Prof. Shalva Mikeladze

(16(29).03.1895, Telavi, - 27.08. 1976, Tbilisi)



EDUCATION AND SCIENTIFIC DEGREES

1903-1905 Pupil of Telavi private school
1905-1910 Pupil of Telavi city school
1910-1915 Pupil of Baku vocational secondary mechanical and building school
1915-1916 Student of Petrograd Electrotechnical Institute
1916-1917 Student of Petrograd Military Engineering Higher School
1920-1929 Student of physical and mathematical faculty of Tbilisi State University
1935 Was awarded Doctor of Science (Phys.-Math) degree by Tbilisi State University
1935 Conferred the rank of professor



POSITIONS HELD AND ACADEMIC EXPERIENCE

1917 Commander of telegraph platoon of Caucasian engineer batallion (Aleksandropol, Armenia)
1917-1918 Chief of military engineering park, 4th Caucasian engineer batallion (Khnis-Kala, Turkey)
1918-1924 Commander of telegraph subdivision of engineer battalion; chief of communication unit of 1st Georgian infantry division; commander of separate communications subdivision; inspector of communications course under division (Tbilisi)
1924-1927 Technician; chief technician, head of technical bureau of Tbilisi Administration for Electrical Structures
1927-1929 Engineer at Zemo Avchala Hydroelectric Power Station
1929-1932 Lecturer at: State Polytechnical Institute; Transcaucasian Institute of Transport Engineers; Tbilisi State University
1932-1933 Docent of: Tbilisi State University; Transcaucasian Institute of Transport Engineers
1933-1935 Was sent to V. A. Steklov Mathematical Institute of Academy of Sciences of USSR (Leningrad)
1935-1946 Professor of Institute of Railroad Transport Engineers; head of theoretical mechanics and higher mathematics chair
1935-1970 Professor of Tbilisi State University
1935-1937 Research specialist; senior research specialist of Tbilisi A. M. Razmadze Mathematical Institute of Academy of Sciences of Georgian SSR
1937-1976 Head of computational mathematics department at Tbilisi Mathematical Institute of Academy of Sciences of georgian SSR
1946-1952 Professor of Tbilisi A. S. Pushkin Pedagogical Institute; head of mathematical analysis chair
1944-1952 Consulting professor of Tbilisi A. V. Vinter Research Institute of Structures and Hydropower Engineering
1954-1955 Head of mathematics chair at physical faculty of Tbilisi State University
1956-1970 Head of approximate analysis and computing technique chair at mechanical and mathematical faculty of Tbilisi State University
1962-1967 Head of computational mathematics problem laboratory under mechanical and mathematical faculty of Tbilisi State University
1976 Scientific consultant of mechanics sector of Tbilisi Mathematical Institute of Academy of Sciences of Georgian SSR



RESEARCH INTERESTS

Problems of interpolation and approximation of functions; numerical differentiation and integration; solution of numerical equations; solution of differential and integral equations; methods of approximate solutions of mechanics problems.



MEMBERSHIP IN SCIENTIFIC ACADEMIES



PRIZES AND AWARDS



EDITORIAL ACTIVITIES

1951-1964 Member of Editorial Board of the "Trudy Tbiliss. Matematicheskogo Instituta"



MAIN PUBLICATIONS

(i) Monographs

  1. Numerical methods of integration of partial differential equations. (Russian) Izd. Akad. Nauk SSSR, M.-L., 1936, pp.108.
  2. Theory and practice of interpolation. (Georgian) Izd. Akad. Nauk Gruzin. SSR, Tbilisi, 1946, pp.393.
  3. Some problems of structural mechanics. (Russian) Gostekhizdat, M.-L., 1948, pp.267.
  4. Numerical integration. (Russian) Uspekhi matem. nauk (N.S.) 3(1948), No. 6(28), 3-88.
  5. New methods of integration of differential equations and their application to problems in the theory of elasticity. (Russian) Gostekhizdat, M.-L., 1951, pp.291.
  6. Numerical methods of mathematical analysis. (Russian) Gostekhizdat, Moscow, 1953, pp.527.
  7. Some problems of structural mechanics. (Chinese) Sci. Publ., Peking, 1956, pp.306.
  8. Numerical methods of mathematical analysis. (Chinese) Sci. Publ., Peking, 1957, pp.638.
  9. Solution of numerical equations. (Russian) Metsnieraba, Tbilisi, 1965, pp.270.

