**M.
Burgin **

S C I E N T I F I C P U B L I C A T I O N S

**M A T H E M A T I C S **

**Books and booklets are in bold letters **

* *

1.
*Imbedding
a group amalgam with some property into
a group with the same property,* Mathematics of the

2. *Imbedding an amalgam of groups into a group,* VIII All-Union Colloquium on General Algebra,

3. *Categories with involution and correspondences
in *g*-categories*, IX All-Union
Algebraic Colloquium,

4. *Generalized free and permutation products of
groups*, IX All-Union Algebraic Colloquium,

5. *Some properties of the generalized free
products and imbedding of group amalgams*, Math. of the

6. *The Freiheitssatz in some varieties of linear *W*-algebras and
*W*-rings*, Russian Mathematical Surveys, 1969, v. 24, No. 1, pp. 27-38 (translated from Russian)

7.
g-*categories and categories with involution*,
Russian Mathematical Surveys, 1969, v. 24, No. 2, pp. 221-222 (in Russian)

8.
*P-products
of linear *W*-algebras*, X All-Union Algebraic Colloquium,

9. *Principal objects in abelian categories and the
related torsion*, X All-Union Algebraic Colloquium,

10. *Categories of relations over semiabelian
categories,* Notices of
the

11. *Gruppoid of linear *W*-algebras varieties*,
Russian Mathematical Surveys, 1970, v. 25, No. 3, pp. 263-264 (in Russian)

12. *Homological algebra in G-primitive *g*-categories*, Doklady of the
Academy of Science of Belorussia, 1970, v. 14, No. 7, pp. 585-587 (in Russian)

13.
*Permutational
products of linear *W*-algebras*,* * Soviet Math. Izvestiya,
1970, v. 4, No. 3, pp. 977-999
(translated from Russian)

14.
*Categories
with involution and relations in *g*-categories*, Transactions of the Moscow Mathematical
Society, 1970, v. 22 (1972) , pp. 161-228
(translated from Russian, AMS, 1972)

15. *Free epimorphic images of free linear *W*-algebras*, Conference on Algebra, Mathematical Logic and
Computational Mathematics,

16.
*Linear *W*-algebras with zero grade identities*, XI All-Union Algebraic Colloquium,

17.
*Some
problems of the theory of topological
algebras*, XI
All-Union Algebraic Colloquium,

18.
*Free
decompositions with a common subobject*, XI All-Union Algebraic Colloquium,

19.
*Wreath
products of linear *W*-algebras*, Mathematics, Izvestiya VUZOV, 1971, No.6,
pp. 9-17 (translated from Russian:
Soviet Mathematics, 1971, v. 15, No. 6)

**20. ***Correspondences,
central ideals and homological algebra
in ***g***-categories***, **, 24 p. (in Russian)

21. *Free topological groups and universal algebras*, Notices of the

22.
*Free
quotients of free linear *W*-algebras*, Matematicheskiye
Zametki, 1972, v. 11, No. 5, pp. 537-544
(translated from Russian)

23. *Schreier varieties of linear *W*-algebras*, Russian Mathematical Surveys, 1972, v. 27,
No. 5, pp. 227-228 (in Russian)

24.
*Linear *W*-algebras over commutative rings and attainable varieties*, Vestnik of the

25.
*Some
properties of subalgebras in varieties of linear *W*-algebras*, Soviet Mathematics - Sbornik, 1972, v. 12, No. 1 (v. 87, No. 1) ,
pp .67-82 (translated from
Russian, in collaboration)

26.
*Subalgebras
of the free topological algebras*, VI All-Union Topological Conference,

27. *Topological algebras with continuous operations*, VI
All-Union Topological Conference,

28.
*Linear *W*-algebras and the Freiheitssatz*, Vestnik of the Moscow
University, 1972, v.27, No. 5, pp. 72-77
(in Russian)

29. *Central extensions in *

30.
*Free
products of linear *W*-algebras*, Russian
Mathematical Surveys, 1973, v. 28, No. 6, p. 195 (in Russian)

31.
*Topological
algebras with continuous operations*, Notices of the

32.
*Subalgebras
of the free products of linear *W*-algebras*, Transactions
of the Moscow Mathematical
Society, 1973, v. 29 (1976) , pp.
101-117 (translated from
Russian, AMS, 1976)

33.
*Malcev
postulate for the free products of topological groups*,
III All-Union Symposium for general topology,

34. *Schreier varieties of linear algebras*,
Soviet Mathematics - Sbornik, 1974, v. 22, No. 4 (v. 93, No. 4), pp. 555-573 (translated from Russian)

35.
*Free
products in the varieties of groups*,
Vestnik of the

36. *Kurosh varieties of linear algebras*, II All-Union Symposium on the theory of
rings, modules and algebras,

