# Georgii Nikolaevich Polozii's publications

We list those publications by Georgii Nikolaevich Polozii that we have been able to find; they come from various different sources. Let us note that his name appears as Polozii, Polozhii, and Polozhij with initials either G N, or G M. We have, however, put all the publications down as having G N Polozii as the author. We have omitted some translations and works which he edited, but this still means that the 98 listed below is a little short of the 111 publications figure (which does include translations and works which he edited) which appears in some of his obituaries.

1. G N Polozii, On $p$-analytic functions of a complex variable (Russian), Doklady Akad. Nauk SSSR (N.S.) 58 (7) (1947), 1275-1278.

2. G N Polozii, On the application of the generalized derivative to a class of quasi-conformal mappings (Russian), Doklady Akad. Nauk SSSR (N.S.) 63 (1948), 615-618.

3. G N Polozii, Singular points and residues of p-analytic functions of a complex variable (Russian), Doklady Akad. Nauk SSSR (N.S.) 60 (5) (1948), 769-772.

4. G N Polozii, A new method for the solution of some mixed problems of the plane theory of elasticity (Russian), Doklady Akad. Nauk SSSR (N.S.) 66 (1949), 177-180.

5. G N Polozii, On a method for the solution of certain mixed problems of the theory of thin plates (Russian), Doklady Akad. Nauk SSSR (N.S.) 66 (1949), 353-356.

6. G N Polozii, A generalization of Cauchy's integral formula (Russian), Mat. Sbornik N.S. 24(66) (1949), 375-384.

7. G N Polozii, Solution of the third basic problem of the plane theory of elasticity for an infinite plane with a square opening (Russian), Akad. Nauk SSSR. Prikl. Mat. Meh. 13 (1949), 297-306.

8. G N Polozii, The solution of some problems of the plane theory of elasticity for regions with angular points (Russian), Ukrain. Mat. Zurnal 1 (4) (1949), 16-41.

9. G N Polozii, Solution of the third fundamental problem of the plane theory of elasticity for an arbitrary finite convex polygon (Russian), Doklady Akad. Nauk SSSR (N.S.) 73 (1950), 49-52.

10. G N Polozii, Application of boundary problems of the theory of functions to the solution of the third problem of the plane theory of elasticity for an infinite plane with triangular and regular polygonal openings (Russian), Ukrain. Mat. Zurnal 2 (3) (1950), 115-124.

11. G N Polozii, On the motion of the boundary points of mapped regions (Russian) Uspehi Matem. Nauk (N.S.) 7 6(52) (1952), 203-205.

12. G N Polozii, The theorem on conservation of domain for certain elliptic systems of differential equations and its applications, Mat. Sbornik N.S. 32(74) (1953), 485-492.

13. G N Polozii, The method of movement of boundary points and majorant regions in the theory of filtration (Russian), Ukrain. Mat. Z. 5 (1953), 380-400.

14. G N Polozii, A theorem on the correspondence of boundaries and variational theorems for certain elliptic systems of differential equations (Russian), Dokl. Akad. Nauk SSSR (N.S.) 95 (1954), 927-930.

15. G N Polozii, Theorems on variation of plane and axially symmetric filtration in homogeneous and inhomogeneous media. The method of area invariance (Russian), Ukrain. Mat. Z. 6 (1954), 333-348.

16. K Breus and G N Polozii, Obituary: Vadim Even'evic D'yacenko (Russian), Ukrain. Mat. Z. 6 (1954), 367-370.

17. G N Polozii, Variational-topological theorems on boundary problems of the theory of torsion of shafts of variable cross-section. The method of preservation of domain and of majorizing domains (Russian), Izv. Akad. Nauk SSSR. Ser. Mat. 19 (1955), 245-270.

18. G N Polozii, Conformal mapping of simply connected and doubly connected regions and the determination of the Christoffel-Schwarz constants by means of a mathematical apparatus (Russian), Dokl. Akad. Nauk SSSR (N.S.) 104 (1955), 15-18.

19. G N Polozii, Effective solution of a problem on approximate conformal mapping of simply connected and doubly connected regions and determination of the Christoffel-Schwarz constants by means of electrohydrodynamical analogies (Russian), Ukrain. Mat. Z. 7 (1955), 423-432.

