Ways of development of mathematical analysis at Tula State Lev Tolstoy Pedagogical University (to the 70th anniversary of the formation of the Department of Mathematical Analysis)
https://doi.org/10.22405/2226-8383-2021-22-5-270-306
Abstract
In the fall of 1938, the Tula State Pedagogical Institute (later renamed the L. N. Tolstoy Tula State Pedagogical University) was organized. The staff of the institute consisted of invited
teachers from other cities. This circumstance determined the entire educational process, since the disciplines were read in compressed blocks and in a short time. One of the three faculties
was physics and mathematics with the only department of mathematics and physics. In the fall of 1939, the faculty managed to invite young scientists-mathematicians, specialists in the
field of mathematical analysis and differential equations. They were the spouses P. V. Soloviev and V. M. Gushchina. Both of them - natives of the Tula region, received their education
and defended their PhD theses in Moscow. P. V. Soloviev had good scientific results and as a scientist could have created a school of mathematical analysis at the faculty, but in 1941
the war broke out, and he volunteered for the front, where he died in 1943. In 1950, two mathematical departments were separated from the Department of Mathematics and Physics,
one of which was the Department of Mathematical Analysis. The first head of the Department of Mathematical Analysis was Professor S. P. Sluginov, who was in Tula on visits from Moscow,
and the staff of the department consisted of 8 people. In June 1951, the department was headed by a well-known scientist in the field of the theory of functions, Doctor of Physical
and Mathematical Sciences, Professor V. I. Levin. The formation of postgraduate studies at the department and faculty is associated with his name. The first graduate of the department’s
postgraduate studies, who successfully defended her thesis for the degree of candidate of physical and mathematical sciences, was S. N. Levina, a student of Professor V. I. Levin. The students
of Professor V. I. Levin were many graduates of TSPU named after L. N. Tolstoy, who later worked at the department. In the 1960s, the scientific and pedagogical component of the Department of Mathematical Analysis was strengthened: associate professors V. I. Antropova (1964), V. I. Rybakov (1969) and A. S. Simonov (1971). Over the years, among the teachers of the department there were first-class specialists who left a noticeable mark in mathematics, but the department achieved the greatest success in the 1970s-80s. This was due to the provision of highly qualified personnel. The article traces the development of mathematical analysis at the faculty through the history of the department, as well as through the activities of its heads and teachers.
About the Author
Igor Vasil’evich DenisovRussian Federation
doctor of physical and mathematical sciences, professor
References
1. 1948, “Mathematics in the USSR for thirty years, 1917–1947“, Gostekhizdat, Moscow, 1044 p.
2. 1959, “Mathematics in the USSR for forty years, 1917–1957: in 2 volumes V. 1: Review articles“,
3. Fizmatgiz, Moscow, 1002 p.
4. 1959, “Mathematics in the USSR for forty years, 1917–1957: in 2 volumes. V. 2: Biobibliography“,
5. Fizmatgiz, Moscow, 821 p.
6. 1970, “Mathematics in the USSR 1958–1967. Volume Two: Biobibliography. Issue 2. M–Z“,
7. Nauka, Moscow , 762 p.
8. 1969, “Mathematics in the USSR 1958–1967. Volume Two: Biobibliography. Issue 1. A–L“,
9. Nauka, M , 814 p.
10. Bazilevich, I. E., Bolotovsky, B. M., Godunova E. K. & Markushevich A. I. 1970, “Viktor
11. Iosifovich Levin (on the occasion of his sixtieth birthday)“, Uspekhi Mat.Nauk., vol. 25, no. 1
12. (151), pp. 205-210.
13. Denisov, I. V., Dobrovolsky, N. M., Rebrova, I.Yu. & Chubarikov V. N. 2012, “To the 80th
14. anniversary of Alexander Sergeevich Simonov “, Chebyshev collection, V. 13, no. 3 (43), pp.
15. -115.
16. Ricker, W. J. 1998, “Rybakov’s theorem in Frechet spaces and completeness of 𝑙1 – spaces“,
17. Austral. Math. Soc. (Series A), no. 64, pp. 247-252.
18. Fernandez, A. & Naranjo, F. 1997, “Rybakov’s theorem for vector measures in Frechet spaces“,
19. Indag. Math. (New Series), no. 8, pp. 33-42.
20. 1973, “Vector and Operator Valued Measures and Applications“, Editors Don H. Tucker, Hugh
21. B. Maynard (Department of Mathematics, University of Utah, Salt Lake City, Utah), pages
22.
23. 1975, “Notas de Matematica (58): Vector Measures and Control Systems“, Series: North-
24. Holland Mathematics Studies, volume 20, pages 169.
25. 2002, Handbook of Measure Theory, volume I, pages 249.
26. Soloviev, P. V. 1939, “Fonctions de Green des Equations Paraboliques“, Comptes Rendus
27. (Doklady) de l’Academie des Sciences de l’URSS, v. XXIV, no. 2, pp. 107-109.
28. Soloviev, P. V. 1939, “On periodic solutions of some linear equations of the fourth order“, Dokl.
29. Academy of Sciences of the USSR, vol. 25, pp. 729-732.
30. Soloviev, P. V. 1939, “Solution of equations of elliptic and parabolic type for small domains“,
31. Matem. Sat., vol. 5 (47), pp. 473-486.
32. Soloviev, P. V. 1939, “Solution of a parabolic equation with variable coefficients“, Uchen. app.
33. univ. M. , no. 15, pp. 81-94.