37. *Topological linear *W*-algebras*, II All-Union Symposium on the theory of
rings, modules and algebras,

38.
*S-bounded
products of linear *W*-algebras*, Matematicheskiye
Issledovaniya, 1974, v. 16, No. 3, pp. 39-52
(in Russian)

39.
*The
cancellation law and accessible classes of linear *W*-algebras*, Matematicheskiye Zametki,
1974, v. 13, No. 6, pp. 467-478
(translated from Russian)

40.
*Free
products in group varieties, * Russian Mathematical Surveys, 1974, v.29, No. 6, pp. 159-160 (in Russian)

41. *Identities in linear *W*-algebras*, Vestnik of the

42.
*Linear *W*-algebras, * Russian Mathematical Surveys, 1975, v. 30,
No. 4, pp. 61-106
(translated from Russian, in collaboration)

43. *The set of Schreier varieties of linear *W*-algebras*, Vestnik of the

44. *Multiplication of varieties of linear *W*-algebras*,
Mathematics, Izvestiya VUZov, 1976, No. 5, pp. 3-14 (translated from Russian: Soviet
Mathematics, 1976, v. 20, No. 5)

45.
*Varieties
of linear *W*-algebras*, Russian
Mathematical Surveys, 1976, v. 31, No. 4, pp. 255-256 (in Russian)

46.
*Relative
closures and preclosures on sets*, Vestnik of the Moscow University, 1976, No. 6, p. 121 (in Russian, in collaboration)

47.
*Free
subalgebras of topological algebras*, Notices of the

48. *Non-classical models of natural numbers*,
Russian Mathematical Surveys, 1977, v. 32, No. 6, pp. 209-210 (in Russian)

49. *Some properties of the set of Schreier
varieties of linear *W*-algebras*, Notices of the American Mathematical
Society, 1979, v.26, No. 2

50. *Free sums of principal objects*,
Notices of the American Mathematical Society, 1979, v.26, No. 3

51.
*Compactly
generated algebras with continuous operations*, International
Topological Conference,

52. *Algebras with continuous systems of operations
freely generated by *k_{w}*-spaces*, IV Symposium on General
Topology, Tiraspol, 1979, pp. 147-151 (in Russian)

53. *Preclosures
and closures of relations*, in "Problems of optimal algorithm
realization",

54. *Representation of linear* W-*algebras as products*, Mathematics:
Izvestiya VUZov, 1980, v. 24, No. 10, pp. 6-14 (translated from Russian: Soviet Mathematics, 1980, v. 24,
No. 10, pp.1-12)

55. *Free algebras with continuous systems of
operations*, Russian Mathematical Surveys, 1980, v.35, No. 3, pp.
147-151 (translated from Russian)

56. *Reduction of algebras with infinite sets of
operations*, Abstracts presented to the American Mathematical
Society, 1980, v. 1, No. 4

57. *Some toirsions in abelian categories with
principal objects*, Abstracts presented to the American
Mathematical Society, 1980, v. 1, No. 5

58.
*Dual
arithmetics*, Abstracts presented to the American Mathematical
Society, 1980, v. 1, No. 6

59. *Kurosh varieties of linear *W-*algebras,* in "Problems of group
theory and homological algebra",

60. *Some generalizations of the theorems of Cauchy
and d'Alembert*, Abstracts presented to the American Mathematical
Society, 1981, v. 2, No. 1

61.
*Decision
problems for linear *W*-algebras*, Abstracts presented to the American
Mathematical Society, 1981, v. 2, No. 2

62. *Generalized Freiheitssatz in linear *W-*algebras with graded presentation*,
Abstracts presented to the American Mathematical Society, 1981, v. 2, No. 3

63.
*Residual
properties of linear *W*-algebras*, Abstracts presented
to the American Mathematical Society, 1981, v. 2, No. 6

64. *Schreier and Kurosh varieties of Lie triple
systems*, Abstracts presented to the American Mathematical
Society, 1981, v. 2, No. 7

65. *Operations induced by replic complete classes
of linear * W*-algebras*, XVI All-Union Algebraic Conference,

66. *On autoprojective principal objects*, Abstracts presented to the American
Mathematical Society, 1982, v. 3, No. 2

67. *Decompositions of principally *q*-generated objects*, Abstracts
presented to the American Mathematical Society, 1982, v. 3, No. 3

68. *Subsemigroups of free products in varieties
of semigroups*, Abstracts presented to the American
Mathematical Society, 1982, v. 3, No. 5

69.
*Named
sets and their subsets,* VI
All-Union Conference in Mathematical Logic,

70. *Algorithmic problems in linear algebras*,
All-Union Symposium on Theory of Rings, Modules and Algebras, Novosibirsk,
1982, pp. 24-25 (in Russian)