20. G N Polozii, On an addendum to a theorem on motion of boundary points.(Russian) Ukrain. Mat. Z. 7 (1955), 339-342.

21. G N Polozii, On some comparison theorems for boundary problems of torsion of prismatic bars (Ukrainian), Akad. Nauk Ukrain. RSR. Prikl. Mat. 1 (1955), 391-399.

22. G N Polozii, Method of solution of the problem of the bending of prismatic rods (Ukrainian), Akad. Nauk Ukrain. RSR. Prikl. Meh. 2 (1956), 257-269.

23. G N Polozii, General solution of the problem of contact with a rigid edge for an arbitrary polygon and an arbitrary polygonal aperture (Russian), Kiiv. Derz. Univ. Nauk Zap. 16 (2) (1957) = Kiev. Gos. Univ. Mat. Sb. 9 (1957), 35-51.

24. G N Polozii, On the question of $(p, q)$-analytical functions of a complex variable and their applications (Russian), Acad. Républ. Popul. Roum., Rev. Math. Pur. Appl. 2 (1957), 331-361.

25. G N Polozii, On certain overall characteristics of the stressed state when prismatic rods are acted upon by a bending force (Russian), Dokl. Akad. Nauk SSSR 114 (1957), 45-48.

26. G N Polozii, A method of solving integral equations (Russian), Dokl. Akad. Nauk SSSR (N.S.) 118 (1958), 876-878.

27. G N Polozii and V S Cemeris, On the application of $p$-analytic functions in the axisymmetrical theory of elasticity (Ukrainian), Dopovidi Akad. Nauk Ukrain. RSR 1958 (1958), 1284-1287.

28. G N Polozii, A method of solving integral equations (Russian), Dokl. Akad. Nauk SSSR 118 (1958), 876-878.

29. G N Polozii, A method of solution of integral equations (Russian), Izv. Akad. Nauk SSSR. Ser. Mat. 23 (1959), 295-312.

30. G N Polozii, A numerical method of solving boundary value problems for partial differential equations (Russian), Dokl. Akad. Nauk SSSR 134 (1960), 39-41.

31. G N Polozii, A numerical method of solving boundary value problems for partial differential equations, Soviet Math. Dokl. 1 (1960), 1016-1019.

32. G N Polozii, (p, q)-analytic functions of a complex variable and some of their applications (Russian), in Issledovaniya po sovremennym problemam teorii funkcii kompleksnogo peremennogo (Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1960), 483-515.

33. G N Polozii, N A Pakhareva, I Z Stepanenko, P S Bondarenko and I M Velikoivanenko, Mathematical laboratory (Russian) (Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1960), 512 pages.

34. G N Polozii, A new method for the numerical solution of boundary problems for elliptical partial differential equations (Ukrainian), Dopovidi Akad. Nauk Ukrain. RSR 1960 (1960), 1579-1853.

35. G N Polozii, On a new method of a numerical solution of boundary-value problems for elliptic differential equations (Russian), Ukrain. Mat. Z. 12 (1960), 308-323.

36. G N Polozii, Explicit relations for equations in partial finite differences. II (Ukrainian), Visnik Kiiv. Univ. 1960 (3) (1960), Ser. Mat. Meh. vyp. 2 (1961), 11-46.

37. G N Polozii and A M Kijasko, Application of $p$-analytical functions to the solution of boundary problems of the momentless shell theory (Ukrainian), Prikladna Meh. 7 (1961), 362-369.

38. G N Polozii and V S Chemeris, On integral equations of axially symmetric elasticity theory (Russian), Issled. Sovrem. Probl. Teor. Funkts. Kompleksn. Perem., IV. Vses. Konf. Mosk. Univ. 1958 (1961), 399-412.

39. G N Polozii and P I Calenko, The strip method for solving integral equations (Ukrainian), Dopovidi Akad. Nauk Ukrain. RSR 1962 (1962), 427-431.

40. G N Polozii, Numerical solution of two- and three-dimensional boundary-value problems of mathematical physics and functions of a discrete argument (Russian) (Izdat. Kiev. Univ., Kiev, 1962), 161 pages.

41. G N Polozii, Boundary-value problems in the axisymmetric theory of elasticity. The method of $p$-analytic functions of a complex variable (Russian), Ukrain. Mat. Z. 15 (1963), 25-45.

