     Received May 3, 1990
 85. DIRAF
     Ordered Affine Spaces Defined in Terms of Directed Parallelity - part I
      by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
     Received May 4, 1990
 86. AFF_1
     Parallelity and Lines in Affine Spaces
      by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
     Received May 4, 1990
 87. AFF_2
     Classical Configurations in Affine Planes
      by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
     Received April 13, 1990
 88. AFF_3
     Affine Localizations of Desargues Axiom
      by Eugeniusz Kusak, Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
     Received April 26, 1990
 89. FINSEQOP
     Binary Operations Applied to Finite Sequences
      by Czes{\l}aw Byli\'nski
     Received May 4, 1990
 90. SETWOP_2
     Semigroup operations on finite subsets
      by Czes{\l}aw Byli\'nski
     Received May 4, 1990
 91. COLLSP
     The Collinearity Structure
      by Wojciech Skaba
     Received May 9, 1990
 92. RVSUM_1
     The Sum and Product of Finite Sequences of Real Numbers
      by Czes{\l}aw Byli\'nski
     Received May 11, 1990
 93. CQC_LANG
     A Classical First Order Language
      by Czes{\l}aw Byli\'nski
     Received May 11, 1990
 94. PASCH
     Classical and Non--classical Pasch Configurations in Ordered Affine Planes
      by Henryk Oryszczyszyn, Krzysztof Pra\.zmowski and
         Ma{\l}gorzata Pra\.zmowska
     Received May 16, 1990
 95. REAL_LAT
     The Lattice of Real Numbers. The Lattice of Real Functions
      by Marek Chmur
     Received May 22, 1990
 96. TDGROUP
     A Construction of an Abstract Space of Congruence of Vectors
      by Grzegorz Lewandowski and Krzysztof Pra\.zmowski
     Received May 23, 1990
 97. CQC_THE1
     A First-Order Predicate Calculus.
     Axiomatics, the Consequence Operation and a Concept of Proof
      by Agata Darmochwa{\l}
     Received May 25, 1990
 98. PARTFUN2
     Partial Functions from a Domain to a Domain
      by Jaros{\l}aw Kotowicz
     Received May 31, 1990
 99. RFUNCT_1
     Partial Functions from a Domain to the Set of Real Numbers
      by Jaros{\l}aw Kotowicz
     Received May 27, 1990
100. ORDINAL4
     Increasing and Continuous Ordinal Sequences
      by Grzegorz Bancerek
     Received May 31, 1990
101. TRANSGEO
     Transformations in Affine Spaces
      by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
     Received May 31, 1990
102. CAT_2
     Subcategories and Products of Categories
      by Czes{\l}aw Byli\'nski
     Received May 31, 1990
103. MARGREL1
     Many-Argument Relations
      by Edmund Woronowicz
     Received June 1, 1990
104. VALUAT_1
     Interpretation and Satisfiability in the First Order Logic
      by Edmund Woronowicz
     Received June 1, 1990
105. PROB_2
     Probability. Independence of Events and Conditional Probability
      by Andrzej N\c{e}dzusiak
     Received June 1, 1990
106. TRANSLAC
     Translations in Affine Planes
      by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
     Received June 12, 1990
107. RPR_1
     Introduction to Probability
      by Jan Popio{\l}ek
     Received June 13, 1990
108. ANPROJ_1
     A Construction of Analytical Projective Space
      by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
     Received June 15, 1990
109. ANPROJ_2
     Projective Spaces - Part I
      by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
     Received June 15, 1990
110. RCOMP_1
     Topological Properties of Subsets in Real Numbers
      by Konrad Raczkowski and Pawe{\l} Sadowski
     Received June 18, 1990
111. RFUNCT_2
     Properties of Real Functions
      by Jaros{\l}aw Kotowicz
     Received June 18, 1990
112. FCONT_1
     Real Function Continuity
      by Konrad Raczkowski and Pawe{\l} Sadowski
     Received June 18, 1990
113. FCONT_2
     Real Function Uniform Continuity
      by Jaros{\l}aw Kotowicz and Konrad Raczkowski
     Received June 18, 1990
114. FDIFF_1
     Real Function Differentiability
      by Konrad Raczkowski and Pawe{\l} Sadowski
     Received June 18, 1990
115. ROLLE
     Average Value Theorems for Real Functions of One Variable
      by Jaros{\l}aw Kotowicz, Konrad Raczkowski and Pawe{\l} Sadowski
     Received June 18, 1990
116. VECTSP_2
     Construction of Rings and Left-, Right-, and Bi-Modules over a Ring
      by Micha{\l} Muzalewski
     Received June 20, 1990
117. REALSET2
     Properties of Fields
      by J\'ozef Bia{\l}as
     Received June 20, 1990
118. FILTER_0
     Filters - Part I. Implicative Lattices
      by Grzegorz Bancerek
     Received July 3, 1990
119. GROUP_1
     Groups
      by Wojciech A. Trybulec
     Received July 3, 1990
120. INT_2
     The Divisibility of Integers and Integer Relatively Primes
      by Rafa{\l} Kwiatek and Grzegorz Zwara
     Received July 10, 1990
121. ALGSTR_1
     From Loops to Abelian Multiplicative Groups with Zero
      by Micha{\l} Muzalewski and Wojciech Skaba
     Received July 10, 1990
122. RAT_1
     Basic Properties of Rational Numbers
      by Andrzej Kondracki
     Received July 10, 1990
123. RLVECT_3
     Basis of Real Linear Space
      by Wojciech A. Trybulec
     Received July 10, 1990
124. VECTSP_3
     Finite Sums of Vectors in Vector Space
      by Wojciech A. Trybulec
     Received July 12, 1990
     Has been removed on June 30, 2010
125. GROUP_2
     Subgroup and Cosets of Subgroups. Lagrange theorem
      by Wojciech A. Trybulec
     Received July 23, 1990
126. VECTSP_4
     Subspaces and Cosets of Subspaces in Vector Space
      by Wojciech A. Trybulec
     Received July 27, 1990
127. VECTSP_5
     Operations on Subspaces in Vector Space
      by Wojciech A. Trybulec
     Received July 27, 1990
128. VECTSP_6
     Linear Combinations in Vector Space
      by Wojciech A. Trybulec
     Received July 27, 1990
129. VECTSP_7
     Basis of Vector Space
      by Wojciech A. Trybulec
     Received July 27, 1990
130. NEWTON
     Factorial and Newton coeffitients
      by Rafa{\l} Kwiatek
     Received July 27, 1990
131. ANALMETR
     Analytical Metric Affine Spaces and Planes
      by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
     Received August 10, 1990
132. ANPROJ_3
     Projective Spaces - part II
      by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
     Received August 10, 1990
     Has been removed on March 7, 1995
133. ANPROJ_4
     Projective Spaces - part III
      by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
     Received August 10, 1990
     Has been removed on March 7, 1995
134. ANPROJ_5
     Projective Spaces - part IV
      by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
     Received August 10, 1990
     Has been removed on March 7, 1995
135. ANPROJ_6
     Projective Spaces - part V
      by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
     Received August 10, 1990
     Has been removed on March 7, 1995
136. ANPROJ_7
     Projective Spaces - part VI
      by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
     Received August 10, 1990
     Has been removed on March 7, 1995
137. NET_1
     Some Elementary Notions of the Theory of Petri Nets
      by Waldemar Korczy\'nski
     Received August 10, 1990
138. GROUP_3
     Classes of Conjugation. Normal Subgroups
      by Wojciech A. Trybulec
     Received August 10, 1990
139. ZF_LANG1
     Replacing of Variables in Formulas of ZF Theory
      by Grzegorz Bancerek
     Received August 10, 1990
140. ZF_REFLE
     The Reflection Theorem
      by Grzegorz Bancerek
     Received August 10, 1990
141. FINSOP_1
     Binary Operations on Finite Sequences
      by Wojciech A. Trybulec
     Received August 10, 1990
142. LATTICE2
     Finite Join and Finite Meet, and Dual Lattices
      by Andrzej Trybulec
     Received August 10, 1990
143. ZFREFLE1
     Consequences of the Reflection Theorem
      by Grzegorz Bancerek
     Received August 13, 1990
144. PROJDES1
     Desargues Theorem In Projective 3-Space
      by Eugeniusz Kusak
     Received August 13, 1990
145. LIMFUNC1
     The Limit of a Real Function at Infinity. Halflines.
     Real Sequence Divergent to Infinity
      by Jaros{\l}aw Kotowicz
     Received August 20, 1990
146. LIMFUNC2
     One-Side Limits of a Real Function at a Point
      by Jaros{\l}aw Kotowicz
     Received August 20, 1990
147. GROUP_4
     Lattice of Subgroups of a Group. Frattini Subgroup
      by Wojciech A. Trybulec
     Received August 22, 1990
148. REAL_2
     Equalities and Inequalities in Real Numbers. Continuation of Real_1
      by Andrzej Kondracki
     Received September 5, 1990
     Has been removed on December 19, 2008
149. CARD_4
     Countable Sets and Hessenberg's Theorem
      by Grzegorz Bancerek
     Received September 5, 1990
150. LIMFUNC3
     The Limit of a Real Function at a Point
      by Jaros{\l}aw Kotowicz
     Received September 5, 1990
151. LIMFUNC4
     The Limit of a Composition of Real Functions
      by Jaros{\l}aw Kotowicz
     Received September 5, 1990
152. CONNSP_2
     Locally Connected Spaces
      by Beata Padlewska
     Received September 5, 1990
153. ALGSEQ_1
     Construction of Finite Sequences over Ring and Left-, Right-,
     and Bi-Modules over a Ring
      by Micha{\l} Muzalewski and Les{\l}aw W. Szczerba
     Received September 13, 1990
154. TOLER_1
     Relations of Tolerance
      by Krzysztof Hryniewiecki
     Received September 20, 1990
155. NORMSP_1
     Real Normed Space
      by Jan Popio{\l}ek
     Received September 20, 1990
156. SCHEME1
     Schemes of Existence of some Types of Functions
      by Jaros{\l}aw Kotowicz
     Received September 21, 1990
157. PREPOWER
     Integer and Rational Exponents
      by Konrad Raczkowski
     Received September 21, 1990
158. HOMOTHET
     Homotheties and Shears in Affine Planes
      by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
     Received September 21, 1990
159. AFVECT0
     Directed Geometrical Bundles and Their Analytical Representation
      by Grzegorz Lewandowski, Krzysztof Pra\.zmowski and Bo\.zena Lewandowska
     Received September 24, 1990
160. ZFMODEL2
     Definable Functions
      by Grzegorz Bancerek
     Received September 26, 1990
161. LUKASI_1
     Propositional Calculus
      by Grzegorz Bancerek, Agata Darmochwa\l and Andrzej Trybulec
     Received September 26, 1990
162. COMPLSP1
     Complex Spaces
      by Czes{\l}aw Byli\'nski and Andrzej Trybulec
     Received September 27, 1990
163. REALSET3
     Several Properties of Fields. Field Theory
      by J\'ozef Bia{\l}as
     Received September 27, 1990
164. SUPINF_1
     Infimum and Supremum of the Set of Real Numbers. Measure Theory
      by J\'ozef Bia{\l}as
     Received September 27, 1990
165. SUPINF_2
     Series of Positive Real Numbers. Measure Theory
      by J\'ozef Bia{\l}as
     Received September 27, 1990
166. ALGSTR_2
     From Double Loops to Fields
      by Wojciech Skaba and Micha{\l} Muzalewski
     Received September 27, 1990
167. METRIC_3
     Metrics in Cartesian Product
      by Stanis{\l}awa Kanas and Jan Stankiewicz
     Received September 27, 1990
168. SUB_METR
     Submetric Spaces - Part I
      by Adam Lecko and Mariusz Startek
     Received September 27, 1990
     Has been removed on March 23, 2010
169. METRIC_2
     On Pseudometric Spaces
      by Adam Lecko and Mariusz Startek
     Received September 28, 1990
170. POWER
     Real Exponents and Logarithms
      by Konrad Raczkowski and Andrzej N\c{e}dzusiak
     Received October 1, 1990
171. HESSENBE
     Hessenberg Theorem
      by Eugeniusz Kusak and Wojciech Leo\'nczuk
     Received October 2, 1990
172. MULTOP_1
     Three-Argument Operations and Four-Argument Operations
      by Michal Muzalewski and Wojciech Skaba
     Received October 2, 1990
173. INCPROJ
     Incidence Projective Spaces
      by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
     Received October 4, 1990
174. AFVECT01
     One-Dimensional Congruence of Segments, Basic Facts and Midpoint Relation
      by Barbara Konstanta, Urszula Kowieska, Grzegorz Lewandowski and
         Krzysztof Pra\.zmowski
     Received October 4, 1990
175. NORMFORM
     Algebra of Normal Forms
      by Andrzej Trybulec
     Received October 5, 1990
176. O_RING_1
     Ordered Rings - Part I
      by Micha{\l} Muzalewski and Les{\l}aw W. Szczerba
     Received October 11, 1990
177. O_RING_2
     Ordered Rings - Part II
      by Micha{\l} Muzalewski and Les{\l}aw W. Szczerba
     Received October 11, 1990
     Has been removed on January 22, 2007
178. O_RING_3
     Ordered Rings - Part III
      by Micha{\l} Muzalewski and Les{\l}aw W. Szczerba
     Received October 11, 1990
     Has been removed on January 22, 2007
179. MCART_2
     N-Tuples and Cartesian Products for n=5
      by Micha{\l} Muzalewski and Wojciech Skaba
     Received October 13, 1990
     Has been removed on December 9, 2011
180. MCART_3
     Tuples and Cartesian Products for n=6
      by Michal Muzalewski and Wojciech Skaba
     Received October 15, 1990
     Has been removed on March 3, 2009
181. MCART_4
     Tuples and Cartesian Products for n=7
      by Michal Muzalewski and Wojciech Skaba
     Received October 15, 1990
     Has been removed on December 18, 2007
182. MCART_5
     Tuples and Cartesian Products for n=8
      by Michal Muzalewski and Wojciech Skaba
     Received October 15, 1990
     Has been removed on March 3, 2008
183. MCART_6
     Tuples and Cartesian Products for n=9
      by Michal Muzalewski and Wojciech Skaba
     Received October 15, 1990
     Has been removed on December 8, 2007
184. ALGSTR_3
     Ternary Fields
      by Micha{\l} Muzalewski and Wojciech Skaba
     Received October 15, 1990
185. MEASURE1
     The $\sigma$-additive Measure Theory
      by J\'ozef Bia{\l}as
     Received October 15, 1990
186. PROJRED1
     Incidence Projective Space (a reduction theorem in a plane)
      by Eugeniusz Kusak and Wojciech Leo\'nczuk
     Received October 16, 1990
187. MOD_1
     Groups, Rings, Left- and Right-Modules
      by Micha{\l} Muzalewski and Wojciech Skaba
     Received October 22, 1990
     Has been removed on September 23, 2008
188. LMOD_1
     Finite Sums of Vectors in Left Module over Associative Ring
      by Micha{\l} Muzalewski and Wojciech Skaba
     Received October 22, 1990
     Has been removed on January 6, 1995
189. LMOD_2
     Submodules and Cosets of Submodules in Left Module over Associative Ring
      by Micha{\l} Muzalewski and Wojciech Skaba
     Received October 22, 1990
     Has been removed on May 13, 1995
190. LMOD_3
     Operations on Submodules in Left Module over Associative Ring
      by Micha{\l} Muzalewski and Wojciech Skaba
     Received October 22, 1990
     Has been removed on May 13, 1995
191. LMOD_4
     Linear Combinations in Left Module over Associative Ring
      by Micha{\l} Muzalewski and Wojciech Skaba
     Received October 22, 1990
     Has been removed on November 19, 2003
192. LMOD_5
     Linear Independence in Left Module over Domain
      by Micha{\l} Muzalewski and Wojciech Skaba
     Received October 22, 1990
     Has been removed on January 1, 2015
193. RMOD_1
     Finite Sums of Vectors in Right Module over Associative Ring
      by Michal Muzalewski and Wojciech Skaba
     Received October 22, 1990
     Has been removed on November 19, 2003
194. RMOD_2
     Submodules and Cosets of Submodules in Right Module over Associative Ring
      by Michal Muzalewski and Wojciech Skaba
     Received October 22, 1990
195. RMOD_3
     Operations on Submodules in Right Module over Associative Ring
      by Michal Muzalewski and Wojciech Skaba
     Received October 22, 1990
196. RMOD_4
     Linear Combinations in Right Module over Associative Ring
      by Michal Muzalewski and Wojciech Skaba
     Received October 22, 1990
197. RMOD_5
     Linear Independence in Right Module over Domain
      by Michal Muzalewski and Wojciech Skaba
     Received October 22, 1990
     Has been removed on June 26, 2008
198. PROCAL_1
     Calculus of Propositions
      by Jan Popio{\l}ek and Andrzej Trybulec
     Received October 23, 1990
199. CQC_THE2
     Calculus of Quantifiers. Deduction Theorem
      by Agata Darmochwa\l
     Received October 24, 1990
200. GEOMTRAP
     A Construction of Analytical Ordered Trapezium Spaces
      by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
     Received October 29, 1990
201. PROJRED2
     On Projections in Projective Planes. Part II
      by Eugeniusz Kusak, Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
     Received October 31, 1990
202. CONAFFM
     Metric-Affine Configurations in Metric Affine Planes -  Part I
      by Jolanta \'Swierzy\'nska and Bogdan \'Swierzy\'nski
     Received October 31, 1990
203. CONMETR
     Metric-Affine Configurations in Metric Affine Planes - Part II
      by Jolanta \'Swierzy\'nska and Bogdan \'Swierzy\'nski
     Received October 31, 1990
204. PAPDESAF
     Fanoian, Pappian and Desarguesian Affine Spaces
      by Krzysztof Pra\.zmowski
     Received November 16, 1990
205. PARDEPAP
     Elementary Variants of Affine Configurational Theorems
      by Krzysztof Pra\.zmowski and Krzysztof Radziszewski
     Received November 30, 1990
206. SEMI_AF1
     Semi-Affine Space
      by Eugeniusz Kusak and Krzysztof Radziszewski
     Received November 30, 1990
207. AFF_4
     Planes in Affine Spaces
      by Wojciech Leo\'nczuk, Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
     Received December 5, 1990
208. GRAPH_1
     Graphs
      by Krzysztof Hryniewiecki
     Received December 5, 1990
209. ZF_FUND1
     Mostowski's Fundamental Operations - Part I
      by Andrzej Kondracki
     Received December 17, 1990
210. AFPROJ
     A Projective Closure and Projective Horizon of an Affine Space
      by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
     Received December 17, 1990
211. SCHEMS_1
     Schemes
      by Stanis\l aw T. Czuba
     Received December 17, 1990
212. HEYTING1
     Algebra of Normal Forms Is a Heyting Algebra
      by Andrzej Trybulec
     Received January 3, 1991
213. TREES_2
     K\"onig's Lemma
      by Grzegorz Bancerek
     Received January 10, 1991
214. FCONT_3
     Monotonic and Continuous Real Function
      by Jaros{\l}aw Kotowicz
     Received January 10, 1991
215. FDIFF_2
     Real Function Differentiability - Part II
      by Jaros{\l}aw Kotowicz and Konrad Raczkowski
     Received January 10, 1991
216. PRELAMB
     Preliminaries to the Lambek Calculus
      by Wojciech Zielonka
     Received February 13, 1991
217. OPPCAT_1
     Opposite Categories and Contravariant Functors
      by Czes\l aw Byli\'nski
     Received February 13, 1991
218. ZF_FUND2
     Mostowski's Fundamental Operations - Part II
      by Grzegorz Bancerek and Andrzej Kondracki
     Received February 15, 1991
219. EUCLMETR
     Fundamental Types of Metric Affine Spaces
      by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
     Received April 17, 1991
220. FILTER_1
     Filters - Part II. Quotient Lattices Modulo Filters and
     Direct Product of Two Lattices
      by Grzegorz Bancerek
     Received April 19, 1991
221. CONMETR1
     Shear Theorems and Their Role in Affine Geometry
      by Jolanta \'Swierzy\'nska and Bogdan \'Swierzy\'nski
     Received April 19, 1991
222. SERIES_1
     Series
      by Konrad Raczkowski and Andrzej N\c{e}dzusiak
     Received October 15, 1990
223. NAT_LAT
     The Lattice of Natural Numbers and The Sublattice of it.
     The Set of Prime Numbers
      by Marek Chmur
     Received April 26, 1991
224. GROUP_5
     Commutator and Center of a Group
      by Wojciech A. Trybulec
     Received May 15, 1991
225. NATTRA_1
     Natural Transformations. Discrete Categories
      by Andrzej Trybulec
     Received May 15, 1991
226. MATRIX_1
     Matrices. Abelian Group of Matrices
      by Katarzyna Jankowska
     Received June 8, 1991
227. PCOMPS_1
     Paracompact and Metrizable Spaces
      by Leszek Borys
     Received June 8, 1991
228. MIDSP_2
     Atlas of Midpoint Algebra
      by Micha{\l} Muzalewski
     Received June 21, 1991
229. MEASURE2
     Several Properties of the $\sigma$-additive Measure
      by J\'ozef Bia{\l}as
     Received July 3, 1991
230. METRIC_4
     Metrics in the Cartesian Product - Part II
      by Stanis\l awa Kanas and Adam Lecko
     Received July 8, 1991
     Has been removed on March 30, 2010
231. ALI2
     Fix Point Theorem for Compact Spaces
      by Alicia de la Cruz
     Received July 17, 1991
232. QUIN_1
     Quadratic Inequalities
      by Jan Popio\l ek
     Received July 19, 1991
233. BHSP_1
     Introduction to Banach and Hilbert spaces - Part I
      by Jan Popio{\l}ek
     Received July 19, 1991
234. BHSP_2
     Introduction to Banach and Hilbert spaces - Part II
      by Jan Popio{\l}ek
     Received July 19, 1991
235. BHSP_3
     Introduction to Banach and Hilbert spaces - Part III
      by Jan Popio{\l}ek
     Received July 19, 1991
236. ENS_1
     Category Ens
      by Czes{\l}aw Byli\'nski
     Received August 1, 1991
237. BORSUK_1
     A Borsuk Theorem on Homotopy Types
      by Andrzej Trybulec
     Received August 1, 1991
238. FUNCT_6
     Cartesian Product of Functions
      by Grzegorz Bancerek
     Received September 30, 1991
239. MODAL_1
     Introduction to Modal Propositional Logic
      by Alicia de la Cruz
     Received September 30, 1991
240. TBSP_1
     Totally Bounded Metric Spaces
      by Alicia de la Cruz
     Received September 30, 1991
241. GRCAT_1
     Categories of Groups
      by Michal Muzalewski
     Received October 3, 1991
242. GROUP_6
     Homomorphisms and Isomorphisms of Groups. Quotient Group
      by Wojciech A. Trybulec and Micha{\l} J. Trybulec
     Received October 3, 1991
243. MOD_2
     Rings and Modules - Part II
      by Michal Muzalewski
     Received October 18, 1991
244. MOD_3
     Free Modules
      by Michal Muzalewski
     Received October 18, 1991
245. ANALORT
     Oriented Metric-Affine Plane - Part I
      by Jaroslaw Zajkowski
     Received October 24, 1991
246. EUCLID
     The Euclidean Space
      by Agata Darmochwa{\l}
     Received November 21, 1991
247. TOPMETR
     Metric Spaces as Topological Spaces - Fundamental Concepts
      by Agata Darmochwa{\l} and Yatsuka Nakamura
     Received November 21, 1991
248. HEINE
     Heine--Borel's Covering Theorem
      by Agata Darmochwa{\l} and Yatsuka Nakamura
     Received November 21, 1991
249. TOPMETR2
     Some Facts about Union of Two Functions and Continuity of Union of Functions
      by Yatsuka Nakamura and Agata Darmochwa{\l}
     Received November 21, 1991
250. TOPREAL1
     The Topological Space ${\calE}^2_{\rm T}$.