34. Soloviev, P. V. 1939, “Some remarks on periodic solutions of nonlinear equations of hyperbolic
35. type“, Izvestiya AN SSSR. Department of Mathematical and Natural Sciences. Mathematical
36. series, pp. 149-164.
37. Soloviev, P. V. 1941, “On a boundary value problem in the theory of analytic functions“, Dokl.
38. Academy of Sciences of the USSR, vol. 33, pp. 190-192.
39. Sluginov, S.P. 1910, “The theory of radicals“, N. M. Chizhova, Tipo-lit, Kazan, 20 p.
40. Sluginov, S.P. 1914, “"Nouvelles annalles de matematiques"dirige par C.-A. Laisant,
41. C. Bourlet, R. Bricard. Paris, : Review. 1913“, Centre. typography, Kazan, 10 p.
42. Sluginov, S.P. 1910, “Proportions and progression“, N. M. Chizhova, Tipo-lit, Kazan, 37 p.
43. Sluginov, S.P. 1912, “O. M. Suvorov: Biog. feature article“, Imp. University, Tipo-lit, Kazan,
44. p.
45. Sluginov, S.P. 1912, “Curvilinear integrals and their development“, Imp. University, Tipo-lit,
46. Kazan, 30 p.
47. Sluginov, S.P. 1912, “Mixed Algebraic Problems: Repeat. course of all dep. algebra for students
48. of grades 7 and 8 gymnasiums and 6 cells. real. uch-sch“, Kazan. ped. museum, Kazan, 146 p.
49. Sluginov, S.P. 1913, “Functional calculus“, Imp. University, Tipo-lit, Kazan, 22 p.
50. Sluginov, S.P. 1913, “Fundamentals of number theory: Lectures, cheat. to Kazan. University“,
51. V. F. Markelov and V. A. Sharonov, Kazan, 150 p.
52. Sluginov, S.P. 1914, “Application of the principle of algebraic reciprocity in the theory of
53. fractions and the theory of radicals“, Centre. typography, Kazan, 8 p.
54. Sluginov, S.P. 1914, “The theory of analytic functions“, Imp. University, Tipo-lit, Kazan, 175
55. p.
56. Sluginov, S.P. 1914, “Physionistic flow in geometry: [Dokl., Chit. in a meeting Phys.-mat.
57. commission. 4 oct. 1913]“, Imp. University, Tipo-lit, Kazan, 16 p.
58. Sluginov, S.P. 1915, “Review of the work of Ya. M. Shatunovsky "Der grosste gemeinschaftliche
59. teiler von algebraischen zahlen zweiter ordnung negativer diskkriminante und die zerkegung
60. dieser zahlen in primfaktoren". (Common greatest divisor of 2nd order algebraic numbers with
61. negative discriminant and decomposition of these numbers into initial factors). Leipzig, 1912“,
62. Imp. University, Tipo-lit, Kazan, 8 p.
63. Sluginov, S.P. 1916, “On the axioms of geometry“, Centre. typography, Kazan, 16 p.
64. Sluginov, S.P. 1916, “The main course of higher algebra: Part 1“, Imp. University, Tipo-lit,
65. Kazan
66. Sluginov, S.P. 1922, “The most important theorems of metric geometry and their connection
67. with each other; Foundations of flat trigonometry“, Typ. Economic Council, Samara, 8 p.
68. Sluginov, S.P. 1922, “The most important theorems of metric geometry and their connection
69. with each other“, Typ. Economic Council, Samara, 8 p.
70. Sluginov, S.P. 1923, “Some applications of the theory of analytic functions; The main course
71. of higher algebra: Part 2, Chapter 3“, Himself. state un-t, Samara. . P. 83–118.
72. Sluginov, S.P. 1924, “Lectures on Introduction to Analysis“, Perm, 227 p.
73. Sluginov, S.P. 1925, “The beginnings of mathematical analysis“, Publishing house of Gosrossnab,
74. Perm.
75. Sluginov, S.P. 1927, “D. N. Zeiliger, professor of mechanics at Kazan State University: (On
76. the occasion of the 40th anniversary of his scientific, pedagogical and social activities)“, Typ.
77. "Permpromkombinata Perm, 6 p.
78. Sluginov, S.P. 1927, “To the 45th anniversary of the scientific and pedagogical activity of prof.
79. G. K. Suslova“, Typ. "Permpromkombinata Perm, 5 p.
80. Levin, V. I. 1932, “Comment on the simple illustrations of the unit circle“, Jahresber DMV, №
81. , pp. 68-70.
82. Levin, V. I. 1933, “On the sections of power series which are bounded with their first derivative
83. in the unit circle“, Sitzber BMG, № 32, pp. 53-59.
84. Levin, V. I. 1934, “A contribution to the Milloux-Landauschen set“, Jahresber DMV, № 44, pp.
85. -265.
86. Levin, V. I. 1934, “A contribution to the coefficient problem of simple functions“, Math. Z., №
87. , pp. 306-311.
88. Levin, V. I. 1934, “On the sums of coefficients of some classes of power series“, Math. Z., № 38,
89. pp. 565-590.
