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 Rư 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]/

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