     Arcs, Line Segments and Special Polygonal Arcs
      by Agata Darmochwa{\l} and Yatsuka Nakamura
     Received November 21, 1991
251. GR_CY_1
     Cyclic Groups and Some of Their Properties - Part I
      by Dariusz Surowik
     Received November 22, 1991
252. ISOCAT_1
     Isomorphisms of Categories
      by Andrzej Trybulec
     Received November 22, 1991
253. CQC_SIM1
     Similarity of Formulae
      by Agata Darmochwa{\l} and Andrzej Trybulec
     Received November 22, 1991
254. RINGCAT1
     Category of Rings
      by Micha{\l} Muzalewski
     Received December 5, 1991
255. MODCAT_1
     Category of Left Modules
      by Micha{\l} Muzalewski
     Received December 12, 1991
256. FDIFF_3
     Real Function One-Side Differantiability
      by Ewa Burakowska and Beata Madras
     Received December 12, 1991
257. METRIC_6
     Sequences in Metric Spaces
      by Stanis{\l}awa Kanas and Adam Lecko
     Received December 12, 1991
258. TOPREAL2
     The Topological Space ${\calE}^2_{\rm T}$. Simple Closed Curves
      by Agata Darmochwa{\l} and Yatsuka Nakamura
     Received December 30, 1991
259. TSEP_1
     Separated and Weakly Separated Subspaces of Topological Spaces
      by Zbigniew Karno
     Received January 8, 1992
260. SYSREL
     Some Properties of Binary Relations
      by Waldemar Korczy\'nski
     Received January 17, 1992
261. FF_SIEC
     Definitions of Petri Net - Part I
      by Waldemar Korczy\'nski
     Received January 31, 1992
262. E_SIEC
     Definitions of Petri Net - Part II
      by Waldemar Korczy\'nski
     Received January 31, 1992
263. S_SIEC
     Definitions of Petri Net - Part III
      by Waldemar Korczy\'nski
     Received January 31, 1992
     Has been removed on November 19, 2003
264. L_HOSPIT
     The de l'Hospital Theorem
      by Ma{\l}gorzata Korolkiewicz
     Received February 20, 1992
265. COMMACAT
     Comma Category
      by Grzegorz Bancerek and Agata Darmochwa\l
     Received February 20, 1992
266. LANG1
     Context-Free Grammar - Part 1
      by Patricia L. Carlson and Grzegorz Bancerek
     Received February 21, 1992
267. MEASURE3
     Completeness of the $\sigma$-Additive Measure. Measure Theory
      by J\'ozef Bia{\l}as
     Received February 22, 1992
268. BHSP_4
     Series in Banach and Hilbert Spaces
      by El\.zbieta Kraszewska and Jan Popio{\l}ek
     Received April 1, 1992
269. CAT_3
     Products and Coproducts in Categories
      by Czes{\l}aw Byli\'nski
     Received May 11, 1992
270. MATRIX_2
     Transpose Matrices and Groups of Permutations
      by Katarzyna Jankowska
     Received May 20, 1992
     Has been removed on November 10, 2013
271. LATTICE3
     Complete Lattices
      by Grzegorz Bancerek
     Received May 13, 1992
272. TMAP_1
     Continuity of Mappings over the Union of Subspaces
      by Zbigniew Karno
     Received May 22, 1992
273. SEQFUNC
     Functional Sequence from a Domain to a Domain
      by Beata Perkowska
     Received May 22, 1992
274. MIDSP_3
     Reper Algebras
      by Micha{\l} Muzalewski
     Received May 28, 1992
275. GR_CY_2
     Isomorphisms of Cyclic Groups. Some Properties of Cyclic Groups
      by Dariusz Surowik
     Received June 5, 1992
276. ISOCAT_2
     Some Isomorphisms Between Functor Categories
      by Andrzej Trybulec
     Received June 5, 1992
277. TDLAT_1
     The Lattice of Domains of a Topological Space
      by Toshihiko Watanabe
     Received June 12, 1992
278. LMOD_6
     Submodules
      by Micha{\l} Muzalewski
     Received June 19, 1992
279. DIRORT
     Oriented Metric-Affine Plane - Part II
      by Jaros{\l}aw Zajkowski
     Received June 19, 1992
280. MOD_4
     Opposite Rings, Modules and their Morphisms
      by Micha{\l} Muzalewski
     Received June 22, 1992
281. MEASURE4
     Properties of Caratheodor's Measure
      by J\'ozef Bia{\l}as
     Received June 25, 1992
282. TDLAT_2
     Completeness of the Lattices of Domains of a Topological Space
      by Zbigniew Karno and Toshihiko Watanabe
     Received July 16, 1992
283. PCOMPS_2
     On Paracompactness of Metrizable Spaces
      by Leszek Borys
     Received July 23, 1992
284. TREAL_1
     The Brouwer Fixed Point Theorem for Intervals
      by Toshihiko Watanabe
     Received August 17, 1992
285. CARD_5
     On Powers of Cardinals
      by Grzegorz Bancerek
     Received August 24, 1992
286. TOPREAL3
     Basic Properties of Connecting Points with Line Segments in ${\calE}^2_{\rm T}$
      by Yatsuka Nakamura and Jaros{\l}aw Kotowicz
     Received August 24, 1992
287. TOPREAL4
     Connectedness Conditions Using Polygonal Arcs
      by Yatsuka Nakamura and Jaros{\l}aw Kotowicz
     Received August 24, 1992
288. GOBOARD1
     Introduction to Go-Board - Part I. Basic Notations
      by Jaros{\l}aw Kotowicz and Yatsuka Nakamura
     Received August 24, 1992
289. GOBOARD2
     Introduction to Go-Board - Part II.
     Go-Board Determined by Finite Sequence of point from ${\calE}^2_{\rm T}$
      by Jaros{\l}aw Kotowicz and Yatsuka Nakamura
     Received August 24, 1992
290. GOBOARD3
     Properties of Go-Board - Part III
      by Jaros{\l}aw Kotowicz and Yatsuka Nakamura
     Received August 24, 1992
291. GOBOARD4
     Go-Board Theorem
      by Jaros{\l}aw Kotowicz and Yatsuka Nakamura
     Received August 24, 1992
292. JORDAN1
     The Jordan's Property for Certain Subsets of the Plane
      by Yatsuka Nakamura and Jaros{\l}aw Kotowicz
     Received August 24, 1992
293. TDLAT_3
     The Lattice of Domains of an Extremally Disconnected Space
      by Zbigniew Karno
     Received August 27, 1992
294. AMI_1
     A Mathematical Model of CPU
      by Yatsuka Nakamura and Andrzej Trybulec
     Received October 14, 1992
     Has been removed on April 7, 2011 (partially covered by EXTPRO_1)
295. CAT_4
     Cartesian Categories
      by Czes{\l}aw Byli\'nski
     Received October 27, 1992
296. VFUNCT_1
     Algebra of Vector Functions
      by Hiroshi Yamazaki and Yasunari Shidama
     Received October 27, 1992
297. TSEP_2
     On a Duality Between Weakly Separated Subspaces of Topological Spaces
      by Zbigniew Karno
     Received November 9, 1992
298. PETRI
     Basic Petri Net Concepts.
     Place/Transition Net Structure, Deadlocks, Traps, Dual Nets
      by Pauline N. Kawamoto, Yasushi Fuwa and Yatsuka Nakamura
     Received November 27, 1992
299. FIN_TOPO
     Finite Topological Spaces. Finite Topology Concepts and Neighbourhoods
      by Hiroshi Imura and Masayoshi Eguchi
     Received November 27, 1992
300. TREES_3
     Sets and Functions of Trees and Joining Operations of Trees
      by Grzegorz Bancerek
     Received November 27, 1992
301. FVSUM_1
     Sum and Product of Finite Sequences of Elements of a Field
      by Katarzyna Zawadzka
     Received December 29, 1992
302. AMI_2
     On a Mathematical Model of Programs
      by Yatsuka Nakamura and Andrzej Trybulec
     Received December 29, 1992
303. UNIALG_1
     Basic Notation of Universal Algebra
      by Jaros{\l}aw Kotowicz, Beata Madras and Ma{\l}gorzata Korolkiewicz
     Received December 29, 1992
304. COH_SP
     Coherent Space
      by Jaros{\l}aw Kotowicz and Konrad Raczkowski
     Received December 29, 1992
305. MONOID_0
     Monoids
      by Grzegorz Bancerek
     Received December 29, 1992
306. MONOID_1
     Monoid of Multisets and Subsets
      by Grzegorz Bancerek
     Received December 29, 1992
307. PRVECT_1
     Product of Families of Groups and Vector Spaces
      by Anna Lango and Grzegorz Bancerek
     Received December 29, 1992
308. MEASURE5
     Properties of the Intervals of Real Numbers
      by J\'ozef Bia{\l}as
     Received January 12, 1993
309. RLVECT_4
     Subspaces of Real Linear Space Generated by One, Two, or Three Vectors
     and Their Cosets
      by Wojciech A. Trybulec
     Received February 24, 1993
310. LMOD_7
     Domains of Submodules, Join and Meet of Finite Sequences of Submodules
     and Quotient Modules
      by Micha{\l} Muzalewski
     Received March 29, 1993
311. RFINSEQ
     Functions and Finite Sequences of Real Numbers
      by Jaros{\l}aw Kotowicz
     Received March 15, 1993
312. RFUNCT_3
     Properties of Partial Functions from a Domain to the Set of Real Numbers
      by Jaros{\l}aw Kotowicz and Yuji Sakai
     Received March 15, 1993
313. TOPS_3
     Remarks on Special Subsets of Topological Spaces
      by Zbigniew Karno
     Received April 6, 1993
314. TEX_1
     On Discrete and Almost Discrete Topological Spaces
      by Zbigniew Karno
     Received April 6, 1993
315. MATRIX_3
     The Product of Matrices of Elements of a Field and Determinants
      by Katarzyna Zawadzka
     Received May 17, 1993
316. REARRAN1
     Introduction to Theory of Rearrangment
      by Yuji Sakai and Jaros{\l}aw Kotowicz
     Received May 22, 1993
317. PBOOLE
     Manysorted Sets
      by Andrzej Trybulec
     Received July 7, 1993
318. UNIALG_2
     Subalgebras of the Universal Algebra. Lattices of Subalgebras
      by Ewa Burakowska
     Received July 8, 1993
319. HAHNBAN
     Hahn Banach Theorem
      by Bogdan Nowak and Andrzej Trybulec
     Received July 8, 1993
320. LATTICE4
     Homomorphisms of Lattices \\ Finite Join and Finite Meet
      by Jolanta Kamie\'nska and Jaros\l aw Stanis\l aw Walijewski
     Received July 14, 1993
321. OPENLATT
     Representation Theorem for Heyting Lattices
      by Jolanta Kamie\'nska
     Received July 14, 1993
322. LOPCLSET
     Representation Theorem for Boolean Algebras
      by Jaros{\l}aw Stanis{\l}aw Walijewski
     Received July 14, 1993
323. AMI_3
     Some Remarks on Simple Concrete Model of Computer
      by Andrzej Trybulec and Yatsuka Nakamura
     Received October 8, 1993
324. AMI_4
     Euclide Algorithm
      by Andrzej Trybulec and Yatsuka Nakamura
     Received October 8, 1993
325. SCM_1
     Development of Terminology for {\bf SCM}
      by Grzegorz Bancerek and Piotr Rudnicki
     Received October 8, 1993
326. PRE_FF
     Two Programs for {\bf SCM}. Part I - Preliminaries
      by Grzegorz Bancerek and Piotr Rudnicki
     Received October 8, 1993
327. FIB_FUSC
     Two Programs for {\bf SCM}. Part II - Proofs
      by Grzegorz Bancerek and Piotr Rudnicki
     Received October 8, 1993
328. TREES_4
     Joining of Decorated Trees
      by Grzegorz Bancerek
     Received October 8, 1993
329. BINARITH
     Binary Arithmetics. Addition
      by Takaya Nishiyama and Yasuho Mizuhara
     Received October 8, 1993
330. BOOLMARK
     Basic Concepts for Petri Nets with Boolean Markings.
     Boolean Markings and the Firability/Firing of Transitions
      by Pauline N. Kawamoto, Yasushi Fuwa and Yatsuka Nakamura
     Received October 8, 1993
331. DTCONSTR
     On Defining Functions on Trees
      by Grzegorz Bancerek and Piotr Rudnicki
     Received October 12, 1993
332. PRALG_1
     Product of Family of Universal Algebras
      by Beata Madras
     Received October 12, 1993
333. ALG_1
     Homomorphisms of algebras. Quotient Universal Algebra
      by Ma{\l}gorzata Korolkiewicz
     Received October 12, 1993
334. FREEALG
     Free Universal Algebra Construction
      by Beata Perkowska
     Received October 20, 1993
335. COMSEQ_1
     Complex Sequences
      by Agnieszka Banachowicz and Anna Winnicka
     Received November 5, 1993
336. TEX_2
     Maximal Discrete Subspaces of Almost Discrete Topological Spaces
      by Zbigniew Karno
     Received November 5, 1993
337. TEX_3
     On Nowhere and Everywhere Dense Subspaces of Topological Spaces
      by Zbigniew Karno
     Received November 9, 1993
338. AMI_5
     On the Decomposition of the States of SCM
      by Yasushi Tanaka
     Received November 23, 1993
339. BINTREE1
     On Defining Functions on Binary Trees
      by Grzegorz Bancerek and Piotr Rudnicki
     Received December 30, 1993
340. SCM_COMP
     A compiler of arithmetic expressions for { \bf SCM }
      by Grzegorz Bancerek and Piotr Rudnicki
     Received December 30, 1993
341. MEASURE6
     Some Properties of the Intervals
      by J\'{o}zef Bia\l{}as
     Received February 5, 1994
342. BINARI_2
     Binary Arithmetics.Addition and Subtraction of Integers
      by Yasuho Mizuhara and Takaya Nishiyama
     Received March 18, 1994
343. BOOLEALG
     Boolean Properties of Lattices
      by Agnieszka Julia Marasik
     Received March 28, 1994
344. MSUALG_1
     Many Sorted Algebras
      by Andrzej Trybulec
     Received April 21, 1994
345. AUTGROUP
     On the Group of Inner Automorphisms
      by Artur Korni{\l}owicz
     Received April 22, 1994
346. MSUALG_2
     Subalgebras of a Many Sorted Algebra. Lattice of Subalgerbas
      by Ewa Burakowska
     Received April 25, 1994
347. PRALG_2
     Products of Many Sorted Algebras
      by Beata Madras
     Received April 25, 1994
348. MSUALG_3
     Homomorphisms of Many Sorted Algebras
      by Ma{\l}gorzata Korolkiewicz
     Received April 25, 1994
349. MSAFREE
     Free Many Sorted Universal Algebra. Lattice of Subalgerbas
      by Beata Perkowska
     Received April 27, 1994
350. T_0TOPSP
     $T_0$ Topological Spaces
      by Mariusz \.Zynel and Adam Guzowski
     Received May 6, 1994
351. MSUALG_4
     Many Sorted Quotient Algebra
      by Ma{\l}gorzata Korolkiewicz
     Received May 6, 1994
352. QUANTAL1
     Quantales
      by Grzegorz Bancerek
     Received May 9, 1994
353. TOPRNS_1
     Sequences in $R^n$
      by Agnieszka Sakowicz , Jaros{\l}aw Gryko and Adam Grabowski
     Received May 10, 1994
354. SPPOL_1
     Extremal Properties of Vertices on Special Polygons I
      by Yatsuka Nakamura and Czes\law Byli\'nski
     Received May 11, 1994
355. RELOC
     Relocatability
      by Yasushi Tanaka
     Received June 16, 1994
356. TEX_4
     Maximal Anti-Discrete Subspaces of Topological Spaces
      by Zbigniew Karno
     Received July 26, 1994
357. TSP_1
     On Kolmogorov Topological Spaces
      by Zbigniew Karno
     Received July 26, 1994
358. TSP_2
     Maximal Kolmogorov Subspaces of a Topological Space as Stone
     Retracts of the Ambient Space
      by Zbigniew Karno
     Received July 26, 1994
359. PROJPL_1
     Projective { P } lanes
      by Micha{\l} Muzalewski
     Received July 28, 1994
360. SGRAPH1
     the formalisation of simple graphs
      by Yozo Toda
     Received September 8, 1994
361. GRSOLV_1
     Solvable Groups
      by Katarzyna Zawadzka
     Received October 23, 1994
362. FILTER_2
     Ideals
      by Grzegorz Bancerek
     Received October 24, 1994
363. CAT_5
     Categorial Categories and Slice Categories
      by Grzegorz Bancerek
     Received October 24, 1994
364. PRE_CIRC
     Preliminaries to Circuits, I
      by Yatsuka Nakamura , Piotr Rudnicki , Andrzej Trybulec
       and Pauline N. Kawamoto
     Received November 17, 1994
365. FSM_1
     Minimization of finite state machines
      by Miroslava Kaloper and Piotr Rudnicki
     Received November 18, 1994
366. TREES_9
     Subtrees
      by Grzegorz Bancerek
     Received November 25, 1994
367. MSATERM
     Terms over many sorted universal algebra
      by Grzegorz Bancerek
     Received November 25, 1994
368. DECOMP_1
     On the Decomposition of the Continuity
      by Marian Przemski
     Received December 12, 1994
369. MSAFREE1
     A Scheme for Extensions of Homomorphisms of Manysorted
     Algebras
      by Andrzej Trybulec
     Received December 13, 1994
370. MSUHOM_1
     The Correspondence Between Homomorphisms of Universal Algebra
     & Manysorted Algebra
      by Adam Grabowski
     Received December 13, 1994
371. MSAFREE2
     Preliminaries to Circuits, II
      by Yatsuka Nakamura , Piotr Rudnicki , Andrzej Trybulec and Pauline N. Kawamoto
     Received December 13, 1994
372. AUTALG_1
     On the Group of Automorphisms of Universal Algebra & Many
     Sorted Algebra
      by Artur Korni{\l}owicz
     Received December 13, 1994
373. CIRCUIT1
     Introduction to Circuits, I
      by Yatsuka Nakamura , Piotr Rudnicki , Andrzej Trybulec and Pauline N. Kawamoto
     Received December 15, 1994
374. CANTOR_1
     The Cantor Set
      by Alexander Yu. Shibakov and Andrzej Trybulec
     Received January 9, 1995
375. CQC_THE3
     Logical Equivalence of Formulae
      by Oleg Okhotnikov
     Received January 24, 1995
376. FINSEQ_5
     Some Properties of Restrictions of Finite Sequences
      by Czes\law Byli\'nski
     Received January 25, 1995
377. SPPOL_2
     Special Polygons
      by Czes\law Byli\'nski and Yatsuka Nakamura
     Received January 30, 1995
378. MEASURE7
     The One-Dimensional Lebesgue Measure As an Example of a
     Formalization in the Mizar Language of the Classical
     Definition of a Mathematical Object
      by J\'ozef Bia{\l}as
     Received February 4, 1995
379. ALTCAT_1
     Categories without Uniqueness of { \bf cod } and { \bf dom }
      by Andrzej Trybulec
     Received February 28, 1995
380. EXTENS_1
     Extensions of Mappings on Generator Set
      by Artur Korni{\l}owicz
     Received March 23, 1995
381. CIRCUIT2
     Introduction to Circuits, II
      by Yatsuka Nakamura , Piotr Rudnicki , Andrzej Trybulec and Pauline N. Kawamoto
     Received April 10, 1995
382. MBOOLEAN
     Definitions and Basic Properties of Boolean & Union of Many
     Sorted Sets
      by Artur Korni{\l}owicz
     Received April 27, 1995
383. CIRCCOMB
     Combining of Circuits
      by Yatsuka Nakamura and Grzegorz Bancerek
     Received May 11, 1995
384. GRAPH_2
     Vertex sequences induced by chains
      by Yatsuka Nakamura and Piotr Rudnicki
     Received May 13, 1995
385. VECTSP_8
     On the Lattice of Subspaces of Vector Space
      by Andrzej Iwaniuk
     Received May 23, 1995
386. LATSUBGR
     On the Lattice of Subgroups of a Group
      by Janusz Ganczarski
     Received May 23, 1995
387. UNIALG_3
     On the Lattice of Subalgebras of a Universal Algebra
      by Miros{\l}aw Jan Paszek
     Received May 23, 1995
388. FINSEQ_6
     On the Decomposition of Finite Sequences
      by Andrzej Trybulec
     Received May 24, 1995
389. GOBOARD5
     Decomposing a Go Board into Cells
      by Yatsuka Nakamura and Andrzej Trybulec
     Received May 26, 1995
390. INDEX_1
     Indexed Category
      by Grzegorz Bancerek
     Received June 8, 1995
391. MATRLIN
     Associated Matrix of Linear Map
      by Robert Milewski
     Received June 30, 1995
392. GOBOARD6
     On the Geometry of a Go-board
      by Andrzej Trybulec
     Received July 9, 1995
393. WEIERSTR
     The Theorem of Weierstrass
      by J\'ozef Bia\las and Yatsuka Nakamura
     Received July 10, 1995
394. URYSOHN1
     Dyadic Numbers and $T_4$ Topological Spaces
      by J\'ozef Bia\las and Yatsuka Nakamura
     Received July 29, 1995
395. FACIRC_1
     Full Adder Circuit. Part { I }
      by Grzegorz Bancerek and Yatsuka Nakamura
     Received August 10, 1995
396. COHSP_1
     Continuous, Stable, and Linear Maps of Coherence Spaces
      by Grzegorz Bancerek
     Received August 30, 1995
397. PZFMISC1
     Some Basic Properties of Many Sorted Sets
      by Artur Korni{\l}owicz
     Received September 29, 1995
398. TREES_A
     Replacement of Subtrees in a Tree
      by Oleg Okhotnikov
     Received October 1, 1995
399. PUA2MSS1
     Minimal Manysorted Signature for Partial Algebra
      by Grzegorz Bancerek
     Received October 1, 1995
400. QC_LANG4
     The Subformula Tree of a Formula of the First Order
     Language
      by Oleg Okhotnikov
     Received October 2, 1995
401. VECTSP_9
     Steinitz Theorem and Dimension of a Vector Space
      by Mariusz \.Zynel
     Received October 6, 1995
402. GOBOARD7
     On the Go Board of a Standard Special Circular Sequence
      by Andrzej Trybulec
     Received October 15, 1995
403. ENDALG
     On the Monoid of Endomorphisms of Universal Algebra \& Many
     Sorted Algebra
      by Jaros{\l}aw Gryko
     Received October 17, 1995
404. GOBOARD8
     More on Segments on a Go Board
      by Andrzej Trybulec
     Received October 17, 1995
405. MSSUBFAM
     Certain Facts about Families of Subsets of Many Sorted Sets
      by Artur Korni{\l}owicz
     Received October 27, 1995
406. TRIANG_1
     On the concept of the triangulation
      by Beata Madras
     Received October 28, 1995
407. GOBOARD9
     Left and Right Component of the Complement of a Special
     Closed Curve
      by Andrzej Trybulec
     Received October 29, 1995
408. REWRITE1
     Reduction Relations
      by Grzegorz Bancerek
     Received November 14, 1995
409. MSUALG_5
     Lattice of Congruences in a Many Sorted Algebra
      by Robert Milewski
     Received January 11, 1996
410. FUNCT_7
     Miscellaneous Facts about Functions
      by Grzegorz Bancerek and Andrzej Trybulec
     Received January 12, 1996
411. ALTCAT_2
     Examples of Category Structures.Subcategories
      by Andrzej Trybulec
     Received January 22, 1996
412. ORDERS_3
     On the Category of Posets
      by Adam Grabowski
     Received January 22, 1996
413. SCMFSA_1
     An Extension of { \bf SCM }
      by Andrzej Trybulec , Yatsuka Nakamura and Piotr Rudnicki
     Received February 3, 1996
414. CONNSP_3
     Components and Unions of Components
      by Yatsuka Nakamura and Andrzej Trybulec
     Received February 5, 1996
415. SCMFSA_2
     The { \bf SCM_FSA } computer
      by Andrzej Trybulec , Yatsuka Nakamura and Piotr Rudnicki
     Received February 7, 1996
416. CLOSURE1
     On the Many Sorted Closure Operator and the Many Sorted
     Closure System
      by Artur Korni{\l}owicz
     Received February 7, 1996
417. SCMFSA_3
     Computation in { \bf SCM_FSA }
      by Andrzej Trybulec and Yatsuka Nakamura
     Received February 7, 1996
418. CLOSURE2
     On the Closure Operator and the Closure System of Many
     Sorted Sets
      by Artur Korni{\l}owicz
     Received February 7, 1996
419. MSUALG_6
     Translations and Endomorphisms in Many Sorted Algebras.Stable
     Equational Theories
      by Grzegorz Bancerek
     Received February 9, 1996
420. MSUALG_7
     More on the Lattice of Many Sorted Equivalence Relations
      by Robert Milewski
     Received February 9, 1996
421. SCMFSA_4
     Modifying addresses of instructions of { \bf SCM_FSA }
      by Andrzej Trybulec and Yatsuka Nakamura
     Received February 14, 1996
422. MSSCYC_1
     The correspondence between monotonic many sorted signatures
