Sobolev of the Euler School
This is a short overview of the origins of distribution theory as well as the life of Sergei Sobolev (1908--1989) and his contribution to the formation of the modern outlook of mathematics.
math.HO↗
arXiv subjects
S. S. Kutateladze
Publications and source records attributed to S. S. Kutateladze.
What Is Boolean Valued Analysis?
This is a brief overview of the basic techniques of Boolean valued analysis.
math.LO↗
Pareto Optimality and Isoperimetry
Under study is the new class of geometrical extremal problems in which it is required to achieve the best result in the presence of conflicting goals; e.g., given the surface area of a convex body $\mathfrak x$, we try to maximize the volume of $\mathfrak x$ and minimize the width of $\mathfrak x$ simultaneously. These problems are addressed along the lines of multiple criteria decision making.
math.MG↗
The Wickstead Problem
In 1977 Anthony Wickstead raised the question of the conditions for all band preserving linear operators to be order bounded in a vector lattice. This article overviews the main ideas and results on the Wickstead problem and its variations, focusing primarily on the case of band preserving operators in a universally complete vector lattice.
math.FA↗
A trivial formalization of the theory of grossone
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.
math.GM↗
Nonstandard Models and Optimization
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.
math.OC↗
Sobolev and Schwartz: Two Fates and Two Fames
This is a brief overview of the lives and contributions of S.L. Sobolev and L. Schwartz, the cofounders of distribution theory.
math.HO↗
Interaction of Order and Convexity
This is an overview of merging the techniques of Riesz space theory and convex geometry.
math.FA↗
Abstract Convexity and Cone-Vexing Abstractions
This talk is a write-up on some origins of abstract convexity and afew vexing limitations on the range of abstraction in convexity.
math.FA↗
Leibniz's Definition of Monad
This is a short discussion of the definition of monad which was given by G.W. Leibniz in his "Monadology."
math.GM↗
Boolean Methods in the Theory of Vector Lattices
This is an overview of the recent results of interaction of Boolean valued analysis and vector lattice theory.
math.FA↗
Saunders Mac Lane, the Knight of Mathematics
This is a short obituary of Saunders Mac Lane (1909--2005).
math.HO↗
Apology of Euclid
This is a short apology of the style of the Elements by Euclid and Bourbaki.
math.GM↗
On Grothendieck Subspaces
The modulus of an order bounded functional on a Riesz space is the sum of a pair of Riesz homomorphisms if and only if the kernel of this functional is a Grothendieck subspace of the ambient Riesz space. An operator version of this fact is given.
math.FA↗
Blaschke addition and convex polyhedra
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 volume of convex bodies (in particular, convex polyhedra with parallel faces) as well as description of a software for visualization of polyhedra with prescribed outward normals and face areas.
math.MG↗