90. Levin, V. I. 1935, “Some remarks on the coefficients of simple functions“, Proc. London Math.
91. Soc., № 39, pp. 467-480.
92. Levin, V. I. 1935, “On some integral inequalities involving periodic functions“, J. London Math.
93. Soc., № 10, pp. 45-48.
94. Levin, V. I. 1936, “On the two-parameter extension and analogue of Hilbert’s inequality“, J.
95. London Math. Soc., № 1, pp. 119-124.
96. Levin, V. I. 1937, “Two remarks on Hilbert’s double series theorem“, J. Indian Math. Soc. , v.
97. , № 3, pp. 111-115.
98. Levin, V. I. 1937, “Two remarks on van der Corput’s generalizations of Knopp’s inequality“,
99. Kon. Akad. Van Wetensch, Amsterdam, v. 40, № 5, pp. 429-431.
100. Levin, V. I. 1938, “On inequalities. I“, Mat. collection, № 3 (45), pp. 341-346.
101. Levin, V. I. 1938, “On inequalities. II“, Mat. collection, № 4 (46), pp. 309-324.
102. Levin, V. I. 1938, “On inequalities. III“, Mat. collection, № 4 (46), pp. 325-332.
103. Levin, V. I. 1938, “On inequalities. IV“, Izvestia of the Academy of Sciences of the USSR.
104. Department of Mathematical and Natural Sciences. Mathematical series, vol. 36, pp. 525-542.
105. Levin, V. I. 1944, “On one continual analogue of the Maclaurin series“, Izvestia of the Academy
106. of Sciences of the USSR. Department of Mathematical and Natural Sciences. Mathematical
107. series, v. 42, pp. 51-53.
108. Levin, V. I. 1948, “Sharp constants in Carlson-type inequalities“, Dokl. Academy of Sciences
109. of the USSR, v. 59, pp. 635-638.
110. Levin, V. I. 1948, “Fourier series and integrals. Elements of operational calculus“, Soviet radio,
111. M., 116 p.
112. Levin, V. I. 1950, “Concerning a problem of S. Ramanujan“, Uspekhi Mat. sciences, v. 5, no. 3
113. (37), pp. 161-166.
114. Levin, V. I. 1951, “A limiting estimate for the accuracy of asymptotic expansions of a certain
115. class of functions“, Dokl. Academy of Sciences of the USSR, vol. 80, pp. 13-16.
116. Levin, V. I. & Grosberg, Yu. M. 1951, “Differential equations of mathematical physics“,
117. Gostekhizdat, M.-L., 576 p.
118. Levin, V. I. & Fuks, B. A. 1951, “Complex variable functions and some of their applications“,
119. Gostekhizdat, M.-L., 308 p.
120. Levin, V. I. 1953, “Limit estimate of the accuracy of asymptotic expansions of a certain class
121. of functions“, Trudy Inst. Moscow. mat. society, vol. 2, pp. 383-395.
122. Levin, V. I. 1953, “On the training of teachers of mathematics in pedagogical institutes, report
123. No. 3“, Ed. APN RSFSR, pp. 1-16.
124. Levin, V. I. 1954, “Estimation of some numerical series“, Uspekhi Mat. sciences, v. 9, No. 4
125. (62), pp. 191-194.
126. Levin, V. I. 1954, “On some determinants composed of members of a higher order arithmetic
127. progression“, Uch. app. Tula state ped. in-t, № 5, pp. 73-75.
128. Levin, V. I. 1954, “Definitions of elementary transcendental functions in terms of integral
129. representations“, Uch. app. Tula state ped. in-t, № 5, pp. 76-105.
130. Levin, V. I. 1955, “Methodical instructions for the program for the course "Mathematical
131. analysis"(for the 1st year of physics and mathematics faculties of pedagogical institutes)“,
132. Uchpedgiz, M., pp. 1-56.
133. Levin, V. I. 1956, “Methods of Mathematical Physics. Textbook for physics and mathematics
134. faculties of pedagogical institutes (1st edition)“, Uchpedgiz, M., 238 p.
135. Levin, V. I. 1957, “Generalization of the arithmetic-geometric mean“, Matem. education, no. 2,
136. pp. 195-204.
137. Levin, V. I. 1958, “An elementary proof of a theorem in the theory of means“, Matem. education,
138. no. 3, pp. 177-181.
139. Levin, V. I. 1958, “The main questions of teaching mathematical disciplines in correspondence
140. departments and razrazny and razrarazheniya“, Correspondence pedagogical education, no. 15,
141. pp. 5-18.
142. Levin, V. I. 1959, “Some questions of teaching mathematics in secondary school“, Matem.
143. education, no. 4, pp. 145-150.
144. Levin, V. I. 1964, “Equations of mathematical physics“, Nauka, Moscow, 287 p.
145. Levin, V. I. & Godunova, E. K. 1965, “Generalization of Carlson’s inequality“, Matem.
146. collection, v. 67 (109), pp. 643-646.
147. Levin, V. I. & Godunova, E. K. 1966, “Some qualitative questions of heat conduction“, Zhurnal
148. Vychisl. mat. and mat. physics, vol. 6, pp. 1097-1103.
149. Levin, V. I. & Pereturin , A. F. 1966, “The interaction of physics and mathematics“, Physics
150. at school, no. 6, pp. 15-21.