     and well-founded graphs
      by Czes{\l}aw Byli\'nski and Piotr Rudnicki
     Received February 14, 1996
423. SCMFSA_5
     Relocability for { \bf SCM_FSA }
      by Andrzej Trybulec and Yatsuka Nakamura
     Received February 22, 1996
424. MSUALG_8
     More on the Lattice of Congruences in a Many Sorted Algebra
      by Robert Milewski
     Received March 6, 1996
425. MSSCYC_2
     The correspondence between monotonic many sorted signatures
     and well founded graphs. Part II
      by Czes{\l}aw Byli\'nski and Piotr Rudnicki
     Received April 10, 1996
426. FUNCTOR0
     Functors for Alternative Categories
      by Andrzej Trybulec
     Received April 24, 1996
427. FUNCTOR1
     Basic Properties about Functor Structures
      by Claus Zinn and Wolfgang Jaksch
     Received April 24, 1996
428. SCMFSA_7
     Some Multi-instructions defined by sequence of instructions
     of SCM+FSA
      by Noriko Asamoto
     Received April 24, 1996
429. PRALG_3
     More on Products of Many Sorted Algebras
      by Mariusz Giero
     Received April 29, 1996
430. GOBRD10
     Adjacency Concept for Pairs of Natural Numbers
      by Yatsuka Nakamura and Andrzej Trybulec
     Received June 10, 1996
431. MSALIMIT
     Inverse Limits of Many Sorted Algebras
      by Adam Grabowski
     Received June 11, 1996
432. MSUALG_9
     On the Trivial Many Sorted Algebras and Many Sorted
     Congruences
      by Artur Korni\l owicz
     Received June 11, 1996
433. MSINST_1
     Examples of Category Structures
      by Adam Grabowski
     Received June 11, 1996
434. SCMFSA6A
     On the compositions of macro instructions
      by Andrzej Trybulec , Yatsuka Nakamura and Noriko Asamoto
     Received June 20, 1996
435. SF_MASTR
     Memory handling for SCM+FSA
      by Piotr Rudnicki and Andrzej Trybulec
     Received July 18, 1996
436. GOBRD11
     Some Topological Properties of Cells in Rý
      by Yatsuka Nakamura and Andrzej Trybulec
     Received July 22, 1996
437. SCMFSA6B
     On the compositions of macro instructions, Part II
      by Noriko Asamoto , Yatsuka Nakamura , Piotr Rudnicki and Andrzej Trybulec
     Received July 22, 1996
438. GOBRD12
     The First Part of Jordan's Theorem for Special Polygons
      by Yatsuka Nakamura and Andrzej Trybulec
     Received July 22, 1996
439. SCMFSA6C
     On the compositions of macro instructions, Part III
      by Noriko Asamoto , Yatsuka Nakamura , Piotr Rudnicki and Andrzej Trybulec
     Received July 22, 1996
440. SCMFSA7B
     Constant assignment macro instructions of SCM+FSA, Part II
      by Noriko Asamoto
     Received August 27, 1996
441. SCMFSA8A
     Conditional branch macro instructions of SCM+FSA, Part
     I(preliminary)
      by Noriko Asamoto
     Received August 27, 1996
442. SCMFSA8B
     Conditional branch macro instructions of SCM+FSA, Part II
      by Noriko Asamoto
     Received August 27, 1996
443. YELLOW_0
     Bounds in Posets and Relational Substructures
      by Grzegorz Bancerek
     Received September 10, 1996
444. WAYBEL_0
     Directed Sets, Nets, Ideals, Filters, and Maps
      by Grzegorz Bancerek
     Received September 12, 1996
445. KNASTER
     Fix-points in complete lattices
      by Piotr Rudnicki and Andrzej Trybulec
     Received September 16, 1996
446. YELLOW_1
     Boolean Posets, Posets under Inclusion and Products of
     Relational Structures
      by Adam Grabowski and Robert Milewski
     Received September 20, 1996
447. YELLOW_2
     Properties of Relational Structures, Posets, Lattices and Maps
      by Mariusz \.Zynel and Czes{\l}aw Byli\'nski
     Received September 20, 1996
448. WAYBEL_1
     Galois Connections
      by Czes\law Byli\'nski
     Received September 25, 1996
449. YELLOW_3
     Cartesian Products of Relations and Relational Structures
      by Artur Korni{\l}owicz
     Received September 25, 1996
450. YELLOW_4
     Definitions and Properties of the Join and Meet of Subsets
      by Artur Korni{\l}owicz
     Received September 25, 1996
451. WAYBEL_2
     Meet - continuous Lattices
      by Artur Korni{\l}owicz
     Received October 10, 1996
452. WAYBEL_3
     The "Way-Below" Relation
      by Grzegorz Bancerek
     Received October 11, 1996
453. WAYBEL_4
     Auxiliary and Approximating Relations
      by Adam Grabowski
     Received October 21, 1996
454. TWOSCOMP
     2's Complement Circuit. Part I.Boolean Operators and 2's
     Complement Circuit Properties
      by Katsumi Wasaki and Pauline N. Kawamoto
     Received October 25, 1996
455. WAYBEL_5
     The Equational Characterization
      by Mariusz \.Zynel
     Received October 25, 1996
456. YELLOW_5
     Miscellaneous Facts about Relation Structure
      by Agnieszka Julia Marasik
     Received November 8, 1996
457. YELLOW_6
     Moore-Smith Convergence
      by Andrzej Trybulec
     Received November 12, 1996
458. YELLOW_7
     Duality in Relation Structures
      by Grzegorz Bancerek
     Received November 12, 1996
459. WAYBEL_6
     Irreducible and Prime Elements
      by Beata Madras
     Received December 1, 1996
460. WAYBEL_7
     Prime Ideals and Filters
      by Grzegorz Bancerek
     Received December 1, 1996
461. WAYBEL_8
     Algebraic Lattices
      by Robert Milewski
     Received December 1, 1996
462. JORDAN3
     Reconstructions of Special Sequences
      by Yatsuka Nakamura and Roman Matuszewski
     Received December 10, 1996
463. COMSEQ_2
     Conjugate Sequences, Bounded Complex Sequences and Convergent
     Complex Sequences
      by Adam Naumowicz
     Received December 20, 1996
464. WAYBEL_9
     On The Topological Properties of Meet-Continuous Lattices
      by Artur Korni{\l}owicz
     Received December 20, 1996
465. INSTALG1
     Institution of Many-sorted Algebras, Part { I } : Signature
     Reduct of an Algebra
      by Grzegorz Bancerek
     Received December 30, 1996
466. YELLOW_8
     Baire Spaces, Sober Spaces
      by Andrzej Trybulec
     Received January 8, 1997
467. WAYBEL10
     Closure Operators and Subalgebras
      by Grzegorz Bancerek
     Received January 15, 1997
468. CATALG_1
     Algebra of Morphisms
      by Grzegorz Bancerek
     Received January 28, 1997
469. WAYBEL11
     Scott Topology
      by Andrzej Trybulec
     Received January 29, 1997
470. WAYBEL12
     On the Baire Category Theorem
      by Artur Korni{\l}owicz
     Received February 5, 1997
471. ALTCAT_3
     Basic properties of objects and morphisms.In categories
     without Uniqueness of { \bf cod } and { \bf dom }
      by Beata Madras
     Received February 14, 1997
472. ABIAN
     Abian's Fixed Point Theorem
      by Piotr Rudnicki and Andrzej Trybulec
     Received February 22, 1997
473. WELLFND1
     On same equivalents of well-foundedness
      by Piotr Rudnicki and Andrzej Trybulec
     Received February 25, 1997
474. WAYBEL13
     Algebraic and Arithmetic Lattices
      by Robert Milewski
     Received March 4, 1997
475. JORDAN4
     Subsequences of Standard Special Circular Sequences in
     ${\cal E}^2_{\rm T}$
      by Yatsuka Nakamura , Roman Matuszewski and Adam Grabowski
     Received May 12, 1997
476. SUBSTLAT
     Lattice of Substitutions
      by Adam Grabowski
     Received May 21, 1997
477. EQUATION
     Equations in Many Sorted Algebras
      by Artur Korni{\l}owicz
     Received May 30, 1997
478. FUNCTOR2
     Category of Functors between Alternative Categories
      by Robert Nieszczerzewski
     Received June 12, 1997
479. YONEDA_1
     Yoneda Embedding
      by Miros{\l}aw Wojciechowski
     Received June 12, 1997
480. GCD_1
     The correctness of the Generic Algorithms of Brown and Henrici
     concerning Addition and Multiplication in Fraction Fields
      by Christoph Schwarzweller
     Received June 16, 1997
481. BIRKHOFF
     Birkhoff Theorem for Many Sorted Algebras
      by Artur Korni{\l}owicz
     Received June 19, 1997
482. CLOSURE3
     Algebraic Operation on Subsets of Many Sorted Sets
      by Agnieszka Julia Marasik
     Received June 23, 1997
483. COMSEQ_3
     Convergence and the Limit of Complex Sequences. Series
      by Yasunari Shidama and Artur Korni{\l}owicz
     Received June 25, 1997
484. RLVECT_5
     The Steinitz Theorem and the Dimension of a Real Linear
     Space
      by JingChao Chen
     Received July 1, 1997
485. GRAPH_3
     Euler circuits and paths
      by Yatsuka Nakamura and Piotr Rudnicki
     Received July 29, 1997
486. PSCOMP_1
     Bounding boxes for compact sets in ${\calE}^2$
      by Czes{\l}aw Byli\'nski and Piotr Rudnicki
     Received July 29, 1997
487. WAYBEL14
     The Scott topology, Part II
      by Czes{\l}aw Byli\'nski and Piotr Rudnicki
     Received August 27, 1997
488. BORSUK_2
     Introduction to Homotopy Theory
      by Adam Grabowski
     Received September 10, 1997
489. JORDAN5A
     Some Properties of Real Maps
      by Adam Grabowski and Yatsuka Nakamura
     Received September 10, 1997
490. JORDAN5B
     The Ordering of Points on a Curve, Part { I }
      by Adam Grabowski and Yatsuka Nakamura
     Received September 10, 1997
491. JORDAN5C
     The Ordering of Points on a Curve, Part { II }
      by Adam Grabowski and Yatsuka Nakamura
     Received September 10, 1997
492. ALTCAT_4
     On the Categories Without Uniqueness of { \bf cod } and {
     \bf dom } . Some Properties of the Morphisms and the
     Functors
      by Artur Korni{\l}owicz
     Received October 3, 1997
493. SCMFSA8C
     The { \bf loop } and { \bf Times } Macroinstruction for {
     \SCMFSA }
      by Noriko Asamoto
     Received October 29, 1997
494. WAYBEL15
     More on the Algebraic and Arithmetic Lattices
      by Robert Milewski
     Received October 29, 1997
495. JORDAN2B
     Projections in n-Dimensional Euclidean Space to Each
     Coordinates
      by Roman Matuszewski and Yatsuka Nakamura
     Received November 3, 1997
496. TOPREAL5
     Intermediate Value Theorem and Thickness of Simple Closed
     Curves
      by Yatsuka Nakamura and Andrzej Trybulec
     Received November 13, 1997
497. LATTICE5
     J\'onson Theorem
      by Jaros{\l}aw Gryko
     Received November 13, 1997
498. UNIFORM1
     Lebesgue's Covering Lemma, Uniform Continuity and Segmentation
     of Arcs
      by Yatsuka Nakamura and Andrzej Trybulec
     Received November 13, 1997
499. SPRECT_1
     On Rectangular Finite Sequences of the Points of the Plane
      by Andrzej Trybulec and Yatsuka Nakamura
     Received November 30, 1997
500. SPRECT_2
     On the Order on a Special Polygon
      by Andrzej Trybulec and Yatsuka Nakamura
     Received November 30, 1997
501. EULER_1
     Euler's Function
      by Yoshinori Fujisawa and Yasushi Fuwa
     Received December 10, 1997
502. SCMFSA_9
     While Macro Instructions of SCM+FSA
      by Jing-Chao Chen
     Received December 10, 1997
503. JORDAN6
     A Decomposition of Simple Closed Curves and an Order of
     Their Points
      by Yatsuka Nakamura and Andrzej Trybulec
     Received December 19, 1997
504. WSIERP_1
     The Chinese Remainder Theorem
      by Andrzej Kondracki
     Received December 30, 1997
505. FUNCTOR3
     The Composition of Functors and Transformations in
     Alternative Categories
      by Artur Korni{\l}owicz
     Received January 21, 1998
506. WAYBEL16
     Completely-Irreducible Elements
      by Robert Milewski
     Received February 9, 1998
507. WAYBEL17
     Scott-Continuous Functions
      by Adam Grabowski
     Received February 13, 1998
508. NAT_2
     Natural Numbers
      by Robert Milewski
     Received February 23, 1998
509. BINARI_3
     Binary Arithmetics. Binary Sequences
      by Robert Milewski
     Received February 24, 1998
510. BINTREE2
     Full Trees
      by Robert Milewski
     Received February 25, 1998
511. T_1TOPSP
     On $T_{1}$ Reflex of Topological Space
      by Adam Naumowicz and Mariusz {\L}api\'nski
     Received March 7, 1998
512. YELLOW_9
     Bases and Refinements of Topologies
      by Grzegorz Bancerek
     Received March 9, 1998
513. YELLOW10
     The Properties of Product of Relational Structures
      by Artur Korni{\l}owicz
     Received March 27, 1998
514. YELLOW11
     On the Characterization of Modular and Distributive Lattices
      by Adam Naumowicz
     Received April 3, 1998
515. WAYBEL18
     Injective Spaces
      by Jaros{\l}aw Gryko
     Received April 17, 1998
516. YELLOW12
     On the Characterization of Hausdorff Spaces
      by Artur Korni{\l}owicz
     Received April 18, 1998
517. QUOFIELD
     The Field of Quotients over an Integral Domain
      by Christoph Schwarzweller
     Received May 4, 1998
518. FRECHET
     First-countable, Sequential, and Frechet Spaces
      by Bart{\l}omiej Skorulski
     Received May 13, 1998
519. SFMASTR1
     On the Composition of non-parahalting Macro Instructions
      by Piotr Rudnicki
     Received June 3, 1998
520. SCMFSA9A
     The { \bf while } macro instructions of SCM+FSA, Part { II }
      by Piotr Rudnicki
     Received June 3, 1998
521. SFMASTR2
     Another { \bf times } Macro Instruction
      by Piotr Rudnicki
     Received June 4, 1998
522. SFMASTR3
     The { \bf for } (going up) Macro Instruction
      by Piotr Rudnicki
     Received June 4, 1998
523. JORDAN5D
     Bounding Boxes for Special Sequences in ${\calE}^2$
      by Yatsuka Nakamura and Adam Grabowski
     Received June 8, 1998
524. EULER_2
     Euler's Theorem and Small Fermat's Theorem
      by Yoshinori Fujisawa, Yasushi Fuwa and Hidetaka Shimizu
     Received June 10, 1998
525. GROUP_7
     The Product of the Families of the Groups
      by Artur Korni{\l}owicz
     Received June 10, 1998
526. JORDAN7
     On a Dividing Function of the Simple Closed Curve into
     Segments
      by Yatsuka Nakamura
     Received June 16, 1998
527. SCM_HALT
     Initialization Halting Concepts and Their Basic Properties of
     SCM+FSA
      by JingChao Chen and Yatsuka Nakamura
     Received June 17, 1998
528. SCMBSORT
     Bubble Sort on SCM+FSA
      by JingChao Chen and Yatsuka Nakamura
     Received June 17, 1998
529. WAYBEL19
     The Lawson Topology
      by Grzegorz Bancerek
     Received June 21, 1998
530. WAYBEL20
     Kernel Projections and Quotient Lattices
      by Piotr Rudnicki
     Received July 6, 1998
531. WAYBEL21
     Lawson Topology in Continuous Lattices
      by Grzegorz Bancerek
     Received July 12, 1998
532. WAYBEL22
     Representation theorem for free continuous lattices
      by Piotr Rudnicki
     Received July 21, 1998
533. GRAPH_4
     Oriented Simple Chains Included in Oriented Chains
      by Yatsuka Nakamura and Piotr Rudnicki
     Received August 19, 1998
534. JGRAPH_1
     Graph Theoretical Properties of Arcs in the Plane and
     Fashoda Meet Theorem
      by Yatsuka Nakamura
     Received August 21, 1998
535. IDEA_1
     Algebraic group on Fixed-length bit integer and its adaptation
     to {IDEA} Cryptography
      by Yasushi Fuwa and Yoshinori Fujisawa
     Received September 7, 1998
536. TOPGRP_1
     The Definition and Basic Properties of Topological Groups
      by Artur Korni{\l}owicz
     Received September 7, 1998
537. MSSUBLAT
     The Correspondence Between Lattices of Subalgebras of
     Universal Algebras and Many Sorted Algebras
      by Adam Naumowicz and Agnieszka Julia Marasik
     Received September 22, 1998
538. CONLAT_1
     Introduction to Concept Lattices
      by Christoph Schwarzweller
     Received October 2, 1998
539. PARTIT1
     A theory of partitions, { I }
      by Shunichi Kobayashi and Kui Jia
     Received October 5, 1998
540. BVFUNC_1
     A Theory of Boolean Valued Functions and Partitions
      by Shunichi Kobayashi and Kui Jia
     Received October 22, 1998
541. SIN_COS
     Trigonometric Functions and Existence of Circle Ratio
      by Yuguang Yang and Yasunari Shidama
     Received October 22, 1998
542. SPRECT_3
     Some properties of special polygonal curves
      by Andrzej Trybulec and Yatsuka Nakamura
     Received October 22, 1998
543. VECTMETR
     Real Linear-Metric Space and Isometric Functions
      by Robert Milewski
     Received November 3, 1998
544. YELLOW13
     Introduction to Meet-Continuous Topological Lattices
      by Artur Korni{\l}owicz
     Received November 3, 1998
545. WAYBEL23
     Bases of Continuous Lattices
      by Robert Milewski
     Received November 28, 1998
546. SCMRING1
     The Construction of { \bf SCM } over Ring
      by Artur Korni{\l}owicz
     Received November 29, 1998
547. SCMRING2
     The Basic Properties of { \bf SCM } over Ring
      by Artur Korni{\l}owicz
     Received November 29, 1998
548. BVFUNC_2
     A Theory of Boolean Valued Functions and Quantifiers with
     Respect to Partitions
      by Shunichi Kobayashi and Yatsuka Nakamura
     Received December 21, 1998
549. BVFUNC_3
     Predicate Calculus for Boolean Valued Functions, { I }
      by Shunichi Kobayashi and Yatsuka Nakamura
     Received December 21, 1998
550. PEPIN
     Public-Key Cryptography and Pepin's Test for the Primality
     of Fermat Numbers
      by Yoshinori Fujisawa , Yasushi Fuwa and Hidetaka Shimizu
     Received December 21, 1998
551. HEYTING2
     Lattice of Substitutions Is a Heyting Algebra
      by Adam Grabowski
     Received December 31, 1998
552. JORDAN2C
     Bounded Domains and Unbounded Domains
      by Yatsuka Nakamura , Andrzej Trybulec and Czeslaw Bylinski
     Received January 7, 1999
553. REVROT_1
     Rotating and reversing. (Finite sequences)
      by Andrzej Trybulec
     Received January 21, 1999
554. SPRECT_4
     On the components of the complement of a special polygonal curve
      by Andrzej Trybulec and Yatsuka Nakamura
     Received January 21, 1999
555. JORDAN8
     Gauges
      by Czes\law Byli\'nski
     Received January 22, 1999
556. INT_3
     The Ring of Integers, Euclidean Rings and Modulo Integers
      by Christoph Schwarzweller
     Received February 4, 1999
557. GATE_1
     Logic Gates and Logical Equivalence of Adders
      by Yatsuka Nakamura
     Received February 4, 1999
558. FRECHET2
     The Sequential Closure Operator In Sequential and Frechet Spaces
      by Bart{\l}omiej Skorulski
     Received February 13, 1999
559. BORSUK_3
     Properties of the Product of Compact Topological Spaces
      by Adam Grabowski
     Received February 13, 1999
560. TOPREAL6
     Compactness of the Bounded Closed Subsets of TOP-REAL 2
      by Artur Korni{\l}owicz
     Received February 19, 1999
561. HILBERT1
     Hilbert Positive Propositional Calculus
      by Adam Grabowski
     Received February 20, 1999
562. TOPREAL7
     Homeomorphism between [:TOP-REAL i,TOP-REAL j:] and TOP-REAL (i+j)
      by Artur Korni{\l}owicz
     Received February 21, 1999
563. FSCIRC_1
     Full Subtracter Circuit. Part { I }
      by Katsumi Wasaki and Noboru Endou
     Received March 13, 1999
564. GATE_2
     Correctness of Binary Counter Circuits
      by Yuguang Yang , Wasaki Katsumi , Yasushi Fuwa and Yatsuka Nakamura
     Received March 13, 1999
565. GATE_3
     Correctness of Johnson Counter Circuits
      by Yuguang Yang , Wasaki Katsumi , Yasushi Fuwa and Yatsuka Nakamura
     Received March 13, 1999
566. INTEGRA1
     The Definition of Riemann Definite Integral and some Related Lemmas
      by Noboru Endou and Artur Korni{\l}owicz
     Received March 13, 1999
567. SIN_COS2
     Properties of Trigonometric Function
      by Takashi Mitsuishi and Yuguang Yang
     Received March 13, 1999
568. BVFUNC_4
     Predicate Calculus for Boolean Valued Functions, II
      by Shunichi Kobayashi and Yatsuka Nakamura
     Received March 13, 1999
569. BVFUNC_5
     Propositional Calculus for Boolean Valued Functions, I
      by Shunichi Kobayashi and Yatsuka Nakamura
     Received March 13, 1999
570. BVFUNC_6
     Propositional Calculus for Boolean Valued Functions, II
      by Shunichi Kobayashi and Yatsuka Nakamura
     Received March 13, 1999
571. SCMISORT
     Insert Sort on SCM+FSA
      by JingChao Chen
     Received March 13, 1999
572. GATE_4
     Correctness of a Cyclic Redundancy Check Code Generator
      by Yuguang Yang, Katsumi Wasaki, Yasushi Fuwa and Yatsuka Nakamura
     Received April 16, 1999
573. HILBERT2
     Defining by structural induction in the positive propositional language
      by Andrzej Trybulec
     Received April 23, 1999
574. GOBRD13
     Some Properties of Cells on Go Board
      by Czes{\l}aw Byli\'nski
     Received April 23, 1999
575. BVFUNC_7
     Propositional Calculus For Boolean Valued Functions, III
      by Shunichi Kobayashi
     Received April 23, 1999
     Has been removed on November 10, 2013
576. BVFUNC_8
     Propositional Calculus For Boolean Valued Functions, IV
      by Shunichi Kobayashi
     Received April 23, 1999
     Has been removed on November 10, 2013
577. GENEALG1
     Basic Properties of Genetic Algorithm
      by Akihiko Uchibori and Noboru Endou
     Received April 24, 1999
578. BVFUNC_9
     Propositional Calculus for Boolean Valued Functions, { V }
      by Shunichi Kobayashi
     Received May 5, 1999
     Has been removed on November 10, 2013
579. GOBRD14
     Properties of Left-, and Right Components
      by Artur Korni{\l}owicz
     Received May 5, 1999
580. LATTICE6
     Noetherian Lattices
      by Christoph Schwarzweller
     Received June 9, 1999
581. SCMPDS_1
     A Small Computer Model with Push-Down Stack
      by JingChao Chen
     Received June 15, 1999
582. SCMPDS_2
     The SCMPDS Computer and the Basic Semantics of Its Instructions
      by JingChao Chen
     Received June 15, 1999
583. SCMPDS_3
     Computation and Program Shift in the SCMPDS Computer
      by JingChao Chen
     Received June 15, 1999
584. SCMPDS_4
     The Construction and shiftability of Program Blocks for SCMPDS
      by JingChao Chen
     Received June 15, 1999
585. SCMPDS_5
     Computation of Two Consecutive Program Blocks for SCMPDS
      by JingChao Chen
     Received June 15, 1999
586. SCMPDS_6
     The Construction and Computation of Conditional Statements for SCMPDS
      by JingChao Chen
     Received June 15, 1999
587. SCMP_GCD
     Recursive Euclide Algorithm
      by JingChao Chen
     Received June 15, 1999
588. WAYBEL24
     Scott-Continuous Functions, Part II
      by Adam Grabowski
     Received June 22, 1999
589. YELLOW14
     Some Properties of Isomorphism between Relational Structures.
