Related papers: Representation Theorem for Multivariable Totally S…
We construct a canonical irreducible representation for the orthofermion algebra of arbitrary order, and show that every representation decomposes into irreducible representations that are isomorphic to either the canonical representation…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
We define antidomain operations for algebras of multiplace partial functions. For all signatures containing composition, the antidomain operations and any subset of intersection, preferential union and fixset, we give finite equational or…
This paper investigates best-worst choice probabilities (picking the best and the worst alternative from an offered set). It is shown that non-negativity of best-worst Block-Marschak polynomials is necessary and sufficient for the existence…
When filtering a topological space by a single parameter, the theory of quiver representations provides a complete framework for decomposing the resulting persistence module to obtain its barcode. This is achieved by interpreting the…
We study the theory of representations of a multiparameter deformation of the function algebra of a simple algebraic group (as defined by Reshetikhin) when the quantum parameter is a root of unity. We extend the technics of De…
In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…
We investigate the representation of symmetric polynomials as a sum of squares. Since this task is solved using semidefinite programming tools we explore the geometric, algebraic, and computational implications of the presence of discrete…
The two function theories of monogenic and of slice monogenic functions have been extensively studied in the literature and were developed independently; the relations between them, e.g. via Fueter mapping and Radon transform, have been…
In this paper we first prove a general representation theorem for generators of backward stochastic differential equations (BSDEs for short) by utilizing a localization method involved with stopping time tools and approximation techniques,…
It is a remarkable fact that for many statistics on finite sets of combinatorial objects, the roots of the corresponding generating function are each either a complex root of unity or zero. These and related polynomials have been studied…
Motivated by partition regularity problems of homogeneous quadratic equations, we prove multiple recurrence and convergence results for multiplicative measure preserving actions with iterates given by rational sequences involving…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…
We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way…
We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…
We show that the monodromy operator at infinity plus the decomposition of the homology given by the vanishing cycles completely determine the homology monodromy representation of any complex polynomial.
In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…
This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…
A relation algebra is measurable if the identity element is a sum of atoms, and the square x;1;x of each subidentity atom x is a sum of non-zero functional elements. These functional elements form a group Gx. We prove that a measurable…