151. Levin, V. I. 1966, “Orthogonal families of plane curves“, Mathematics at school, No. 2, P. 13-24.
152. Levin, V. I. 1968, “Ramanujan is the mathematical genius of India“, Knowledge, M., 47 p.
153. Levin, V. I. & Godunova, E. K. 1967, “On a Maroni inequality“, Mat. notes, v. 2, no. 2, pp.
154. -224.
155. Levin, V. I., Godunova, E. K. & Chebaevskaya, I. V. “New research on functional inequalities.
156. Materials of the 6th Interuniversity Phys.-Math. scientific conference of the Far East“, vol. 3.
157. Levin, V. I. & Godunova, E. K. 1968, “A general class of inequalities containing Steffensen’s
158. inequality“, Mat. notes, vol. 3, no. 3, pp. 339-344.
159. Levin, V. I. 1960, “The life and work of the Indian mathematician S. Ramanujan“, Historicalmat.
160. issled., № 13, pp. 335-378.
161. Gushchina, V. M. 1954, “On a class of nonlinear integral equations“, Uch. app. Tula state ped.
162. in-t, № 5, pp. 107-128.
163. Gushchina, V. M. 1960, “Existence and uniqueness theorems for nonlinear integral equations
164. of general form“, Uch. app. Tula state ped. in-t, № 7, pp. 224-245.
165. Simonov, A. S. 1963, “Fourier’s method for one integro-differential equation of elliptic type“,
166. Tr. Sci. unite. phys.-math. fac. universities Dal. Vost., Nn. 3, pp. 70-74.
167. Simonov, A. S. 1965, “A priori estimates for integro-differential equations“, Tr. Sci. combined.
168. teachers phys.-math. fac. ped. in-tov Dal. Vost., № 5, pp. 150-165.
169. Kononenko, V. I., Likhtarnikov, L. M. & Simonov, A. S. 1965, “On the sign of the solution of a
170. boundary value problem“, Tr. Sci. combined. teachers phys.-math. fac. ped. in-tov Dal. Vost.,
171. № 5, pp. 59-73.
172. Simonov, A. S. 1965, “On the existence of solutions of some quasilinear elliptic equations“, Tr.
173. Sci. combined. teachers phys.-math. fac. ped. in-tov Dal. Vost., № 5, pp. 166-178.
174. Crane, S. G. & Simonov, A. S. 1966, “A theorem on homeomorphisms“, Dokl. Academy of
175. Sciences of the USSR, vol. 167, № 6, pp. 1226-1228.
176. Simonov, A. S. 1967, “Modification of the Leray–Lions theorem and its application to the
177. solution of nonlinear elliptic equations“, Tr. seminar on func. analysis, Voronezh, № 9, pp.
178. -166.
179. Crane, S. G., Levin, V. I., Kononenko, V. I. & Simonov, A. S. 1985, “L. M. Likhtarnikov“,
180. Mathematics at school, № 3, pp. 77.
181. Vilenkin, N.Ya., Simonov, A. S. & Survillo G. S. 1992, “Program of 10–11 grades with a
182. humanitarian bias“, New model of the school "Dialectics and Ecology Avangard, M ., pp. 248-
183.
184. Simonov, A. S. 1997, “On mathematical models of economics in the school course of
185. mathematics“, Mathematics at school, № 5, pp. 72-75.
186. Simonov, A. S. 1998, “Safety parabola“, Mathematics at school, № 1. pp. 83-90.
187. Simonov, A. S. 1998, “Some applications of geometric progression in economics“, Mathematics
188. at school, № 3, pp. 27-37.
189. Simonov, A. S. 1998, “Interest and banking calculations“, Mathematics at school, № 4, pp.
190. -45.
191. Simonov, A. S. 1998, “Compound interest“, Mathematics at school, № 5, pp. 30-42.
192. Simonov, A. S. 1998, “Today’s cost of tomorrow’s payments“, Mathematics at school, № 6, pp.
193. -37.
194. Simonov, A. S. 1999, “On one way of introducing the concept of a derivative“, Mathematics at
195. school, № 4, pp. 56-63.
196. Simonov, A. S. 2001. “Do not throw out the child with the water“, Mathematics at school, №
197. , pp. 62-64.
198. Simonov, A. S. & Inyutina, E. V. 2001, “Geometric progression in economics“, Mathematics at
199. school, № 5, pp. 17-21.
200. Simonov, A. S. & Ignatieva, N. I. 2001, “On one application of the concept "Derivative"to the
201. solution of economic problems“, Mathematics at school, № 9, pp. 43-52.
202. Simonov, A. S. & Survillo, G. S. 2002, “Planning and tests for grades 8–9 with advanced study
203. of mathematics“, Mathematics at school, № 7.
204. Vilenkin, N.Ya., Simonov, A. S. & Survillo, G. S. 1992, “Algebra–10. For advanced study
205. classes. Part 1 / (textbook, manual, printed on the basis of the decision of the board of
206. the Ministry of Education of the Republic of Khakassia)“, Nauka, Novosibirsk, 81 p.