     On the Product of Topological Spaces
      by Jaros{\l}aw Gryko and Artur Korni{\l}owicz
     Received June 22, 1999
590. JORDAN9
     Cages, external aproximation of Jordan's curve
      by Czes{\l}aw Byli\'nski and Mariusz \.Zynel
     Received June 22, 1999
591. YELLOW15
     Components and Basis of Topological Spaces
      by Robert Milewski
     Received June 22, 1999
592. JORDAN10
     Properties of the External Approximation of Jordan's Curve
      by Artur Korni{\l}owicz
     Received June 24, 1999
593. IRRAT_1
     Irrationality of e
      by Freek Wiedijk
     Received July 2, 1999
594. WAYBEL25
     Injective Spaces, Part { II }
      by Artur Korni{\l}owicz and Jaros{\l}aw Gryko
     Received July 3, 1999
595. BVFUNC10
     Propositional Calculus for Boolean Valued Functions, VI
      by Shunichi Kobayashi
     Received July 14, 1999
     Has been removed on November 10, 2013
596. BVFUNC11
     Predicate Calculus for Boolean Valued Functions, III
      by Shunichi Kobayashi and Yatsuka Nakamura
     Received July 14, 1999
597. CONLAT_2
     A Characterization of Concept Lattices; Dual Concept Lattices
      by Christoph Schwarzweller
     Received August 17, 1999
598. BVFUNC12
     Predicate Calculus for Boolean Valued Functions, IV
      by Shunichi Kobayashi and Yatsuka Nakamura
     Received August 17, 1999
     Has been removed on July 5, 2005
599. BVFUNC13
     Predicate Calculus for Boolean Valued Functions, V
      by Shunichi Kobayashi and Yatsuka Nakamura
     Received August 17, 1999
     Has been removed on July 12, 2010
600. RADIX_1
     Definitions of Radix-2k Signed-Digit number and its adder algorithm
      by Yoshinori Fujisawa and Yasushi Fuwa
     Received September 7, 1999
601. YELLOW16
     Retracts and Inheritance
      by Grzegorz Bancerek
     Received September 7, 1999
602. ALGSPEC1
     Technical Preliminaries to Algebraic Specifications
      by Grzegorz Bancerek
     Received September 7, 1999
603. POLYNOM1
     Multivariate polynomials with arbitrary number of variables
      by Piotr Rudnicki and Andrzej Trybulec
     Received September 22, 1999
604. WAYBEL26
     Continuous Lattices of Maps between T$_0$ Spaces
      by Grzegorz Bancerek
     Received September 24, 1999
605. BVFUNC14
     Predicate Calculus for Boolean Valued Functions, { VI }
      by Shunichi Kobayashi
     Received October 19, 1999
606. BVFUNC15
     Predicate Calculus for Boolean Valued Functions, { VII }
      by Shunichi Kobayashi
     Received October 19, 1999
     Has been removed on February 27, 2003
607. BVFUNC16
     Predicate Calculus for Boolean Valued Functions, { VIII }
      by Shunichi Kobayashi
     Received November 4, 1999
     Has been removed on April 30, 2002
608. BVFUNC17
     Predicate Calculus for Boolean Valued Functions, IX
      by Shunichi Kobayashi
     Received November 4, 1999
     Has been removed on April 10, 2002
609. ASYMPT_0
     Asymptotic notation. Part I: Theory
      by Richard Krueger, Piotr Rudnicki and Paul Shelley
     Received November 4, 1999
610. ASYMPT_1
     Asymptotic notation. Part II: Examples and Problems
      by Richard Krueger, Piotr Rudnicki and Paul Shelley
     Received November 4, 1999
611. BVFUNC18
     Predicate Calculus for Boolean Valued Functions, { X }
      by Shunichi Kobayashi
     Received November 15, 1999
     Has been removed on February 27, 2003
612. BVFUNC19
     Predicate Calculus for Boolean Valued Functions, { XI }
      by Shunichi Kobayashi
     Received November 15, 1999
     Has been removed on February 6, 2003
613. BVFUNC20
     Four Variable Predicate Calculus for Boolean Valued Functions, (1)
      by Shunichi Kobayashi
     Received November 26, 1999
     Has been removed on March 7, 2003
614. BVFUNC21
     Four Variable Predicate Calculus for Boolean Valued Functions, (2)
      by Shunichi Kobayashi
     Received November 26, 1999
     Has been removed on February 27, 2003
615. WAYBEL27
     Function Spaces in the Category of Directed Suprema Preserving Maps
      by Grzegorz Bancerek and Adam Naumowicz
     Received November 26, 1999
616. CFUNCT_1
     Property of Complex Functions
      by Takashi Mitsuishi, Katsumi Wasaki and Yasunari Shidama
     Received December 7, 1999
617. CFCONT_1
     Property of Complex Sequence and Continuity of Complex
     Function
      by Takashi Mitsuishi , Katsumi Wasaki and Yasunari Shidama
     Received December 7, 1999
618. INTEGRA2
     Scalar Multiple of Riemann Definite Integral
      by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
     Received December 7, 1999
619. INTEGRA3
     Darboux's Theorem
      by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
     Received December 7, 1999
620. BVFUNC22
     Five Variable Predicate Calculus for Boolean Valued
     Functions, ( 1 )
      by Shunichi Kobayashi
     Received December 27, 1999
     Has been removed on July 12, 2004
621. BVFUNC23
     Six Variable Predicate Calculus for Boolean Valued Functions, (1)
      by Shunichi Kobayashi
     Received December 27, 1999
     Has been removed on January 4, 2006
622. SCMPDS_7
     The Construction and Computation of For-loop Programs for
     SCMPDS
      by JingChao Chen and Piotr Rudnicki
     Received December 27, 1999
623. BVFUNC24
     Predicate Calculus for Boolean Valued Functions, (12)
      by Shunichi Kobayashi
     Received December 28, 1999
     Has been removed on December 19, 2008
624. WAYBEL28
     Lim-inf Convergence
      by Bart{\l}omiej Skorulski
     Received January 6, 2000
625. WAYBEL29
     The Characterization of Continuity of Topologies
      by Grzegorz Bancerek and Adam Naumowicz
     Received January 6, 2000
626. WAYBEL30
     Meet Continuous Lattices Revisited
      by Artur Korni{\l}owicz
     Received January 6, 2000
627. WAYBEL31
     Weights of Continuous Lattices
      by Robert Milewski
     Received January 6, 2000
628. LATTICE7
     Representation Theorem For Finite Distributive Lattices
      by Marek Dudzicz
     Received January 6, 2000
629. COMPLFLD
     The Field of Complex Numbers
      by Anna Justyna Milewska
     Received January 18, 2000
630. INTEGRA4
     Integrability of Bounded Total Functions
      by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
     Received February 1, 2000
631. RADIX_2
     High-speed algorithms for RSA cryptograms
      by Yasushi Fuwa and Yoshinori Fujisawa
     Received February 1, 2000
632. INTEGRA5
     Definition of Integrability for Partial Functions from REAL
     to REAL and Integrability for Continuous Functions
      by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
     Received March 23, 2000
633. RFUNCT_4
     Introduction to Several Concepts of Convexity and
     Semicontinuity for Function from REAL to REAL
      by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
     Received March 23, 2000
634. AMISTD_1
     Standard Ordering of Instruction Locations
      by Andrzej Trybulec , Piotr Rudnicki and Artur Korni{\l}owicz
     Received April 14, 2000
635. AMISTD_2
     On the Composition of Macro Instructions of Standard
     Computers
      by Artur Korni{\l}owicz
     Received April 14, 2000
636. SCMRING3
     The Properties of Instructions of { \bf SCM } over Ring
      by Artur Korni{\l}owicz
     Received April 14, 2000
637. CARD_FIL
     Basic facts about inaccessible and measurable cardinals
      by Josef Urban
     Received April 14, 2000
638. POLYNOM2
     Evaluation of Multivariate Polynomials
      by Christoph Schwarzweller and Andrzej Trybulec
     Received April 14, 2000
639. POLYNOM3
     The Ring of Polynomials
      by Robert Milewski
     Received April 17, 2000
640. POLYEQ_1
     Solving Roots of Polynomial Equations of Degree 2 and 3
     with Real Coefficients
      by Xiquan Liang
     Received May 18, 2000
641. FUZZY_1
     Concept of Fuzzy Set and Membership Function and Basic
     Properties of Fuzzy Set Operation
      by Takashi Mitsuishi , Noboru Endou and Yasunari Shidama
     Received May 18, 2000
642. FUZZY_2
     Basic Properties of Fuzzy Set Operation and Membership
     Function
      by Takashi Mitsuishi , Katsumi Wasaki and Yasunari Shidama
     Received May 22, 2000
643. HAHNBAN1
     Hahn Banach Theorem in the Vector Space over the Field of
     Complex Numbers
      by Anna Justyna Milewska
     Received May 23, 2000
644. YELLOW17
     The Tichonov Theorem
      by Bart{\l}omiej Skorulski
     Received May 23, 2000
645. WAYBEL32
     On the Order-consistent Topology of Complete and Uncomplete
     Lattices
      by Ewa Gr\c{a}dzka
     Received May 23, 2000
646. PENCIL_1
     On Segre's Product of Partial Line Spaces
      by Adam Naumowicz
     Received May 29, 2000
647. POLYNOM4
     Evaluation of Polynomials
      by Robert Milewski
     Received June 7, 2000
648. SCMPDS_8
     The Construction and Computation of While-loop Programs for
     SCMPDS
      by JingChao Chen
     Received June 14, 2000
649. SCPISORT
     Insert Sort on SCMPDS
      by JingChao Chen
     Received June 14, 2000
650. SCPQSORT
     Quick Sort on SCMPDS
      by JingChao Chen
     Received June 14, 2000
651. SCPINVAR
     Justifying the Correctness of Fibonacci Sequence and Euclide
     Algorithm by Loop Invariant
      by JingChao Chen
     Received June 14, 2000
652. ORDERS_4
     On the Isomorphism Between Finite Chains
      by Marta Pruszy\'nska and Marek Dudzicz
     Received June 29, 2000
653. LATTICE8
     J\'onsson Theorem about Representation of Modular Lattices
      by Mariusz {\L}api\'nski
     Received June 29, 2000
654. HILBERT3
     The canonical formulae
      by Andrzej Trybulec
     Received July 4, 2000
655. HEYTING3
     The Incompleteness of the Lattice of Substitutions
      by Adam Grabowski
     Received July 17, 2000
656. COMPTRIG
     Trigonometric Form of Complex Numbers
      by Robert Milewski
     Received July 21, 2000
657. POLYNOM5
     Fundamental Theorem of Algebra
      by Robert Milewski
     Received August 21, 2000
658. FINSEQ_7
     On Replace Function and Swap Function for Finite Sequences
      by Hiroshi Yamazaki , Yoshinori Fujisawa and Yatsuka Nakamura
     Received August 28, 2000
659. GATE_5
     Correctness of the High Speed Array Multiplier Circuits
      by Hiroshi Yamazaki and Katsumi Wasaki
     Received August 28, 2000
660. JCT_MISC
     Miscellaneous { I }
      by Andrzej Trybulec
     Received August 28, 2000
661. CARD_LAR
     Mahlo and inaccessible cardinals
      by Josef Urban
     Received August 28, 2000
662. EXTREAL1
     Basic Properties of Extended Real Numbers
      by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
     Received September 7, 2000
663. MESFUNC1
     Definitions and Basic Properties of Measurable Functions
      by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
     Received September 7, 2000
664. JORDAN1A
     Gauges and Cages
      by Artur Korni{\l}owicz, Robert Milewski, Adam Naumowicz and
       Andrzej Trybulec
     Received September 12, 2000
665. EXTREAL2
     Some Properties of Extended Real Numbers Operations: absolute
     value, min and max
      by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
     Received September 15, 2000
     Has been removed on November 10, 2013
666. FUZZY_3
     Concept of Fuzzy Relation and Basic Properties of Its
     Operation
      by Takashi Mitsuishi , Katsumi Wasaki and Yasunari Shidama
     Received September 15, 2000
     Has been removed on November 22, 2007
667. MESFUNC2
     Measurability of Extended Real Valued Functions
      by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
     Received October 6, 2000
668. JORDAN1B
     Some Properties of Cells and Arcs
      by Robert Milewski , Andrzej Trybulec , Artur Korni{\l}owicz and Adam Naumowicz
     Received October 6, 2000
669. FINTOPO2
     Formal topological spaces
      by Gang Liu , Yasushi Fuwa and Masayoshi Eguchi
     Received October 13, 2000
670. JORDAN1C
     Some Properties of Cells and Gauges
      by Adam Grabowski , Artur Korni{\l}owicz and Andrzej Trybulec
     Received October 13, 2000
671. SPRECT_5
     Again on the Order on a Special Polygon
      by Andrzej Trybulec and Yatsuka Nakamura
     Received October 16, 2000
672. JORDAN1D
     Gauges and Cages. { P } art { II }
      by Artur Korni{\l}owicz and Robert Milewski
     Received November 6, 2000
673. BINOM
     The Binomial Theorem for Algebraic Structures
      by Christoph Schwarzweller
     Received November 20, 2000
674. IDEAL_1
     Ring Ideals
      by Jonathan Backer , Piotr Rudnicki and Christoph Schwarzweller
     Received November 20, 2000
675. HILBASIS
     Hilbert Basis Theorem
      by Jonathan Backer and Piotr Rudnicki
     Received November 27, 2000
676. DYNKIN
     Dynkin's Lemma in Measure Theory
      by Franz Merkl
     Received November 27, 2000
677. TAXONOM1
     Lower Tolerance. {P}reliminaries to {W}roclaw Taxonomy
      by Mariusz Giero and Roman Matuszewski
     Received December 5, 2000
678. YELLOW18
     Concrete Categories
      by Grzegorz Bancerek
     Received January 12, 2001
679. PARTIT_2
     Classes of Independent Partitions
      by Andrzej Trybulec
     Received February 14, 2001
680. URYSOHN2
     Some Properties of Dyadic Numbers and Intervals
      by J\'ozef Bia{\l}as and Yatsuka Nakamura
     Received February 16, 2001
681. URYSOHN3
     Urysohn Lemma
      by J\'ozef Bia{\l}as and Yatsuka Nakamura
     Received February 16, 2001
682. POLYALG1
     The Algebra of Polynomials
      by Ewa Gr\c{a}dzka
     Received February 24, 2001
683. CIRCTRM1
     Circuit Generated by Terms and Circuit Calculating Terms
      by Grzegorz Bancerek
     Received April 10, 2001
684. AMI_6
     On the Instructions of { \bf SCM }
      by Artur Korni{\l}owicz
     Received May 8, 2001
685. AMI_7
     Input and Output of Instructions
      by Artur Korni{\l}owicz
     Received May 8, 2001
     MML Identifier has been changed into AMISTD_4
686. SCMFSA10
     On the Instructions of { \bf SCM+FSA }
      by Artur Korni{\l}owicz
     Received May 8, 2001
687. ROBBINS1
     Robbins Algebras vs. Boolean Algebras
      by Adam Grabowski
     Received June 12, 2001
688. FUZZY_4
     Properties of Fuzzy Relation
      by Noboru Endou , Takashi Mitsuishi and Keiji Ohkubo
     Received June 25, 2001
689. JGRAPH_2
     On Outside Fashoda Meet Theorem
      by Yatsuka Nakamura
     Received July 16, 2001
690. COMPUT_1
     The set of primitive recursive functions
      by Grzegorz Bancerek and Piotr Rudnicki
     Received July 27, 2001
691. TURING_1
     Introduction to Turing Machines
      by Jingchao Chen and Yatsuka Nakamura
     Received July 27, 2001
692. YELLOW19
     On the characterizations of compactness
      by Grzegorz Bancerek , Noboru Endou and Yuji Sakai
     Received July 29, 2001
693. WAYBEL33
     Compactness of Lim-inf Topology
      by Grzegorz Bancerek and Noboru Endou
     Received July 29, 2001
694. YELLOW20
     Miscellaneous Facts about Functors
      by Grzegorz Bancerek
     Received July 31, 2001
695. YELLOW21
     Categorial Background for Duality Theory
      by Grzegorz Bancerek
     Received August 1, 2001
696. MSAFREE3
     Yet another construction of free algebra
      by Grzegorz Bancerek and Artur Korni{\l}owicz
     Received August 8, 2001
697. WAYBEL34
     Duality Based on Galois Connection. Part I
      by Grzegorz Bancerek
     Received August 8, 2001
698. JORDAN1E
     Upper and Lower Sequence of a Cage
      by Robert Milewski
     Received August 8, 2001
699. POLYNOM6
     On polynomials with coefficients in a ring of polynomials
      by Barbara Dzienis
     Received August 10, 2001
700. PENCIL_2
     On Cosets in Segre's Product of Partial Linear Spaces
      by Adam Naumowicz
     Received August 14, 2001
701. JGRAPH_3
     On the Simple Closed Curve Property of the Circle and the
     Fashoda Meet Theorem for It
      by Yatsuka Nakamura
     Received August 20, 2001
702. PYTHTRIP
     Pythagorean triples
      by Freek Wiedijk
     Received August 26, 2001
703. JORDAN1F
     Some Remarks on Finite Sequences on Go-boards
      by Adam Naumowicz
     Received August 29, 2001
704. JORDAN1G
     Upper and Lower Sequence on the Cage. Part II
      by Robert Milewski
     Received September 28, 2001
705. AFINSQ_1
     Zero Based Finite Sequences
      by Tetsuya Tsunetou , Grzegorz Bancerek and Yatsuka Nakamura
     Received September 28, 2001
706. JORDAN1H
     More on External Approximation of a Continuum
      by Andrzej Trybulec
     Received October 7, 2001
707. TOPREAL8
     More on the Finite Sequences on the Plane
      by Andrzej Trybulec
     Received October 25, 2001
708. POLYNOM7
     More About Polynomials: Monomials and Constant Polynomials
      by Christoph Schwarzweller
     Received November 28, 2001
709. FSM_2
     On state machines of calculating type
      by Hisayoshi Kunimune , Grzegorz Bancerek and Yatsuka Nakamura
     Received December 3, 2001
710. TAXONOM2
     Hierarchies and Classifications of Sets
      by Mariusz Giero
     Received December 28, 2001
711. JGRAPH_4
     Fan Homeomorphisms in the Plane
      by Yatsuka Nakamura
     Received January 8, 2002
712. RCOMP_2
     Half Open Intervals in Real Numbers
      by Yatsuka Nakamura
     Received February 1, 2002
     Has been removed on December 19, 2008
713. JORDAN1I
     Some Remarks on Clockwise Oriented Sequences on Go-boards
      by Adam Naumowicz and Robert Milewski
     Received March 1, 2002
714. DICKSON
     Dickson's lemma
      by Gilbert Lee and Piotr Rudnicki
     Received March 12, 2002
715. BAGORDER
     On Ordering of Bags
      by Gilbert Lee and Piotr Rudnicki
     Received March 12, 2002
716. CIRCCMB2
     Combining of Multi Cell Circuits
      by Grzegorz Bancerek , Shin'nosuke Yamaguchi and Yasunari Shidama
     Received March 22, 2002
717. FACIRC_2
     Full Adder Circuit. Part { II }
      by Grzegorz Bancerek , Shin'nosuke Yamaguchi and Katsumi Wasaki
     Received March 22, 2002
718. JORDAN1J
     Upper and Lower Sequence on the Cage, Upper and Lower Arcs
      by Robert Milewski
     Received April 5, 2002
719. FIB_NUM
     Fibonacci Numbers
      by Robert M. Solovay
     Received April 19, 2002
720. JORDAN11
     Preparing the Internal Approximations of Simple Closed Curves
      by Andrzej Trybulec
     Received May 21, 2002
721. JORDAN12
     On the General Position of Special Polygons
      by Mariusz Giero
     Received May 27, 2002
722. JORDAN13
     Introducing Spans
      by Andrzej Trybulec
     Received May 27, 2002
723. JGRAPH_5
     General {F}ashoda {M}eet {T}heorem for Unit Circle
      by Yatsuka Nakamura
     Received June 24, 2002
724. JORDAN14
     Properties of the Internal Approximation of {J}ordan's Curve
      by Robert Milewski
     Received June 27, 2002
725. CIRCCMB3
     Preliminaries to Automatic Generation of Mizar Documentation for Circuits
      by Grzegorz Bancerek and Adam Naumowicz
     Received July 26, 2002
726. JORDAN15
     Properties of the Upper and Lower Sequence on the Cage
      by Robert Milewski
     Received August 1, 2002
727. BORSUK_4
     On the Decompositions of Intervals and Simple Closed Curves
      by Adam Grabowski
     Received August 7, 2002
728. JORDAN1K
     On the Minimal Distance Between Set in {E}uclidean Space
      by Andrzej Trybulec
     Received August 19, 2002
729. TOPMETR3
     Sequences of Metric Spaces and an Abstract Intermediate Value Theorem
      by Yatsuka Nakamura and Andrzej Trybulec
     Received September 11, 2002
730. JORDAN16
     On the Decomposition of a Simple Closed Curve into Two Arcs
      by Andrzej Trybulec and Yatsuka Nakamura
     Received September 16, 2002
731. JORDAN17
     The Ordering of Points on a Curve, Part {III}
      by Artur Korni{\l}owicz
     Received September 16, 2002
732. JORDAN18
     The Ordering of Points on a Curve, Part {IV}
      by Artur Korni{\l}owicz
     Received September 16, 2002
733. OSALG_1
     Order Sorted Algebras
      by Josef Urban
     Received September 19, 2002
734. OSALG_2
     Subalgebras of a Order Sorted Algebra. {L}attice of Subalgebras
      by Josef Urban
     Received September 19, 2002
735. OSALG_3
     Homomorphisms of Order Sorted Algebras
      by Josef Urban
     Received September 19, 2002
736. OSALG_4
     Order Sorted Quotient Algebra
      by Josef Urban
     Received September 19, 2002
737. OSAFREE
     Free Order Sorted Universal Algebra
      by Josef Urban
     Received September 19, 2002
738. RUSUB_1
     Subspaces and Cosets of Subspace of Real Unitary Space
      by Noboru Endou, Takashi Mitsuishi and Yasunari Shidama
     Received October 9, 2002
739. RUSUB_2
     Operations on Subspaces in Real Unitary Space
      by Noboru Endou, Takashi Mitsuishi and Yasunari Shidama
     Received October 9, 2002
740. RUSUB_3
     Linear Combinations in Real Unitary Space
      by Noboru Endou, Takashi Mitsuishi and Yasunari Shidama
     Received October 9, 2002
741. RUSUB_4
     Dimension of Real Unitary Space
      by Noboru Endou, Takashi Mitsuishi and Yasunari Shidama
     Received October 9, 2002
742. SIN_COS3
     Trigonometric Functions on Complex Space
      by Takashi Mitsuishi, Noboru Endou and Yasunari Shidama
     Received October 10, 2002
743. RUSUB_5
     Topology of Real Unitary Space
      by Noboru Endou, Takashi Mitsuishi and Yasunari Shidama
     Received October 25, 2002
744. ARMSTRNG
     Armstrong's Axioms
      by William W. Armstrong, Yatsuka Nakamura and Piotr Rudnicki
     Received October 25, 2002
745. CONVEX1
     Convex Sets and Convex Combinations
      by Noboru Endou, Takashi Mitsuishi and Yasunari Shidama
     Received November 5, 2002
746. VECTSP10
     Quotient Vector Spaces and Functionals
      by Jaros{\l}aw Kotowicz
     Received November 5, 2002
747. BILINEAR
     Bilinear Functionals in Vector Spaces
      by Jaros{\l}aw Kotowicz
     Received November 5, 2002
748. HERMITAN
     Hermitan Functionals. {C}anonical Construction of Scalar Product in
     Quotient Vector Space
      by Jaros{\l}aw Kotowicz
     Received November 12, 2002
749. NECKLACE
     The Class of Series-Parallel Graphs, {I}
      by Krzysztof Retel
     Received November 18, 2002
750. TERMORD
     Term Orders
      by Christoph Schwarzweller
     Received December 20, 2002
751. POLYRED
     Polynomial Reduction
      by Christoph Schwarzweller
     Received December 20, 2002
752. PNPROC_1
     Processes in {P}etri nets
      by Grzegorz Bancerek, Mitsuru Aoki, Akio Matsumoto and Yasunari Shidama
     Received December 20, 2002
753. RADIX_3
     Improvement of Radix-$2^k$ Signed-Digit Number for High Speed Circuit
      by Masaaki Niimura and Yasushi Fuwa
     Received January 3, 2003
754. RADIX_4
     High Speed Adder Algorithm with Radix-$2^k$ SD_Sub Number
      by Masaaki Niimura and Yasushi Fuwa
     Received January 3, 2003
755. GRAPH_5
     The Underlying Principle of {D}ijkstra's Shortest Path Algorithm
      by Jingchao Chen and Yatsuka Nakamura
     Received January 7, 2003
756. HAUSDORF
     On the {H}ausdorff Distance Between Compact Subsets
      by Adam Grabowski
     Received January 27, 2003
757. CHAIN_1
     Chains on a Grating in Euclidean Space
      by Freek Wiedijk
     Received January 27, 2003
758. BHSP_5
     Bessel's Inequality
      by Hiroshi Yamazaki, Yasunari Shidama and Yatsuka Nakamura
     Received January 30, 2003
759. BINARI_4
     A Representation of Integers by Binary Arithmetics
     and Addition of Integers
      by Hisayoshi Kunimune and Yatsuka Nakamura
     Received January 30, 2003
760. EUCLID_2
     The Inner Product of Finite Sequences and of Points of $n$-dimensional
     Topological Space
      by Kanchun and Yatsuka Nakamura
     Received February 3, 2003
761. POLYEQ_2
     Solving Roots of Polynomial Equation of Degree 4 with Real Coefficients
      by Xiquan Liang
     Received February 3, 2003
762. WAYBEL35
     Morphisms Into Chains, Part {I}
      by Artur Korni{\l}owicz
     Received February 6, 2003
763. BVFUNC25
     Propositional Calculus for Boolean Valued Functions, {VII}
      by Shunichi Kobayashi
     Received February 6, 2003
764. OPOSET_1
     Basic Notions and Properties of Orthoposets
      by Markus Moschner
     Received February 11, 2003
765. JGRAPH_6
     General {F}ashoda Meet Theorem for Unit Circle and Square
      by Yatsuka Nakamura
     Received February 25, 2003
766. BHSP_6
     On Some Properties of Real {H}ilbert Space, {I}
      by Hiroshi Yamazaki, Yasumasa Suzuki, Takao Inou\'e and Yasunari Shidama
     Received February 25, 2003