71. *Principally generated objects in abelian
categories*, XVII All-Union Algebraic Conference,

72. *Extensions of Relations*, in
"Mathematical Linguistics and Theory of Algorithms,"

73.
*Operators
of closure for relations and binary operations*, in "Operation research and Automated
Control Systems,"

74.
*Subobjects
in the categories of named sets,* Abstracts presented to the American Mathematical Society, 1983,
v. 4, No. 2 (in collaboration)

75. *On Greg's paradox in taxonomy*, Abstracts presented to the American
Mathematical Society, 1983, v. 4, No. 3

76. *Named sets and their categories*,
Abstracts presented to the American Mathematical Society, 1983, v. 4, No.
3 (in collaboration)

77. *Named power-sets*, Abstracts presented to the American
Mathematical Society, 1983, v. 4, No. 4 (in collaboration)

78. *Multicardinals*,
Abstracts presented to the American Mathematical Society, 1983, v. 4, No. 7

79. *Some properties of abelian categories with
principal objects*, Theory of Semigroups and its Applications,

80.
*Representation
of Algebraic and Topological Constructions by Means of Generalized Connected
Relations, *in* * "Properties of Semigroups,"

81. *Homomorphisms of a vector space into itself*, Abstracts presented to the American
Mathematical Society, 1984, v. 5, No. 1

82. $-*varieties and their homomorphisms*,
Abstracts presented to the American Mathematical Society, 1984, v. 5, No. 2

83. *Some aspects of multicombinatorics*, Abstracts presented to the American
Mathematical Society, 1984, v. 5, No. 4

84. *Functors in categories of named sets*, Abstracts presented to the American
Mathematical Society, 1984, v. 5, No. 7

85.
*Principally
generated radicals in abelian categories*,* *in "Problems of group theory and homological algebra,"

86. *Galois Grouppoids*, XVIII All-Union Algebraic Conference, pt. 1,

87. *Approximation of Linear Algebras and Grouppoids*, in "Algebraic systems with one action
and relation,"

88.
*Strict
Kurosh varieties of semigroups*, Semigroup Theory and its Applications,

89. *New aspects of multicombinatorics*,
Abstracts presented to the American Mathematical Society, 1985, v. 6, No. 2

90. *Functional bisequences*,
Abstracts presented to the American Mathematical Society, 1985, v. 6, No. 3

91. *Order cardinality of named sets*,
Abstracts presented to the American Mathematical Society, 1985, v. 6, No. 4

92. 2-*distributions*, Abstracts presented to
the American Mathematical Society, 1985, v. 6, No. 5

93. *Abstract theory of properties,* in "Non-classical Logics,"

94.
*Mathematics*, in "Philosophical Dictionary,"

95.
*Theory
of Categories*, in
"Philosophical Dictionary,"

96.
*Probability
Theory*, in "Philosophical Dictionary,"

97.
*Catastrophe
Theory*, in
"Philosophical Dictionary,"

98.
*Mathematical
Constructivism*, in
"Philosophical Dictionary,"

99.
*Constructive
Logic*, in "Philosophical Dictionary,"

100. *Continuum,* in
"Philosophical Dictionary,"

101. *Operations on spaces of distributions*, Abstracts presented to the American
Mathematical Society, 1986, v. 7, No. 1

102. *Algebras of d-distributions*,
Abstracts presented to the American Mathematical Society, 1986, v. 7, No. 2

103. *Universality of algebras of distributions*,
Abstracts presented to the American Mathematical Society, 1986, v. 7, No.3

104. *Upper multicardinals*,
Abstracts presented to the American Mathematical Society, 1986, v. 7, No.4

105. *Logical deductive varieties*,
Abstracts presented to the American Mathematical Society, 1986, v. 7, No. 6

106. *Quantifiers in Theory of Properties*, in "Nonstandard Semantics of
Non-classical Logics,"

107. *Cardinality of named sets and multicardinal
numbers,* VIII
All-Union conference on Mathematical
Logic,

108. *Operations
with named sets*, in "Ordered sets and lattices,"

109. *Logical model varieties*,
Abstracts presented to the American Mathematical Society, 1987, v. 8, No. 1

110. *Compactness Theorem for logical varieties*, Abstracts presented to the American
Mathematical Society, 1987, v. 8, No. 3

111. *Spaces of *D*-numbers*, Abstracts presented to the American Mathematical
Society, 1987, v.8, No.4

112. *Generalized measures and integration*, Abstracts presented to the American
Mathematical Society, 1987, v. 8, No. 5

113. *Induced generalized measures*,
Abstracts presented to the American Mathematical Society, 1987, v. 8, No. 6

114. *Functor semantics in categories of named sets, *in
"Rationality, Reasoning, Communication,"