207. Vilenkin, N.Ya. & Simonov, A. S. 1992, “Mathematical analysis of functions of several
208. variables. In 3 parts. Part 1. Basic structures of mathematical analysis“, Alpha, Moscow, 58 p.
209. Vilenkin, N.Ya. & Simonov, A. S. 1992, “Mathematical analysis of functions of several
210. variables. In 3 parts. Part 2. Differential calculus of functions of several variables“, Alpha,
211. Moscow, 79 p.
212. Vilenkin, N.Ya. & Simonov, A. S. 1992, “Mathematical analysis of functions of several
213. variables. In 3 parts. Part 3. Integral calculus of functions of several variables“, Alpha, Moscow,
214. p.
215. Vilenkin, N.Ya., Simonov, A. S. & Survillo, G. S. 1993, “Algebra–10. For advanced liberal arts
216. classes. Part II / Ministry of Education of the Russian Federation, Abakan state. ped. in-t
217. them. N.F. Katanov“, Editorial office of the publishing department of the A.I. N.F. Katanova,
218. Abakan, 165 p.
219. Vilenkin, N.Ya., Simonov, A. S. , Survillo, G. S. & Kudryavtsev, A. I. 1996, “Algebra–9:
220. A textbook for students in schools and classes with advanced study of mathematics. /
221. Recommended by the Main Directorate for the Development of General Secondary Education
222. of the Ministry of Education of the Russian Federation. Included in the federal textbook
223. package“, Education, Moscow, 384 p.
224. Simonov, A. S. 1999, “Economics in Mathematics Lessons: Textbook (recommended by the
225. Ministry of Education of the Russian Federation)“, School–Press, M .
226. Vilenkin, N.Ya., Simonov, A. S. , Survillo, G. S. & Kudryavtsev, A. I. 2011, “Algebra–9. A
227. textbook for grade 9 students with an in-depth study of mathematics, Recommended by the
228. Ministry of Education and Science of the Russian Federation“, Education, Moscow, Issue 8.
229. Chernov, V. M. 1959, “Limit relations for some integral transformations“, Uch. app. Correspondence
230. ped. in-t., M., № 3, pp. 103-143.
231. Chernov, V. M. 1961, “Some limit relations for the two-sided Laplace transform and their
232. applications“, Izv. universities. Mathematics, № 4, pp. 125-136.
233. Chernov, V. M. 1962, “Some properties of the two-sided two-dimensional Laplace transform“,
234. Izv. universities. Mathematics, № 5, pp. 115-127.
235. Chernov, V. M. 1963, “Some questions of operational calculus based on the two-sided twodimensional
236. Laplace - Carson transform“, Izv. universities. Mathematics, № 2, pp. 140-151.
237. Chernov, V. M. 1965, “Asymptotic properties of the two-dimensional Laplace transform“, Izv.
238. universities. Mathematics, № 1, pp. 158-167.
239. Vasin, L.A., Gorodnichev, S. V. & Lutsenko, A. G. 2013, “Formation of a portfolio of orders
240. in the absence of uncertainty“, Bulletin of the Tula State University. Economic and legal
241. sciences, no. 3, pp. 3-11.
242. Lutsenko, A. G. 2006, “Control elements (controls) in the MMathcad system as an instrumental
243. basis for the development of controlled visual teaching aids and their use in the educational
244. process“, Bulletin of the Tula State University. Series: Mathematics. Mechanics. Computer
245. science,. V. 12. No. 5. P. 173.
246. Lutsenko, A. G. 2006, “Computer modeling in teaching mathematics to future economists“,
247. Bulletin of the Moscow City Pedagogical University. Series: Informatics and informatization
248. of education, no. 7, pp. 121.
249. Lutsenko, A. G. 2005, “Experience of using the Mathcad 11 system in teaching higher
250. mathematics“, Mathematics in higher education, no. 3, pp. 53-64.
251. Lutsenko, A. G. 2004, “Guided visual teaching aids in mathematical analysis“, Pedagogical
252. informatics, no. 4, pp. 67-74.
253. Lutsenko, A. G. 1985, “On injective Boolean spaces“, Uspekhi Mat. sciences, v. 40, no. 4, pp.
254.
255. Lutsenko, A. G. 1982, “On retracts DT“, Mathematical Notes, v. 31, no. 3, pp. 433.
256. Denisov, I. V. 1982, “Asymptotic solution of an irregularly singular equation in a Banach
257. space“, Uspekhi Mat. sciences, vol. 37, no. 5, pp. 181-182.
258. Denisov, I. V. 1982, “On the number of cuts for a singular equation“, Approximate methods for
259. the study of differential equations and their applications: Collection of scientific papers, KSU,
260. Kuibyshev, pp. 45-46.
261. Denisov, I. V. 1982, “On the asymptotic solution of differential equations in a Banach space,
262. unsolved with respect to the derivative“, Computational mathematics and mathematical
263. physics: Collection of scientific papers, Moscow State Pedagogical Institute named after
264. V. I. Lenin, M ., pp. 77-84.
265. Denisov, I. V. 1985, “Differential equations with a finite meromorphic operator coefficient in a
266. Banach space“, Dokl. AN SSSR, vol. 282, no. 6, pp. 1289-1293.
267. Denisov, I. V. 1991, “On the asymptotic expansion of the solution of a singularly perturbed
268. elliptic equation in a rectangle“, Asymptotic methods of the theory of singularly perturbed
269. equations and ill-posed problems: Collection of scientific works, Ilim, Bishkek, pp. 37.
