相关论文: A three-factor product construction for mutually o…
Suppose $f\in L^1(\mathbb{R}^d)$, $\Lambda\subset\mathbb{R}^d$ is a finite union of translated lattices such that $f+\Lambda$ tiles with a weight. We prove that there exists a lattice $L\subset{\mathbb{R}}^d$ such that $f+L$ also tiles,…
Ouroboros functions have shown some interesting properties when subjected to conventional operations. The aim of this paper is to continue our investigation and prove some additional properties of these functions. Using algebraic methods,…
It has been proven that the lozenge tilings of a quartered hexagon on the triangular lattice are enumerated by a simple product formula. In this paper we give a new proof for the tiling formula by using Kuo's graphical condensation. Our…
A generalization of the Macdonald polynomials depending upon both commuting and anticommuting variables has been introduced recently. The construction relies on certain orthogonality and triangularity relations. Although many…
We apply column generation to approximating complex structured objects via a set of primitive structured objects under either the cross entropy or L2 loss. We use L1 regularization to encourage the use of few structured primitive objects.…
Latin squares are well studied combinatorial objects. In this paper we generalize the concept and propose new objects like Latin triangles, free Latin squares, Latin tetrahedra, free Latin cubes, etc. We start with a classic definition of…
The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras…
We describe a logarithmic tensor product theory for certain module categories for a ``conformal vertex algebra.'' In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not…
We prove an explicit formula for the tensor product with itself of an irreducible complex representation of the symmetric group defined by a rectangle of height two. We also describe part of the decomposition for the tensor product of…
We investigate several properties of Kronecker (direct, tensor) products of graphs that are planar and $3$-connected (polyhedral, $3$-polytopal). This class of graphs was recently characterised and constructed by the second author [15]. Our…
In this paper we consider the topological products of modal logics of S4.1 and S4. We prove that it is equal to the fusion of logics S4.1 and S4 plus one additional axiom. We also show that this product is decidable. This is an example of a…
Consider a one-parameter family of smooth Riemannian metrics on a two-sphere, $\mathscr{S}$. By choosing a one-parameter family of smooth lapse and shift, these Riemannian two-spheres can always be assembled into smooth Riemannian…
It is well-known that orthogonal polynomials on the real line satisfy a three-term recurrence relation and conversely every system of polynomials satisfying a three-term recurrence relation is orthogonal with respect to some positive Borel…
The Kauffman bracket skein algebra of a surface is a generalization of the Jones polynomial invariant for links and plays a principal role in the Witten-Reshetikhin- Turaev topological quantum field theory. However, the multiplicative…
We develop a new method for constructing "good" designs for computer experiments. The method derives its power from its basic structure that builds large designs using small designs. We specialize the method for the construction of…
We propose a deep learning approach to the obstacle problem inspired by the first-order system least-squares (FOSLS) framework. This method reformulates the problem as a convex minimization task; by simultaneously approximating the…
In three-dimensional Euclidean geometry, the scalar product produces a number associated to two vectors, while the vector product computes a vector perpendicular to them. These are key tools of physics, chemistry and engineering and…
We introduce a triple coproduct for knots on surfaces, providing a commutative framework that decomposes a single-component diagram into three components (Section 2). This construction is motivated by the interplay between intersection…
We derive explicit rational generating functions for weighted tilings of $2k\times n$ rectangles by straight $k\times 1$ tiles. Our approach combines a decomposition by fault lines with a Hadamard-product framework. Tools from algebraic…
We introduce a new multiplication for the polytope algebra, defined via the intersection of polytopes. After establishing the foundational properties of this intersection product, we investigate finite-dimensional subalgebras that arise…