115. *Functor operations in varieties of linear *W*-algebras*, Theory of Semigroups and its Applications,
No. 7,

116. *Algebraic structures of distributions*,* *Doklady of the

117. *Functional integrals and **w**-integration*, Abstracts presented to the American Mathematical
Society, 1988, v. 9, No. 1

118. *Categories as systems of named sets*,
Abstracts presented to the American Mathematical Society, 1988, v. 9, No. 2

119. *Functors as mappings of named sets*,
Abstracts presented to the American Mathematical Society, 1988, v. 9, No. 3

120. *Counting operations on named sets* ,
Abstracts presented to the American Mathematical Society, 1988, v. 9, No. 4

121. *First order model theories*,
Abstracts presented to the American Mathematical Society, 1988, v. 9, No. 5

122. *Asymptotic series and **w**-numbers*, Abstracts presented to the
American Mathematical Society, 1988, v. 9, No. 6

123. *Arithmetic hierarchy and inductive Turing
machines,* Notices of
the Academy of Sciences of the USSR, 1988, 299, No. 3, pp. 530-533 (translated from Russian: v. 37, No.2, pp.
390-393)

124. *Categorical named sets*,
Abstracts presented to the American Mathematical Society, 1989, v. 10, No. 2

125. *Rules of composition and c-categories*, Abstracts presented to the American
Mathematical Society, 1989, v. 10, No. 3

126. *Topological, algebraic and logical Varieties as
named sets*, Abstracts presented to the American Mathematical
Society, 1989, v. 10, No. 5

127. *Existential and universal properties*, Abstracts presented to the American
Mathematical Society, 1989, v. 10, No. 6

128. *Hypermeasures and hyperintegration, * Doklady of the

129. *Concepts, Types and the Theory of Abstract
Properties*, X All-Union Conference for Mathematical Logic,

130. *Arithmetic of the multicardinal numbers, * X All-Union Conference for Mathematical
Logic,

131. *Extensions of scientific theories and named
sets, * X All-Union
Conference for Mathematical Logic,

132. *Theory of Named Sets as a Foundational Basis for Mathematics*, in "Structures in Mathematical
Theories,"

133. *Information and language*,
Abstracts presented to the American Mathematical Society, 1990, v. 11, No. 1

134. *Formal (syntactical) calculi of properties*,
Abstracts presented to the American Mathematical Society, 1990, v. 11, No. 3

135. *Generalized product-measures*,
Abstracts presented to the American Mathematical Society, 1990, v. 11, No. 4

136. *Projective operations in named sets*, Abstracts presented to the American
Mathematical Society, 1990, v. 11, No. 5

137. *Exact formal calculi of properties*,
Abstracts presented to the American Mathematical Society, 1990, v. 11, No. 6

138. *Infinite-valued measures and integration, *XVI
School on theory of operators in functional spaces, Nijnii Novgorod, 1991,
p.28 (in Russian)

139. *Dynamic information theory*,
Abstracts presented to the American Mathematical Society, 1991, v. 12, No. 1

140. *Measures of information*,
Abstracts presented to the American Mathematical Society, 1991, v. 12, No. 3

141. *Independent exposition of named sets theory*,
Abstracts presented to the American Mathematical Society, 1991, v. 12, No. 4

142. *Approximation of fuzzy logics by logical
varieties*, Abstracts presented to the American Mathematical
Society, 1991, v. 12, No. 6

143. *On the Hahn-Banach theorem for
hyperfunctionals,* Doklady of the Ukrainian Academy of Sciences, 1991, No. 7, pp. 9-14 (in Russian, in Ukrainian)

144. *Hyperfunctionals in linear spaces*,
Abstracts presented to the American Mathematical Society, 1991, v. 12, No. 5

145. *Fuzzy optimization on matrix sets*, EURO XI, 11 European Congress on Operational
Research, Aachen, 1991, p. 39

146. *Categories, semigroups and named sets,*
Semigroup Theory and Applications,

147. *Named set compositions in categories*, in "Problems of group theory and
homological algebra,"

148. *Continuity Measures of Mappings of Topological
Spaces, * IX International Conference on Topology and
its Applications Kiev, 1992, p. 63
(in collaboration)

149. *Topological spaces of extrafunctions*, IX International Conference on Topology and its
Applications,

150. *Fuzzy sets as named sets, *Fuzzy sets and systems,
1992, v. 46, No. 2, pp. 189-192 (in collaboration)

151. *Topological Characterization of Hypernumbers*, VIII Summer Conference on General Topology and
Applications,

152. *Continuity Defect for Mappings of Topological
Spaces, * VIII Summer
Conference on General Topology and Applications,

153. *Towards the theory of continuity defect and
continuity measure for mappings of metric spaces*, in "Matematika,"