270. Denisov, I. V. 1995, “Quasilinear singularly perturbed elliptic equations in a rectangle“,
271. Computational Mathematics and Mathematical Physics, v. 35, no. 11, pp. 1341-1350.
272. Denisov, I. V. 1996, “On asymptotic solutions of singularly perturbed parabolic equations with
273. nonlinearities“, Theory and applications of small parameter methods: Collection of scientific
274. works, OIAE, Obninsk, pp. 32.
275. Denisov, I. V. 1996, “A boundary - value problem for a quasilinear singularly perturbed
276. parabolic equation in a rectangle“, Computational Mathematics and Mathematical Physics,
277. v. 36, no. 10, pp. 1367-1380.
278. Denisov, I. V. 1996, “An estimate of the residual term in the asymptotic form of the solution
279. of a boundary-value problem“, Computational Mathematics and Mathematical Physics, v. 36,
280. no. 12, pp. 1693-1696.
281. Denisov, I. V. 1998, “The first boundary value problem for a linear parabolic equation in space“,
282. Differential Equations, v. 34, no. 12, pp. 1620-1628.
283. Denisov, I. V. 1999, “The problem of finding the dominant term of the corner part of the
284. asymptotics of the solution to a singularly perturbed elliptic equation with a nonlinearity“,
285. Computational Mathematics and Mathematical Physics, v. 39, no. 5, pp. 747-759.
286. Denisov, I. V. 2000, “On the classes of functions defined by functional inequalities“, Bulletin of
287. the Tula State University. Series “Mathematics. Mechanics. Computer science", vol. 6, no. 1,
288. pp. 79-84.
289. Denisov, I. V. 2001, “The corner boundary layer in nonlinear singularly perturbed elliptic
290. equations“, Computational Mathematics and Mathematical Physics, v. 41, No. 3, P. 362-378.
291. Denisov, I.V. 2004, “The corner boundary layer in nonmonotone singularly perturbed
292. boundary value problems with nonlinearities“, Computational Mathematics and Mathematical
293. Physics, v. 44, No. 9, P. 1592-1610.
294. Denisov, I. V. 2008, “Corner boundary layer in nonlinear singularly perturbed elliptic
295. problems“, Computational Mathematics and Mathematical Physics, v. 48, No. 1, P. 59-75.
296. Denisov, I. V. 2009, “On some classes of functions“, Chebyshev collection, v. X, no. 2 (30), P.
297. -108.
298. Denisov, I. V., Denisova, T.Yu. & Rodionov, A. V. 2012, “Angular boundary layer in nonlinear
299. singularly perturbed parabolic equations“, Chebyshevskii sbornik, v. 13, no. 3 (43), P. 28-46.
300. Butuzov, V. F. & Denisov, I. V. 2014, “Corner Boundary Layer in Nonlinear Elliptic Problems
301. Containing First Order Derivatives“, Automatic Control and Computer Sciences, vol. 48, No.
302. , P. 459-477.
303. Denisov, I. V. 2017, “Angular Boundary Layer in Boundary Value Problems for Singularly
304. Perturbed Parabolic Equations with Quadratic Nonlinearity“, Computational Mathematics
305. and Mathematical Physics, v. 57, № 2, P. 253-271.
306. Denisov, I. V. 2018, “Corner Boundary Layer in Boundary Value Problems for Singularly
307. Perturbed Parabolic Equations with Monotonic Nonlinearity“, Computational Mathematics
308. and Mathematical Physics, v. 58, № 4, P. 562-571.
309. Denisov, I. V. & Denisov, A. I. 2019, “Mathematical models of combustion processes“, Bulletin
310. of the Russian Academy of Natural Sciences. Published by the Russian Academy of Natural
311. Sciences, Vol. 19, No. 2, P. 64-66.
312. Denisov, I. V. & Denisov, A. I. 2019, “Corner Boundary Layer in Boundary Value Problems for
313. Singularly Perturbed Parabolic Equations with Nonlinearities“, Computational Mathematics
314. and Mathematical Physics, v. 59, № 1, P. 96-111.
315. Denisov, I. V. & Denisov, A. I. 2019, “Corner Boundary Layer in Boundary Value Problems for
316. Singularly Perturbed Parabolic Equations with Nonmonotonic Nonlinearities“, Computational
317. Mathematics and Mathematical Physics, v. 59, № 9, P. 1518-1527.
318. Denisov, I. V. &Dobrovolsky, N. M. 2019, “Life and scientific activity of Albert Rubenovich
319. Yesayan“, Chebyshev collection, Vol. 20, No. 1 (69), P. 432-436.
320. Denisov, I. V. & Denisov, A. I. 2020, “Mathematical models of combustion processes“, Itogi
321. Nauki i Tekhniki. Series Contemporary mathematics and its applications. Thematic reviews.
322. VINITI RAN, Vol. 185, pp. 82-88.
323. Denisov, I. V. 2021, “Corner Boundary Layer in Boundary Value Problems for Singularly
324. Perturbed Parabolic Equations with Cubic Nonlinearities“, Computational Mathematics and
325. Mathematical Physics, v. 61, № 2, pp. 242-253.
326. Denisov, I.V. 2021, “Corner Boundary Layer in Boundary Value Problems with Nonlinearities
327. Having Stationary Points“, Computational Mathematics and Mathematical Physics, v. 61, № .
328. , pp. 1855-1863.