767. FSCIRC_2
     Full Subtracter Circuit. Part {II}
      by Shin'nosuke Yamaguchi, Grzegorz Bancerek and Katsumi Wasaki
     Received February 25, 2003
768. GRAPHSP
     Dijkstra's Shortest Path Algorithm
      by Jing-Chao Chen
     Received March 17, 2003
769. RSSPACE
     Real Linear Space of Real Sequences
      by Noboru Endou, Yasumasa Suzuki and Yasunari Shidama
     Received April 3, 2003
770. RSSPACE2
     Hilbert Space of Real Sequences
      by Noboru Endou, Yasumasa Suzuki and Yasunari Shidama
     Received April 3, 2003
771. INTPRO_1
     Intuitionistic Propositional Calculus in the Extended Framework
     with Modal Operator, Part I
      by Takao Inou\'e
     Received April 3, 2003
772. CONVEX2
     Some Properties for Convex Combinations
      by Noboru Endou, Yasumasa Suzuki and Yasunari Shidama
     Received April 3, 2003
773. BHSP_7
     On Some Properties of Real {H}ilbert Space, {II}
      by Hiroshi Yamazaki, Yasumasa Suzuki, Takao Inou\'e and Yasunari Shidama
     Received April 17, 2003
774. COMPLEX2
     Inner Products and Angles of Complex Numbers
      by Wenpai Chang, Yatsuka Nakamura and Piotr Rudnicki
     Received May 29, 2003
775. EUCLID_3
     Angle and Triangle in {E}uclidian Topological Space
      by Akihiro Kubo and Yatsuka Nakamura
     Received May 29, 2003
776. NECKLA_2
     The Class of Series-Parallel Graphs, {II}
      by Krzysztof Retel
     Received May 29, 2003
777. GROEB_1
     Characterization and Existence of {G}r\"obner Bases
      by Christoph Schwarzweller
     Received June 11, 2003
778. GROEB_2
     Construction of {G}r\"obner bases. S-Polynomials and Standard
     Representations
      by Christoph Schwarzweller
     Received June 11, 2003
779. BORSUK_5
     On the Subcontinua of a Real Line
      by Adam Grabowski
     Received June 12, 2003
780. KURATO_1
     On the {K}uratowski Closure-Complement Problem
      by Lilla Krystyna Bagi\'nska and Adam Grabowski
     Received June 12, 2003
781. CONVEX3
     Convex Hull, Set of Convex Combinations and Convex Cone
      by Noboru Endou and Yasunari Shidama
     Received June 16, 2003
782. ROBBINS2
     On the Two Short Axiomatizations of Ortholattices
      by Wioletta Truszkowska and Adam Grabowski
     Received June 28, 2003
783. CONVFUN1
     Definition of Convex Function and {J}ensen's Inequality
      by Grigory E. Ivanov
     Received July 17, 2003
784. ABCMIZ_0
     On semilattice structure of {M}izar types
      by Grzegorz Bancerek
     Received August 8, 2003
785. EUCLID_4
     Lines in $n$-Dimensional Euclidean Spaces
      by Akihiro Kubo
     Received August 8, 2003
786. RSSPACE3
     Banach Space of Absolute Summable Real Sequences
      by Yasumasa Suzuki, Noboru Endou and Yasunari Shidama
     Received August 8, 2003
787. EUCLID_5
     Cross Products and Tripple Vector Products in 3-dimensional Euclidian Space
      by Kanchun, Hiroshi Yamazaki and Yatsuka Nakamura
     Received August 8, 2003
788. MATRIX_4
     Calculation of Matrices of Field Elements. Part {I}
      by Yatsuka Nakamura and Hiroshi Yamazaki
     Received August 8, 2003
789. LFUZZY_0
     Lattice of Fuzzy Sets
      by Takashi Mitsuishi and Grzegorz Bancerek
     Received August 12, 2003
790. KURATO_2
     On the {K}uratowski Limit Operators
      by Adam Grabowski
     Received August 12, 2003
791. JORDAN_A
     On the Segmentation of a Simple Closed Curve
      by Andrzej Trybulec
     Received August 18, 2003
792. MEMBERED
     On the Sets Inhabited by Numbers
      by Andrzej Trybulec
     Received August 23, 2003
793. BINARI_5
     On the Calculus of Binary Arithmetics
      by Shunichi Kobayashi
     Received August 23, 2003
     Has been removed on June 30, 2010
794. SCMPDS_9
     SCMPDS Is Not Standard
      by Artur Korni{\l}owicz and Yasunari Shidama
     Received September 27, 2003
795. JORDAN19
     On the Upper and Lower Approximations of the Curve
      by Robert Milewski
     Received September 27, 2003
796. RFINSEQ2
     Sorting Operators for Finite Sequences
      by Yatsuka Nakamura
     Received October 17, 2003
797. RADIX_5
     Magnitude Relation Properties of Radix-$2^k$ SD Number
      by Masaaki Niimura and Yasushi Fuwa
     Received November 7, 2003
798. RADIX_6
     High Speed Modulo Calculation Algorithm with Radix-$2^k$ SD Number
      by Masaaki Niimura and Yasushi Fuwa
     Received November 7, 2003
799. LFUZZY_1
     Transitive Closure of Fuzzy Relations
      by Takashi Mitsuishi and Grzegorz Bancerek
     Received November 23, 2003
800. ROUGHS_1
     Basic Properties of Rough Sets and Rough Membership Function
      by Adam Grabowski
     Received November 23, 2003
801. PRGCOR_1
     Correctness of Non Overwriting Programs. {P}art {I}
      by Yatsuka Nakamura
     Received December 5, 2003
802. AMISTD_3
     A Tree of Execution of a Macroinstruction
      by Artur Korni{\l}owicz
     Received December 10, 2003
803. LOPBAN_1
     Banach Space of Bounded Linear Operators
      by Yasunari Shidama
     Received December 22, 2003
804. UPROOTS
     Little {B}ezout Theorem (Factor Theorem)
      by Piotr Rudnicki
     Received December 30, 2003
805. UNIROOTS
     Primitive Roots of Unity and Cyclotomic Polynomials
      by Broderick Arneson and Piotr Rudnicki
     Received December 30, 2003
806. WEDDWITT
     Witt's Proof of the {W}edderburn Theorem
      by Broderick Arneson, Matthias Baaz and Piotr Rudnicki
     Received December 30, 2003
807. RSSPACE4
     Banach Space of Bounded Real Sequences
      by Yasumasa Suzuki
     Received January 6, 2004
808. POLYEQ_3
     Solving Complex Roots of Polynomial Equation of Degree 2 and 3 with
     Complex Coefficients
      by Yuzhong Ding and Xiquan Liang
     Received January 26, 2004
809. CLVECT_1
     Complex Linear Space and Complex Normed Space
      by Noboru Endou
     Received January 26, 2004
810. LOPBAN_2
     The {B}anach Algebra of Bounded Linear Operators
      by Yasunari Shidama
     Received January 26, 2004
811. CSSPACE
     Complex Linear Space of Complex Sequences
      by Noboru Endou
     Received January 26, 2004
812. JORDAN20
     Behaviour of an Arc Crossing a Line
      by Yatsuka Nakamura
     Received January 26, 2004
813. FINTOPO3
     Some Set Series in Finite Topological Spaces. {F}undamental Concepts
     for Image Processing
      by Masami Tanaka and Yatsuka Nakamura
     Received January 26, 2004
814. LOPBAN_3
     The Series on {B}anach Algebra
      by Yasunari Shidama
     Received February 3, 2004
815. SIN_COS4
     Formulas And Identities of Trigonometric Functions
      by Pacharapokin Chanapat, Kanchun and Hiroshi Yamazaki
     Received February 3, 2004
816. NECKLA_3
     The Class of Series-Parallel Graphs, {III}
      by Krzysztof Retel
     Received February 3, 2004
817. SCMRING4
     Relocability for { \bf SCM } over Ring
      by Artur Korni{\l}owicz and Yasunari Shidama
     Received February 6, 2004
818. CLVECT_2
     Convergent Sequences in Complex Unitary Space
      by Noboru Endou
     Received February 10, 2004
819. RECDEF_2
     Recursive Definitions. {P}art {II}
      by Artur Korni{\l}owicz
     Received February 10, 2004
820. LOPBAN_4
     The Exponential Function on {B}anach Algebra
      by Yasunari Shidama
     Received February 13, 2004
821. NAT_3
     Fundamental {T}heorem of {A}rithmetic
      by Artur Korni{\l}owicz and Piotr Rudnicki
     Received February 13, 2004
822. CSSPACE2
     Hilbert Space of Complex Sequences
      by Noboru Endou
     Received February 24, 2004
823. CSSPACE3
     Banach Space of Absolute Summable Complex Sequences
      by Noboru Endou
     Received February 24, 2004
824. TAYLOR_1
     The {T}aylor Expansions
      by Yasunari Shidama
     Received February 24, 2004
825. CLOPBAN1
     Complex {B}anach Space of Bounded Linear Operators
      by Noboru Endou
     Received February 24, 2004
826. CSSPACE4
     Complex Banach Space of Bounded Complex Sequences
      by Noboru Endou
     Received March 18, 2004
827. FINSEQ_8
     Concatenation of Finite Sequences Reducing Overlapping Part and an
     Argument of Separators of Sequential Files
      by Hirofumi Fukura and Yatsuka Nakamura
     Received March 18, 2004
828. CLVECT_3
     Cauchy Sequence of Complex Unitary Space
      by Yasumasa Suzuki and Noboru Endou
     Received March 18, 2004
829. CFUNCDOM
     Complex Valued Function's Space
      by Noboru Endou
     Received March 18, 2004
830. CLOPBAN2
     Banach Algebra of Bounded Complex Linear Operators
      by Noboru Endou
     Received March 18, 2004
831. SIN_COS5
     Formulas And Identities of Trigonometric Functions
      by Yuzhong Ding and Xiquan Liang
     Received March 18, 2004
832. POLYEQ_4
     Solving the Roots of the Special Polynomial Equation with Real
     Coefficients
      by Yuzhong Ding and Xiquan Liang
     Received March 18, 2004
833. BORSUK_6
     Algebraic Properties of Homotopies
      by Adam Grabowski and Artur Korni{\l}owicz
     Received March 18, 2004
834. TOPALG_1
     The Fundamental Group
      by Artur Korni{\l}owicz, Yasunari Shidama and Adam Grabowski
     Received March 18, 2004
835. NFCONT_1
     The Continuous Functions on Normed Linear Spaces
      by Takaya Nishiyama, Keiji Ohkubo and Yasunari Shidama
     Received April 6, 2004
836. NFCONT_2
     The Uniform Continuity of Functions on Normed Linear Spaces
      by Takaya Nishiyama, Artur Korni{\l}owicz and Yasunari Shidama
     Received April 6, 2004
837. CLOPBAN3
     Series on Complex {B}anach Algebra
      by Noboru Endou
     Received April 6, 2004
838. CLOPBAN4
     Exponential Function on Complex {B}anach Algebra
      by Noboru Endou
     Received April 6, 2004
839. TOPALG_2
     The Fundamental Group of Convex Subspaces of TOP-REAL n
      by Artur Korni{\l}owicz
     Received April 20, 2004
840. TOPREAL9
     Intersections of Intervals and Balls in TOP-REAL n
      by Artur Korni{\l}owicz and Yasunari Shidama
     Received May 10, 2004
841. FIB_NUM2
     Some Properties of {F}ibonacci Numbers
      by Magdalena Jastrz\c{e}bska and Adam Grabowski
     Received May 10, 2004
842. HALLMAR1
     The {H}all {M}arriage {T}heorem
      by Ewa Romanowicz and Adam Grabowski
     Received May 11, 2004
843. NDIFF_1
     The Differentiable Functions on Normed Linear Spaces
      by Hiroshi Imura, Morishige Kimura and Yasunari Shidama
     Received May 24, 2004
844. FIB_NUM3
     Lucas Numbers and Generalized {F}ibonacci Numbers
      by Piotr Wojtecki and Adam Grabowski
     Received May 24, 2004
845. LATSUM_1
     The Operation of Addition of Relational Structures
      by Katarzyna Romanowicz and Adam Grabowski
     Received May 24, 2004
846. NAGATA_1
     The {N}agata-Smirnov Theorem. {P}art {I}
      by Karol P\c{a}k
     Received May 31, 2004
847. GROUP_8
     Properties of Groups
      by Gijs Geleijnse and Grzegorz Bancerek
     Received May 31, 2004
848. CATALAN1
     Catalan Numbers
      by Dorota Cz\c{e}stochowska and Adam Grabowski
     Received May 31, 2004
849. SHEFFER1
     Axiomatization of {B}oolean Algebras Based on Sheffer Stroke
      by Violetta Kozarkiewicz and Adam Grabowski
     Received May 31, 2004
850. SHEFFER2
     Short {S}heffer Stroke-Based Single Axiom for {B}oolean Algebras
      by Aneta {\L}ukaszuk and Adam Grabowski
     Received May 31, 2004
851. NDIFF_2
     Differentiable Functions on Normed Linear Spaces. {P}art {II}
      by Hiroshi Imura, Yuji Sakai and Yasunari Shidama
     Received June 4, 2004
852. PRGCOR_2
     Logical Correctness of Vector Calculation Programs
      by Takaya Nishiyama, Hirofumi Fukura and Yatsuka Nakamura
     Received July 13, 2004
853. FINTOPO4
     Continuous Mappings between Finite and One-Dimensional Finite Topological
     Spaces
      by Hiroshi Imura, Masami Tanaka and Yatsuka Nakamura
     Received July 13, 2004
854. NAGATA_2
     The {N}agata-Smirnov Theorem. {P}art {II}
      by Karol P\c{a}k
     Received July 22, 2004
855. TOPALG_3
     On the Isomorphism of Fundamental Groups
      by Artur Korni{\l}owicz
     Received July 30, 2004
856. VFUNCT_2
     Algebra of Complex Vector Valued Functions
      by Noboru Endou
     Received August 20, 2004
857. NCFCONT1
     Continuous Functions on Real and Complex Normed Linear Spaces
      by Noboru Endou
     Received August 20, 2004
858. TOPALG_4
     On the Fundamental Groups of Products of Topological Spaces
      by Artur Korni{\l}owicz
     Received August 20, 2004
859. SERIES_2
     Partial Sum of Some Series
      by Ming Liang and Yuzhong Ding
     Received September 25, 2004
860. SUBSTUT1
     Substitution in First-Order Formulas: Elementary Properties
      by Patrick Braselmann and Peter Koepke
     Received September 25, 2004
861. SUBLEMMA
     Coincidence Lemma and Substitution Lemma
      by Patrick Braselmann and Peter Koepke
     Received September 25, 2004
862. SUBSTUT2
     Substitution in First-Order Formulas -- Part II. {T}he Construction of
     First-Order Formulas
      by Patrick Braselmann and Peter Koepke
     Received September 25, 2004
863. CALCUL_1
     A Sequent Calculus for First-Order Logic
      by Patrick Braselmann and Peter Koepke
     Received September 25, 2004
864. CALCUL_2
     Consequences of the Sequent Calculus
      by Patrick Braselmann and Peter Koepke
     Received September 25, 2004
865. HENMODEL
     Equivalences of Inconsistency and {H}enkin Models
      by Patrick Braselmann and Peter Koepke
     Received September 25, 2004
866. GOEDELCP
     G{\"o}del's Completeness Theorem
      by Patrick Braselmann and Peter Koepke
     Received September 25, 2004
867. BVFUNC26
     Propositional Calculus for Boolean Valued Functions, {VIII}
      by Shunichi Kobayashi
     Received September 25, 2004
     Has been removed on November 10, 2013
868. HOLDER_1
     H\"older's Inequality and {M}inkowski's Inequality
      by Yasumasa Suzuki
     Received September 25, 2004
869. LP_SPACE
     The Banach Space $l^p$
      by Yasumasa Suzuki
     Received September 25, 2004
870. MESFUNC3
     Lebesgue Integral of Simple Valued Function
      by Yasunari Shidama and Noboru Endou
     Received September 25, 2004
871. SIN_COS6
     Inverse Trigonometric Functions Arcsin and Arccos
      by Artur Korni{\l}owicz and Yasunari Shidama
     Received September 25, 2004
872. JORDAN21
     On Some Points of a Simple Closed Curve
      by Artur Korni{\l}owicz
     Received October 6, 2004
873. JORDAN22
     On Some Points of a Simple Closed Curve. {P}art {II}
      by Artur Korni{\l}owicz and Adam Grabowski
     Received October 6, 2004
874. NCFCONT2
     Uniform Continuity of Functions on Normed Complex Linear Spaces
      by Noboru Endou
     Received October 6, 2004
875. RLTOPSP1
     Introduction to Real Linear Topological Spaces
      by Czes{\l}aw Byli\'nski
     Received October 6, 2004
876. TOPREALA
     Some Properties of Rectangles on the Plane
      by Artur Korni{\l}owicz and Yasunari Shidama
     Received October 18, 2004
877. TOPREALB
     Some Properties of Circles on the Plane
      by Artur Korni{\l}owicz and Yasunari Shidama
     Received October 18, 2004
878. PENCIL_3
     On the Characterization of Collineations of the Segre Product of Strongly
     Connected Partial Linear Spaces
      by Adam Naumowicz
     Received October 18, 2004
879. PENCIL_4
     Spaces of Pencils, {G}rassmann Spaces, and Generalized {V}eronese
     Spaces
      by Adam Naumowicz
     Received November 8, 2004
880. TOPGEN_1
     On the Boundary and Derivative of a Set
      by Adam Grabowski
     Received November 8, 2004
881. GROEB_3
     Construction of {G}r\"obner Bases: Avoiding S-Polynomials -- Buchberger's
     First Criterium
      by Christoph Schwarzweller
     Received December 10, 2004
882. MATRIX_5
     A Theory of Matrices of Complex Elements
      by Wenpai Chang, Hiroshi Yamazaki and Yatsuka Nakamura
     Received December 10, 2004
883. TOPGEN_2
     On the characteristic and weight of a topological space
      by Grzegorz Bancerek
     Received December 10, 2004
884. TOPGEN_3
     On constructing topological spaces and Sorgenfrey line
      by Grzegorz Bancerek
     Received December 10, 2004
885. PARTFUN3
     On the Real Valued Functions
      by Artur Korni{\l}owicz
     Received December 10, 2004
886. ROBBINS3
     Formalization of Ortholattices via Orthoposets
      by Adam Grabowski and Markus Moschner
     Received December 28, 2004
887. JGRAPH_7
     Fashoda Meet Theorem for Rectangles
      by Yatsuka Nakamura and Andrzej Trybulec
     Received January 3, 2005
888. MATHMORP
     Preliminaries to Mathematical Morphology and Its Properties
      by Yuzhong Ding and Xiquan Liang
     Received January 7, 2005
889. JORDAN23
     Subsequences of Almost, Weakly and Poorly One-to-one Finite Sequences
      by Robert Milewski
     Received February 1, 2005
890. GLIB_000
     Alternative Graph Structures
      by Gilbert Lee and Piotr Rudnicki
     Received February 22, 2005
891. GLIB_001
     Walks in a Graph
      by Gilbert Lee
     Received February 22, 2005
892. GLIB_002
     Trees: Connected, Acyclic Graphs
      by Gilbert Lee
     Received February 22, 2005
893. GLIB_003
     Weighted and Labeled Graphs
      by Gilbert Lee
     Received February 22, 2005
894. GLIB_004
     Proof of Dijkstra's Shortest Path Algorithm & Prim's Minimum Spanning
     Tree Algorithm
      by Gilbert Lee and Piotr Rudnicki
     Received February 22, 2005
895. GLIB_005
     Proof of Ford/Fulkerson's Maximum Network Flow Algorithm
      by Gilbert Lee
     Received February 22, 2005
896. RCOMP_3
     Properties of Connected Subsets of the Real Line
      by Artur Korni{\l}owicz
     Received February 22, 2005
897. TOPALG_5
     The Fundamental Group of the Circle
      by Artur Korni{\l}owicz
     Received February 22, 2005
898. BROUWER
     Brouwer Fixed Point Theorem for Disks on the Plane
      by Artur Korni{\l}owicz and Yasunari Shidama
     Received February 22, 2005
899. STIRL2_1
     Stirling Numbers of the Second Kind
      by Karol P\c{a}k
     Received March 15, 2005
900. SETLIM_1
     Limit of Sequence of Subsets
      by Bo Zhang, Hiroshi Yamazaki and Yatsuka Nakamura
     Received March 15, 2005
901. ISOMICHI
     The Properties of Supercondensed Sets, Subcondensed Sets and Condensed Sets
      by Magdalena Jastrz\c{e}bska and Adam Grabowski
     Received March 31, 2005
902. RELSET_2
     Properties of First and Second Order Cutting of Binary Relations
      by Krzysztof Retel
     Received April 25, 2005
903. COMPLSP2
     The Inner Product and Conjugate of Finite Sequences of Complex Numbers
      by Wenpai Chang, Hiroshi Yamazaki and Yatsuka Nakamura
     Received April 25, 2005
904. RINFSUP1
     Inferior Limit and Superior Limit of Sequences of Real Numbers
      by Bo Zhang, Hiroshi Yamazaki and Yatsuka Nakamura
     Received April 29, 2005
905. SIN_COS7
     Formulas And Identities of Inverse Hyperbolic Functions
      by Fuguo Ge, Xiquan Liang and Yuzhong Ding
     Received May 24, 2005
906. EUCLIDLP
     Lines on Planes in $n$-Dimensional Euclidean Spaces
      by Akihiro Kubo
     Received May 24, 2005
907. CARD_FIN
     Cardinal Numbers and Finite Sets
      by Karol P\c{a}k
     Received May 24, 2005
908. SETLIM_2
     Some Equations Related to the Limit of Sequence of Subsets
      by Bo Zhang, Hiroshi Yamazaki and Yatsuka Nakamura
     Received May 24, 2005
909. SERIES_3
     On the Partial Product of Series and Related Basic Inequalities
      by Fuguo Ge and Xiquan Liang
     Received July 6, 2005
910. FINTOPO5
     Homeomorphism between Finite Topological Spaces, Two-Dimensional Lattice
     Spaces and a Fixed Point Theorem
      by Masami Tanaka, Hiroshi Imura and Yatsuka Nakamura
     Received July 6, 2005
911. TAYLOR_2
     The {M}aclaurin Expansions
      by Akira Nishino and Yasunari Shidama
     Received July 6, 2005
912. FDIFF_4
     Several Differentiable Formulas of Special Functions
      by Yan Zhang and Xiquan Liang
     Received July 6, 2005
913. PROB_3
     Set Sequences and Monotone Class
      by Bo Zhang, Hiroshi Yamazaki and Yatsuka Nakamura
     Received August 12, 2005
914. FILEREC1
     A Theory of Sequential Files
      by Hirofumi Fukura and Yatsuka Nakamura
     Received August 12, 2005
915. CIRCLED1
     Circled Sets, Circled Hull, and Circled Family
      by Fahui Zhai, Jianbing Cao and Xiquan Liang
     Received August 30, 2005
916. TOPGEN_4
     On the {B}orel Families of Subsets of Topological Spaces
      by Adam Grabowski
     Received August 30, 2005
917. MESFUNC4
     Linearity of {L}ebesgue Integral of Simple Valued Function
      by Noboru Endou and Yasunari Shidama
     Received September 14, 2005
918. JGRAPH_8
     The {F}ashoda Meet Theorem for Continuous Mappings
      by Yatsuka Nakamura, Andrzej Trybulec and Artur Korni{\l}owicz
     Received September 14, 2005
919. TIETZE
     Tietze {E}xtension {T}heorem
      by Artur Korni{\l}owicz, Grzegorz Bancerek and Adam Naumowicz
     Received September 14, 2005
920. JORDAN24
     Homeomorphisms of {J}ordan Curves
      by Adam Naumowicz and Grzegorz Bancerek
     Received September 15, 2005
921. JORDAN
     Jordan's Curve Theorem
      by Artur Korni{\l}owicz
     Received September 15, 2005
922. MATRIXC1
     The Inner Product and Conjugate of Matrix of Complex Numbers
      by Wenpai Chang, Hiroshi Yamazaki and Yatsuka Nakamura
     Received October 10, 2005
923. SERIES_4
     Partial Sum and Partial Product of Some Series
      by Jianbing Cao, Fahui Zhai and Xiquan Liang
     Received November 7, 2005
924. FDIFF_5
     Some Differentiable Formulas of Special Functions
      by Jianbing Cao, Fahui Zhai and Xiquan Liang
     Received November 7, 2005
925. SIN_COS8
     Formulas and Identities of Hyperbolic Functions
      by Pacharapokin Chanapat and Hiroshi Yamazaki
     Received November 7, 2005
926. TOPGEN_5
     Niemytzki Plane -- an Example of {T}ychonoff Space Which Is Not $T_4$
      by Grzegorz Bancerek
     Received November 7, 2005
927. SERIES_5
     On the Partial Product and Partial Sum of Series and Related Basic
     Inequalities
      by Fuguo Ge and Xiquan Liang
     Received November 23, 2005
928. FDIFF_6
     Several Differentiable Formulas of Special Functions -- Part {II}
      by Yan Zhang, Bo Li and Xiquan Liang
     Received November 23, 2005
929. BINARI_6
     On the Calculus of Binary Arithmetics, Part {II}
      by Shunichi Kobayashi
     Received November 23, 2005
     Has been removed on November 30, 2006
930. PROB_4
     The Relevance of Measure and Probability and Definition of Completeness
     of Probability
      by Bo Zhang, Hiroshi Yamazaki and Yatsuka Nakamura
     Received November 23, 2005
931. MATRIX_6
     Some Properties Of Some Special Matrices
      by Xiaopeng Yue, Xiquan Liang and Zhongpin Sun
     Received December 7, 2005
932. GFACIRC1
     Generalized Full Adder Circuits (GFAs). {P}art {I}
      by Shin'nosuke Yamaguchi, Katsumi Wasaki and Nobuhiro Shimoi
     Received December 7, 2005
933. RING_1
     Quotient Rings
      by Artur Korni{\l}owicz
     Received December 7, 2005
934. REAL_NS1
     Completeness of the Real {E}uclidean Space
      by Noboru Endou and Yasunari Shidama
     Received December 28, 2005
935. MATRIX_7
     Determinant of Some Matrices of Field Elements
      by Yatsuka Nakamura
     Received January 4, 2006
936. MATRIX_8
     Some Properties Of Some Special Matrices, Part {II}
      by Xiaopeng Yue, Dahai Hu, Xiquan Liang and Zhongpin Sun
     Received January 4, 2006
937. MATRIX_9
     On the Permanent of a Matrix
      by Ewa Romanowicz and Adam Grabowski
     Received January 4, 2006
938. MATRIXR1
     A Theory of Matrices of Real Elements
      by Yatsuka Nakamura, Nobuyuki Tamura and Wenpai Chang
     Received February 20, 2006
939. MOEBIUS1
     On the Properties of the {M}\"obius Function
      by Magdalena Jastrz\c{e}bska and Adam Grabowski
     Received March 21, 2006
940. FDIFF_7
     Several Differentiation Formulas of Special Functions -- Part {III}
      by Bo Li, Yan Zhang and Xiquan Liang
     Received March 22, 2006
941. NAT_4
     Pocklington's Theorem and {B}ertrand's Postulate
      by Marco Riccardi
     Received May 17, 2006
942. MESFUNC5
     Integral of Measurable Function
      by Noboru Endou and Yasunari Shidama
     Received May 24, 2006
943. REAL_3
     Simple Continued Fractions and Their Convergents
      by Bo Li, Yan Zhang and Artur Korni{\l}owicz
     Received August 18, 2006
944. CHORD
     Chordal Graphs
      by Broderick Arneson and Piotr Rudnicki
