Related papers: The Ostrowski Expansions Revealed
We explore possibilities and limitations of a purely topological approach to the Dvoretzky Theorem.
We give a counterexample to a conjecture made by Cigler, Jerman and Wojciechowski stating that all posets are conclusive. We also provide combinatorial characterizations for conclusiveness of finite posets and the existence of outer…
We give two algorithms that allow to get arbitrary precision asymptotics for the harmonic potential of a random walk.
We develop new adaptive algorithms for variational inequalities with monotone operators, which capture many problems of interest, notably convex optimization and convex-concave saddle point problems. Our algorithms automatically adapt to…
A new generalization of the classical separate algebraicity theorem is suggested and proved.
We give a complete classification of Dembowski-Ostrom polynomials from the composition of Dickson polynomials of arbitrary kind and monomials over finite fields. Moreover, by using a variant of the Weil bound for the number of points of…
In this paper, we establish some new inequalities of Ostrowski's type for functions whose derivatives in absolute value are the class of s-convex. Some applications for special means of real numbers are also provided. Finally, some error…
In this work we mainly prove the existence and pathwise uniqueness of solutions to general backward doubly stochastic differential equations with jumps appearing in both forward and backward integral parts. Several comparison theorems under…
In this note, we establish new an inequality of Ostrowski-type for double integrals involving functions of two independent variables by using fairly elementary analysis.
We introduce and study $\alpha$-embedded sets and apply them to generalize the Kuratowski Extension Theorem.
In this note we present variants of Kostov's theorem on a versal deformation of a parabolic point of a complex analytic $1$-dimensional vector field. First we provide a self-contained proof of Kostov's theorem, together with a proof that…
We investigate gauge anomalies in the context of orbifold conformal field theories. Such anomalies manifest as failures of modular invariance in the constituents of the orbifold partition function. We review how this irregularity is…
We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, orthogonal logarithmic functions, and transmuted orthogonal polynomials
We consider some special type extensions of an arbitrary Lie algebra, which we call universal extensions. We show that these extensions are in one-to-one correspondence with finite dimensional associative commutative algebras. We also…
We prove that all entire transcendental entire functions have infinite topological entropy.
Double coverings of the orthogonal groups of the real and complex spaces are considered. The relation between discrete transformations of these spaces and fundamental automorphisms of Clifford algebras is established, where an isomorphism…
We generalize Rado's extension theorem to complex spaces.
In this article, we collected more than thirty theorems on expansions of iterated Ito and Stratonovich stochastic integrals, which have been formulated and proved by the author in the period from 1997 to 2025. These theorems open up a new…
The paper contains an exposition of part of topology using partitions of unity. The main idea is to create variants of the Tietze Extension Theorem and use them to derive classical theorems. This idea leads to a new result generalizing…
Using the correspondence between a cycle up-down permutation and a pair of matchings, we give a combinatorial proof of the enumeration of alternating permutations according to the given peak set.