329. Levina, S. N. 1957, “On the solution of the equation of oscillations on the entire axis of time“,
330. Reports of the Academy of Sciences of the USSR, Vol. 114, No. 6, pp. 18-20.
331. Levina, S. N. 1960, “Operator solution of some problems of mathematical physics on the whole
332. time axis“, Uch. app. Ped. institute, Tula, No. 7, pp. 113-137.
333. Levina, S. N. 1965, “On one problem on the entire time axis“, Volzh. mat. sb., No. 3, P. 207-210.
334. Efimova, N. S. 1960, “Double asymptotic expansions“, Uch. app. Ped. institute, Tula, No. 7,
335. pp. 98-112.
336. Isaeva, L. V. 1965, “Solution of the Cauchy problem for the equation“, Volzh. mat. sb., No. 3,
337. pp. 289-295.
338. Antropova, V. I. 1954, “Mikhail Vasilievich Ostrogradsky“, Bulletin of the Higher School, No.
339. , P. 49-50.
340. Antropova, V. I. 1955, “Public lectures on integral calculus M. V. Ostrogradsky“, Proceedings
341. of Ying-that history of natures. and tech., No. 5, P. 304-320.
342. Antropova, V. I. 1957, “On the history of M. V. Ostrogradskii’s integral theorem“, Proceedings
343. of Ying-that history of natures. and tech., No. 17, P. 229-269.
344. Antropova, V. I. 1957, “On the works of Fourier, Ostrogradsky, and Poisson on heat conduction
345. and liquids“, Problems of the history of natural sciences. and tech., No. 3, pp. 49-61.
346. Antropova, V. I. 1958, “Notes. In the book "Ostrogradskiy M. V. Selected Works„‘, P. 484-495.
347. Antropova, V. I. 1959, “Comments (No. 51-103). In the book "Ostrogradskiy M. V. Complete
348. collection of works 1“, Kiev, pp. 269-284.
349. Antropova, V. I. 1961, “Comments and notes to "Notes of integral calculus"of
350. M. V. Ostrogradskiy. In the book «Mikhail Vasilievich Ostrogradsky, 1862–1962», M., P. 253-
351.
352. Antropova, V. I. 1963, “The first systematic courses in potential theory. On Sat. "Question.
353. History Phys.-Math. N. ”“, M., P. 139-140.
354. Antropova, V. I. 1965, “Notes to the "Memoir on the Propagation of Heat Inside Solids"by
355. M. V. Ostrogradskii“, Istor.-Matem. research., M., No. 16, P. 97-126.
356. Antropova, V. I. 1966, “On the geometric method of "Mathematical principles of natural
357. philosophy"I. Newton“, Istor.-Matem. research., M., No. 17, P. 205-228.
358. Rybakov, V. I. 2007, “Asplund Space: Another Criterion“, Math. Notes, 82: 1, 104-109.
359. Rybakov, V. I. 2004, “Banach Spaces with the PC Property“, Math. Notes, 76: 4, 525-533.
360. Rybakov, V. I. 2003, “Yet Another Class of Namioka Spaces“, Math. Notes, 73: 2, 244-248.
361. Rybakov, V. I. 1996, “Pettis integrability of Stone transforms“, Math. Notes, 60: 2, 175-185.
362. Rybakov, V. I. 1996, “On convergence on the boundary of the unit ball in dual space“, Math.
363. Notes, 59: 5, 543-546.
364. Rybakov, V. I. 1993, “On resultant-preserving functionals“, Math. Notes, 54: 1, 710-712.
365. Rybakov, V. I. 1984, “A certain refinement of a theorem of Namioka and m-admissible sets“,
366. Math. Notes, 35: 4, 316-323.
367. Rybakov, V. I. 1983, “Banach spaces with k- and m-admissible sets“, Math. Notes, 33: 1, 25-32.
368. Rybakov, V. I. 1978, “Universal measurability of the identity mapping of a Banach space in
369. certain topologies“, Math. Notes, 23: 2, 164-168.
370. Rybakov, V. I. 1977, “Certain properties of measures on a normed space possessing the property
371. RN“, Math. Notes, 21: 1, 45-50.
372. Rybakov, V. I. 1975, “Certain cases of the reduction of the study of weakly integrable functions
373. to the study of Pettis-integrable functions, Soviet Math. (Iz. VUZ), 19:11, 84-86.
374. Rybakov, V. I. 1975, “A generalization of the Bochner integral to locally convex spaces“, Math.
375. Notes, 18: 4, 933-938.
376. Rybakov, V. I. 1975, “The separation from a vector measure of the part representable by a
377. Bochner integral“, Math. Notes, 17: 5, 476-482.
378. Rybakov, V. I. 1973, “Vector measures with values in locally convex spaces“, Funct. Anal.
379. Appl., 7: 4, 339-340.
380. Rybakov, V. I. 1971, “On conditional mathematical expectations for functions integrable in
381. the Pettis sense“, Math. Notes, 10: 5, 764-767.