42. G N Polozii, A fundamental integral representation for p-analytic functions with characteristic $p = x^{k}$ (Russian), Ukrain. Mat. Z. 16 (1964), 254-259.

43. G N Polozii, Remarks on the fundamental integral representation of p-analytic functions with characteristic $p = x^{k}$ (Ukrainian), Dopovidi Akad. Nauk Ukrain. RSR 1964 (1964), 839-841.

44. G N Polozii, On the representation of p-harmonic functions by harmonic functions and their derivatives (Ukrainian), Dopovidi Akad. Nauk Ukrain. RSR 1964 (1964), 1277-1280.

45. G N Polozii and E M Prikhod'ko, On the application of the summary representation method to the numerical solution of biharmonic problems (Russian), Teor. Obolochek i Plastin, Tr. IV. Vsesoyuzn. Konf., Erevan 1962 (1964), 808-814.

46. G N Polozii, The equations of mathematical physics (Russian) (Izdat. "Vyssaja Skola'', Moscow, 1964), 559 pages.

47. G N Polozii, On the representation of $p$-analytic functions in terms of analytic functions and their derivatives (Ukrainian), Dopovidi Akad. Nauk Ukrain. RSR 1964 (1964), 986-991.

48. G N Polozii and P I Calenko, Solution of integral equations by the band method (Russian), in Problems Math. Phys. And Theory of Functions (Russian) (Izdat. Akad. Nauk Ukrain. SSR, Kiev, 1964), 124-144.

49. G N Polozii, On the representation of $p$-analytic functions as linear combinations of analytic functions and their first and second derivatives (Russian), Sibirsk. Mat. Z. 5 (1964), 1326-1332.

50. G N Polozii, Limit values and inversion formulas along the cuts of the fundamental integral representation for p-analytic functions with characteristic $p = x^{k}$. I (Russian), Ukrain. Mat. Z. 16 (1964), 631-656.

51. G N Polozii, On solving boundary value problems by the use of $p$-analytic functions with characteristic $p = x^{k}$ in bipolar and modified bipolar coordinates (Ukrainian), Visnik kiiv. Univ. 1964 (6) (1964), 3-13.

52. G N Polozii and A F Ulitko, On inversion formulae for the fundamental integral representation of $p$-analytic functions with characteristic $p = x^{k}$ (Russian), Prikladna. Meh. 1 (1) (1965), 39-51.

53. G N Polozii, Limit values and inversion formulas along the cuts of the fundamental integral representation of $p$-analytic functions with characteristic $p = x^{k}$. II (Russian), Ukrain. Mat. Z. 17 (2) (1965), 61-87.

54. G N Polozii, The solution of the fundamental biharmonic problem for a wide class of regions by the method of summary representations (Russian), Prikladna. Meh. 1 (12) (1965), 1-8.

55. G N Polozii, Applications of $p$-analytic functions and $(p, q)$-analytic functions (Russian), in Appl. Theory of Functions in Continuum Mechanics, Proc. Internat. Sympos., Tbilisi, 1963, I, Mechanics of Solids (Russian) (Izdat. "Nauka'', Moscow, 1965), 309-326

56. G N Polozii, Generalization of the theory of analytic functions of a complex variable. p-analytic and (p, q)-analytic functions and some of their applications (Russian) (Izdat. Kiev. Univ., Kiev, 1965), 442 pages.

57. G N Polozii and O M Prihod'ko, Transformation formulae for summary representations (Ukrainian), Visnik Kiiv. Univ. 1965 (7) (1965), 3-15.

58. G N Polozii and A A Skorobagat'ko, On a certain class of formulas of summary representations (Russian), Vycisl. Mat. (Kiev) Vyp. 1 (1965), 20-40.

59. G N Polozii, Die Löung von Randwertaufgaben $p$-analytischer Funktionen mit der Charakteristik $p = x^{k}$ für gewisse kanonische Gebiete, Wiss. Z. Karl-Marx-Univ. Leipzig Math.-Natur. Reihe 14 (1965), 475-495.

60. G N Polozii, The method of summary representation for numerical solution of problems of mathematical physics (Pergamon Press, Oxford-New York-Paris, 1965), 283 pages.

