Results 41 to 50 of about 22,180 (168)

Certain Summation and Operational Formulas Involving Gould–Hopper–Lambda Polynomials

Mathematics
This manuscript introduces the family of Gould–Hopper–Lambda polynomials and establishes their quasi-monomial properties through the umbral method. This approach serves as a powerful mechanism to analyze the characteristic of multi-variable special ...
Maryam Salem Alatawi
doaj   +1 more source

Summability in a monomial for some classes of singularly perturbed partial differential equations [PDF]

Publicacions Matemàtiques, 2021
The aim of this paper is to continue the study of asymptotic expansions and summability in a monomial in any number of variables. In particular we characterize these expansions in terms of bounded derivatives and we develop tauberian theorems for the summability processes involved.
openaire   +6 more sources

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

Advanced Intelligent Discovery, EarlyView.
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley   +1 more source

A Simplified Game for Resolution of Singularities [PDF]

, 2014
We will describe a combinatorial game that models the problem of resolution of singularities of algebraic varieties over a field of characteristic zero.
Schicho, Josef
core  

A bordered Chekanov-Eliashberg algebra

, 2010
Given a front projection of a Legendrian knot $K$ in $\mathbb{R}^{3}$ which has been cut into several pieces along vertical lines, we assign a differential graded algebra to each piece and prove a van Kampen theorem describing the Chekanov-Eliashberg ...
Sivek, Steven
core   +1 more source

Meromorphic differential equations having all monomials as solutions [PDF]

Archiv der Mathematik, 1992
In this paper one considers ordinary differential equations with meromorphic coefficients of the form \(F(y(x),y^{(1)}(x),\dots,y^{(r)}(x))=0\), where \(F(Y_ 0,Y_ 1,\dots,Y_ r)\) is a polynomial in the variables \(Y_ 0,\dots,Y_ r\) with coefficients in the field \(\mathbb{C}\{x\}[x^{-1}]\) of convergent Laurent series in \(x\) over \(\mathbb{C}\).
openaire   +3 more sources

Controlling Dynamical Systems Into Unseen Target States Using Machine Learning

Advanced Intelligent Systems, EarlyView.
Parameter‐aware next‐generation reservoir computing enables efficient, data‐driven control of dynamical systems across unseen target states and nonstationary transitions. The approach suppresses transient behavior while navigating system collapse scenarios with minimal training data—over an order of magnitude less than traditional methods.
Daniel Köglmayr, Alexander Haluszczynski, Christoph Räth   +2 more
wiley   +1 more source

Techniques for the study of singularities with applications to resolution of 2-dimensional schemes

, 2011
We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.Comment: 26 pages; minor changes have been ...
A. Altman, A. Benito, A. Bravo, A. Bravo, Angélica Benito, E. Bierstone, H. Hauser, H. Hauser, H. Hironaka, H. Kawanoue, H. Kawanoue, J. Giraud, J. Giraud, J. Lipman, J. Włodarczyk, O.E. Villamayor, O.E. Villamayor, O.E. Villamayor U., O.E. Villamayor U., O.E. Villamayor U., Orlando E. Villamayor U., R. Narasimhan, R. Narasimhan, S. Abhyankar, S. Abhyankar, S. Abhyankar, S. Abhyankar, S. Encinas, S. Encinas, S.D. Cutkosky, T.T. Moh, V. Cossart, V. Cossart, V. Cossart, V. Cossart, V. Cossart   +35 more
core   +1 more source

Self‐Similar Blowup for the Cubic Schrödinger Equation

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We give a rigorous proof for the existence of a finite‐energy, self‐similar solution to the focusing cubic Schrödinger equation in three spatial dimensions. The proof is computer‐assisted and relies on a fixed point argument that shows the existence of a solution in the vicinity of a numerically constructed approximation.
Roland Donninger, Birgit Schörkhuber
wiley   +1 more source

Free resolutions via Gr\"obner bases [PDF]

, 2011
For associative algebras in many different categories, it is possible to develop the machinery of Gr\"obner bases. A Gr\"obner basis of defining relations for an algebra of such a category provides a "monomial replacement" of this algebra.
Dotsenko, Vladimir, Khoroshkin, Anton
core