Professor Niko Vekua

(10. 08. 1913, village Akhuti - 16. 04. 1993, Tbilisi)



EDUCATION AND SCIENTIFIC DEGREES

1920-1928 Pupil of seven-year Akhuti school
1928-1931 Pupil of Kutaisi Agricultural Technical Secondary School
1932-1937 Student of Tbilisi State University, Faculty of Physics and Mathematics.
1937 Diploma in Mathematics, Tbilisi State University
1938-1941 Post-graduate student of Tbilisi Mathematical Institute
1941 Ph.D. in Mathematics, Tbilisi Mathematical Institute
1946 Dr. Sci. (Phys. & Math.), Tbilisi Mathematical Institute
1947 Conferred the rank of professor



POSITIONS HELD AND ACADEMIC EXPERIENCE

1931-1933 Teacher of Akhuti seven-year school
1937-1938 Director of Akhuti secondary school
1938-1941 Assistant of Tbilisi State University
1941-1942 Junior researcher of Tbilisi Mathematical Institute
1941-1947 Docent of Tbilisi State University
1942-1957 Senior researcher of Tbilisi Mathematical Institute
1948-1951 Dean of Faculty of Physics and Mathematics of Tbilisi State University
1957-1989 Head of the Department of Mathematical Physics Equations of Tbilisi Mathematical Institute
1963-1993 Head of the Chair of Theoretical Mechanics of Tbilisi State University
1977-1989 Director of A. Razmadze Mathematical Institute of Georgian Academy of Sciences



RESEARCH INTERESTS

Boundary value problems of analytical functions, differential and integro-differential equations with a small parameter and their applications to the potential theory and mathematical physics.



MEMBERSHIP IN SCIENTIFIC ACADEMIES



PRIZES AND AWARDS



MEMBERSHIP IN SCIENTIFIC SOCIETIES



EDITORIAL ACTIVITIES

1977-1986 Member of Editorial Board of the journal "Trudy Tbiliss. Matematicheskogo Instituta"
1964-1968 Member of Editorial Board of the journal "Trudy Tbiliss. Universiteta"



MAIN PUBLICATIONS

(i) Monographs

  1. Systems of singular integral equations and some boundary value problems. (Russian) Gos. Izd. tekhn.-teoret. lit., M.-L., 1950, pp. 252.
  2. Systems of singular integral equations. P. Noordhoff-Groninger-Holland, 1967, pp. 216.
  3. Systems of singular integral equations and some boundary value problems. (Russian) M., Nauka, 1970, pp. 379.
  4. Some problems of the theory of differential equations and applications to mechanics. M., Nauka, 1991, pp. 255.