61. G N Polozii, On a modification of the formula of summary representations of the generalized biharmonic equation (Russian), Prikladna. Meh. 2 (4) (1966), 1-6.

62. G N Polozii, Remark on a class of $p$-analytic functions connected with axially symmetric problems in the theory of elasticity (Russian), Prikladna. Meh. 2 (11) (1966), 123-126.

63. G N Polozii and V L Makarov, On the question of the summary representation formulas for an axially symmetric potential (Ukrainian), Visnik Kiiv. Univ. 1966 (8) (1966), 11-20.

64. G N Polozii, On eigenvalues of certain biharmonic problems (Ukrainian), Visnik Kiiv. Univ. 1966 (8) (1966), 3-10.

65. G N Polozii, N A Pachariewa, I Z Stiepanienko, P S Bondarienko and I M Wielikoiwanienko, Metody przyblizonych obliczen (Wydawnictwa Naukowo-Techniczne, Warsaw, 1966), 487 pages.

66. G N Polozii, Some questions concerning the method of summary representation (Russian), Vycisl. Mat. (Kiev) Vyp. 2 (1966), 31-52.

67. A A Skorobogat'ko and G N Polozii, Remark on a class of summary representation formulas (Russian), Vycisl. Mat. (Kiev) Vyp. 2 (1966), 144-153.

68. G N Polozii, A remark on the basic integral representation of $p$-analytic functions with characteristic $p = x^{k}$ (Russian), Vycisl. Prikl. Mat. (Kiev) Vyp. 4 (1966), 145-151.

69. G N Polozii, Numerische Lösung von Randwertproblemen der mathematischen Physik und Funktionen diskreten Arguments (B G Teubner Verlagsgesellschaft, Leipzig, 1966), 270 pages.

70. G N Polozii and I M Lyashenko, Eigenvalues of the finite-differences Laplace operator for regions consisting of rectangles (Ukrainian), Dopovidi Akad. Nauk Ukrain. RSR Ser. A 1967 (1967), 31-35.

71. G N Polozii and I M Lyashenko, On the theory of the eigenvalues of Laplace's difference operator for domains that are composed of rectangles (Russian), Vycislit. Prikl. Mat., Mezhvedomst. Nauchn. Sb. 3 (1967), 3-31.

72. B M Bublik and G N Polozii, Eigenvalues of the basic biharmonic problem for a rectangle (Ukrainian), Dopovidi Akad. Nauk Ukrain. RSR Ser. A 1967 (1967), 3-6.

73. B M Bublik and G N Polozii, On boundary value problems and eigenvalues of the generalized biharmonic equation (Russian), Vychisl. Prikl. Mat., Mezhvedomst. Nauchn. Sb. 3 (1967), 68-85.

74. G N Polozii, Inversion formulas for the fundamental integral representation of $x^{k}$-analytic functions of $z = x + iy$, $k$ any odd integer (Ukrainian), Dopovidi Akad. Nauk Ukrain. RSR Ser. A 1967 (1967), 315-319.

75. G N Polozii, On $p$-analytic functions with logarithmically harmonic characteristic $p$ (Ukrainian), Dopovidi Akad. Nauk Ukrain. RSR Ser. A 1967 (1967), 503-506.

76. G N Polozii, Inversion formulas along arbitrary contours of the principal integral representation of $p$-analytic functions (Russian), Ukrain. Mat. Z. 19 (5) (1967), 87-95.

77. G N Polozii, Solution of boundary value problems for $p$-analytic functions with characteristic $p = x^{k}$ for certain canonical domains (Russian), Bull. Kiev. Univ. Special Issue Sci. Papers Sci. Kiev and Leipzig Univ (Russian) (Izdat. Kiev. Univ., Kiev, 1967), 131-166.

78. G N Polozii, Inversion formulas for the fundamental integral representation of $p$-analytic functions of $z = x + iy$ with characteristic $p = x^{k}$ (Russian), Dokl. Akad. Nauk SSSR 177 (1967), 40-43.

79. G N Polozii, Inversion formulas for the fundamental integral representation of $p$-analytic functions of $z = x + iy$ with characteristic $p = x^{k}$, Sov. Math. Dokl. 8 (1967), 1370-1376.

