On conjugate functions and trigonometric series

The present paper is an abstract of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Physical and Mathematical Sciences. The dissertation was defended on June 30, 1967 before the Academic Council of the Faculty of Mechanics and Mathematics of the M. V. Lomonosov Moscow State University. The official opponents were Professor A. V. Efimov, Doctor of Physical and Mathematical Sciences, Professor V. A. Il'in, Doctor of Physical and Mathematical Sciences, and Professor G. P. Tolstov, Doctor of Physical and Mathematical Sciences.Translated from Matematicheskie Zametki, Vol. 2, No. 6, pp. 695–702, December, 1967.     

On the theory of linear systems of ordinary differential equations

Author's abstract of dissertation for the attainment of the scientific degree of Doctor of the Physical and Mathematical Sciences. Dissertation defended May 24, 1968 at the sitting of the Council of the Mechanical and Mathematical Faculty of the M. V. Lomonosov State University.Official opponents: Doctor of the Physical and Mathematical Sciences D. V. Anosov, Doctor of the Physical and Mathematical Sciences Professor R. é Vinograd, and Doctor of the Physical and Mathematical Sciences Professor Ya. G. Sinai.Translated from Matematicheskie Zametki, Vol. 4, No. 4, pp. 483–490, October, 1968.     

Infinite solvable and finitely approximable groups

Author's abstract of a dissertation presented as a requirement for the academic degree of Doctor of Physical and Mathematical Sciences. The dissertation was defended on June 21, 1974 at a meeting of the Academic Council of the Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR. Official opponents: Professor Yu. L. Ershov, Professor S. I. Adyan, and Professor A. I. Starostin.     

Investigations of multidimensional,infinite-dimensional and limit theorems of the theory of probabilities

Author's abstract of a dissertation in competition for the scientific degree of Doctor of Physical-Mathematical Sciences. The dissertation was defended on May 30, 1968 at a meeting of the Scientific Council of the V. A. Steklov Mathematical Institute, Academy of Sciences of the USSR. The official opponents were: V. S. Korolyuk, Corresponding Member, Academy of Sciences of the Ukrainian SSR, A. V. Skorokhod, Corresponding Member, Academy of Sciences of the Ukrainian SSR, and V. A. Statulyavichus, Doctor of Physical-Mathematical Sciences.Translated from Matematicheskie Zametki, Vol. 4, No. 5, pp. 611–619, November, 1968.     

Investigation of boundary value problems for elliptic systems of first order

This paper is the author's abstract of a dissertation submitted for the degree of Doctor of Physicomathematical Sciences. The dissertation was defended November 2, 1972 at a session of the Scientific Council of the V. A. Steklov Mathematical Institute of the Academy of Sciences, USSR. Official referees: Corresponding Member of the Academy of Sciences of the USSR Professor A. V. Bitsadze, Corresponding Member of the Academy of Sciences of the USSR Professor M. M. Lavrent'ev, and Doctor of Physicomathematical Sciences, Professor P. I. Lizorkin.Translated from Matematicheskie Zametki, Vol. 14, No. 2, pp. 291–304, August, 1973.     

Generalized Liouville differentiation and the method of multiplicators in imbedding theory for function classes

Author's review of his dissertation for the degree of doctor of the physico-mathematical sciences. Dissertation defended May 23, 1968, at the Mathematical Institute of the Academy of Sciences of the USSR.Official opponents: Doctor of Phys.-Math Sciences V. P. Il'in, Doctor of Phys.-Math Sciences I. A. Kipriyanov, and Doctor of Phys.-Math Sciences L. N. Slobodetskii.Translated from Matematicheskie Zametki, Vol. 4, No. 4, pp. 467–482, October, 1968.     

Spaces of kinematic type

The present paper is based on the author's dissertation for the degree of Doctor of Mathematical Physics. The dissertation was defended on November 27, 1969, at a meeting in the V. A. Steklov Institute of Soviet Mathematics, Academy of Sciences of the USSR. The official referees were Academician A. D. Aleksandrov, Doctor of Mathematical Physics, Professor Yu. F. Borisov, and Doctor of Mathematical Physics, Professor V. A. Efremovich.Translated from Matematicheskie Zametki, Vol. 7, No. 5, pp. 641–653, May, 1970.     