154. *Logical varieties and the Gödel theorem*, XI International conference on mathematical
logic,

155. *Incompleteness Theorem for Logical Varieties*, Abstracts presented to the American
Mathematical Society, 1992, v. 13, No. 1

156. *On one theorem of neoclassical analysis*, Abstracts presented to the American
Mathematical Society, 1992, v. 13, No. 3

157. *Nonstandard Function Theory*,
Abstracts presented to the American Mathematical Society, 1992, v. 13, No. 4

158. *Construction Axioms for Nonstandard Analysis*,
Abstracts presented to the American Mathematical Society, 1992, v. 13, No. 5

159. *Construction axioms for hypernumbers*,
Abstracts presented to the American Mathematical Society, 1992, v. 13, No. 6

160. *Algebraic Structures of Multicardinal Numbers*, in "Problems of group theory and
homological algebra,"

161. *Spaces of extrafunctions*,
Abstracts presented to the American Mathematical Society, 1993, v. 14, No. 2

162. *Expressive possibilities of deductive methods
in mathematics, * XIX World Congress of Philosophy, Abstracts,
v.1,

163. *Fuzzy continuous mappings*,
Abstracts presented to the American Mathematical Society, 1993, v. 14, No. 3
(in collaboration)

164. *Two approaches to continuity measure*,
Abstracts presented to the American Mathematical Society, 1993, v. 14, No. 3

165. *Universal theory of integration: General
approach*, Abstracts presented to the American Mathematical
Society, 1993, v. 14, No. 5

166. *An Axiomatic System for the Theory of Named
Sets,* Theory of Semigroups and its Applications, No.11,

167. *Universal theory of integration: Riemann model*,
Abstracts presented to the American Mathematical Society, 1993, v. 14, No. 6

168. *Space-time manifold as a dynamic scale*,
Abstracts presented to the American Mathematical Society, 1993, v. 14, No. 7

169. *Differential Calculus For Extrafunctions*, Doklady of the

170. *Fuzzification of the theory of continuous
functions,* Fuzzy Sets
and Systems, 1994, v. 62, No. 1, pp. 71-81
(in collaboration)

171. *Hypernumbers and fuzzy convergence*,
Abstracts presented to the American Mathematical Society, 1994, v.15, No.1

172. *Problems of mathematical analysis teaching:
from classical to neoclassical analysis*, International Congress of Mathematicians,

173. *Cardinal typology of sets,* Abstracts presented to the American
Mathematical Society, 1994, v.15, No. 4
(in collaboration)

174. *Sequences, series and hypernumbers*,
Abstracts presented to the American Mathematical Society, 1994, v.15, No. 5

175. *Law of inverse ratio*,
Abstracts presented to the American Mathematical Society, 1994, v.15, No.7

176. *Logical Modeling of Scientific Theories*, Theories and Models in Scientific Processes,

177. *Fundamental Base of the Theory of Triads,*
Idea, 1994, No. 2, pp. 32-45 (in
Ukrainian)

178. *Dynamic scales in unified theories*, Abstracts presented to the American
Mathematical Society, 1995, v. 16, No. 1

179. *Local and global integration*,
Abstracts presented to the American Mathematical Society, 1995, v. 16, No. 2

180. *A new criterion of continuity of real functions*,
Abstracts presented to the American Mathematical Society, 1995, v.16, No. 2

181. *Generalized Baire theorem*,
Abstracts presented to the American Mathematical Society, 1995, v.16, No. 3

182. *Formal Theory of Time*,
Abstracts presented to the American Mathematical Society, 1995, v.16, No. 3

183. *Universal theory of integration: Daniel
integral*, Abstracts presented to the American Mathematical
Society, 1995, v.16, No. 4

184. *Hypermetrics and hyperspaces*, Abstracts presented to the American
Mathematical Society, 1995, v.16, No. 4

185. *A method of solution of operator equations by
means of the theory of hypernumbers*, Doklady of the National
Academy of Sciences of Ukraine, 1995, No. 8, pp. 27-30 (in Russian, in collaboration)

186. *Neoclassical Analysis: Fuzzy Continuity and
Convergence*, Fuzzy Sets and Systems, 1995 v.75, No. 2, pp.
291-299

187. *Integral Calculus for Extrafunctions*, Doklady of the National Academy of Sciences
of Ukraine, 1995, No. 11, pp. 14-17

188. *Similarity loops in time*, Abstracts presented to the American
Mathematical Society, 1996, v.17, No. 1

189. *Universal theory of differentiation: General
approach*, Abstracts
presented to the American Mathematical Society, 1996, v.17, No. 1

190. *Leibnitz-Newton theorem in the universal theory
of integration*, Abstracts presented to the American Mathematical Society,
1997, v.18, No. 1