    (ii) Papers


  5. Volterra type equations with an integral in the sense of Adamar. (Georgian) Soobshch. Gruz. Filiala AN SSSR, 1(1940), No. 17, 501-508.
  6. Remarks concerning the Fourier method (with D. Kharazov). (Russian) Soobshch. Gruz. Filiala AN SSSR, 1(1940), No. 9, 647-650.
  7. Integral equations of Volterra type with an integral in the sense of Adamar. (Russian) Trudy Tbiliss. Mat. Inst., 7(1940), 113-146.
  8. On the limiting passage from dynamical to stationary processes in the boundary value problems of heat conductivity. (Russian) Soobshch. Gruz. Filiala AN SSSR, 1(1940), No. 9, 651-657.
  9. On one class of singular integral equations and some boundary value problems of the potential theory. (Georgian) Trudy Tbiliss. Mat. Inst., 10(1941), 73-92.
  10. On one boundary value problem of the theory of functions of a complex variable (with D. Kveselava). (Russian) Soobshch. AN GSSR, (1941), No. 3, 233-240.
  11. On one boundary value problem of the theory of functions of a complex variable and its application to the solution of a system of singular integral equations (with D. Kveselava). (Russian) Trudy Tbiliss. Mat. Inst., 9(1941), 33-48.
  12. On the solution of a mixed boundary value problem of the Newtonian potential theory for a multi-connected domain. (Russian) Soobshch. AN GSSR, 3(1942), No. 8, 753-758.
  13. To the theory of systems of singular integral equations with the Cauchy type kernels. (Russian) Soobshch. AN GSSR, 4(1943), No. 3, 207-214.
  14. The Riemann boundary value problem for several unknown functions and its application to the systems of singular integral equations (with N. Muskhelishvili). (Russian) Trudy Tbiliss. Mat. Inst., 12(1943), 1-46.
  15. On one boundary value problem of Riemann with discontinuous coefficients for systems of analytic functions. (Georgian) Soobshch. AN GSSR, 5(1944), No. 5, 473-482.
  16. The Riemann problem with discontinuous coefficients for several unknown functions. (Georgian) Soobshch. AN GSSR, 5(1944), No. 1, 1-10.
  17. To the theory of systems of singular integral equations with discontinuous coefficients. (Georgian) Soobshch. AN GSSR, 5(1944), No. 2, 125-134.
  18. On one mixed boundary value problem of the theory of analytic functions. (Georgian) Soobshch. AN GSSR, 6(1945), No. 4, 245-254.
  19. Singular integral equation of general type with discontinuous coefficients. (Georgian) Soobshch. AN GSSR, 6(1945), No. 1, 3-10.
  20. A system of singular integral equations of general type with discontinuous coefficients. (Georgian) Soobshch. AN GSSR, 6(1945), No. 3, 185-194.
  21. The Hilbert boundary value problem with rational coefficients for several unknowns. (Georgian) Soobshch. AN GSSR, 7(1945), No. 9-10, 565-572.
  22. One remark on a system of singular integral equations. (Georgian) Trudy Tbiliss. Univ., 30a(1947), 31-38.
  23. The Riemann-Hilbert boundary value problem for systems of analytic functions. (Georgian) Trudy Tbiliss. Mat. Inst., 14(1947), 1-15.
  24. The generalized Hilbert boundary value problem for several unknown functions. (Georgian) Soobshch. AN GSSR, 8(1947), No. 9-10, 575-582.
  25. On one generalized system of singular integral equations. (Georgian) Soobshch. AN GSSR, 9(1947), No. 3, 153-160.
  26. Generalized Hilbert boundary value problem for several unknown functions. (Georgian) Trudy Tbiliss. Mat. Inst., 16(1948), 81-83.
  27. On some boundary value problems of the theory of logarithmic potential. (Georgian) Trudy Tbiliss. Univ., 34 a-v(1949), 311-327.
  28. The Hilbert boundary value problem and systems of singular integral equations in the case of piecewise smooth contours. (Georgian) Trudy Tbiliss. Mat. Inst., 17(1949), 29-49.
  29. On one boundary value problem of the theory of functions of a complex variable. (Georgian) Trudy Tbiliss. Mat. Inst., 17(1949), 41-46.
  30. The Hilbert boundary value problem for several unknown functions in the case of non-connected domains. (Georgian) Soobshch. AN GSSR, 11(1950), No. 9, 533-544.
  31. On one Hilbert problem with continuous coefficients and its application to singular integral equations. (Russian) Trudy Tbiliss. Mat. Inst., 18(1951), 307-313.
  32. The Carleman boundary value problem for several unknown functions. (Georgian) Soobshch. AN GSSR, 13(1952), No. 1, 9-14.
  33. On one boundary value problem of the theory of functions of a complex variable for several unknown functions. (Russian) Izvestia Akad. Nauk SSSR, 16(1952), No. 2, 157-180.
  34. On one problem on the theory of functions of a commplex variable. (Russian) Dokl. Akad. Nauk SSSR, 86(1952), No. 3, 457-460.
  35. On one generalized problem of the theory of functions of a complex variable. (Georgian) Trudy Tbiliss. Univ., 52(1954), 1-9.
  36. On one boundary value problem of linear conjugation. (Russian) Dokl. Akad. Nauk SSSR, 94(1954), No. 2, 173-176.
  37. On one boundary value problem of linear conjugation for several unknown functions with prescribed displacements. (Georgian) Trudy Tbiliss. Mat. Inst., 21(1955), 169-189.
  38. On one boundary value problem of linear conjugation for several unknown function. (Russian) Trudy Tbiliss. Univ., 56(1956), 75-80
