Related papers: A streamlined difference ring theory: Indefinite n…
Active feedback between geometry and physics is woven throughout the study of Nature at its fundamental level, and is of key importance in string theory. Methods of complex algebraic geometry in particular have brought about an unrivaled…
Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial coefficients and also all the sequences with…
Teleparallel gravity offers a path to resolve a number of longstanding issues in general relativity by re-interpreting gravitation as an artifact of torsion rather than curvature. The present work deals with cosmological solutions in an…
In this survey article we present difference field algorithms for symbolic summation. Special emphasize is put on new aspects in how the summation problems are rephrased in terms of difference fields, how the problems are solved there, and…
Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition. This is useful because complexity can be significantly reduced and the treatment of large-scale data sets…
Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…
In this paper by exploiting critical point theory, the existence of two distinct nontrivial solutions for a nonlinear algebraic system with a parameter is established. Our goal is achieved by requiring an appropriate behavior of the…
We characterize the set of planar locally finite Cayley graphs, and give a finite representation of these graphs by a special kind of finite state automata called labeling schemes. As a result, we are able to enumerate and describe all…
We develop an analogue of universal algebra in which generating symbols are interpreted as relations. We prove a variety theorem for these relational algebraic theories, in which we find that their categories of models are precisely the…
Take a multiplicative monoid of sequences in which the multiplication is given by Hadamard product. The set of linear combinations of interleaving monoid elements then yields a ring. For hypergeometric sequences, the resulting ring is a…
We give an overview on recent results concerning additive unit representations. Furthermore the solutions of some open questions are included. The central problem is whether and how certain rings are (additively) generated by their units.…
We introduce a new topological invariant of a rigidly-compactly generated tensor-triangulated category and two new notions of support. The first is based on smashing subcategories: it is unknown whether the frame of smashing subcategories…
For simply-laced quivers, we consider the fixed-point subalgebra of the quiver Hecke algebra under the homogeneous sign map. This leads to a new family of algebras we call alternating quiver Hecke algebras. We give a basis theorem and a…
We consider the irregular strip packing problem of rasterized shapes, where a given set of pieces of irregular shapes represented in pixels should be placed into a rectangular container without overlap. The rasterized shapes provide simple…
Signed networks, characterized by edges labeled as either positive or negative, offer nuanced insights into interaction dynamics beyond the capabilities of unsigned graphs. Central to this is the task of identifying the maximum balanced…
We provide several characterizations of ring-shaped rotationally symmetric solutions to the Serrin problem in arbitrary dimensions.
We extend the existing skew polynomial representations of matrix algebras which are direct sum of matrix spaces over division rings. In this representation, the sum-rank distance between two tuples of matrices is captured by a weight…
Motivated by an open problem from graph drawing, we study several partitioning problems for line and hyperplane arrangements. We prove a ham-sandwich cut theorem: given two sets of n lines in R^2, there is a line l such that in both line…
We provide a theory to establish the existence of nonzero solutions of perturbed Hammerstein integral equations with deviated arguments, being our main ingredient the theory of fixed point index. Our approach is fairly general and covers a…
In this work some nonlinear integral equation is studied. This equation has arisen in the (super)string field theory and cosmology. In this work it is proved that some boundary problem for this equation has a solution.