Dual Entwining Structures and Dual Entwined Modules

In this note we introduce and investigate the concepts of dual entwining structures and dual entwined modules. This generalizes the concepts of dual Doi–Koppinen structures and dual Doi–Koppinen modules introduced (in the infinite case over rings) by the author in his dissertation. Presented by A. VerschorenMathematics Subject Classifications (2000) 16W30, 18E15.Jawad Y. Abuhlail: Current address: Department of Mathematical Sciences, P.O. Box 5046, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Saudi Arabia.     

Resonance theorems and functional series

Self-referred dissertation in competition for the academic doctor's degree in physico-mathematical sciences (printed with elisions). The dissertation was defended on May 7, 1971 at the teaching council of the mechanics-mathematics faculty of the Moscow State University. The official opponents were: Dr. Physico-Mathematical Sciences, Prof. N. P. Kuptsov, Dr. Physico-Mathematical Sciences, Prof. A. M. Olevskii, and Corresponding Member of the Academy of Sciences of the Armenian SSR, Dr. Physico-Mathematical Sciences, Prof. A. A. Talalyan.Translated from Matematicheskie Zametki, Vol. 10, No. 5, pp. 583–595, November, 1971.The author extends hearty thanks to Prof. P. L. Ul'yanov for purposeful scientific conferences on the results of the dissertation.     

Some extremal problems of theory of quadrature and approximation of functions

This is the author-review of the dissertation presented for the degree of the Doctor of Physicomathematical Sciences. The dissertation was defended on March 13, 1975 in a meeting of the scientists of the V. A. Steklov Mathematics Institute of the Academy of Sciences of the USSR. The official opponents were Doctor of Physicomathematical Sciences Prof. N. S. Bakhvalov, Doctor of Physicomathematical Sciences Prof. P. K.Suetin, and Doctor of Physicomathematical Sciences Prof. S. B. Stechkin.Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 299–311, February, 1976.     

Classes of functions and Fourier coefficients with respect to complete orthonormal systems

This is the author review of a dissertation presented in the competition for the academic degree of Doctor of Physicomathematical Sciences. The dissertation was defended on October 10, 1974 in a meeting of the academic council of the V. A. Steklov Mathematics Institute of the Academy of Sciences of the USSR. The official opponents were: A. A. Talalyan, Corresponding Member of the Academy of Sciences of the Armenian SSR; N. P. Kuptsov, Doctor of Physicomathematical Sciences; and E. M. Nikishin, Doctor of Physicomathematical Sciences.Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 445–463, September, 1976.     

Extremal functional interpolation and approximation by splines

This article is the author's abstract of his dissertation for the degree Doctor of Physico-mathematical Science. The dissertation was defended on April 22, 1974 at the meeting of the Academic Council for the award of higher degrees in mathematics and mechanics at the Novosibirsk State University. Official opponents were: Academician N. N. Yanenko, Corresponding Member of the Academy of Sciences of the Ukrainian SSR, Doctor of Physicomathematical Sciences; Professor N. P. Korenchuk, Doctor of Physicomathematical Sciences; Professor G. Sh. Rubinshtein.Translated from Matematicheskie Zametki, Vol. 16, No. 5, pp. 843–854, November, 1974.     

The theory of thermal potentials and its applications

A review by the author of his dissertation presented for the academic degree of doctor of physico-mathematical sciences. A defense of the dissertation was given on February 29, 1968 before the science committee of the V. A. Steklov Institute of Mathematics of the Academy of Sciences of the USSR. Official challengers were A. V. Bitsadze and A. A. Samarskii, Corresponding Members of the Academy of Sciences of the USSR, and V. P. Mikhailov, Doctor of Physico-Mathematical Sciences.Translated from Matematicheskie Zametki, Vol. 4, No.1, pp. 113–123, July, 1968.     