     Received August 18, 2006
945. FINTOPO6
     Connectedness and Continuous Sequences in Finite Topological Spaces
      by Yatsuka Nakamura
     Received August 18, 2006
946. MATRPROB
     The Definition of Finite Sequences and Matrices of Probability, and
     Addition of Matrices of Real Elements
      by Bo Zhang and Yatsuka Nakamura
     Received August 18, 2006
947. FDIFF_8
     Several Differentiation Formulas of Special Functions -- Part {IV}
      by Bo Li and Peng Wang
     Received September 29, 2006
948. DIFF_1
     Difference and Difference Quotient
      by Bo Li, Yan Zhang and Xiquan Liang
     Received September 29, 2006
949. POLYNOM8
     Multiplication of Polynomials using {D}iscrete {F}ourier {T}ransformation
      by Krzysztof Treyderowski and Christoph Schwarzweller
     Received October 12, 2006
950. MATRIX10
     Some Special Matrices of Real Elements and Their Properties
      by Xiquan Liang, Fuguo Ge and Xiaopeng Yue
     Received October 19, 2006
951. HURWITZ
     Schur's Theorem on the Stability of Networks
      by Agnieszka Rowi\'nska-Schwarzweller and Christoph Schwarzweller
     Received October 19, 2006
952. MESFUNC6
     Integral of Real-valued Measurable Function
      by Yasunari Shidama and Noboru Endou
     Received October 27, 2006
953. CATALAN2
     The {C}atalan Numbers. {P}art {II}
      by Karol P\c{a}k
     Received October 31, 2006
954. QUATERNI
     The Quaternion Numbers
      by Xiquan Liang and Fuguo Ge
     Received November 14, 2006
955. MODELC_1
     Model Checking, Part {I}
      by Kazuhisa Ishida
     Received November 14, 2006
956. LEXBFS
     Recognizing Chordal Graphs: Lex BFS and MCS
      by Broderick Arneson and Piotr Rudnicki
     Received November 17, 2006
957. INTEGRA6
     Integrability and the Integral of Partial Functions from $\Bbb R$ into
     $\Bbb R$
      by Noboru Endou, Yasunari Shidama and Masahiko Yamazaki
     Received November 17, 2006
958. NORMSP_2
     Baire's Category Theorem and Some Spaces Generated from Real Normed Space
      by Noboru Endou, Yasunari Shidama and Katsumasa Okamura
     Received November 21, 2006
959. NUMERAL1
     On the Representation of Natural Numbers in Positional Numeral Systems
      by Adam Naumowicz
     Received December 31, 2006
960. BCIALG_1
     Several Classes of {BCI}-algebras and Their Properties
      by Yuzhong Ding
     Received February 23, 2007
961. FLANG_1
     Formal Languages -- Concatenation and Closure
      by Micha{\l} Trybulec
     Received March 9, 2007
962. MATRIX11
     Basic Properties of Determinants of Square Matrices over a Field
      by Karol P\c{a}k
     Received March 21, 2007
963. COMBGRAS
     Combinatorial {G}rassmannians
      by Andrzej Owsiejczuk
     Received April 16, 2007
964. GROUP_9
     The {J}ordan-H\"older Theorem
      by Marco Riccardi
     Received April 20, 2007
965. FLANG_2
     Regular Expression Quantifiers -- $m$ to $n$ Occurrences
      by Micha{\l} Trybulec
     Received June 6, 2007
966. INTEGRA7
     Riemann Indefinite Integral of Functions of Real Variable
      by Yasunari Shidama, Noboru Endou, Katsumi Wasaki and Katuhiko Kanazashi
     Received June 6, 2007
967. PDIFF_1
     Partial Differentiation on Normed Linear Spaces $ {\cal R}^n$
      by Noboru Endou, Yasunari Shidama and Keiichi Miyajima
     Received June 6, 2007
968. FDIFF_9
     Several Differentiation Formulas of Special Functions -- Part {V}
      by Peng Wang and Bo Li
     Received July 9, 2007
969. PRVECT_2
     The Product Space of Real Normed Spaces and Its Properties
      by Noboru Endou, Yasunari Shidama and Keiichi Miyajima
     Received July 9, 2007
970. AOFA_000
     Mizar Analysis of Algorithms: Preliminaries
      by Grzegorz Bancerek
     Received July 9, 2007
971. ENTROPY1
     Definition and Some Properties of Information Entropy
      by Bo Zhang and Yatsuka Nakamura
     Received July 9, 2007
972. REWRITE2
     String Rewriting Systems
      by Micha{\l} Trybulec
     Received July 17, 2007
973. MATRIXR2
     Determinant and Inverse of Matrices of Real Elements
      by Nobuyuki Tamura and Yatsuka Nakamura
     Received July 17, 2007
974. RANKNULL
     The Rank+Nullity Theorem
      by Jesse Alama
     Received July 31, 2007
975. LAPLACE
     Laplace Expansion
      by Karol P\c{a}k and Andrzej Trybulec
     Received August 13, 2007
976. MATRIX12
     Some Properties of Line and Column Operations on Matrices
      by Xiquan Liang, Tao Sun and Dahai Hu
     Received August 13, 2007
977. GROUP_10
     The Sylow Theorems
      by Marco Riccardi
     Received August 13, 2007
978. COMPACT1
     Alexandroff One Point Compactification
      by Czeslaw Bylinski
     Received August 13, 2007
979. ARROW
     Arrow's Impossibility Theorem
      by Freek Wiedijk
     Received August 13, 2007
980. BCIALG_2
     Congruences and Quotient Algebras of {BCI}-algebras
      by Yuzhong Ding and Zhiyong Pang
     Received August 28, 2007
981. INT_4
     Linear Congruence Relation and Complete Residue Systems
      by Xiquan Liang, Li Yan and Junjie Zhao
     Received August 28, 2007
982. INTEGRA8
     Several Integrability Formulas of Special Functions
      by Cuiying Peng, Fuguo Ge and Xiquan Liang
     Received August 28, 2007
983. MATRIX13
     Basic Properties of the Rank of Matrices over a Field
      by Karol P\c{a}k
     Received August 28, 2007
984. PCS_0
     Basic Operations on Preordered Coherent Spaces
      by Klaus E. Grue and Artur Korni{\l}owicz
     Received August 28, 2007
985. RINFSUP2
     Inferior Limit, Superior Limit and Convergence of Sequences of Extended
     Real Numbers
      by Hiroshi Yamazaki, Noboru Endou, Yasunari Shidama and Hiroyuki Okazaki
     Received August 28, 2007
986. BCIALG_3
     Several Classes of {BCK}-algebras and Their Properties
      by Tao Sun, Dahai Hu and Xiquan Liang
     Received September 19, 2007
987. FDIFF_10
     Several Differentiation Formulas of Special Functions -- Part {VI}
      by Bo Li and Pan Wang
     Received September 19, 2007
988. BSPACE
     The Vector Space of Subsets of a Set Based on Symmetric Difference
      by Jesse Alama
     Received October 9, 2007
989. POLYFORM
     Euler's Polyhedron Formula
      by Jesse Alama
     Received October 9, 2007
990. LOPBAN_5
     Uniform Boundedness Principle
      by Hideki Sakurai, Hisayoshi Kunimune and Yasunari Shidama
     Received October 9, 2007
991. INT_5
     Gauss Lemma and Law of Quadratic Reciprocity
      by Li Yan, Xiquan Liang and Junjie Zhao
     Received October 9, 2007
992. FLANG_3
     Regular Expression Quantifiers -- at least $m$ Occurrences
      by Micha{\l} Trybulec
     Received October 9, 2007
993. COMPL_SP
     Complete Spaces
      by Karol P\c{a}k
     Received October 12, 2007
994. DIFF_2
     Difference and Difference Quotient -- Part {II}
      by Bo Li, Yanping Zhuang and Xiquan Liang
     Received October 25, 2007
995. MESFUNC7
     The First Mean Value Theorem for Integrals
      by Keiko Narita, Noboru Endou and Yasunari Shidama
     Received October 30, 2007
996. MESFUNC8
     Egoroff's Theorem
      by Noboru Endou, Yasunari Shidama and Keiko Narita
     Received October 30, 2007
997. BCIALG_4
     BCI-Algebras with Condition (S) and Their Properties
      by Tao Sun, Junjie Zhao and Xiquan Liang
     Received November 24, 2007
998. GFACIRC2
     Stability of n-bit Generalized Full Adder Circuits (GFAs). Part {II}
      by Katsumi Wasaki
     Received December 18, 2007
999. MATRIX15
     Solutions of Linear Equations
      by Karol P\c{a}k
     Received December 18, 2007
1000. HELLY
     Helly property for subtrees
      by Jessica Enright and Piotr Rudnicki
     Received January 10, 2008
1001. EUCLID_6
     Heron's Formula and Ptolemy's Theorem
      by Marco Riccardi
     Received January 10, 2008
1002. INT_7
     Uniqueness of factoring an integer and multiplicative group $Z/pZ^{*}$
      by Hiroyuki Okazaki and Yasunari Shidama
     Received January 31, 2008
1003. BCIIDEAL
     Ideals of BCI-Algebras and Their Properties
      by Chenglong Wu and Yuzhong Ding
     Received March 3, 2008
1004. C0SP1
     Banach Algebra of Bounded Functionals
      by Yasunari Shidama, Hikofumi Suzuki and Noboru Endou
     Received March 3, 2008
1005. CONVEX4
     Convex Sets and Convex Combinations on Complex Linear Spaces
      by Hidenori Matsuzaki, Noboru Endou and Yasunari Shidama
     Received March 3, 2008
1006. QUATERN2
     Inner Products, Group, Ring of Quaternion Numbers
      by Fuguo Ge
     Received March 18, 2008
1007. HFDIFF_1
     Several Higher Differentiation Formulas of Special Functions
      by Junjie Zhao, Xiquan Liang and Li Yan
     Received March 18, 2008
1008. SIN_COS9
     Inverse Trigonometric Functions Arctan and Arccot
      by Xiquan Liang and Bing Xie
     Received March 18, 2008
1009. SINCOS10
     Inverse Trigonometric Functions Arcsec1, Arcsec2, Arccosec1 and Arccosec2
      by Bing Xie, Xiquan Liang and Fuguo Ge
     Received March 18, 2008
1010. MESFUNC9
     The Lebesgue Monotone Convergence Theorem
      by Noboru Endou, Keiko Narita and Yasunari Shidama
     Received March 18, 2008
1011. AOFA_I00
     Mizar Analysis of Algorithms: Algorithms over Integers
      by Grzegorz Bancerek
     Received March 18, 2008
1012. MATRIX14
     Invertibility of Matrices of Field Elements
      by Yatsuka Nakamura, Kunio Oniumi and Wenpai Chang
     Received April 2, 2008
1013. RAMSEY_1
     Ramsey's Theorem
      by Marco Riccardi
     Received April 18, 2008
1014. ABCMIZ_1
     Towards the construction of a model of Mizar concepts
      by Grzegorz Bancerek
     Received April 21, 2008
1015. MODELC_2
     Model Checking, Part II
      by Kazuhisa Ishida
     Received April 21, 2008
1016. INT_6
     Modular Integer Arithmetic
      by Christoph Schwarzweller
     Received May 13, 2008
1017. BCIALG_5
     General Theory of Quasi-Commutative BCI-algebras
      by Tao Sun, Weibo Pan, Chenglong Wu and Xiquan Liang
     Received May 13, 2008
1018. MATRIXJ1
     Block Diagonal Matrices
      by Karol P\c{a}k
     Received May 13, 2008
1019. MATRLIN2
     Linear Map of Matrices
      by Karol P\c{a}k
     Received May 13, 2008
1020. ROBBINS4
     Orthomodular Lattices
      by El\.zbieta M\c{a}dra and Adam Grabowski
     Received June 27, 2008
1021. AFINSQ_2
     Basic Properties and Concept of Selected Subsequence of Zero Based Finite
     Sequences
      by Yatsuka Nakamura and Hisashi Ito
     Received June 27, 2008
1022. VECTSP11
     Eigenvalues of a Linear Transformation
      by Karol P\c{a}k
     Received July 11, 2008
1023. MATRIXJ2
     Jordan Matrix Decomposition
      by Karol P\c{a}k
     Received July 11, 2008
1024. MESFUN10
     Fatou's Lemma and the {L}ebesgue's Convergence Theorem
      by Noboru Endou, Keiko Narita and Yasunari Shidama
     Received July 22, 2008
1025. INTEGR10
     Extended {R}iemann Integral of Functions of Real Variable and One-sided
     {L}aplace Transform
      by Masahiko Yamazaki, Hiroshi Yamazaki, Yasunari Shidama and Yatsuka Nakamura
     Received July 22, 2008
1026. MESFUN6C
     Integral of Complex-Valued Measurable Function
      by Keiko Narita, Noboru Endou and Yasunari Shidama
     Received July 30, 2008
1027. MATROID0
     Introduction to Matroids
      by Grzegorz Bancerek and Yasunari Shidama
     Received July 30, 2008
1028. PDIFF_2
     Partial Differentiation of Real Binary Functions
      by Bing Xie, Xiquan Liang, Hongwei Li and Yanping Zhuang
     Received August 5, 2008
1029. MODELC_3
     Model Checking, Part {III}
      by Kazuhisa Ishida and Yasunari Shidama
     Received August 19, 2008
1030. MATRIX16
     Basic Properties of Circulant Matrices and Anti-circular Matrices
      by Xiaopeng Yue and Xiquan Liang
     Received August 26, 2008
1031. LPSPACE1
     On $L^1$ Space Formed by Real-valued Partial Functions
      by Yasushige Watase, Noboru Endou and Yasunari Shidama
     Received August 26, 2008
1032. BCIALG_6
     {BCI}-Homomorphisms
      by Yuzhong Ding, Fuguo Ge and Chenglong Wu
     Received August 26, 2008
1033. FTACELL1
     Stability of the 4-2 Binary Addition Circuit Cells. Part {I}
      by Katsumi Wasaki
     Received August 28, 2008
1034. FDIFF_11
     Several Differentiation Formulas of Special Functions -- Part {VII}
      by Fuguo Ge and Bing Xie
     Received September 23, 2008
1035. LOPBAN_6
     Open Mapping Theorem
      by Hideki Sakurai, Hisayoshi Kunimune and Yasunari Shidama
     Received September 23, 2008
1036. EUCLID_7
     The Real Vector Spaces of Finite Sequences Are Finite Dimensional
      by Yatsuka Nakamura, Artur Korni{\l}owicz, Nagato Oya
        and Yasunari Shidama
     Received September 23, 2008
1037. INTEGRA9
     Several Integrability Formulas of Some Functions, Orthogonal Polynomials
     and Norm Functions
      by Bo Li, Yanping Zhuang, Bing Xie and Pan Wang
     Received October 14, 2008
1038. INTEGR11
     Several Integrability Formulas of Special Functions -- Part {II}
      by Bo Li, Yanping Zhuang, Yanhong Men and Xiquan Liang
     Received October 14, 2008
1039. QUATERN3
     Some Operations on Quaternion Numbers
      by Bo Li, Pan Wang, Xiquan Liang and Yanping Zhuang
     Received October 14, 2008
1040. PETRI_2
     Cell Petri Net Concepts
      by Mitsuru Jitsukawa, Pauline N. Kawamoto, Yasunari Shidama and Yatsuka Nakamura
     Received October 14, 2008
1041. VALUED_2
     Arithmetic Operations on Functions from Sets into Functional Sets
      by Artur Korni{\l}owicz
     Received October 15, 2008
1042. CFDIFF_1
     Complex Function Differentiability
      by Chanapat Pacharapokin, Hiroshi Yamazaki, Yasunari Shidama and Yatsuka Nakamura
     Received November 4, 2008
1043. KOLMOG01
     Kolmogorov's Zero-one Law
      by Agnes Doll
     Received November 4, 2008
1044. PDIFF_3
     Second-order Partial Differentiation of Real Binary Functions
      by Bing Xie, Xiquan Liang and Xiuzhuan Shen
     Received December 16, 2008
1045. MESFUN7C
     The Measurability of Complex-Valued Functional Sequences
      by Keiko Narita, Noboru Endou and Yasunari Shidama
     Received December 16, 2008
1046. MEMBER_1
     Collective Operations on Number-Membered Sets
      by Artur Korni{\l}owicz
     Received December 19, 2008
1047. POLYEQ_5
     Solution of Cubic and Quartic Equations
      by Marco Riccardi
     Received March 3, 2009
1048. NAT_5
     The Perfect Number Theorem and Wilson's Theorem
      by Marco Riccardi
     Received March 3, 2009
1049. RANDOM_1
     Probability on Finite Set and Real Valued Random Variables
      by Hiroyuki Okazaki and Yasunari Shidama
     Received March 17, 2009
1050. MESFUN9C
     Lebesgue's Convergence Theorem of Complex-Valued Function
      by Keiko Narita, Noboru Endou and Yasunari Shidama
     Received March 17, 2009
1051. METRIZTS
     Basic Properties of Metrizable Topological Spaces
      by Karol P\c{a}k
     Received March 31, 2009
1052. GR_CY_3
     Properties of Primes and Multiplicative Group of a Field
      by Kenichi Arai and Hiroyuki Okazaki
     Received April 7, 2009
1053. CFDIFF_2
     Cauchy-Riemann Differential Equations of Complex Functions
      by Hiroshi Yamazaki, Yasunari Shidama, Chanapat Pacharapokin and Yatsuka Nakamura
     Received April 7, 2009
1054. MEASURE8
     The Hopf Extension Theorem of Measure
      by Noboru Endou, Hiroyuki Okazaki and Yasunari Shidama
     Received April 7, 2009
1055. REWRITE3
     Labelled State Transition Systems
      by Micha{\l} Trybulec
     Received May 5, 2009
1056. DIST_1
     Probability on Finite and Discrete Set and Uniform Distribution
      by Hiroyuki Okazaki
     Received May 5, 2009
1057. INTEGR15
     Riemann Integral of Functions $\mathbbbR$ into $\mathbbbR^n$
      by Keiichi Miyajima and Yasunari Shidama
     Received May 5, 2009
1058. FUNCT_8
     Basic properties of even and odd functions
      by Bo Li and Yanhong Men
     Received May 25, 2009
1059. FSM_3
     Equivalence of Epsilon, Nondeterministic [Finite] Automata and Deterministic
     [Finite] Automata
      by Micha{\l} Trybulec
     Received May 25, 2009
1060. TOPDIM_1
     Small {I}nductive {D}imension of {T}opological {S}paces
      by Karol P\c{a}k
     Received June 29, 2009
1061. GROUP_11
     On Rough Subgroup of a Group
      by Xiquan Liang and Dailu Li
     Received August 7, 2009
1062. TOPDIM_2
     Small Inductive Dimension of Topological Spaces, Part {II}
      by Karol P\c{a}k
     Received August 7, 2009
1063. DILWORTH
     Dilworth's Decomposition Theorem for Posets
      by Piotr Rudnicki
     Received September 17, 2009
1064. INTEGR1C
     Complex Integral
      by Masahiko Yamazaki, Hiroshi Yamazaki, Katsumi Wasaki and Yasunari Shidama
     Received October 10, 2009
1065. INTERVA1
     On the Lattice of Intervals and Rough Sets
      by Adam Grabowski and Magdalena Jastrz\c{e}bska
     Received October 10, 2009
1066. FUNCT_9
     Basic Properties of Periodic Functions
      by Bo Li, Yanhong Men, Dailu Li and Xiquan Liang
     Received October 10, 2009
1067. EUCLID_8
     Vector Function and its Differentiation Formulas in 3-dimensional Euclidean
     Spaces
      by Xiquan Liang, Piqing Zhao and Ou Bai
     Received October 10, 2009
1068. ORDINAL5
     Epsilon Numbers and Cantor Normal Form
      by Grzegorz Bancerek
     Received October 20, 2009
1069. C0SP2
     Banach Algebra of Continuous Functionals
      by Kanazashi Katuhiko, Noboru Endou and Yasunari Shidama
     Received October 20, 2009
1070. ALGSTR_4
     Free Magmas
      by Marco Riccardi
     Received October 20, 2009
1071. INTEGR12
     Integrability Formulas -- Part {I}
      by Bo Li and Na Ma
     Received November 7, 2009
1072. PDIFF_4
     Partial Differentiation of Real Ternary Functions
      by Takao Inou\'e, Bing Xie and Xiquan Liang
     Received November 7, 2009
1073. POSET_1
     Fix-point Theorem for Continuous Functions on Chain-complete Posets
      by Kazuhisa Ishida and Yasunari Shidama
     Received November 10, 2009
1074. GRNILP_1
     Nilpotent Groups
      by Dailu Li, Xiquan Liang and Yanhong Men
     Received November 10, 2009
1075. DIFF_3
     Difference and Difference Quotient -- Part {III}
      by Xiquan Liang and Ling Tang
     Received November 17, 2009
1076. ABCMIZ_A
     A Model of Mizar Concepts -- Unification
      by Grzegorz Bancerek
     Received November 20, 2009
1077. FIB_NUM4
     Representation of the {F}ibonacci and {L}ucas Numbers in Terms of
     the Floor and Ceiling Functor
      by Magdalena Jastrz\c{e}bska
     Received November 30, 2009
1078. EUCLID_9
     The Correspondence Between $n$-dimensional {E}uclidean Space and the
     Product of $n$ Real Lines
      by Artur Korni{\l}owicz
     Received November 30, 2009
1079. RLAFFIN1
     Affine Independence in Vector Spaces
      by Karol P\c{a}k
     Received December 18, 2009
1080. SIMPLEX0
     Abstract Simplicial Complexes
      by Karol P\c{a}k
     Received December 18, 2009
1081. RVSUM_2
     The Sum and Product of Finite Sequences of Complex Numbers
      by Keiichi Miyajima and Takahiro Kato
     Received January 12, 2010
1082. PDIFF_5
     Second-order Partial Differentiation of Real Ternary Functions
      by Takao Inou\'e
     Received January 26, 2010
1083. INTEGR13
     Integrability Formulas -- Part {II}
      by Bo Li, Na Ma and Xiquan Liang
     Received February 4, 2010
1084. INTEGR14
     Integrability Formulas -- Part {III}
      by Bo Li and Na Ma
     Received February 4, 2010
1085. LPSPACE2
     On $L^p$ Space Formed by Real-valued Partial Functions
      by Yasushige Watase, Noboru Endou and Yasunari Shidama
     Received February 4, 2010
1086. TOPS_4
     Miscellaneous Facts about Open Functions and Continuous Functions
      by Artur Korni{\l}owicz
     Received February 9, 2010
1087. TOPREALC
     On the Continuity of Some Functions
      by Artur Korni{\l}owicz
     Received February 9, 2010
1088. RLAFFIN2
     The Geometric Interior in Real Linear Spaces
      by Karol P\c{a}k
     Received February 9, 2010
1089. SIMPLEX1
     Sperner's Lemma
      by Karol P\c{a}k
     Received February 9, 2010
1090. CARDFIN2
     Counting Derangements, Counting Non Bijective Functions and the Birthday
     Problem
      by Cezary Kaliszyk
     Received February 23, 2010
1091. INTEGR16
     Riemann Integral of Functions $\mathbbbR$ into $\mathbbbC$
      by Keiichi Miyajima, Takahiro Kato and Yasunari Shidama
     Received February 23, 2010
1092. PDIFF_6
     Differentiation of Vector-Valued Functions on $n$-Dimensional Real Normed
     Linear Spaces
      by Takao Inou\'e, Noboru Endou and Yasunari Shidama
     Received February 23, 2010
1093. RANDOM_2
     Probability Measure on Discrete Spaces and Algebra of Real Valued Random
     Variables
      by Hiroyuki Okazaki and Yasunari Shidama
     Received March 16, 2010
1094. PDIFF_7
     Partial Differentiation of Vector-Valued Functions on $n$-Dimensional Real
     Normed Linear Spaces
      by Takao Inou\'e, Adam Naumowicz, Noboru Endou and Yasunari Shidama
     Received April 22, 2010
1095. GROUPP_1
     Some Properties of $p$-Groups and Commutative $p$-Groups
      by Xiquan Liang and Dailu Li
     Received April 29, 2010
1096. INTEGR18
     Riemann Integral of Functions from $\mathbbbR$ into Real Normed Space
      by Keiichi Miyajima, Takahiro Kato and Yasunari Shidama
     Received May 20, 2010
1097. GROUP_12
     Normal Subgroup of Product of Groups
      by Hiroyuki Okazaki, Kenichi Arai and Yasunari Shidama
     Received July 2, 2010
1098. MYCIELSK
     The {M}ycielskian of a Graph
      by Piotr Rudnicki and Lorna Stewart
     Received July 2, 2010
1099. DIFF_4
     Difference and Difference Quotient -- Part {IV}
      by Xiquan Liang, Ling Tang and Xichun Jiang
     Received July 12, 2010
1100. MFOLD_1
     The Definition of Topological Manifolds
      by Marco Riccardi
     Received August 17, 2010
1101. NFCONT_3
     More on Continuous Functions on Normed Linear Spaces
      by Hiroyuki Okazaki, Noboru Endou and Yasunari Shidama
     Received August 17, 2010
1102. PRVECT_3
     Cartesian Products of Family of Real Linear Spaces
      by Hiroyuki Okazaki, Noboru Endou and Yasunari Shidama
     Received August 17, 2010
1103. RLVECT_X
     Formalization of Integral Linear Space
      by Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
     Received August 17, 2010
1104. PDIFF_8
     Partial Differentiation, Differentiation and Continuity on $n$-Dimensional
     Real Normed Linear Spaces
      by Takao Inou\'e, Adam Naumowicz, Noboru Endou and Yasunari Shidama
     Received October 13, 2010
1105. NDIFF_3
     Differentiable Functions into Real Normed Spaces
      by Hiroyuki Okazaki, Noboru Endou, Keiko Narita and Yasunari Shidama
     Received October 13, 2010
1106. CGAMES_1
     Conway's Games and Some of Their Basic Properties
      by Robin Nittka
     Received October 13, 2010
1107. ORDINAL6
     Veblen Hierarchy
      by Grzegorz Bancerek
     Received October 18, 2010
1108. EXCHSORT
     Sorting by Exchanging
      by Grzegorz Bancerek
     Received October 18, 2010
1109. MATRTOP1
     Linear Transformations of Euclidean Topological Spaces
      by Karol P\kak
     Received October 26, 2010
1110. MATRTOP2
     Linear Transformations of Euclidean Topological Spaces. Part {II}
      by Karol P\kak
     Received October 26, 2010
1111. LTLAXIO1
     The Axiomatization of Propositional Linear Time Temporal Logic
      by Mariusz Giero
     Received November 20, 2010
1112. CC0SP1
     Banach Algebra of Bounded Complex-Valued Functionals
      by Katuhiko Kanazashi, Hiroyuki Okazaki and Yasunari Shidama
     Received November 20, 2010
1113. MAZURULM
     Mazur-Ulam Theorem
      by Artur Korni{\l}owicz
     Received December 21, 2010
1114. EC_PF_1
     Set of Points on Elliptic Curve in Projective Coordinates
      by Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
     Received December 21, 2010
1115. RLAFFIN3
     Continuity of Barycentric Coordinates in Euclidean Topological Spaces
      by Karol P\kak
     Received December 21, 2010
1116. SIMPLEX2
     Brouwer Fixed Point Theorem for Simplexes
      by Karol P\kak
     Received December 21, 2010
1117. BROUWER2
     Brouwer Fixed Point Theorem in the General Case
      by Karol P\kak
     Received December 21, 2010
1118. FOMODEL0
     Preliminaries to Classical First-order Model Theory
      by Marco B. Caminati
     Received December 29, 2010
1119. FOMODEL1
     Definition of first order language with arbitrary alphabet. Syntax of
     terms, atomic formulas and their subterms.