    (ii) Papers


  10. Investigation of an equation of the form um-pun-q=0. (Georgian) Izv. Inzhen.-Stroit. Inst. Gruzii, 1(1932), 83-99.
  11. A note on the Raabe and Schlömilch convergence criteria. (Georgian) Izv. Zakavkazsk. Industr. Inst., 1(1934), 115-118.
  12. To the question of an approximate solution of an equation by expandion the root into a series. (Russian) Izv. Zakavkazsk. Industr. Inst., 1(1934), 21-47.
  13. On the numerical integration of partial differential equations. (Russian) Izv. AN SSSR,(1934), No. 6, 819-842.
  14. On new algorithms of numerical integration of ordinary differential equations. (Russian) Izv. AN SSSR,(1934), No. 8, 1187-1224.
  15. On the numerical solution of integral equations. (Russian) Izv. AN SSSR,(1935), No. 2, 255-300.
  16. On the roots of a function defined by a differential equation. (Russian) Izv. AN SSSR,(1935), No. 4, 559-586.
  17. On the numerical integration of some differential equations of mathematical physics. (Russian) Trudy II Vsesojuznogo Mat. s'ezda, 2,L., 1936, 388-393.
  18. On the numerical integration of Laplace and Poisson equations. (Russian) Dokl. AN SSSR, 14(1937), No.4, 181-182.
  19. On the numerical solution of the differential equation 2u/x2 + 2u/y2 + 2u/z2 = j(x,y,z). (Russian) Dokl.AN SSSR, 14(1937), No. 4, 177-179.
  20. Investigation of mechanical quadratures formulas. (Russian) Trudy Tbiliss. Mat. Inst., 2(1937), 43-108.
  21. On a residual term of a series providing some root of the equation um-pun-q=0. (Georgian) Izv. Gruz. Industr. Inst., 5(1937), 1-14.
  22. On the numerical solution of Laplace and Poisson differential equations. (Russian) Izv. AN SSSR, (1938), No. 2, 271-292.
  23. On the integration of differential equations by the difference method. (Russian) Izv. AN SSSR,(1939), No. 5-6, 627-642.
  24. Generalization of the method of numerical integration of differential equations by means of mechanical quadrature formulas. (Russian) Trudy Tbiliss. Mat. Inst., 7(1940), 47-63.
  25. To the question of numerical integration of partial differential equations by means of nets. (Russian) Soobshch. Gruz. Filiala AN SSSR, 1(1940), No. 4, 249-254.
  26. To the question of solution of boundary value problems by the difference method. (Russian) Dokl. AN SSSR, 28(1940), No. 5, 401-403.
  27. On the numerical integration of elliptic and parabolic type equations. (Russian) Izv. AN SSSR, 5(1941), No. 1, 57-74.
  28. On the divided differences with repeated values of the argument. (Russian) Trudy Tbiliss. Mat. Inst., 9(1941), 49-60.
  29. On the approximate integration of linear differential equations with discontinuous coefficients.(Russian) Soobshch. AN GSSR, 3 (1942 ), No. 7 , 633 - 639 .
  30. Quadrature formulas using differences.(Russian) Soobshch. AN GSSR, 3 (1942 ), No. 10 , 1001 - 1003 .
  31. New formulas for the numerical integration of differential equations. (Russian) Soobshch. AN GSSR, 4 (1943 ), No. 3 ,215 - 218 .
  32. On formulas for mechanical cubatures, containing partial derivatives of the integrand.(Russian) Soobshch. AN GSSR, 4 (1943 ), No. 4 , 297 - 300 .
  33. New finite difference equations for the computation of rectangular plates, freely supported along the boundaries. (Russian) Soobshch. AN GSSR, 4 (1943 ), No. 8 , 737 - 744 .