**191. ***Non-Diophantine
Arithmetics or is it Possible that 2+2 is not Equal to 4?*** **(in
Russian)

192. *Calculus of Abstract Properties, * International conference "Smirnov's

193. *Approaches to the Notion of the Actual Infinity in Mathematics*, in
"Infinity in Mathematics,"

194. *Stratified Universal Algebras*, International Algebraic Conference dedicated
to the Memory of Prof. L.M.Gluskin,

195. *Hypernormed Spaces and Algebras*, International Algebraic Conference dedicated
to the Memory of Prof. L.M.Gluskin,

196. *Logical Varieties and Covarieties*, in "Methodological and Theoretical
Problems of Mathematics and Information
and Computer Sciences,"

197. *Superposition of Fuzzy Continuous Functions,* in "Methodological and Theoretical
Problems of Mathematics and Information and Computer Sciences," Ukrainian
Academy of Information Sciences,

198. *Extended Fixed Point Theorem,* in
"Methodological and Theoretical Problems of Mathematics and Information
and Computer Sciences," Ukrainian

199. *Functions with finite fluctuation,* Abstracts presented to the American
Mathematical Society, 1997, v. 18, No. 3
(in collaboration)

200. *Foundations of Mathematics Revisited*,
Abstracts presented to the American Mathematical Society, 1997, v.18, No. 2

201. *Discontinuous Topology*, Abstracts presented to the American
Mathematical Society, 1997, v. 18, No. 2

202. *Relativized fuzzy continuious functions*, Abstracts presented to the American
Mathematical Society, 1997, v.18, No. 2

203. *Fuzzy fixed point theorem*,
Abstracts presented to the American Mathematical Society, 1997, v. 18, No. 4

204. *On
the Nature and Essence of Mathematics,***Kiev,
**(in Russian)

205. *Finite and Infinite*, in
"On the Nature and Essence of**
**Mathematics, Appendix,"

206. *Spaces of the Fuzzy Continuous Functions,* in "On the Nature and Essence of** **Mathematics, Appendix," Ukrainian
Academy of Information Sciences,

207. *One-sided Defects of Continuity and Fuzzy
Continuous Functions*, in "On the Nature and Essence of** **Mathematics, Appendix," Ukrainian
Academy of Information Sciences,

208. *Multicombinatorics: Combinatorial Problems in
the Theory of Named Sets*, in "On the Nature and Essence of** **Mathematics, Appendix,"

209. *Paraconsistent Logics and Logical Varieties,* in
"On the Nature and Essence of** **Mathematics,
Appendix,"

210. *Weak Deductive Covarieties, *Abstracts presented to the
American Mathematical Society, 1998, v.19, No. 2

211. *Fuzzy Continuity in Analysis, * 7^{th} International Scientific
Kravchuk Conference, Kyiv, 1998, p.
72 (in Ukrainian, in collaboration)

212. *Extended Fuzzy Continuity*, Abstracts presented to the American
Mathematical Society, 1999, v.20, No. 1

213. *Fuzzy Contractions and Fixed Points*,
Abstracts presented to the American Mathematical Society, 1999, v.20, No. 2, p.
392 (942^{nd} AMS Meeting,

214. *Categories and Populations*, Abstracts presented to the American
Mathematical Society, 1999, v.20, No. 2, p. 414

215. *Relatively Continuous Mappings of Topological
Spaces*, Abstracts of
the 14^{th} Summer Conference on General Topology and Applications,

216. *Related Hypernumbers*, Abstracts presented to the American
Mathematical Society, 1999, v.20, No. 4, p. 699

217. *Fuzzy Completeness of Metric Spaces*, Abstracts presented to the American
Mathematical Society, 1999, v.20, No. 4, pp. 699-700

218. *General Approach to Continuity Measures*, Fuzzy Sets and Systems, 1999, v. 105, No. 2,
pp. 225-231

219. *Theory of Hypernumbers and Feynman Integrals*,
Abstracts presented to the American Mathematical Society, 2000, v.21, No. 1, p.
71

220. *General Compactness Theorem*, Abstracts presented to the American
Mathematical Society, 2000, v.21, No. 1, p. 249

221. *Axiomatic Representation of the Enhanced
Banzhaf Power Index*, in “11^{th} International Conference
on Game Theory”, Book of Abstracts, Stony Brook, 2000, pp. 17-18 (in collaboration)

222. *Extremum Criteria in Neoclassical Analysis*, Abstracts presented to the American Mathematical
Society, 2000, v.21, No. 3, p. 424

223. *Differentiation in Neoclassical Analysis*, Abstracts presented to the American
Mathematical Society, 2000, v.21, No. 3, p. 501

224. *A Historical Perspective in Teaching Science
and Mathematics*, The Journal of Interdisciplinary Studies, v.
13, Fall 2000, pp. 1-11

225. *Theory of Fuzzy Limits*, Fuzzy Sets and Systems, 2000, v. 115, No. 3,
pp. 433-443

226. *Enhanced Banzhaf Power Index and its
Mathematical Properties*, Department of Economics and Mathematics,
University of California, Los Angeles, Report W - 797, 2000, 33 p.
(in collaboration)

227. *Differential Intermediate Value Theorem*,
Abstracts presented to the American Mathematical Society, 2001, v.22, No. 1, p.
269

228. *Extrafunctions, Distributions, and Nonsmooth
Analysis*, University of California, Los Angeles, Mathematics
Report Series, MRS Report 01-02, 2001, 48 p.