      by Marco B. Caminati
     Received December 29, 2010
1120. FOMODEL2
     First order languages: syntax, part two; semantics.
      by Marco B. Caminati
     Received December 29, 2010
1121. FOMODEL3
     Free interpretation, quotient interpretation and substitution of a letter
     with a term for first order languages.
      by Marco B. Caminati
     Received December 29, 2010
1122. FOMODEL4
     Sequent calculus, derivability, provability. Goedel's completeness theorem.
      by Marco B. Caminati
     Received December 29, 2010
1123. CAYLEY
     Cayley's Theorem
      by Artur Korni{\l}owicz
     Received December 29, 2010
1124. BOR_CANT
     Borel-Cantelli Lemma
      by Peter Jaeger
     Received January 31, 2011
1125. NFCONT_4
     More on the Continuity of Real Functions
      by Keiko Narita, Artur Korni{\l}owicz and Yasunari Shidama
     Received February 22, 2011
1126. STACKS_1
     Representation Theorem for Stacks
      by Grzegorz Bancerek
     Received February 22, 2011
1127. FINANCE1
     Elementary Introduction to Stochastic Finance in Discrete Time
      by Peter Jaeger
     Received March 22, 2011
1128. FVALUAT1
     Valuation Theory, Part {I}
      by Grzegorz Bancerek, Hidetsune Kobayashi and Artur Korni{\l}owicz
     Received April 7, 2011
1129. CC0SP2
     Banach Algebra of Complex-Valued Continuous Functionals and Space of
     Complex-valued Continuous Functionals with Bounded Support
      by Katuhiko Kanazashi, Hiroyuki Okazaki and Yasunari Shidama
     Received May 30, 2011
1130. MATRTOP3
     The Rotation Group
      by Karol P\kak
     Received May 30, 2011
1131. NDIFF_5
     Differentiable Functions on Normed Linear Spaces
      by Yasunari Shidama
     Received June 2, 2011
1132. MFOLD_2
     Planes and Spheres as Topological Manifolds. Stereographic Projection
      by Marco Riccardi
     Received June 6, 2011
1133. ZMODUL01
     $\mathbb Z$-modules
      by Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
     Received September 5, 2011
1134. MORPH_01
     Morphology for Image Processing, Part {I}
      by Hiroshi Yamazaki, Czes\l aw Byli\'nski and Katsumi Wasaki
     Received September 21, 2011
1135. NDIFF_4
     The Differentiable Functions from $\mathbbR$ into ${\mathbbR}^n$
      by Keiko Narita, Artur Korni\l owicz and Yasunari Shidama
     Received September 28, 2011
1136. MATRIX17
     Some Basic Properties of Some Special Matrices, Part {III}
      by Xiquan Liang and Tao Wang
     Received October 23, 2011
1137. INTEGR19
     Riemann Integral of Functions from $\mathbbbR$ into $n$-dimensional Real
     Normed Space
      by Keiichi Miyajima, Artur Korni{\l}owicz and Yasunari Shidama
     Received October 27, 2011
1138. EC_PF_2
     Operations of Points on Elliptic Curve in Projective Coordinates
      by Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima and Yasunari Shidama
     Received November 3, 2011
1139. TOPALG_6
     Fundamental Group of $n$-sphere for $n \geq 2$
      by Marco Riccardi and Artur Korni{\l}owicz
     Received November 3, 2011
1140. BORSUK_7
     The {B}orsuk-Ulam Theorem
      by Artur Korni{\l}owicz and Marco Riccardi
     Received November 3, 2011
1141. PDIFF_9
     Higher Order Partial Differentiation
      by Noboru Endou, Hiroyuki Okazaki and Yasunari Shidama
     Received November 20, 2011
1142. DESCIP_1
     Formalization of the Data Encryption Standard
      by Hiroyuki Okazaki and Yasunari Shidama
     Received November 30, 2011
1143. MMLQUERY
     Semantic of MML Query
      by Grzegorz Bancerek
     Received December 18, 2011
1144. MENELAUS
     Routh's, {M}enelaus' and Generalized {C}eva's Theorems
      by Boris A. Shminke
     Received January 16, 2012
1145. SCMYCIEL
     Simple Graphs as Simplicial Complexes: the {M}ycielskian of a Graph
      by Piotr Rudnicki and Lorna Stewart
     Received February 8, 2012
1146. NTALGO_1
     Extended Euclidean Algorithm and CRT Algorithm
      by Hiroyuki Okazaki, Yosiki Aoki and Yasunari Shidama
     Received February 8, 2012
1147. RATFUNC1
     Introduction to Rational Functions
      by Christoph Schwarzweller
     Received February 8, 2012
1148. QC_TRANS
     Transition of Consistency and Satisfiability under Language Extensions
      by Julian J. Schl\"oder and Peter Koepke
     Received May 7, 2012
1149. GOEDCPUC
     The G\"odel Completeness Theorem for Uncountable Languages
      by Julian J. Schl\"oder and Peter Koepke
     Received May 7, 2012
1150. ZMODUL02
     Quotient Module of $\mathbb Z$-module
      by Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
     Received May 7, 2012
1151. LTLAXIO2
     The Derivations of Temporal Logic Formulas
      by Mariusz Giero
     Received May 7, 2012
1152. LTLAXIO3
     The Properties of Sets of Temporal Logic Subformulas
      by Mariusz Giero
     Received May 7, 2012
1153. LTLAXIO4
     Weak Completeness Theorem for Propositional Linear Time Temporal Logic
      by Mariusz Giero
     Received May 7, 2012
1154. FRIENDS1
     The Friendship Theorem
      by Karol P\kak
     Received May 15, 2012
1155. MSAFREE4
     Free Term Algebras
      by Grzegorz Bancerek
     Received May 15, 2012
1156. DIST_2
     Posterior Probability on Finite Set
      by Hiroyuki Okazaki
     Received July 4, 2012
1157. INT_8
     Basic Properties of Primitive Root and Order Function
      by Na Ma and Xiquan Liang
     Received August 6, 2012
1158. LOPBAN_7
     Banach's Continuous Inverse Theorem and Closed Graph Theorem
      by Hideki Sakurai, Hiroyuki Okazaki and Yasunari Shidama
     Received August 6, 2012
1159. ZMODUL03
     Free $\mathbb Z$-module
      by Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
     Received August 6, 2012
1160. CAYLDICK
     Cayley-Dickson Construction
      by Artur Korni{\l}owicz
     Received August 6, 2012
1161. ORDEQ_01
     Contracting Mapping on Normed Linear Space
      by Keiichi Miyajima, Artur Korni{\l}owicz and Yasunari Shidama
     Received August 19, 2012
1162. ALTCAT_5
     Products in Categories without Uniqueness of { \bf cod } and { \bf dom }
      by Artur Korni{\l}owicz
     Received August 19, 2012
1163. AOFA_A00
     Program Algebra over an Algebra
      by Grzegorz Bancerek
     Received August 27, 2012
1164. GROUP_14
     Isomorphisms of Direct Products of Finite Cyclic Groups
      by Kenichi Arai, Hiroyuki Okazaki and Yasunari Shidama
     Received August 27, 2012
1165. LPSPACC1
     On $L^1$ Space Formed by Complex-valued Partial Functions
      by Yasushige Watase, Noboru Endou and Yasunari Shidama
     Received August 27, 2012
1166. AOFA_A01
     Analysis of Algorithms: An Example of a Sort Algorithm
      by Grzegorz Bancerek
     Received November 9, 2012
1167. CKSPACE1
     The $C^k$ Space
      by Katuhiko Kanazashi, Hiroyuki Okazaki and Yasunari Shidama
     Received November 9, 2012
1168. RANDOM_3
     Random Variables and Product of Probability Spaces
      by Hiroyuki Okazaki and Yasunari Shidama
     Received December 1, 2012
1169. MMLQUER2
     The Semantics of MML Query -- Ordering
      by Grzegorz Bancerek
     Received December 1, 2012
1170. HURWITZ2
     A Test for the Stability of Networks
      by Agnieszka Rowi\'nska-Schwarzweller and Christoph Schwarzweller
     Received January 17, 2013
1171. ROUGHS_2
     Relational Formal Characterization of Rough Sets
      by Adam Grabowski
     Received January 17, 2013
1172. GROUP_17
     Isomorphisms of Direct Products of Finite Commutative Groups
      by Hiroyuki Okazaki, Hiroshi Yamazaki and Yasunari Shidama
     Received January 31, 2013
1173. NBVECTSP
     $n$-dimensional Binary Vector Spaces
      by Kenichi Arai and Hiroyuki Okazaki
     Received April 17, 2013
1174. TOPGEN_6
     Some Properties of the {S}orgenfrey Line and the {S}orgenfrey Plane
      by Adam J.J. St. Arnaud and Piotr Rudnicki
     Received April 17, 2013
1175. NUMERAL2
     More on Divisibility Criteria for Selected Primes
      by Adam Naumowicz and Rados{\l}aw Piliszek
     Received May 19, 2013
1176. NDIFF_6
     Differentiation in Normed Spaces
      by Noboru Endou and Yasunari Shidama
     Received May 19, 2013
1177. NUMPOLY1
     Polygonal Numbers
      by Adam Grabowski
     Received May 19, 2013
1178. GAUSSINT
     Gaussian Integers
      by Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima and Yasunari Shidama
     Received May 19, 2013
1179. TOPALG_7
     Commutativeness of Fundamental Groups of Topological Groups
      by Artur Korni{\l}owicz
     Received May 19, 2013
1180. HUFFMAN1
     Constructing Binary {H}uffman Tree
      by Hiroyuki Okazaki, Yuichi Futa and Yasunari Shidama
     Received June 18, 2013
1181. INTEGR20
     Riemann Integral of Functions from $\mathbbbR$ into Real {B}anach Space
      by Keiko Narita, Noboru Endou and Yasunari Shidama
     Received June 18, 2013
1182. MOEBIUS2
     On Square-free Numbers
      by Adam Grabowski
     Received July 12, 2013
1183. DBLSEQ_1
     Double Sequences and Limits
      by Noboru Endou, Hiroyuki Okazaki and Yasunari Shidama
     Received August 31, 2013
1184. AESCIP_1
     Formalization of the Advanced Encryption Standard -- Part {I}
      by Kenichi Arai and Hiroyuki Okazaki
     Received October 7, 2013
1185. INTEGR21
     The Linearity of Riemann Integral on Functions from $\mathbbbR$ into Real
     {B}anach Space
      by Keiko Narita, Noboru Endou and Yasunari Shidama
     Received October 7, 2013
1186. CAT_6
     Object-Free Definition of Categories
      by Marco Riccardi
     Received October 7, 2013
1187. GROUP_18
     Isomorphisms of Direct Products of Cyclic Groups of Prime-power Order
      by Hiroshi Yamazaki, Hiroyuki Okazaki, Kazuhisa Nakasho and Yasunari Shidama
     Received October 7, 2013
1188. LATTICEA
     Prime Filters and Ideals in Distributive Lattices
      by Adam Grabowski
     Received October 7, 2013
1189. PREFER_1
     Introduction to Formal Preference Spaces
      by Eliza Niewiadomska and Adam Grabowski
     Received October 7, 2013
1190. ALTCAT_6
     Coproducts in Categories without Uniqueness of { \bf cod } and { \bf
     dom}
      by Maciej Goli\'nski and Artur Korni{\l}owicz
     Received December 8, 2013
1191. PETRI_3
     Formulation of Cell Petri Nets
      by Mitsuru Jitsukawa, Pauline N. Kawamoto and Yasunari Shidama
     Received December 8, 2013
1192. NDIFF_7
     Isometric Differentiable Functions on Real Normed Space
      by Yuichi Futa, Noboru Endou and Yasunari Shidama
     Received December 31, 2013
1193. ORDEQ_02
     Differential Equations on Functions from $\mathbbR$ into Real {B}anach
     Space
      by Keiko Narita, Noboru Endou and Yasunari Shidama
     Received December 31, 2013
1194. ZMODUL04
     Submodule of free $\mathbb Z$-module
      by Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
     Received December 31, 2013
1195. POSET_2
     Definition of Flat Poset and Existence Theorems for Recursive Call
      by Kazuhisa Ishida, Yasunari Shidama and Adam Grabowski
     Received February 11, 2014
1196. TIETZE_2
     Tietze Extension Theorem for $n$-dimensional Spaces
      by Karol P\kak
     Received February 11, 2014
1197. BROUWER3
     Brouwer Invariance of Domain Theorem
      by Karol P\kak
     Received February 11, 2014
1198. PETRI_DF
     The Formalization of Decision Free {P}etri Net
      by Pratima K. Shah, Pauline N. Kawamoto and Mariusz Giero
     Received March 31, 2014
1199. ABSRED_0
     Abstract Reduction Systems and Idea of {K}nuth {B}endix Completion
     Algorithm
      by Grzegorz Bancerek
     Received March 31, 2014
1200. DBLSEQ_2
     Double Series and Sums
      by Noboru Endou
     Received March 31, 2014
1201. DUALSP01
     Dual Spaces and Hahn-Banach's Theorem
      by Keiko Narita, Noboru Endou and Yasunari Shidama
     Received March 31, 2014
1202. SRINGS_1
     Semiring of Sets
      by Roland Coghetto
     Received March 31, 2014
1203. SRINGS_2
     Semiring of Sets: Examples
      by Roland Coghetto
     Received March 31, 2014
1204. ROUGHS_4
     Topological Interpretation of Rough Sets
      by Adam Grabowski
     Received March 31, 2014
1205. HILBERT4
     Pseudo-canonical Formulae are Classical
      by Marco B. Caminati and Artur Korni{\l}owicz
     Received May 25, 2014
1206. LAGRA4SQ
     Lagrange's Four-Square Theorem
      by Yasushige Watase
     Received June 4, 2014
1207. NAT_6
     Proth Numbers
      by Christoph Schwarzweller
     Received June 4, 2014
1208. BALLOT_1
     Bertrand's Ballot Theorem
      by Karol P\kak
     Received June 13, 2014
1209. MSAFREE5
     Term Context
      by Grzegorz Bancerek
     Received June 13, 2014
1210. RVSUM_3
     Cauchy Mean Theorem
      by Adam Grabowski
     Received June 13, 2014
1211. GTARSKI1
     Tarski Geometry Axioms
      by William Richter, Adam Grabowski and Jesse Alama
     Received June 16, 2014
1212. GRAPH_3A
     A Note on the Seven Bridges of K\"onigsberg Problem
      by Adam Naumowicz
     Received June 16, 2014
1213. MFOLD_0
     Topological Manifolds
      by Karol P\kak
     Received June 16, 2014
1214. ZMODUL05
     Rank of Submodule, Linear Transformations and Linearly Independent Subsets
     of $\mathbb Z$-module
      by Kazuhisa Nakasho, Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
     Received July 10, 2014
1215. FINANCE2
     Events of Borel Sets, Construction of Borel Sets and Random Variables
     for Stochastic Finance
      by Peter Jaeger
     Received July 10, 2014
1216. NEWTON01
     Some Remarkable Identities Involving Numbers
      by Rafa{\l} Ziobro
     Received September 5, 2014
1217. NORMSP_3
     Topological Properties of Real Normed Space
      by Kazuhisa Nakasho, Yuichi Futa and Yasunari Shidama
     Received September 15, 2014
1218. AOFA_L00
     Algebraic Approach to Algorithmic Logic
      by Grzegorz Bancerek
     Received September 15, 2014
1219. LATTAD_1
     Formalization of Generalized Almost Distributive Lattices
      by Adam Grabowski
     Received September 26, 2014
1220. VSDIFF_1
     Difference of Function on Vector Space over $\mathbbF$
      by Kenichi Arai, Ken Wakabayashi and Hiroyuki Okazaki
     Received September 26, 2014
1221. ZMODUL06
     Torsion $\mathbb Z$-module and Torsion-free $\mathbb Z$-module
      by Yuichi Futa, Hiroyuki Okazaki, Kazuhisa Nakasho and Yasunari Shidama
     Received November 29, 2014
1222. RING_2
     The First Isomorphism Theorem and Other Properties of Rings
      by Artur Korni{\l}owicz and Christoph Schwarzweller
     Received November 29, 2014
1223. DUALSP02
     Bidual Spaces and Reflexivity of Real Normed Spaces
      by Keiko Narita, Noboru Endou and Yasunari Shidama
     Received November 29, 2014
1224. EUCLID10
     Some Facts about Trigonometry and Euclidean Geometry
      by Roland Coghetto
     Received November 29, 2014
1225. FUZNUM_1
     The Formal Construction of Fuzzy Numbers
      by Adam Grabowski
     Received December 31, 2014
1226. CAT_7
     Categorical Pullbacks
      by Marco Riccardi
     Received December 31, 2014
1227. GROUP_19
     Definition and Properties of Direct Sum Decomposition of Groups
      by Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki and Yasunari Shidama
     Received December 31, 2014
1228. ZMATRLIN
     Matrix of $\mathbb Z$-module
      by Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
     Received February 18, 2015
1229. SRINGS_3
     $\sigma$-ring and $\sigma$-algebra of Sets
      by Noboru Endou, Kazuhisa Nakasho and Yasunari Shidama
     Received February 18, 2015
1230. NORMSP_4
     Separability of Real Normed Spaces and Its Basic Properties
      by Kazuhisa Nakasho and Noboru Endou
     Received February 26, 2015
1231. GROUP_20
     Equivalent Expressions of Direct Sum Decomposition of Groups
      by Kazuhisa Nakasho, Hiroyuki Okazaki, Hiroshi Yamazaki and Yasunari Shidama
     Received February 26, 2015
1232. EUCLID11
     Morley's Trisector Theorem
      by Roland Coghetto
     Received March 26, 2015
1233. FLEXARY1
     Flexary Operations
      by Karol P\kak
     Received March 26, 2015
1234. EULRPART
     {E}uler's {P}artition {T}heorem
      by Karol P\kak
     Received March 26, 2015
1235. DIOPHAN1
     Introduction to {D}iophantine Approximation
      by Yasushige Watase
     Received April 19, 2015
1236. SRINGS_4
     Finite Product of Semiring of Sets
      by Roland Coghetto
     Received April 19, 2015
1237. NELSON_1
     Two Axiomatizations of {N}elson Algebras
      by Adam Grabowski
     Received April 19, 2015
1238. GROUP_1A
     Groups -- Additive Notation
      by Roland Coghetto
     Received April 30, 2015
1239. POLNOT_1
     Polish Notation
      by Taneli Huuskonen
     Received April 30, 2015
1240. GRZLOG_1
     Grzegorczyk's Logics, Part 1
      by Taneli Huuskonen
     Received April 30, 2015
1241. CARDFIL2
     Convergent Filter Bases
      by Roland Coghetto
     Received June 30, 2015
1242. ASYMPT_2
     Polynomially Bounded Sequences and Polynomial Sequences
      by Hiroyuki Okazaki and Yuichi Futa
     Received June 30, 2015
1243. NEWTON02
     Fermat's Little Theorem via Divisibility of {N}ewton's Binomial
      by Rafa{\l} Ziobro
     Received June 30, 2015
1244. DUALSP03
     Weak Convergence and Weak* Convergence
      by Keiko Narita, Noboru Endou and Yasunari Shidama
     Received July 1, 2015
1245. DUALSP04
     The Orthogonal Projection and {R}iesz Representation Theorem
      by Keiko Narita, Noboru Endou and Yasunari Shidama
     Received July 1, 2015
1246. DBLSEQ_3
     Extended Real Valued Double Sequence and Its Convergence
      by Noboru Endou
     Received July 1, 2015
1247. CARDFIL3
     Summable Family in a Commutative Group
      by Roland Coghetto
     Received August 14, 2015
1248. FINTOPO7
     Topology from Neighbourhoods
      by Roland Coghetto
     Received August 14, 2015
1249. ZMODUL07
     Torsion-part of $\mathbb Z$-module
      by Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
     Received August 14, 2015
1250. MEASURE9
     Construction of Measure from Semialgebra of Sets
      by Noboru Endou
     Received August 14, 2015
1251. PETERSON
     Event-based Proof of the Mutual Exclusion Property of {P}eterson's
     Algorithm
      by Ievgen Ivanov, Mykola Nikitchenko and Uri Abraham
     Received August 14, 2015
1252. RING_3
     Characteristic of Rings; Prime Fields
      by Christoph Schwarzweller and Artur Korni{\l}owicz
     Received August 14, 2015
1253. CAT_8
     Exponential Objects
      by Marco Riccardi
     Received August 15, 2015
1254. ASYMPT_3
     Algebra of Polynomially Bounded Sequences and Negligible Functions
      by Hiroyuki Okazaki
     Received August 15, 2015
1255. LTLAXIO5
     Propositional Linear Time Temporal Logic with Initial Semantics
      by Mariusz Giero
     Received October 22, 2015
1256. LATSTONE
     Stone Lattices
      by Adam Grabowski
     Received October 22, 2015
1257. FINANCE3
     Modelling Real World Using Stochastic Processes and Filtration
      by Peter Jaeger
     Received December 30, 2015
1258. EUCLID12
     Circumcenter, Circumcircle, and Centroid of a Triangle
      by Roland Coghetto
     Received December 30, 2015
1259. EUCLID13
     Altitude, Orthocenter of a Triangle and Triangulation
      by Roland Coghetto
     Received December 30, 2015
1260. ZMODUL08
     Divisible $\mathbb Z$-modules
      by Yuichi Futa and Yasunari Shidama
     Received December 30, 2015
1261. ZMODLAT1
     Lattice of $\mathbb Z$-module
      by Yuichi Futa and Yasunari Shidama
     Received December 30, 2015