  34. On the problem of longitudinal bending of rectlinear bars within the limits of elasticity. (Russian) Trudy Tbiliss. Mat. Inst., 12(1943), 175-213.
  35. On the numerical integration of a function depending on a parameter. (Georgian) Soobshch. AN GSSR, 5 (1944 ), No. 6 , 575 - 583 .
  36. On a method of numerical differentiation. (Georgian) Soobshch. AN GSSR, 5 ( 1944 ), No. 7 , 663-666.
  37. A new method for the calculation of the trajectory of the center of gravity of a projectile. (Georgian) Soobshch. AN GSSR, 5 ( 1944 ), No. 9 , 861-865.
  38. Application of a formula of numerical differentiation to the calculation of the trajectory of the center of gravity of an artillery schell. (Georgian) Soobshch. AN GSSR, 5 (1944 ), No. 10 , 959-964 .
  39. An approximate method for the integration of the differential equation for the bending of a beam. (Georgian) Soobshch. AN GSSR, 6 (1945 ), No. 2 , 97-104.
  40. On numerical integration. (Russian) Doklady AN SSSR, 49(1945), No.3, 167-168.
  41. On the subtabulation of matematical tables. (Georgian) Soobshch. AN GSSR, 6 ( 1945 ), No. 6 , 397-405 .
  42. On a process of interpolation for functions of two variables. (Georgian) Soobshch. AN GSSR, 6 ( 1945 ), No. 7 , 503-509 .
  43. General equation of elastic line of a beam. (Russian) Doklady AN SSSR, 50(1945), No...., 117-119.
  44. Solution of boundary value problems by means of the generalized Maclaurin formula. (Russian) Dokl. AN SSSR, 52(1946), No. 9, 759-761.
  45. Investigation of the bending of a bar, taking into account the influence of shifts on bendings. (Russian) Soobshch. AN GSSR, 7 ( 1946 ), No. 8 , 529-533 .
  46. A new method of calculating non-cut beams. (Russian) Soobshch. AN GSSR, 7 ( 1946 ), No. 9-10 , 627-632.
  47. Discontinuous solutions of ordinary linear differential equations. (Russian) Dokl. AN SSSR, 55(1947), No. 9, 801-804.
  48. Discontinuous solutions of differential equations and their application to calculating elements of bar deformation. (Russian) Trudy Tbiliss. Gosud. Pedagogich. Inst., 4(1947), 1-16.
  49. On the evaluation of determinants whose elements are polinomials. (Russian) AN SSSR. Prikl. Mat. Meh., 12(1948), No.2, 219-222.
  50. Longitudinal-transverse bending of a beam on an elastic foundation. (Russian) Doklady AN SSSR, 59(1948), No.3, 451-454.
  51. New formulas for the numerical integration of differential equations. (Russian) Doklady AN SSSR, 61(1948), No.5, 789-790.
  52. New quadrature formulas and their application to the integration of differential equations. (Russian) Doklady AN SSSR, 61(1948), No.4, 613-615.
  53. A new formula for the numerical solution of a Poisson equation. (Russian) Trudy Tbiliss. Gosud. Pedagogich. Inst., 5(1948), 1-5.
  54. The numerical integration of differential equations by means of summation formulas. (Russian) Doklady AN SSSR, 65(1949), No.2, 125-128.
  55. A new method for the solution of characteristic value problems. (Russian) Doklady AN SSSR, 66(1949), No.4, 553-556.
  56. A new integral method of solution of boundary problems. (Russian) Soobshch. AN GSSR, 12 ( 1951), No. 7 , 393-396 .
  57. On approximate solution of integral equations of Volterra type. (Russian) Trudy Tbiliss. Mat. Inst., 18(1951), 315-325.
  58. A new method of approximate calculation of a critical force. (Russian) Izv. Tbil. Nauchno-Issled. Inst. Sooruzhenii i Gidroenergetiki, 4(1951), 47-56.
