Related papers: Macaulay inverse systems revisited
This paper, being the sequel of [An inverse problem in Polya-Schur theory. I. Non-genegerate and degenerate operators], studies a class of linear ordinary differential operators with polynomial coefficients called \emph{exactly solvable};…
This paper contains the details and complete proofs of our earlier announcement in math.AG/9907004 . We construct a general semiregularity map for algebraic cycles as asked for by S. Bloch in 1972. The existence of such a semiregularity map…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
Directed topology was introduced as a model of concurrent programs, where the flow of time is described by distinguishing certain paths in the topological space representing such a program. Algebraic invariants which respect this…
This is a self-contained tour of the Conley index and connection matrices. The starting point is Conley's fundamental theorem of dynamical systems. There is a short stop at the necessary topological background, before we proceed to the…
This review provides an introduction to - and overview of - the current state of the art in neural-network based regularization methods for inverse problems in imaging. It aims to introduce readers with a solid knowledge in applied…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
This thesis is divided into three parts. The first part deals with cylindric plane partitions. The second with lambda-determinants and the third with commutators in semi-circular systems. For more detailed abstract please see inside.…
Transfer learning has recently become the dominant paradigm of machine learning. Pre-trained models fine-tuned for downstream tasks achieve better performance with fewer labelled examples. Nonetheless, it remains unclear how to develop…
This is the second paper in a series of three papers. In the first paper of the series, "Artinian Gorenstein algebras with linear resolutions", (arXiv:1306.2523, J. of Algebra, to appear) we prove that it is possible to give the minimal…
The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular…
In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new…
In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems,…
The aim of this work is to prove inverse formulas for Laplace transform on semilattices of open-and-compact sets in a both discrete and non-discrete cases. These are partial answers to a question posed by Yu.~I.~Lyubich.
We introduce an orbifold induction procedure which provides a systematic construction of cyclic orbifolds, including their twisted sectors. The procedure gives counterparts in the orbifold theory of all the current-algebraic constructions…
In the 90's a collection of Plethystic operators were introduced in [3], [7] and [8] to solve some Representation Theoretical problems arising from the Theory of Macdonald polynomials. This collection was enriched in the research that led…
The initial motivation of this text was to provide an up to date translation of the monograph [45] written in french by the first author, taking account of more recent developments of infinite dimensional dynamics based on the…
The question of how Algebra can be used to solve dynamical systems and characterize chaos was first posed in a fertile mathematical context by Ziglin, Morales, Ramis and Sim\'o using differential Galois theory. Their study was aimed at…
This note deals with the direct and inverse spectral analysis for a class of infinite band symmetric matrices. This class corresponds to operators arising from difference quations with usual and inner boundary conditions. We give a…
Cosmology is a well established research area in physics while dynamical systems are well established in mathematics. It turns out that dynamical system techniques are very well suited to study many aspects of cosmology. The aim of this…