1262. MEASUR10
     Product Pre-Measure
      by Noboru Endou
     Received December 31, 2015
1263. GROUP_21
     Conservation Rules of Direct Sum Decomposition of Groups
      by Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki and Yasunari Shidama
     Received December 31, 2015
1264. BAGORD_2
     On Multiset Ordering
      by Grzegorz Bancerek
     Received December 31, 2015
1265. COUSIN
     Cousin's Lemma
      by Roland Coghetto
     Received December 31, 2015
1266. SRINGS_5
     Chebyshev Distance
      by Roland Coghetto
     Received December 31, 2015
1267. ROUGHS_3
     Binary Relations-Based Rough Sets -- An Automated Approach
      by Adam Grabowski
     Received February 15, 2016
1268. GTARSKI2
     Tarski Geometry Axioms -- Part {II}
      by Roland Coghetto and Adam Grabowski
     Received June 30, 2016
1269. TOPMETR4
     Compactness in Metric Spaces
      by Kazuhisa Nakasho, Keiko Narita and Yasunari Shidama
     Received June 30, 2016
1270. CARDFIL4
     Double Sequences and Iterated Limits in Regular Space
      by Roland Coghetto
     Received June 30, 2016
1271. NEWTON03
     Prime Factorization of Sums and Differences of Two Like Powers
      by Rafa{\l} Ziobro
     Received June 30, 2016
1272. INTEGR22
     Riemann-Stieltjes Integral
      by Keiko Narita, Kazuhisa Nakasho and Yasunari Shidama
     Received June 30, 2016
1273. UNIFORM2
     Quasi-uniform Space
      by Roland Coghetto
     Received June 30, 2016
1274. UNIFORM3
     Uniform Space
      by Roland Coghetto
     Received June 30, 2016
1275. RING_4
     Some Algebraic Properties of Polynomial Rings
      by Christoph Schwarzweller, Artur Korni{\l}owicz and Agnieszka Rowinska-Schwarzweller
     Received June 30, 2016
1276. ANPROJ_8
     Homography in $\mathbbRP^2$
      by Roland Coghetto
     Received October 18, 2016
1277. INTEGR23
     The Basic Existence Theorem of Riemann-Stieltjes Integral
      by Kazuhisa Nakasho, Keiko Narita and Yasunari Shidama
     Received October 18, 2016
1278. NEWTON04
     On Subnomials
      by Rafa{\l} Ziobro
     Received October 18, 2016
1279. LEIBNIZ1
     Leibniz's Series for Pi
      by Karol P\kak
     Received October 18, 2016
1280. PL_AXIOM
     The Axiomatization of Propositional Logic
      by Mariusz Giero
     Received October 18, 2016
1281. ALGNUM_1
     Algebraic Numbers
      by Yasushige Watase
     Received December 15, 2016
1282. NIVEN
     Niven's Theorem
      by Artur Korni{\l}owicz and Adam Naumowicz
     Received December 15, 2016
1283. MEASUR11
     Fubini's Theorem on Measure
      by Noboru Endou
     Received February 23, 2017
1284. POLYDIFF
     Differentiability of Polynomials over Reals
      by Artur Korni{\l}owicz
     Received February 23, 2017
1285. LIOUVIL1
     Introduction to {L}iouville Numbers
      by Adam Grabowski and Artur Korni{\l}owicz
     Received February 23, 2017
1286. LIOUVIL2
     All Liouville Numbers are Transcendental
      by Artur Korni{\l}owicz, Adam Naumowicz and Adam Grabowski
     Received February 23, 2017
1287. ANPROJ_9
     Group of Homography in Real Projective Plane
      by Roland Coghetto
     Received March 17, 2017
1288. REALALG1
     Ordered Rings and Fields
      by Christoph Schwarzweller
     Received March 17, 2017
1289. ZMODLAT2
     Embedded Lattice and Properties of {G}ram Matrix
      by Yuichi Futa and Yasunari Shidama
     Received March 17, 2017
1290. POLYVIE1
     Vieta's Formula about the Sum of Roots of Polynomials
      by Artur Korni{\l}owicz and Karol P\kak
     Received May 25, 2017
1291. FUZNORM1
     Basic Formal Properties of Triangular Norms and Conorms
      by Adam Grabowski
     Received June 27, 2017
1292. FINANCE4
     Introduction to Stopping Time in Stochastic Finance Theory
      by Peter Jaeger
     Received June 27, 2017
1293. PASCAL
     Pascal's Theorem in Real Projective Plane
      by Roland Coghetto
     Received June 27, 2017
1294. ORDERS_5
     About Quotient Orders and Ordering Sequences
      by Sebastian Koch
     Received June 27, 2017
1295. BASEL_1
     Basel Problem -- Preliminaries
      by Artur Korni{\l}owicz and Karol P\kak
     Received June 27, 2017
1296. BASEL_2
     Basel Problem
      by Karol P\kak and Artur Korni{\l}owicz
     Received June 27, 2017
1297. ZMODLAT3
     Dual Lattice of $\mathbb Z$-module Lattice
      by Yuichi Futa and Yasunari Shidama
     Received June 27, 2017
1298. VECTSP12
     Isomorphism Theorem on Vector Spaces over a Ring
      by Yuichi Futa and Yasunari Shidama
     Received August 30, 2017
1299. DUALSP05
     F. Riesz Theorem
      by Keiko Narita, Kazuhisa Nakasho and Yasunari Shidama
     Received August 30, 2017
1300. RING_5
     On Roots of Polynomials and Algebraically Closed Fields
      by Christoph Schwarzweller
     Received August 30, 2017
1301. PELLS_EQ
     The Pell's Equation
      by Marcin Acewicz and Karol P\kak
     Received August 30, 2017
1302. NOMIN_1
     Simple named-complex valued nominative data -- definition and basic
     operations
      by Ievgen Ivanov, Mykola Nikitchenko, Andrii Kryvolap and Artur Korni{\l}owicz
     Received August 30, 2017
1303. COUSIN2
     Gauge Integral
      by Roland Coghetto
     Received September 3, 2017
1304. MESFUN11
     Integral of Non Positive Functions
      by Noboru Endou
     Received September 3, 2017
1305. FUZIMPL1
     Formal Introduction to Fuzzy Implications
      by Adam Grabowski
     Received September 3, 2017
1306. REALALG2
     Formally Real Fields
      by Christoph Schwarzweller
     Received November 29, 2017
1307. FINANCE5
     Introduction to Stopping Time in Stochastic Finance Theory: Part {II}
      by Peter Jaeger
     Received November 29, 2017
1308. NDIFF_8
     Implicit Function Theorem -- Part {I}
      by Kazuhisa Nakasho, Yuichi Futa and Yasunari Shidama
     Received November 29, 2017
1309. DIOPHAN2
     Introduction to {D}iophantine Approximation -- Part 2
      by Yasushige Watase
     Received November 29, 2017
1310. GTARSKI3
     {T}arski Geometry Axioms -- Part {III}
      by Roland Coghetto and Adam Grabowski
     Received November 29, 2017
1311. HILB10_1
     The {M}atiyasevich Theorem -- Preliminaries
      by Karol P\kak
     Received November 29, 2017
1312. FINANCE6
     Introduction to Stochastic Finance: Random-Variables and Arbitrage Theory
      by Peter Jaeger
     Received March 27, 2018
1313. PARTPR_1
     Kleene Algebra of Partial Predicates
      by Artur Korni{\l}owicz, Ievgen Ivanov and Mykola Nikitchenko
     Received March 27, 2018
1314. BKMODEL1
     Beltrami-Klein Model, {P}art {I}
      by Roland Coghetto
     Received March 27, 2018
1315. BKMODEL2
     Beltrami-Klein model, Part {II}
      by Roland Coghetto
     Received March 27, 2018
1316. MESFUN12
     Fubini's Theorem for Nonnegative or Nonpositive Functions
      by Noboru Endou
     Received March 27, 2018
1317. MOEBIUS3
     Sequences of Prime Reciprocals -- Preliminaries
      by Adam Grabowski
     Received March 27, 2018
1318. HILB10_2
     Diophantine sets -- Preliminaries
      by Karol P\kak
     Received March 27, 2018
1319. NEWTON05
     Parity as a Property of Integers
      by Rafa{\l} Ziobro
     Received June 29, 2018
1320. GLIB_006
     About Supergraphs, Part {I}
      by Sebastian Koch
     Received June 29, 2018
1321. GLIB_007
     About Supergraphs, Part {II}
      by Sebastian Koch
     Received June 29, 2018
1322. PARTPR_2
     On algebras of algorithms and specifications over uninterpreted data
      by Ievgen Ivanov, Artur Korni{\l}owicz and Mykola Nikitchenko
     Received June 29, 2018
1323. NOMIN_2
     On an algorithmic algebra over simple-named complex-valued nominative data
      by Ievgen Ivanov, Artur Korni{\l}owicz and Mykola Nikitchenko
     Received June 29, 2018
1324. NOMIN_3
     An inference system of an extension of Floyd-Hoare logic for partial
     predicates
      by Ievgen Ivanov, Artur Korni{\l}owicz and Mykola Nikitchenko
     Received June 29, 2018
1325. NOMIN_4
     Partial correctness of GCD algorithm
      by Ievgen Ivanov, Artur Korni{\l}owicz and Mykola Nikitchenko
     Received June 29, 2018
1326. HILB10_3
     Basic Diophantine Relations
      by Marcin Acewicz and Karol P\kak
     Received June 29, 2018
1327. ROUGHS_5
     Formalizing Two Generalized Approximation Operators
      by Adam Grabowski and Micha{\l} Sielwiesiuk
     Received June 29, 2018
1328. ROBBINS5
     On Two Alternative Axiomatizations of Lattices by McKenzie and Sholander
      by Adam Grabowski and Damian Sawicki
     Received June 29, 2018
1329. FINSEQ_9
     Arithmetic Operations on Short Finite Sequences
      by Rafa{\l} Ziobro
     Received September 29, 2018
1330. TOPS_5
     Some Remarks about Product Spaces
      by Sebastian Koch
     Received September 29, 2018
1331. BINARI_6
     Binary Representation of Natural Numbers
      by Hiroyuki Okazaki
     Received September 29, 2018
1332. LOPBAN_8
     Continuity of Bounded Linear Operators on Normed Linear Spaces
      by Kazuhisa Nakasho, Yuichi Futa and Yasunari Shidama
     Received September 29, 2018
1333. MUSIC_S1
     {P}ythagorean Tuning: Pentatonic and Heptatonic Scale
      by Roland Coghetto
     Received September 29, 2018
1334. FUZIMPL2
     Fundamental Properties of Fuzzy Implications
      by Adam Grabowski
     Received September 29, 2018
1335. TOPZARI1
     {Z}ariski {T}opology
      by Yasushige Watase
     Received October 16, 2018
1336. RVSUM_4
     Concatenation of Finite Sequences
      by Rafa{\l} Ziobro
     Received February 27, 2019
1337. LOPBAN_9
     Bilinear Operators on Normed Linear Spaces
      by Kazuhisa Nakasho
     Received February 27, 2019
1338. PDIFFEQ1
     A Simple Example for Linear Partial Differential Equations and Its
     Solution Using the Method of Separation of Variables
      by Sora Otsuki, Pauline N. Kawamoto and Hiroshi Yamazaki
     Received February 27, 2019
1339. LOPBAN10
     Multilinear Operator and Its Basic Properties
      by Kazuhisa Nakasho
     Received February 27, 2019
1340. ANPROJ10
     {C}ross-ratio in Real Vector Space
      by Roland Coghetto
     Received February 27, 2019
1341. LOPBAN11
     Continuity of Multilinear Operator on Normed Linear Spaces
      by Kazuhisa Nakasho and Yasunari Shidama
     Received February 27, 2019
1342. MESFUN13
     Fubini's Theorem
      by Noboru Endou
     Received March 11, 2019
1343. GTARSKI4
     Tarski Geometry Axioms. {P}art {IV } -- Right angle
      by Roland Coghetto and Adam Grabowski
     Received March 11, 2019
1344. NTALGO_2
     Maximum Number of Steps Taken by Modular Exponentiation and Euclidean
     Algorithm
      by Hiroyuki Okazaki, Koich Nagao and Yuichi Futa
     Received March 11, 2019
1345. FIELD_1
     On Roots of Polynomials over K[X]/<p>
      by Christoph Schwarzweller
     Received March 28, 2019
1346. LOPBAN12
     Isomorphisms from the Space of Multilinear Operators
      by Kazuhisa Nakasho
     Received May 27, 2019
1347. LOPBAN13
     Invertible Operators on Banach Spaces
      by Kazuhisa Nakasho
     Received May 27, 2019
1348. NDIFF_9
     Implicit Function Theorem -- Part {II}
      by Kazuhisa Nakasho and Yasunari Shidama
     Received May 27, 2019
1349. FIELD_2
     On Monomorphisms and Subfields
      by Christoph Schwarzweller
     Received May 27, 2019
1350. ORDINAL7
     Natural Addition of Ordinals
      by Sebastian Koch
     Received May 27, 2019
1351. GLIB_008
     About Supergraphs, {P}art {III}
      by Sebastian Koch
     Received May 27, 2019
1352. NOMIN_5
     Partial Correctness of a Factorial Algorithm
      by Adrian Jaszczak and Artur Korni{\l}owicz
     Received May 27, 2019
1353. NOMIN_6
     Partial Correctness of a Power Algorithm
      by Adrian Jaszczak
     Received May 27, 2019
1354. HILB10_4
     Diophantine Sets -- Preliminaries
      by Karol P\kak
     Received May 27, 2019
1355. HILB10_5
     Formalization of the {MRDP } Theorem in the {M}izar System
      by Karol P\kak
     Received May 27, 2019
1356. FIELD_3
     On the Intersection of Fields $F$ with $F[X]$
      by Christoph Schwarzweller
     Received August 29, 2019
1357. FIELD_4
     Field Extensions and {K}ronecker's Construction
      by Christoph Schwarzweller
     Received August 29, 2019
1358. GLIB_009
     Underlying Simple Graphs
      by Sebastian Koch
     Received August 29, 2019
1359. GLIB_010
     About Graph Mappings
      by Sebastian Koch
     Received August 29, 2019
1360. GLIB_011
     About Graph Mappings
      by Sebastian Koch
     Received August 29, 2019
1361. EC_PF_3
     Operations of Points on Elliptic Curve in Affine Coordinates
      by Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
     Received August 29, 2019
1362. AIMLOOP
     {AIM } Loops and the {AIM } Conjecture
      by Chad E. Brown and Karol P\kak
     Received August 29, 2019
1363. ROUGHIF1
     Formal Development of Rough Inclusion Functions
      by Adam Grabowski
     Received August 29, 2019
1364. BKMODEL3
     Beltrami-Klein model, Part {III}
      by Roland Coghetto
     Received December 30, 2019
1365. BKMODEL4
     Beltrami-Klein model, Part {IV}
      by Roland Coghetto
     Received December 30, 2019
1366. GLIBPRE0
     Miscellaneous Graph Preliminaries
      by Sebastian Koch
     Received December 30, 2019
1367. GLIB_012
     About Graph Complements
      by Sebastian Koch
     Received December 30, 2019
1368. WALLACE1
     Stability of the 7-3 Compressor Circuit for {W}allace Tree. Part {I}
      by Katsumi Wasaki
     Received December 30, 2019
1369. RINGFRAC
     {R}ings of {F}ractions and {L}ocalization
      by Yasushige Watase
     Received January 13, 2020
1370. PRSUBSET
     Dynamic Programming for the Subset Sum Problem
      by Hiroshi Fujiwara, Hokuto Watari and Hiroaki Yamamoto
     Received January 13, 2020
1371. MEASUR12
     Reconstruction of the One-Dimensional Lebesgue Measure
      by Noboru Endou
     Received January 13, 2020
1372. ROUGHIF2
     Developing Complementary Rough Inclusion Functions
      by Adam Grabowski
     Received February 26, 2020
1373. NUMBER01
     Elementary Number Theory Problems. {P}art {I}
      by Adam Naumowicz
     Received February 26, 2020
1374. FUZIMPL3
     On Fuzzy Negations Generated by Fuzzy Implications
      by Adam Grabowski
     Received February 26, 2020
1375. FIELD_5
     Renamings and a Condition-free Formalization of {K}ronecker's Construction
      by Christoph Schwarzweller
     Received May 19, 2020
1376. GLIB_013
     Refined Finiteness and Degree properties in Graphs
      by Sebastian Koch
     Received May 19, 2020
1377. GLIB_014
     About Graph Unions and Intersections
      by Sebastian Koch
     Received May 19, 2020
1378. GLUNIR00
     Unification of Graphs and Relations in {M}izar
      by Sebastian Koch
     Received May 31, 2020
1379. NOMIN_7
     Partial Correctness of a Fibonacci Algorithm
      by Artur Korni{\l}owicz
     Received May 31, 2020
1380. COMPLEX3
     Multiplication-related Classes of Complex Numbers
      by Rafal Ziobro
     Received May 31, 2020
1381. CLASSES3
     Grothendieck Universes
      by Karol P\kak
     Received May 31, 2020
1382. LATQUASI
     Formalization of Quasilattices
      by Dominik Kulesza and Adam Grabowski
     Received May 31, 2020
1383. FINTOPO8
     A Case Study of Transport Urysohn's Lemma from TopSpace Defined with 
     Open Sets to TopSpace Defined with Neighborhoods
      by Roland Coghetto
     Received October 25, 2020
1384. COUNTERS
     Extended Natural Numbers and Counters
      by Sebastian Koch
     Received October 25, 2020
1385. FIELD_6
     Ring and Field Adjunctions, Algebraic Elements and Minimal Polynomials
      by Christoph Schwarzweller
     Received October 25, 2020
1386. SEQFUNC2
     Functional Sequence in Norm Space
      by Hiroshi Yamazaki
     Received October 25, 2020
1387. NOMIN_8
     General theory and tools for proving algorithms in nominative data systems
      by Adrian Jaszczak
     Received October 25, 2020
1388. NOMIN_9
     Partial correctness of an algorithm computing Lucas sequences
      by Adrian Jaszczak
     Received October 25, 2020
1389. RINGDER1
     Derivation of Commutative Rings \& {L}eibnitz Formula for Power of 
     Derivation
      by Yasushige Watase
     Received March 30, 2021
1390. NDIFF10
     Inverse Function Theorem -- Part {I}
      by Kazuhisa Nakasho and Yuichi Futa
     Received March 30, 2021
1391. GLIBPRE1
     Miscellaneous Graph Preliminaries, {I}
      by Sebastian Koch
     Received March 30, 2021
1392. FIELD_7
     Algebraic Extensions
      by Christoph Schwarzweller and Agnieszka Rowin\'nska-Schwarzweller
     Received March 30, 2021
1393. C0SP3
     Functional Space Consisted by Continuous Functions on Topological Space
      by Hiroshi Yamazaki, Keiichi Miyajima and Yasunari Shidama
     Received March 30, 2021
1394. NUMBER02
     Elementary Number Theory Problems. {P}art {II}
      by Artur Korni{\l}owicz and Dariusz Surowik
     Received March 30, 2021
1395. PAPPUS
     Pappus's Hexagon Theorem in Real Projective Plane
      by Roland Coghetto
     Received June 30, 2021
1396. LATWAL_1
     On Weakly Associative Lattices and Near Lattices
      by Damian Sawicki and Adam Grabowski
     Received June 30, 2021
1397. ASCOLI
     Ascoli-Arzela's Theorem
      by Hiroshi Yamazaki, Keiichi Miyajima and Yasunari Shidama
     Received June 30, 2021
1398. IDEAL_2
     On Primary Ideals. {P}art {I}
      by Yasushige Watase
     Received June 30, 2021
1399. FUZZY_5
     Some Properties of Membership Functions Composed of Triangle Functions and 
     Piecewise Linear Functions
      by Takashi Mitsuishi
     Received June 30, 2021
1400. REAL_NS2
     Real Vector Space and Related Notions
      by Kazuhisa Nakasho, Hiroyuki Okazaki and Yasunari Shidama
     Received June 30, 2021
1401. FIELD_8
     Splitting Fields
      by Christoph Schwarzweller
     Received June 30, 2021
1402. BINPACK1
     Algorithm NextFit for the Bin Packing Problem
      by Hiroshi Fujiwara, Ryota Adachi and Hiroaki Yamamoto
     Received June 30, 2021
1403. LATTBA_1
     Automatization of {T}ernary {B}oolean {A}lgebras
      by Wojciech Ku\'smierowski and Adam Grabowski
     Received September 30, 2021
1404. ANPROJ11
     Principle of Duality in Real Projective Plane: a Proof of the Converse 
     of {D}esargues' Theorem and a Proof of the Converse of {P}appus' 
     Theorem by Transport
      by Roland Coghetto
     Received September 30, 2021
1405. REAL_NS3
     Finite Dimensional Real Normed Spaces are Proper Metric Spaces
      by Kazuhisa Nakasho, Hiroyuki Okazaki and Yasunari Shidama
     Received September 30, 2021
1406. MESFUN14
     Relationship between the {R}iemann and {L}ebesgue Integrals
      by Noboru Endou
     Received September 30, 2021
1407. INTEGR24
     Improper Integral, Part {I}
      by Noboru Endou
     Received September 30, 2021
1408. HILB10_6
     Prime Representing Polynomial
      by Karol P\kak
     Received November 30, 2021
1409. FIELD_9
     Quadratic Extensions
      by Christoph Schwarzweller and Agnieszka Rowin\'nska-Schwarzweller
     Received November 30, 2021
1410. PRVECT_4
     The 3-fold Product Space of Real Normed Spaces and its Properties
      by Hiroyuki Okazaki and Kazuhisa Nakasho
     Received November 30, 2021
1411. GLIB_015
     About Graph Sums
      by Sebastian Koch
     Received November 30, 2021
1412. INTEGR25
     Improper Integral, Part {II}
      by Noboru Endou
     Received December 8, 2021