  59. Approximate formulas for multiple integrals. (Russian) Soobshch. AN GSSR, 13 ( 1952 ), No. 4 , 193-200 .
  60. Numerical solution of boundary problems for nonlinear ordinary differential equations. (Georgian) Soobshch. AN GSSR, 14 ( 1953 ), No. 3 , 133-137 .
  61. Stability of a rectangular plate of variable thickness at uniaxial stressed state. (Russian) Trudy Tbiliss. Mat. Inst., 19(1953), 211-224.
  62. On the theory of construction of interpolation formulas. (Russian) Doklady AN SSSR, 90(1953), No.4, 503-506.
  63. Expansion of the finite difference of a function in differences of its derivative. (Russian) Doklady AN SSSR, 92(1953), No.3, 479-482.
  64. Approximate formulae for repeated integrals. (Russian) Trudy Voyenno-Morskoi Akademii Korablestroyeniya i Vooruzheniya im. A. N. Krilova (Proc. A. N. Krilov Milit. Navy Ship-Building and Weaponry Acad.) (Jubilee collected works dedicated to the 90th birthday anniversary of A. N. Krilov), (1953), vyp. 6, L., 115-120.
  65. On approximate solution of Cauchy's problem. (Russian) AN SSSR. Prikl. Mat. Meh., 18(1954), No.2, 245-249.
  66. Remarks on the theory of discontinuous solutions of ordinary differential equations. (Russian) Soobshch. AN GSSR, 15 ( 1954 ), No. 10 , 647-654 .
  67. On discontinuous solutions of ordinary quasi-differential equations. (Russian) Doklady AN SSSR, 105(1955), No.4, 641-644.
  68. Numerical solution of the inhomogeneous polyharmonic equation. (Russian) Inzhen. Sb., 23(1956), 190-202.
  69. Numerical integration of differential equations in the complex plane. (Russian) Soobshch. AN GSSR, 17 ( 1956 ), No. 2 , 97-102 .
  70. Formulas of mechanical quadratures for multiple integrals. (Russian) Trudy Tbiliss. Mat. Inst., 22(1956), 277-299.
  71. On one review and its accompanying comment. (Russian) Trudy Tbiliss. Mat. Inst., 22(1956), 319-338.
  72. Quadrature formulas for a regular function. (Russian) Soobshch. AN GSSR, 17 (1956 ), No. 4 , 289-296 .
  73. Approximate formulas for the multiple integral of a regular function. (Russian) Soobshch. AN GSSR, 17 (1956 ), No. 7 , 577-584 .
  74. On one review and its accompanying comment. (Russian) Uspekhi Mat. Nauk, 11(1956), vip. 3(69), 241-242. (an abridged version of Sh. E. Mikeladze's letter published in Trudy Tbiliss. Mat. Inst., 22(1956), 319-338).
  75. Formulae of numerical differentiation and integration of a function. (Russian) Trudy III Vsesojuznogo Mat. s'ezda,Moscow, 1956. Abstracts of section reports. M., Izd.AN SSSR, II(1956), 151-152.
  76. Quadrature formulas for multiple integrals with the greatest possible degree of accuracy. (Russian) Soobshch. AN GSSR, 18 ( 1957 ), No. 1 , 3-10 .
  77. Numerical differentiation in complex region. (Russian) Soobshch. AN GSSR, 18 (1957 ), No. 4 , 385-392 .
  78. Approximate solution of a system of non-linear equations. (Russian) Soobshch. AN GSSR, 20 (1958 ), No. 6 , 647-653 .
  79. Some iterations of higher order. (Russian) Soobshch. AN GSSR, 22 (1959 ), No. 3 , 257-264 .
  80. A general method for numerical solution of differential equations. (Russian) Soobshch. AN GSSR, 22 ( 1959 ), No. 5 , 513-518 .
  81. The method of variation of parameters in the solution of equations. (Russian) Soobshch. AN GSSR, 23 ( 1959 ), No. 1 , 3-9 .
  82. Boundary-value problems and eigenvalue problems for quasi-differential equations. (Russian) Trudy Tbiliss. Mat. Inst., 26(1959), 241-261.