382. Rybakov, V. I. 1970, “Theorem of Bartle, Dunford, and Schwartz concerning vector measures“,
383. Math. Notes, 7: 2, 147-151.
384. Rybakov, V. I. 1968, “The Radon – Nikodym theorem and the representation of vector measures
385. by an integral“, Dokl. AN SSSR, 180: 2, 282-285.
386. Rybakov, V. I. 1968, “On vector measures“, Izv. universities. Mat., 12, 92-101.
387. Manokhin, E. V. 1991, “On K-locally uniformly convex spaces“, Izvestiya Vuzov. Math., No. 5,
388. P. 32-34.
389. Manokhin, E.V. 1998, “T-weakly locally uniform convexity in Banach spaces“, Izvestiya Vuzov.
390. Math., No. 1. P. 51-54.
391. Dobrovolsky, N. M. & “Manokhin, E. V. 1998, Banach spaces of a periodic function“, Izv. TulSU.
392. Ser. Mechanics. Math. Informatics. Tula, V.4, No. 3, P. 56-67.
393. Manokhin, E. V. 2003, “Banach matrices“, Izv. TulSU. Ser. Mechanics. Math. Informatics,
394. Tula, v.9, No. 1, P. 129-141.
395. Manokhin, E. V. 2008, “Some sets in and Young’s constant“, Chebyshev collection, Publishing
396. house of TSPU im. L. N. Tolstoy, Tula, v. 9, No. 1, P. 144-147.
397. Shulyupov, V. A. 1995, “Differential equations describing a closed system containing a term
398. with hysteron“, Mosc. Univ. Math. Bull., 50, No. 2, P. 23-27.
399. Shulyupov, V. A. 1995, “Differential equations describing a closed system containing a link
400. with a hysteron“, Differential Equations, No. 5, P. 914.
401. Dobrovolsky, N. M., Yesayan, A. R. & Shulyupov, V. A. 1999, “Factorial and recursion“, Izv.
402. Tool. state un. Math. Mechanics. Informatics. TulSU, Tula, Vol. 5, No. 1, P. 100-113.
403. Shulyupov, V. A. 2012, “Possible view of a separate semi-trajectory of a two-dimensional
404. autonomous closed-loop system containing a link with a hysteron“, Information technologies,
405. innovations, investments, mathematical methods and models. Interuniversity collection of
406. scientific papers, Tula, P. 177-181.
407. Shulyupov, V. A. 2012, “Qualitative study of a two-dimensional system containing a link with
408. hysterone“, Publishing house of TSPU im. L.N. Tolstoy, Tula, 92 p.
409. Yesayan, A. R., Chubarikov, V. N., Dobrovolsky, N. M. & Shulyupov, V. A. 2010, “Programming
410. in Mathcad by examples“, Publishing house TSPU, Tula, 330 p.
411. Isaeva, N. M. & Subbotina, T. I. 2001, “Mathematical modeling of the relationship between
412. total and direct bilirubin for some liver diseases“, Bulletin of new medical technologies,
413. Publishing house of TulSU, Tula, Vol. IX, No. 1, pp. 34-36.
414. Isaeva, N. M., T. I. Subbotina, & A. A. Yashin. 2006, “Lithogenic properties of bile and the
415. "golden section„‘, Bulletin of new medical technologies, Publishing house of TulSU, Tula, Vol.
416. XIII, No. 4, P. 175-177.
417. Isaeva, N. M., Subbotina, T. I., Khadartsev, A. A. & Yashin, A. A. 2007, “Fibonacci code and
418. the "golden ratio"in experimental pathophysiology and electromagnetobiology“, State Unitary
419. Enterprise NII NMT, NITs "Matrix". Moscow–Tula–Tver: Triada Publishing House.
420. Isaeva, N. M., Kurotchenko, S.P., Savin, E. I., Subbotina, T. I. & Yashin, A. A. 2009, “"Golden
421. section"as a criterion for the severity of pathomorphological changes when the body is
422. exposed to rotating and pulsed running magnetic fields“, Bulletin of new medical technologies,
423. Publishing house of TulSU, Tula, Vol. . XVI, No. 3, P. 38-39.
424. Isaeva, N. M., Ivanov, V. B., Savin, E. I., Subbotina,T. I., Yashin, A. A. & Khasaya, D. A. 2011,
425. “Investigation of the activity of regulation of the aggregate state of blood when exposed to
426. the body of electromagnetic radiation from the standpoint of the "golden section„‘, Bulletin
427. of new medical technologies, Publishing house of TulSU, Tula, Vol. XVIII, No. 4, P. 30-32.
428. Isaeva, N. M., Kupeev, V. G., Savin, E. I., Subbotina, T. I. & Yashin, A. A. 2011, “Application of
429. correlation-regression analysis to study the activity of free-radical processes under the influence
430. of electromagnetic radiation, the introduction of phytomelanin and stem cells“, Bulletin of new
431. medical technologies, Publishing house of TulSU, Tula, Vol. XVIII, No. 4, P. 48-50.
Review
For citations:
Denisov I.V. Ways of development of mathematical analysis at Tula State Lev Tolstoy Pedagogical University (to the 70th anniversary of the formation of the Department of Mathematical Analysis). Chebyshevskii Sbornik. 2021;22(5):270-306. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-5-270-306