229. *Fuzzy Differentiation of Real Function*,
University of California, Los Angeles, Mathematics Report Series, MRS Report
01-03, 2001, 46 p.

230. *Linear Differential Equations and
Extrafunctions*, University of California, Los Angeles, Mathematics
Report Series, MRS Report 01-04, 2001, 35 p. (in collaboration)

231.
*Theory
of Real Hypernumbers*: *Properties
and Axiomatization*, Elsevier, Preprint 0107062, 2001, 42 p. (electronic
edition:
http://www.mathpreprints.com/math/Preprint/ changed to http://www.sciencedirect.com/preprintarchive)

232.
*How
we Count or is it Possible that Two Times Two is not Equal to Four*, Elsevier, Preprint
0108003, 2001, 12 p. (electronic edition:
http://www.mathpreprints.com/math/Preprint/ changed to http://www.sciencedirect.com/preprintarchive)

233. *Classes of Extrafunctions*,
Abstracts presented to the American Mathematical Society, 2001, v.22, No. 2, p.
432-433

234. *Optimization Principle for Coalition Formation
in Political Games*, in “12^{th} International Conference
on Game Theory”, Book of Abstracts, Stony Brook, 2001, p. 14 (in collaboration)

235.
*Fuzzy
Derivatives and Monotonous Functions*, Elsevier, Preprint
0108017, 2001, 36 p. (electronic
edition:
http://www.mathpreprints.com/math/Preprint/ changed to http://www.sciencedirect.com/preprintarchive)

236. *Continuity and Connectedness in Discontinuous
Topology*, University of California, Los Angeles, Mathematics
Report Series, MRS Report 01-06, 2001, 28 p.

237. *Diophantine and Non-Diophantine Aritmetics*: *Operations with Numbers in Science and
Everyday Life*, LANL, Preprint Mathematics GM/0108149, 2001, 27 p. (electronic edition: http://arXiv.org)

238. *Mathematics as a Natural Science*,
Fall Meeting of the Southern California Section of the Mathematical Association
of America, Abstracts, Los Angeles, 2001, p. 6

239.
*Fuzzy
Sets of Strong, Weak, and Conditional Derivatives*,
Elsevier, Preprint 0110014, 2001, 41 p.
(electronic edition:
http://www.mathpreprints.com/math/Preprint/ changed to http://www.sciencedirect.com/preprintarchive)

240. *Measure Dependable Extrafunctions*,
Abstracts presented to the American Mathematical Society, 2001, v.22, No. 4, p.
571-572 (972^{nd} AMS Meeting,
University of California, Irvine, November 10-11, 2001, p. 21)

241. *Generalized Solutions for the Cauchy Problem
for Partial Differential Equations*, Abstracts presented to the
American Mathematical Society, 2001, v.22, No. 4, p. 574 (972^{nd} AMS Meeting, University of
California, Irvine, November 10-11, 2001, p. 23) (in collaboration)

242. *Uncertainty and Imprecision in Analytical
Context*:* Fuzzy Limits
and Fuzzy Derivatives*, International Journal of Uncertainty, Fuzziness and
Knowledge-Based Systems, v. 9, No. 5, 2001, pp. 563-685

243. *Mistakes, Fallacies, and Misconceptions in the
History of Mathematics*, Abstracts presented to the American
Mathematical Society, 2002, v.23, No. 1, p. 198 (Joint Mathematics Meeting, San Diego, California, January 6-9,
2002)

244. *Cauchy-Kowalewski Theorem for Extended
Distributions*, Abstracts presented to the American Mathematical
Society, 2002, v.23, No. 1, p. 97
(Joint Mathematics Meeting, San Diego, California, January 6-9,
2002) (in collaboration)

245. *Extended Distributions and Hyperfunctionals*,
Abstracts presented to the American Mathematical Society, 2002, v.23, No. 1, p.
126 (Joint Mathematics Meeting, San
Diego, California, January 6-9, 2002)

246. *Conditional Convergence and Nearness Based
Limits*, Abstracts of the 6^{th} International
Conference FSTA 2002 on Fuzzy Sets Theory and its Applications, Liptovsky Jan,
Slovak Republic, 2002, pp. 41-42
(in collaboration)

