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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)
Let X be a Riesz space, and let Y be a Kantorovich (or Dedekind complete Riesz) space Y with base a complete Boolean algebra B. In [1] we have described every order bounded operator T from X to Y that may be presented as the difference of some Riesz homomorphisms. An operator T is such a difference if and only if the kernel of the stratum bT of T is a Riesz(More)
This is a short overview of the life of Leonid Kantorovich and his contribution to the formation of the modern outlook on the interaction between mathematics and economics. Kantorovich was born in the family of a venereologist at St. Petersburg on January 19, 1912 (January 6, according to the old Russian style). It is curious that many reference books give(More)
This is an overview of merging the techniques of Riesz space theory and convex geometry. Alexandr Danilovich Alexandrov became the first and foremost Russian geome-ter of the twentieth century. He contributed to mathematics under the slogan: " Retreat to Euclid, " remarking that " the pathos of contemporary mathematics is the return to Ancient Greece. "(More)
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. The union of functional(More)
This is a brief overview of the so-called " Case of Academician Luzin. " Tsunami swept over the Russian mathematical community in 1999 after publication of the book The Case of Academician Nikola˘ ı Nikolaevich Luzin [1]. For the first time it revealed the complete shorthand notes of the meetings of a notorious special Commission of the Academy of Sciences(More)