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.     

Extreme modules over the Weyl algebraA n

Certain classes of simple modules over generalized Weyl algebras (extreme modules, polynomial modules, and modules with strongD-torsion) are classified. For these algebras, analogs of the Bernshtein and Stafford theorems are proved.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 9, pp. 1187–1197, September, 1993.The author expresses his gratitude to Prof. Yu. M. Berezanskii, Prof. Yu. A. Drozd, and Prof. Yu. S. Samoilenko for fruitful discussions and remarks.     

Denumerable state stochastic games with limiting average payoff

We study stochastic games with countable state space, compact action spaces, and limiting average payoff. ForN-person games, the existence of an equilibrium in stationary strategies is established under a certain Liapunov stability condition. For two-person zero-sum games, the existence of a value and optimal strategies for both players are established under the same stability condition.The authors wish to thank Prof. T. Parthasarathy for pointing out an error in an earlier version of this paper. M. K. Ghosh wishes to thank Prof. A. Arapostathis and Prof. S. I. Marcus for their hospitality and support.     

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.     

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.     

Eine an die Nicholsonformel anschliessende asymptotische Entwicklung für Zylinderfunktionen

Ohne Zusammenfassung Habilitationsschrift in der Fakult?t für Mathematik und Physik der Technischen Hochschule Darmstadt. Referent: Prof. Dr.A. Walther, Korreferent: Prof. Dr.C. Schmieden.     

A solution method for regular optimal control problems with state constraints

A method of region analysis is developed for solving a class of optimal control problems with one state and one control variable, including state and control constraints. The performance index is strictly convex with respect to the control variable, while this variable appears only linearly in the state equation. The convexity or linearity assumption of the performance index or the state equation with respect to the state variable is not required.The author would like to express his sincere gratitude to Prof. R. Klötzler, Prof. E. Zeidler, Prof. H. Schumann, Prof. J. Focke, and other colleagues of the Department of Mathematics, Karl Marx University, Leipzig, GDR, for their support during his stay in Leipzig.     

Transformation of incidence structures and sharply multiply transitive permutation sets

In this note we generalize the transformation process introduced in [8]. This generalization allows to find the nonplanar nearfield discovered by H.Karzel and W.Kerby, [5], [6], and the affine Andrè planes.Dedicated to Prof. A.Barlotti and to Prof. L.A.Rosati on their 70th birthdayWork performed under the auspicies of G.N.S.A.G.A. and supported by 40% grants of M.U.R.S.T.     

Über Peano- und Riemann-Ableitungen in der Norm

Ohne ZusammenfassungDie Verfasser danken Herrn Prof. P. L.Butzer sehr für die Anregung zur Behandlung der vorliegenden Probleme und für Sein förderndes Interesse an dieser Arbeit. Dankbar vermerken wir weiter, daß uns die Verwendung der Distributionentheorie von Herrn Prof. H.König in einer schriftlichen Mitteilung vorgeschlagen wurde. Nicht zuletzt möchten wir Herrn Dr. H.Berens für viele fruchtbare Gespräche, insbesondere zum vierten Paragraphen, danken. Die Ergebnisse über die Peano-Ableitung mögen als eine Antwort auf eine Frage von Prof. A.Bruckner an Prof.Butzer bezüglich der Beziehung der Peano-Ableitung zum Thema der Arbeit [3] gesehen werden.     

A proof of the Grothendieck inequality

The fundamental constant of Grothendieck's inequality, defined below, was shown by Grothendieck to be less than sinh π/2=2.301+. We improve the bound slightly, and show that for the positive definite case π/2 suffices. Partially supported by Grant #901-052, Gustavus Adolphus College Research Fund, and a National Science Foundation Summer Traineeship grant. This is based on part of the author's Ph.D. dissertation, University of Minnesota, under Prof. C.A. McCarthy. The author is grateful for Prof. McCarthy's assistance.     

On 2-transitive 3-nets

A 3-net is said to be 2-transitive if it admits a group of direction-preserving automorphisms fixing one of the transversal lines and acting 2-transitively on its points. We classify the 2-transitive finite 3-nets which do not admit a proper 2-transitive 3-subnet, except, possibly, for a subnet of order 2. The result is then extended under a weaker assumption.To Prof. Walter Benz and Prof. Jakob Joussen on their 60^th birthdaywork done within the activity of GNSAGA of CNR and supported by the Italian Ministry for Research and Technology.     

