Related papers: The Ostrowski Expansions Revealed
The article is devoted to some ``strange'' phenomena of representation theory and their interrelations. Cross-projective representations of pairs of anticommutative algebras, alloys, their universal envelopping Lie algebras and their…
The expansion of the closed two-component universe has been considered. The potential barrier of the expansion has been investigated and its overcoming condition has been obtained. The restrictions on the Friedmann integrals, cosmological…
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
It is very fundamental to study irreducible plane curve singularities in algebraic geometry. The contents of the paper consist of three parts, called Part[A], Part[B] and Part[C] with Good Appendix. Our aim is to prove by Part[B] and…
We explain how a slight variant in the use of our recursive algorithm leads to improve the known lower bounds for the absolute trace of a totally positive algebraic integer. We also link the absolute trace of a totally positive algebraic…
Umbral extensions of the stirling numbers of the second kind are considered and the resulting dobinski-like various formulas including new ones are presented. These extensions naturally encompass the two well known q-extensions. The further…
We consider the second Ostrogradsky expansion from the number theory, probability theory, dynamical systems and fractal geometry points of view, and establish several new phenomena connected with this expansion. First of all we prove the…
We study, with the help of a computer program, the Polish Algorithm for finite terms satisfying various algebraic laws, e.g., left distributivity a(bc) = (ab)(ac). While the termination of the algorithm for left distributivity remains open…
We establish some asymptotic expansions for infinite weighted convolutions of distributions having light subexponential tails. Examples are presented, some showing that in order to obtain an expansion with two significant terms, one needs…
We prove in this article the well posedness of non - linear Ordinary Differential Equations (ODE) of first and second order in Orlicz spaces with unbounded domain of definition.
In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].
Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation are investigated. Attention is restricted to solutions that, for the appropriate choice of certain constant parameters, reduce to solutions of the…
We extend the classical Ostrowski numeration systems, closely related to Sturmian words, by allowing a wider range of coefficients, so that possible representations of a number $n$ better reflect the structure of the associated Sturmian…
This article proposes a unified analytical approach leading to a partial resolution of the Erdos-Straus, Sierpinski conjectures, and their generalization. We introduce an equivalent reformulation of these conjectures while constructing two…
We provide a very effective and explicit algorithm of finding a Puiseux expansion of a cuspidal singularity of a plane curve, when this singularity is given in a parametric form.
We estimate whether there is an embedding from one n-dimensional rectangle into another which expands every k-dimensional area. Our estimate is sharp up to a constant factor in each dimension.
A method is presented to construct exactly solvable nonlinear extensions of the Schr\"odinger equation. The method explores a correspondence which can be established under certain conditions between exactly solvable ordinary Schr\"odinger…
We introduce methods that allow to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results…
We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.
We study the uniqueness of optimal solutions to extremal graph theory problems. Lovasz conjectured that every finite feasible set of subgraph density constraints can be extended further by a finite set of density constraints so that the…