Related papers: Group Determinants and Invariant Rings

First, we establish the theory of fractional powers of first order differential operators with zero order terms, obtaining PDE properties and analyzing the corresponding fractional Sobolev spaces. In particular, our study shows that…

We define the concept of a doset Hibi ring and a generalized doset Hibi ring which are subrings of a Hibi ring and are normal affine semigrouprings. We apply the theory of (generalized) doset Hibi rings to analyze the rings of absolute…

In this monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful applications in mathematical physics,…

We define a class of discrete operators that, in particular, include the delta and nabla fractional operators.

Since polynomial regression models are generally quite reliable for data with a linear trend, it is important to note that, in some cases, they may encounter overfitting issues during the training phase, which could result in negative…

For two positive integers $m$ and $n$, we let ${\mathbb H}_n$ be the Siegel upper half plane of degree $n$ and let ${\mathbb C}^{(m,n)}$ be the set of all $m\times n$ complex matrices. In this article, we study differential operators on the…

We give a characterization, in terms of simplicial sets, of Frobenius objects in the category of relations. This result generalizes a result of Heunen, Contreras, and Cattaneo showing that special dagger Frobenius objects in the category of…

Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of…

We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative theory of non-unique factorizations. Topics covered include…

Inversion symmetry is a very non-trivial discrete symmetry of Frobenius manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger transformations of a special ODE associated to a Frobenius manifold. In this paper, we…

We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case…

This article gives a fundamental discussion on variable coefficients, self-adjoint, formally partially hypoelliptic differential operators. A generalization of the results to pseudo differential operators, is given in a following article in…

The purpose of this paper is to begin studying the computation of the nonzero determinant of semigroups within the class of finite semigroups that possesses a pair of non-commutative idempotents. This paper focuses on a class of these…

A class of pseudodifferential operators on the Heisenberg group is defined. As it should be, this class is an algebra containing the class of differential operators. Furthermore, those pseudodifferential operators act continuously on…

If $\fg$ is a semisimple Lie algebra, we describe the prime factors of $\mcU(\fg)$ that have enough finite dimensional modules. The proof depends on some combinatorial facts about the Weyl group which may be of independent interest. We also…

In 2000, Voiculescu proved an algebraic characterization of cyclic gradients of noncommutative polynomials. We extend this remarkable result in two different directions: first, we obtain an analogous characterization of free gradients;…

Here we develop a technique of computing the invariants of $n-$ary forms and systems of forms using the discriminants of corresponding multilinear forms built of their partial derivatives, which should be cosidered as analogues of classical…

This work introduces a new kind of affine semigroups called $P$-semigroups. Within the framework of $\mathcal C$-semigroups, we define a finite-state automaton associated to them. Moreover, this automaton determines whether a $\mathcal…

The most developed aspect of the theory of finite semigroups is their classification in pseudovarieties. The main motivation for investigating such entities comes from their connection with the classification of regular languages via…

We apply a novel method for the equivalence group and its infinitesimal generators to the investigation of invariants of linear ordinary differential equations. First, a comparative study of this method is illustrated by an example. Next,…