相关论文: On Scottish Book Problem 157

A solution of Problem 184 from the Scottish Book is presented.

The paper discusses Problems 8 and 88 posed by Stanislaw Mazur in the Scottish Book. It turns out that negative solutions to both problems are immediate consequences of the results of Section 5 of my paper "Estimates of functions of power…

A negative solution of Problem 188 posed by Max Eidelheit in {\it the Scottish Book} concerning superpositions of separately absolutely continuous functions is presented. We discuss here his and some related problems which have also…

We comment on a Mazur problem from "Scottish Book" concerning second partial derivatives. It is proved that, if a function $f(x,y)$ of real variables defined on a rectangle has continuous derivative with respect to $y$ and for almost all…

We prove that a uniformly bounded system of orthonormal functions satisfying the $\psi_2$ condition: (1) must contain a Sidon subsystem of proportional size, (2) must satisfy the Rademacher-Sidon property, and (3) must have its 5-fold…

Methods are described for the solution of linear inference problems subject to deterministic constraints. The approach builds on work by Backus (1970a,b,c) and Parker (1977), but a range useful advances are suggested to address both…

In this paper we give a closed expression for a multiple factorial series, solving Open Problem 3.137 in a recent book by O. Furdui. The method is based on properties of divided differences. It applies also to similar series and certain…

In his 1981 Fundamental Theorem of Algebra paper Steve Smale initiated the complexity theory of finding a solution of polynomial equations of one complex variable by a variant of Newton's method. In this paper we reconsider his algorithm in…

In the early 2000's the first and second named authors worked for a period of six years in an attempt of proving the Compositional Shuffle Conjecture [1]. Their approach was based on the discovery that all the Combinatorial properties…

Since its original publication in 1916 under the title "The Algebraic Theory of Modular Systems", the book by F. S. Macaulay has attracted a lot of scientists with a view towards pure mathematics (D. Eisenbud,...) or applications to control…

We provide a list of (mainly unsolved) problems in ordered and orderable groups. These were originally compiled 10 years ago by the last two authors. New problems have been added to the list. Progress on some of these is noted and…

A new edition of Walter K. Hayman's 'Research Problems in Function Theory' (1967), containing over five hundred function theory and complex analysis problems, along with all progress updates over the last 51 years. The final publication…

Compositor attribution, the clustering of pages in a historical printed document by the individual who set the type, is a bibliographic task that relies on analysis of orthographic variation and inspection of visual details of the printed…

The 17th of the problems proposed by Steve Smale for the 21st century asks for the existence of a deterministic algorithm computing an approximate solution of a system of $n$ complex polynomials in $n$ unknowns in time polynomial, on the…

This is a work in two parts devoted to solutions of the so-called {\em four Landau's problems} in Number Theory, listed by Edmund Landau at the 1912 International Congress of Mathematics. In Part I the {\em Goldbach's conjecture} is proved.…

In a recent volume of Mathematics Magazine (Vol. 90, No. 3, June 2017) there is an interesting article by Seth Zimmerman, titled Detecting Deficiencies: An Optimal Group Testing Algorithm. The claim in the summary is contradictory to…

Existence and uniqueness of advanced and retarded fundamental solutions (Green's functions) and of global solutions to the Cauchy problem is proved for a general class of first order linear differential operators on vector bundles over…

Computability theory is a discipline in the intersection of computer science and mathematical logic where the fundamental question is: given two mathematical objects X and Y, does X compute Y in principle? In case X and Y are real numbers,…

We consider blind, deterministic, finite automata equipped with a register which stores an element of a given monoid, and which is modified by right multiplication by monoid elements. We show that, for monoids M drawn from a large class…

In this paper we consider nonzero harmonic functions vanishing on some subsets of $\mathbb R^n$. We give a positive solution to Problem 151 from the Scottish Book posed by R. Wavre in 1936. In more detail, we construct a nonzero harmonic…