  39. On one generalized Carleman boundary value problem for several unknown functions. Izvestia Akad. Nauk SSSR, 20(1956), No. 3, 377-384.
  40. On one boundary value problem of linear conjugation. (Georgian) Trudy Tbiliss. Mat. Inst., 24(1957), 125-134.
  41. On one system of singular integro-differential equations and its application to boundary value problems of linear conjugation. (Russian) Trudy Tbiliss. Mat. Inst., 24(1957), 135-147.
  42. On one differential boundary value problem of linear conjugation for several unknown functions in the case of open contours. (Georgian) Soobshch. AN GSSR, 21(1958), No. 5, 513-518.
  43. On one class of singular integral equations solvable effectively (with R. Isakhanov). (Georgian) Soobshch. AN GSSR, 23(1959), No. 3, 257-264.
  44. The Cauchy problem for a singular integro-differential equation. (Russian) Soobshch. AN GSSR, 22(1959), No. 6, 641-648.
  45. On one method of solution of singular integro-differential equations. (Georgian) Soobshch. AN GSSR, 23(1959), No. 2, 129-134.
  46. On one boundary value problem of linear conjugation for several unknown functions. (Georgian) Soobshch. AN GSSR, 22(1959), No. 1, 3-8.
  47. Linear integro-differential equations with small parameters in higher derivatives. (Russian) In: Problemy mekhaniki sploshnoi sredy. Izd. AN SSSR, M., 1961, 92-100.
  48. Systems of linear differential equations with a small parameter. (Georgian) Soobshch. AN GSSR, 29(1962), No. 4, 385-391.
  49. General boundary value problem of linear conjugation of unknown functions with prescribed displacements. (Russian) Trudy Tbiliss. Univ., 84(1962), 23-24.
  50. On the compactness of a family of generalized analytic functions. (Russian) Trudy Tbiliss. Univ., 84(1962), 17-21.
  51. On some integro-differential equations with a small parameter. (Russian) Soobshch. AN GSSR, 36(1964), No. 3, 513-519.
  52. On one differential boundary value problem of linear conjugation with a small parameter. (Russian) Soobshch. AN GSSR, 36(1964), No. 2, 257-260.
  53. On one system of nonlinear differential equations with a small parameter. (Georgian) Trudy Tbiliss. Univ., 110(1965), 25-32.
  54. On one system of integro-differential equations with a small parameter. (Georgian) Trudy Tbiliss. Univ., 117(1966), 249-253.
  55. On one system of nonlinear differential equations with a small parameter. (Georgian) Trudy Tbiliss. Mat. Inst., 33(1967), 21-24.
  56. On one generalized Hilbert boundary value problem for several unknown functions. (Russian) Trudy Tbiliss. Mat. Inst., 34(1968), 5-12.
  57. On one new method of solution of the Hilbert boundary value problem for several unknown functions. (Russian) Soobshch. AN GSSR, 52(1968), No. 1, 17-20.
  58. On one generalized Hilbert boundary value problem for several unknown functions with displacements. (Russian) In: Problemy mekhaniki sploshnoi sredy., M., Nauka, 1972, 11-120.
  59. Application of some I. Plemelj's results to the theory of singular integral equations and to boundary value problems of linear conjugation. Mathematica Balkanica, No. 3, 1973, 583-589.
  60. On some generalized Hilbert boundary value problems for several unknown functions with small parameters and connected with them integral and integro-differential equations. (Russian) Trudy Tbiliss. Mat. Inst., 49(1975), 19-38.
  61. On one Riemann-Hilbert boundary value problem for systems of analytic functions. (Russian) Soobshch. AN GSSR, 88(1977), No. 2, 273-276.
  62. On one nonlinear system of differential equations with a small parameter in derivatives. (Russian) Soobshch. AN GSSR, 85(1977), No. 2, 263-266.
  63. On one system of integro-differential equations with a small parameter and periodic coefficients. (Russian) Soobshch. AN GSSR, 86(1977), No. 1, 17-20.
  64. On one system of nonlinear differential equations with a small parameters in derivatives. (Georgian) Trudy Tbiliss. Mat. Inst., 58(1978), 73-80.
  65. The Riemann-Hilbert boundary value problem for several unknown functions. (Russian) Trudy Inst. Prikl. Mat. Tbiliss. Univ., 5-6(1978), 51-67.
  66. Non-homogeneous Riemann-Hilbert boundary value problem for systems of analytic functions. (Russian) Soobshch. AN GSSR, 89(1978), No. 2, 273-276.
  67. On some meromorphic solutions of homogeneous Riemann-Hilbert boundary value problem for several unknown functions. (Russian) Soobshch. AN GSSR, 89(1978), No. 1, 17-20.
  68. On one system of integro-differential equations with periodic coefficients and small parameters in derivatives. (Russian) Trudy Tbiliss. Mat. Inst., 58(1978), 62-72.
  69. Hilbert boundary value problems for some unknowns functions with rational coefficients. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze AN GSSR, 88(1989), 64-68.
  70. On factorization of some matrix functions (with O. Meunargia). (Russian) Trudy Tbiliss. Mat. Inst. Razmadze AN GSSR, 88(1989), 69-74.
  71. An efficient solution of Hilbert's problem for some matrix functions. (Russian) Soobshch. AN GSSR, 137(1990), No. 2, 241-243.
  72. On the Carleman integral equations. (Russian) Soobshch. AN GSSR, 138(1990), No. 3, 465-468.