  83. Numerical solution of ordinary differential equations by polynomials. (Russian) Trudy Tbiliss. Mat. Inst., 26(1959), 263-284.
  84. Solution of trinomial equations. (Russian) Trudy Tbiliss. Univ., 76(1959), 191-225.
  85. Numerical solution of a heat-transfer equation. (Russian) Trudy Tbiliss. Mat. Inst., 27(1960), 367-410.
  86. Formulas for numerical differentiation. (Russian) Soobshch. AN GSSR, 27 ( 1961 ), No. 6 , 657-662 .
  87. An application of Bernstein polynomials to a problem in structural mechanics. (Russian) Trudy Tbiliss. Mat. Inst., 28(1962), 107-121.
  88. A certain formula and its applications to the numerical solution of ordinary linear second-order differential equations. (Russian) Trudy Tbiliss. Mat. Inst., 29(1963), 283-305.
  89. A new numerical method of solution of ordinary differential equations. (Russian) Soobshch. AN GSSR, 45 ( 1967 ), No. 2 , 289-296 .
  90. Numerical solution of boundary problems for ordinary differential equations in the general case. (Russian) Soobshch. AN GSSR, 47 ( 1967 ), No. 2 , 263-268.
  91. The numerical solution of eigenvalue problems for ordinary linear differential equations with variable coefficients. (Russian) Soobshch. AN GSSR, 49 ( 1968 ), No. 2 , 257-262 .
  92. The numerical solution of nonlinear differential equations which depend on a parameter. (Russian) Soobshch. AN GSSR, 52 (1968), No. 1 , 21-26.
  93. Numerical solution of multipoint boundary value problems for ordinary nonlinear differential equations. (Russian) Soobshch. AN GSSR, 53 ( 1969 ), No. 2 , 269-272.
  94. Discontinuous solutions of ordinary differential equations. (Russian) Soobshch. AN GSSR, 59 ( 1970 ), No. 2 , 269-272 .
  95. Construction of discontinuous solutions of linear differential equations for multipoint boundary value problems. (Russian) Soobshch. AN GSSR, 67 (1972 ), No. 3 , 529-532.
  96. An eigenvalue problem for n'th order linear differential equations. (Russian) Soobshch. AN GSSR, 76 ( 1974 ), No. 1 , 45-48.
  97. On the estimation of the remainder term of the expansion of a piecewise continuous function with piecewise continuous derivatives. (Russian) Soobshch. AN GSSR, 79 ( 1975), No. 3 , 541-544.
  98. Numerical solution of partial differential equations and integral equations. (Russian) Selected papers, V. 1, Metsniereba, Tbilisi, 1979, pp.328.
  99. Numerical analysis and theory of ordinary differential equations.(Russian) Selected papers, V. 2, Metsniereba, Tbilisi, 1980, pp.331.



BIBLIOGRAPHY ON SH. MIKELADZE

  1. Georgian Soviet Encyclopaedia, v. 7, 1984 (Georgian)
  2. Tbilisi University 1918-1968. Tbilisi University Press, Tbilisi, 1968 (Russian)
  3. Mathematics in the USSR for 40 Years. 1917 - 1957 (Russian). V. 2, Gos. Izd. Fiz.-Mat. Liter., 1959.
  4. Mathematics in the USSR. 1958-1967. V. 2, Nauka, Moscow, 1970.
  5. Mathematics in the USSR for 30 Years. 1917-1947. V. 2. Gos. Izd. Telhniko-Teoretich. Lit., Moscow-Leningrad, 1948.
  6. An Essay on the History of Soviet Georgian Science for 25 Years. Izd. AN GSSR, Tbilisi, 1946 (Russian)
  7. Science in Soviet Georgia for 40 Years. Izd. AN GSSR, Tbilisi, 1961.
  8. T. Ebanoidze. Essays on Georgian Mathematicians. Tbilisi, Metsniereba, 1981. (Georgian)
  9. History of the Native Mathematics. Naukova Dumka, Kiev, v. 3, 1968, v. 4 1970 (Russian)