80. G N Polozii, On a problem of the theory of the axially symmetric potential and on the system of the round and the ring die (Russian), Prikl. Mekh. 3 (12) (1967), 16-27.

81. G N Polozii, Formulas of inversion along arbitrary contours for the fundamental integral representation of $p$-analytic functions, Ukrain. Mat. Z. 19 (1967), 578-585.

82. G N Polozii, The basic integral representation of $p$-analytic functions with characteristic $p=e^{\alpha x + \beta}$ and its inversion formulas (Russian), in Problems in the Theory and History of Differential Equations (Russian) ("Naukova Dumka'', Kiev, 1968), 65-81.

83. G N Polozii, Affine transformations of $p$-analytic and $(p, q)$-analytic functions of a complex variable (Russian), Ukrain. Mat. Z. 20 (1968), 325-339.

84. G N Polozii, Affine transformations of $p$-analytic and $(p, q)$-analytic functions of a complex variable, Ukrain. Mat. Z. 20 (1968), 288-298.

85. G N Polozii, Certain questions connected with affine transformations of $p$- and $(p, q)$-analytic functions (Ukrainian), Visnik Kiiv. Univ. 1968 (10) (1968), Ser. Mat. Meh., 7-19.

86. G N Polozii, The solution of a mixed boundary value problem of the theory of axially symmetric potential for a space layer (Russian), Mathematical Physics, No. 5 (1968) (Russian) (Naukova Dumka, Kiev, 1968), 162-168.

87. G N Polozii, The axially symmetric potential of an annular disc and of a system of annular discs (Russian), Vycisl. Prikl. Mat. (Kiev) No. 6 (1968), 3-22.

88. G N Polozii, The $p$-analytic functions with a logarithmically harmonic characteristic $p$ (Russian), Vycisl. Prikl. Mat. (Kiev) No. 5 (1968), 24-37.

89. G N Polozii and M V Nogin, A problem in the theory of axially symmetric potential of two spherical circular discs (Ukrainian), Dopovidi Akad. Nauk Ukrain. RSR Ser. A 1969 (1969), 894-898; 956.

90. G N Polozii, Integral representations of $x^{k}$-analytic functions and of solutions of axisymmetric problems in elasticity theory (Russian), Prikladna. Meh. 5 (4) (1969), 1-17.

91. G N Polozii and V L Makarov, A generalization of the summary representation formulas of an axially symmetric potential, and special functions of a discrete argument of the first and second kind. I (Russian), Vycisl. Prikl. Mat. (Kiev) No. 8 (1969), 80-97.

92. G N Polozii and V L Makarov, A generalization of the summary representation formulas of an axially symmetric potential, and special functions of a discrete argument of the first and second kind. II (Russian), Vycisl. Prikl. Mat. (Kiev) No. 9 (1969), 3-18.

93. G N Polozii, P I Calenko and A A Skorobagat'ko, Computational formulae for the solution of boundary value problems of the Helmholtz and Poisson equations by the method of summary representations. I (Russian), Vycisl. Prikl. Mat. (Kiev) No. 8 (1969), 22-39.

94. G N Polozii and V L Makarov, A generalization of the summary representation formulas for an axially symmetric potential (Russian), Vycisl. Prikl. Mat. (Kiev) No. 7 (1969), 38-56.

95. G N Polozii and O O Kapsivii, Certain properties of the fundamental integral representation of $p$-analytic functions with the characteristic $p = x$ (Ukrainian), Visnik Kiiv. Univ. 1970 (12) (1970), 3-9.

96. G N Polozii, A A Skorobagat'ko and P I Calenko, Computational formulae for the solution of boundary value problems of the Helmholtz and Poisson equations by the method of summary representations. II (Russian), Vycisl. Prikl. Mat. (Kiev) No. 10 (1970), 17-32.

97. G N Polozii and A A Kapsivyi, Problems of linear conjugation of $p$-analytic functions with the characteristic $p = x$ (Russian), Vycisl. Prikl. Mat. (Kiev) No. 10 (1970), 49-66.

98. G N Polozii, Generalization of the theory of analytic functions of a complex variable. $p$-analytic and $(p, q)$-analytic functions and some of their applications (2nd edition) (Russian) ("Naukova Dumka", Kiev, 1973), 424 pages.

Last Updated March 2021