    (iii) Text-books


  73. Theoretical Mechanics. (Georgian) Izd-vo Tbiliss. Univ., 1956, Tbilisi, pp. 432.
  74. Theoretical Mechanics. (Georgian) Tbilisi, "Ganatleba", 1965, pp. 575.
  75. Theoretical Mechanics. I. (Georgian) Izd-vo Tbiliss. Univ., 1970, Tbilisi, pp. 285.
  76. Theoretical Mechanics. II. (Georgian) Izd-vo Tbiliss. Univ., 1970, Tbilisi, pp. 366.



BIBLIOGRAPHY ON N. VEKUA

  1. Science in the Soviet Georgia for 25 years. Mathematics and Physics. Geophysics and Astronomy. Tbilisi, Izd-vo AN GSSR, 1946.
  2. Vekua Nikolai Petrovich. In: Mathematics in the USSR for 40 years. 1917-1957. V. 2. Biobibliography. M., Izd-vo Fiz.-Mat. Liter., 1959, 122-123.
  3. History of our country's mathematics. V. 3. 1917-1967. Kiev, "Naukova Dumka", 1968.
  4. Vekua Nikolai Petrovich. In: Mathematics in the USSR. V. 2. Biobibliography. M., Nauka, 1969, 226-227.
  5. Vekua Nikolai Petrovich. In: History of our country's mathematics. V. 4. 1917-1967. Kiev, "Naukova Dumka", 1970.
  6. The USSR Academy of Sciences and development of the Georgian science. 1924-1974. Tbilisi, Metsniereba, 1974.
  7. Vekua Nikolai Petrovich. Georgian Soviet Encyclopaedia, V. 4, 1979, 346-347.
  8. Vekua Nikolai Petrovich. In: Borodin A.I., Bugai A.S. Biographical Dictionary of Scientists in mathematics. Kiev, "Radjanska Shkola", 1979, 104-105.