Studies in the matrix representability of abstract groups and in matrix groups

The author presents a summary of his dissertation in competition for the academic degree Doctor of Physicomathematical Sciences. The dissertation was defended on April 26, 1972, before the Academic Council of the Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR. The official opponents were Prof. D. M. Smirnov (Doctor of Physicomathematical Sciences), Prof. A. I. Starostin (Doctor of Physicomathematical Sciences of the Belorussian SSR and Doctor of Physicomathematical Sciences), and Prof. A. I. Shirshov (Corresponding Member of the Academy of Sciences of the USSR and Doctor of Physicomathematical Sciences).Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 597–606, October, 1973.     

Local convergence of the diagonalized method of multipliers

In this study, we consider a modification of the method of multipliers of Hestenes and Powell in which the iteration is diagonalized, that is, only a fixed finite number of iterations of Newton's method are taken in the primal minimization stage. Conditions are obtained for quadratic convergence of the standard method, and it is shown that a diagonalization where two Newton steps are taken preserves the quadratic convergence for all multipler update formulas satisfying these conditions.This work constitutes part of the author's doctoral dissertation in the Department of Mathematical Sciences, Rice University, under the direction of Professor R. A. Tapia and was supported in part by ERDA Contract No. E-(40-1)-5046.The author would like to thank Professor Richard Tapia for his comments, suggestions, and discussions on this material.     

Bemerkung zu einer Arbeit von Marshall und Olkin

Ohne ZusammenfassungDiese Arbeit entstand während eines Aufenthalts beim National Research Institute for Mathematical Sciences P.O. Box 395. Pretoria, South Africa.     

Random flows generated by random processes (properties of random flows,level-crossing problems)

Author's summary of a dissertation submitted for the degree of Doctor of Physicomathematical Sciences. The dissertation was defended February 10, 1970, at a meeting of the Scientific Council of the Institute of Applied Mathematics, Academy of Sciences of the USSR. Official opponents: B. V. Gnedenko, Academician of the Academy of Sciences of the USSR, Yu. V. Prokhorov, Corresponding Member of the Academy of Sciences of the USSR, and N. N. Chentsov, Doctor of Physicomathematical Sciences.Translated from Matematicheskie Zametki, Vol. 8, No. 3, pp. 393–407, September, 1970.     

Conjugate functions

This is the author-review of a dissertation for the competition of the academic degree of Doctor of Physicomathematical Sciences (published with abbreviations). The dissertation was defended on June 30, 1976, in the academic council of the A. M. Razmadze Tbilisi Mathematics Institute of the Academy of Sciences of the Georgian SSR. The official opponents were: Professor N. N. Bakhaniya, Doctor of Physicomathematical Sciences; Professor Sh. S. Pkhakadze, Doctor of Physicomathematical Sciences; Professor A. A. Talalyan, Corresponding Member of the Academy of Sciences of the Armenian SSR and Doctor of Physicomathematical Sciences; and Professor S. A. Telyakovskii, Doctor of Physicomathematical Sciences.Translated from Matematicheskie Zametki, Vol. 22, No. 5, pp. 771–783, November, 1977.     

Certain problems of the theory of difference boundary value problems

This is an author's abstract of a dissertation for the degree of doctor of physicomathematical sciences. The dissertation was defended on December 2,1969,at a session of the Scientific Council of the Institute of Applied Mathematics, Academy of Sciences of the USSR. The official opponents were: Doctor of Physicomathematical Sciences Prof. K. I. Babenko, Doctor of Physicomathematical Sciences Prof. N. S. Bakhvalov, and Doctor of Physicomathematical Sciences E. A. Volkov.Translated from Matematicheskie Zametki, Vol. 7, No. 5, pp. 655–663, May, 1970.     

Isometric imbedding in E3 of noncompact domains of nonpositive curvature

Author's abstract of a dissertation for the degree of Doctor of Physicomathematical Sciences. The dissertation was defended on Oct. 21, 1977, at a session of the Specialized Council D 002.38.02 at the V. A. Steklov Mathematics Institute of the Academy of Sciences of the USSR. Official opponents: Academician of the Academy of Sciences of the USSR, Doctor of Physicomathematical Sciences A. V. Pogorelov; Professor, Doctor of Physicomathematical Sciences É. G. Poznyak; Professor, Doctor of Physicomathematical Sciences A. S. Fedenko.Translated from Matematicheskie Zametki, Vol. 25, No. 5, pp. 785–797, May, 1979.