Numerical experiments with ABS algorithms for linear systems on a parallel machine

Numerical results are obtained on sequential and parallel versions of ABS algorithms for linear systems for both full matrices andq-band matrices. The results using the sequential algorithm on full matrices indicate the superiority of a particular implementation of the symmetric algorithm. The condensed form of the algorithm is well suited for implementation in a parallel environment, and results obtained on the IBM 4381 system favor a synchronous implementation over the asynchronous one. Results are obtained from sequential implementations of theLU, Cholesky, and symmetric algorithms of the ABS class forq-band matrices able to reduce memory storage. A simple parallelization of do-loops for calculating components gives interesting performances.This work has been developed in the framework of a collaboration between IBM-ECSEC, Rome, Italy, and the Department of Mathematics of the University of Bergamo, Bergamo, Italy.The author is grateful to Prof. J. Abaffy (University of Economics, Budapest), Prof. L. Dixon (Hatfield Polytechnic), and Prof. E. Spedicato (Department of Mathematics, University of Bergamo) for useful suggestions.     

A variety generated by a finite algebra with 2x 0 subvarieties

As was indicated to me by Prof. A. Wroński, the following problem was suggested by Prof. B. Jónsson: is every subvariety of the variety of a finite algebra generated by a finite algebra? In this paper we solve this problem in the negative by constructing a finite algebra that generates a variety having 2^x ₀ subvarieties.     

Integralgeometrie Ebener Kurvennetze

Ohne Zusammenfassung Vorgelegt von A. Rényi Als Habilitationsschrift von der Mathematisch-Naturwissenschaftlichen Fakultät der Humboldt-Universität zu Berlin angenommen. Referenten: Prof. Dr.H. Reichardt (Berlin) und Prof. Dr.W. Rinow (Greifswald).     

Inverse Interpolation bei den speziellen Funktionen der mathematischen Physik

Zusammenfassung Es wird ein Verfahren mit Fehlerabschätzung zur Bestimmung der Nullstellen einer Funktion angegeben, die einer linearen homogenen Differentialgleichung zweiter Ordnung genügt.Diese Note ist ein erweiterter Teil einer von der Fakultät für Mathematik und Physik der Technischen Hochschule Darmstadt angenommenen Dissertation (Ref.: Prof. Dr. h. C. Dr. A.Walther, Prof. Dr. C.Schmieden). Der Verfasser dankt den Referenten sowie Herrn Prof. Dr. W.Börsch-Sudan für ihre freundliche Unterstützung und einige wertvolle Ratschläge.     

Bemerkungen zum Gesetz der grossen Zahlen

Ohne ZusammenfassungDem Andenken von Prof.A. Rényi gewidmet     

Über Konvergenzsätze,die sich bei der Anwendung eines Differenzenverfahrens auf ein Sturm-Liouvillesches Eigenwertproblem ergeben

Ohne ZusammenfassungDiese Arbeit enthält einen wesentlichen Teil meiner Habilitationsschrift. Die Habilitation erfolgte 1944 zu Darmstadt. Referenten waren die Herren Prof. Dr.L. Collatz und Prof. Dr.A. Walther. Besonders HerrnCollatz habe ich für die Problemstellung und sein ständiges Interesse an dieser Arbeit zu danken.     

On the distance coefficient between isomorphic function spaces

IfX, Y are compact countable metric spaces such thatY contains no subset homeomorphic toX, then for any isomorphismΦ ofC(X) intoC(Y), ‖ φ ‖ ‖ φ⁻¹ ‖≧3. This result and some variants of it are established here, and prove a special case of a conjecture raised in [1]. This is a part of the author’s Ph.D. Thesis prepared at the Hebrew University of Jerusalem, under the supervision of Prof. J. Lindenstrauss. I wish to thank Prof. Lindenstrauss and Prof. A. Dvoretzky for their guidance and the interest they showed in this work.     

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.     

Über die Anwendung von Binärmodellen in der Theorie der Charaktere der symmetrischen Gruppen

Ohne ZusammenfassungHerrn Prof. Dr.A. Walther, Darmstadt, zum 60. Geburtstag.