247. *Theory of Hypernumbers and Extrafunctions:
Functional Spaces and Differentiation*, Discrete Dynamics in
Nature and Society, v. 7, No. 3, 2002, pp. 201-212

248. *Conditional Fuzzy Convergence of Sequences and
Numerical Computation*, Abstracts presented to the American Mathematical
Society, 2002, v.23, No. 4, p. 560
(in collaboration)

249. *Multiplication of Hypernumbers and
Extrafunctions*, Abstracts presented to the American Mathematical
Society, 2003, v.24, No. 3, p. 471 (987^{th}
AMS Meeting, San Francisco State University, San Francisco, California, May
3-4, 2003, p. 44)

250.
*Monotonicity,
Fuzzy Extrema, and Fuzzy Conditional Derivatives of Real Functions*,
University of California, Los Angeles, Mathematics Report Series, MRS Report
03-13, 2003, 73 p.

251. *Fixed Points in Fuzzy Dynamical Systems*,
Abstracts presented to the American Mathematical Society, 2004, v.25, No. 1, p.
97-98 (Joint Mathematics Meeting,
Phoenix, Arizona, January 7-10, 2004)
(in collaboration)

252. *Recurrent Points in Fuzzy Dynamical Systems of
the First Type*, Abstracts presented to the American Mathematical
Society, 2004, v.25, No. 1, p. 106
(Joint Mathematics Meeting, Phoenix, Arizona, January 7-10, 2004)

253. *Fuzzy Fixed Points in Banach Spaces*,
Abstracts presented to the American Mathematical Society, 2004, v.25, No. 1, p.
119 (Joint Mathematics Meeting,
Phoenix, Arizona, January 7-10, 2004)

254. *Named Set Theory Axiomatization*: **T**_{NZ} *Theory*, Elsevier, Preprint 0402024, 2004 (electronic edition:
http://www.mathpreprints.com/math/Preprint/ changed to http://www.sciencedirect.com/preprintarchive)

255. *Unified Foundations of Mathematics*,
Preprint in Mathematics LO/0403186, 2004, 39 p. (electronic edition:
http://arXiv.org)

256. *The fundamental Theorem of Calculus for
infinite intervals*, Abstracts presented to the American
Mathematical Society, 2004, v.25, No. 3, p.
(996^{th} AMS Meeting, University of Southern California, Los
Angeles, California, April 3-4, 2004, p. 29)

257.
*Topological
Spaces of Extended Hypernumbers*, Abstracts presented to the
American Mathematical Society, 2004, v.25, No. 3, p. (996^{th} AMS Meeting, University of Southern
California, Los Angeles, California, April 3-4, 2004, p. 49)

258. *Hyperfunctionals and Generalized Distributions*, in
“Stochastic Processes and Functional Analysis” (Eds. Krinik, A.C. and Swift,
R.J.; A Dekker Series of Lecture Notes in Pure and Applied Mathematics, v.238)
2004, pp. 81 – 119

259. *Fuzzy Optimization of Real Functions*,
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2004,
v. 12, No. 4, pp. 471-497

260. *Compatibility in Logical Varieties*,
Bulletin of Symbolic Logic, 2004, v. 10, No. 2, p. 288 * *(Association for Symbolic
Logic, 2003-2004 Winter Meeting in Phoenix)

261. *PDE and Extrafunctions*,
Rocky Mountain Journal of Mathematics, 2004, v. 34, No. 3, pp. 849-867 (in collaboration)

262. *Discontinuity Structures in Topological Spaces*,
International Journal of Pure and Applied Mathematics, 2004, v. 16, No. 4, pp.
485-513

263. *Nonlinear Cauchy-Kowalewski Theorem in
Extrafunctions*, University of California, Los Angeles, Mathematics
Report Series, MRS Report 05-02, 2005, 40 p.

264. *Series Summation in Hypernumbers*,
University of California, Los Angeles, Mathematics Report Series, MRS Report
05-07, 2005, 27 p.

265. *Fuzzy Conditional Convergence and Nearness
Relations*, Fuzzy Sets and Systems, 2005, v. 149, No. 3, pp.
383-398 (in collaboration)

266. *Calculus versus topology:
comprehension versus abstraction*, Fuzzy
Sets and Systems, 2005, v. 149, No. 3, pp. 413-414 (in collaboration)

267. *Topology in Nonlinear Extensions of
Hypernumbers*, Discrete Dynamics in Nature and Society, v. 10, No.
2, 2005, pp. 145-170

268. *Recurrent Points of Fuzzy Dynamical Systems*,
Journal of Dynamical Systems and Geometric Theories, 2005, v. 3, No. 1, pp.1-14