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This is an extended version of a talk on October 4, 2004 at the research seminar “Differential geometry and applications” (headed by Academician A. T. Fomenko) at Moscow State University. The paper contains an overview of available (but far from well-known) results about the Blaschke addition of convex bodies, some new theorems on the monotonicity of the… (More)

A trivial formalization is given for the informal reasonings presented in a series of papers by Ya.D. Sergeyev on a positional numeral system with an infinitely large base, grossone; the system which is groundlessly opposed by its originator to the classical nonstandard analysis. Mathematics Subject Classification (2000): 26E35.

- E. Yu. Emel’yanov, S. S. Kutateladze
- 2005

An operator T is called Cesàro bounded if supn ‖A T n‖ <∞, power bounded if sup{‖T n‖ : n ∈ N} <∞, and doubly power bounded if sup{‖T n‖ : n ∈ Z} <∞. There exist operators which are Cesàro bounded but not power bounded. An operator T is called mean ergodic if the norm limit lim n→∞ Anx exists for all x ∈ X. Each mean ergodic operator T is Cesàro bounded and… (More)

Boolean valued analysis is applied to deriving operator versions of the classical Farkas Lemma in the theory of simultaneous linear inequalities.

This is an overview of a few possibilities that are open by model theory in applied mathematics. Most attention is paid to the present state and frontiers of the Cauchy method of majorants, approximation of operator equations with finite-dimensional analogs, and the Lagrange multiplier principle in multiobjective decision making. 1. Agenda The union of… (More)

This is a talk on interaction of the techniques of positivity and abstract convexity in functional analysis and the extremal problems of convex geometry. Alexandr Danilovich Alexandrov became the first and foremost Russian geometer of the twentieth century. He contributed to mathematics under the slogan: “Retreat to Euclid,” remarking that “the pathos of… (More)

This is a short overview of the origins of distribution theory as well as the life of Sergĕı Sobolev (1908–1989) and his contribution to the formation of the modern outlook of mathematics. Sergĕı Lvovich Sobolev belongs to the Russian mathematical school and ranks among the scientists whose creativity has produced the major treasures of the world culture.… (More)

This is a brief overview of the lives and contributions of S. L. Sobolev and L. Schwartz, the cofounders of distribution theory. In the history of mathematics there are quite a few persons whom we prefer to recollect in pairs. Listed among them are Euclid and Diophant, Newton and Leibniz, Bolyai and Lobachevskĭı, Hilbert and Poincaré, as well as Bourbaki… (More)

This is a brief overview of the basic techniques of Boolean valued analysis.

This is an overview of a few possibilities that are open by model theory in applied mathematics. The most attention is paid to the present state and frontiers of the Cauchy method of majorants, approximation of operator equations with finite-dimensional analogs, and the Lagrange multiplier principle in multiobjective decision making. DOI:… (More)