Usmanov, Zafar Dzuraevich

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Usmanov, Zafar Dzuraevich
Doctor of physico-mathematical sciences (1974)
Speciality: 01.01.04 (Geometry and topology)
Birth date: 26.08.1937
E-mail: ,
Keywords: partial differential equations of elliptic type; general theory of elliptic systems; generalized Cauchy–Riemann systems with a singular point and a singular line; integral representations of solutions; general theory; boundary value problems differential geometry in Euclidean space; theory of surfaces; intrinsic geometry of surfaces; bending of surfaces; infinitesimal bendings of surfaces with an isolated flat point and a conic point; generalized Christoffel problem application of mathematical methods in different sciences; in sciences on space and time; modelling of an intrinsic time of a process.
UDC: 51-7, 51-71, 513.7, 513.73, 513.736.4, 514.752.43, 514.752.434, 514.752.435, 517.944, 517.956.222, 517.956.223
MSC: 35с15, 35j45, 35j55, 35j70, 53a05, 53b, 53c24


The theory of generalized Cauchy–Riemann systems with a point of singularity of the 1-st order in coefficients, that is an immedate extension of the classical apparatus of the Vekua theory of generalized analytic functions, was developed. On this basis local and global problems in the theory of deformation of surfaces with a flat point as well as their local rigidity and non-rigidity were investigated. Together with the disciples theories of generalized Cauchy–Riemann systems with a point singularity of order greater than one in coefficients (with H. Najmiddinov) and with the 1-st order singularity on a circle (with A. Abdushukurov) were worked out. A certain progress was attained in solution of the extended Christoffel problem in searching convex surfaces with a given sum of conventional radii of curvature determined in a convex surface with an isolated flat point (with A. Khakimov). For an extensive class of processes described by linear and partial differential equations natural metrics similar to the Minkowskii space-time one were constructed. In particular, it enabled to create the natural metrics of the gravitational field, processes of string oscillation, heat conductivity and extension, and some others.


1954–1958 — Student of Moscow State University, Faculty of Mathematics and Mechanics; 1959–1962 — Post-graduate, Department of Mechanics, Moscow State University; 1966 — Ph.D. thesis was defended; 1973 — D.Sci. thesis was defended; 1983 — Professor of Math. (VAK USSR). Author of more than 180 papers in theoretical and applied mathematics including 4 monographs.

1976 — Corresponding member, Tajik Academy of Sciences, Dushanbe; 1981 — Full member, Tajik ACademy of Sciences, Dushanbe; 1997 — Professor, Moscow Power Engineering Institute, Voljski Department; 1999 — Professor, Department of Informatics, Tajik Technological University, Dushanbe; Head of Department "Natural metrics of processes", Vertual Institute of interdisciplinary study of time, Moscow State University.

Main publications:
  1. Z. D. Usmanov, Generalized Cauchy–Riemann systems with a singular point, Pitman Monographs and Surveys in Pure and Applied Mathematics, 85, Longman, Harlow, 1997, 222 p., ISSN 0269-3666, ISBN 0-582-29280-8  mathscinet  zmath
List of publications on Google Scholar

Publications in Math-Net.Ru
1. A. L. Goncharov, S. B. Klimentov, Z. D. Usmanov, “An analogue of Liouville's theorem for a class of systems of Cauchy-Riemann type with singular coefficients”, Vladikavkaz. Mat. Zh., 7:4 (2005),  7–16  mathnet  mathscinet
2. Z. D. Usmanov, “Relationship between manifolds of solutions to generic and model generalized Cauchy–Riemann systems with a singular point”, Mat. Zametki, 66:2 (1999),  302–307  mathnet  mathscinet  zmath; Math. Notes, 66:2 (1999), 240–244  isi
3. Z. D. Usmanov, “The variety of solutions of the singular generalized Cauchy–Riemann System”, Mat. Zametki, 59:2 (1996),  278–283  mathnet  mathscinet  zmath; Math. Notes, 59:2 (1996), 196–200  isi
4. Z. D. Usmanov, “On Efimov surfaces that are rigid 'in the small'”, Mat. Sb., 187:6 (1996),  119–130  mathnet  mathscinet  zmath; Sb. Math., 187:6 (1996), 903–915  isi  scopus
5. Z. D. Usmanov, “The problem of local rigidity in the class $C^\infty$”, Mat. Zametki, 22:5 (1977),  643–648  mathnet  mathscinet  zmath; Math. Notes, 22:5 (1977), 850–853
6. N. V. Efimov, Z. D. Usmanov, “Infinitesimal bending of a surface with a point of flatness”, Dokl. Akad. Nauk SSSR, 208:1 (1973),  28–31  mathnet  mathscinet  zmath
7. Z. D. Usmanov, “A certain class of generalized Cauchy-Riemann systems with a singular point”, Sibirsk. Mat. Zh., 14:5 (1973),  1076–1087  mathnet  mathscinet  zmath; Siberian Math. J., 14:5 (1973), 751–758
8. Z. D. Usmanov, “An effective solution of a certain two-dimensional integral equation with a homogeneous kernel, and its applications”, Differ. Uravn., 8:12 (1972),  2267–2270  mathnet  mathscinet  zmath
9. Z. D. Usmanov, “On a problem concerning the deformation of a surface with a flat point”, Mat. Sb. (N.S.), 89(131):1(9) (1972),  61–82  mathnet  mathscinet  zmath; Math. USSR-Sb., 18:1 (1972), 61–81
10. Z. D. Usmanov, “A boundary value problem for generalized analytic functions with a fixed singular point”, Dokl. Akad. Nauk SSSR, 197:2 (1971),  288–291  mathnet
11. Z. D. Usmanov, “On infinitesimal deformations of surfaces of positive curvature with an isolated flat point”, Mat. Sb. (N.S.), 83(125):4(12) (1970),  596–615  mathnet  mathscinet  zmath; Math. USSR-Sb., 12:4 (1970), 595–614
12. A. I. Achil'diev, Z. D. Usmanov, “Rigidity of a surface with a point of flattening”, Mat. Sb. (N.S.), 73(115):1 (1967),  89–96  mathnet  mathscinet  zmath; Math. USSR-Sb., 2:1 (1967), 77–83
13. L. G. Mikhailov, Z. D. Usmanov, “Infinitesimal bendings of surfaces of revolution with positive curvature having a conic or a parabolic point at the pole”, Dokl. Akad. Nauk SSSR, 166:4 (1966),  791–794  mathnet  mathscinet  zmath

14. V. A. Il'in, S. M. Nikol'skii, B. V. Boyarsky, Z. D. Usmanov, “Abdukhamid Dzhuraevich Dzhuraev (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 47:3(285) (1992),  187–190  mathnet  mathscinet; Russian Math. Surveys, 47:3 (1992), 201–204  isi
15. S. M. Nikol'skii, L. D. Kudryavtsev, Z. D. Usmanov, È. M. Muhamadiev, “Leonid Grigor'evich Mikhailov (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 43:2(260) (1988),  171–172  mathnet  mathscinet; Russian Math. Surveys, 43:2 (1988), 205–207  isi

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