Related papers: A Combinatorial Approach to Involution and delta-R…
We present a more general proof that cyclotomic polynomials are irreducible over Q and other number fields that meet certain conditions. The proof provides a new perspective that ties together well-known results, as well as some new…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
A common generalization of orthomodular lattices and residuated lattices is provided corresponding to bounded lattices with an involution and sectionally extensive mappings. It turns out that such a generalization can be based on integral…
Quaternionic polynomials occur naturally in applications of quaternions in science and engineering, and normalization of quaternionic polynomials is a basic manipulation. Once a Groebner basis is certified for the defining ideal I of the…
In this paper we discourse basises of representable algebras. This question lead to arithmetic problems. We prove algorithmical solvability of exponential-Diophantine equations in rings represented by matrices over fields of positive…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
In this paper, we study properties of polynomials over division rings. Moreover, we present formulas for finding roots of some polynomials
This paper is a survey on the study of the behaviour of the composition of polynomials on the computation of Gr\"obner bases. This survey brings together some works published between 1995 and 2007. The authors of these papers gave answers…
We improve certain degree bounds for Grobner bases of polynomial ideals in generic position. We work exclusively in deterministically verifiable and achievable generic positions of a combinatorial nature, namely either strongly stable…
Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…
Let $k \leq n$ be nonnegative integers and let $\lambda$ be a partition of $k$. S. Griffin recently introduced a quotient $R_{n,\lambda}$ of the polynomial ring $\mathbb{Q}[x_1, \dots, x_n]$ in $n$ variables which simultaneously generalizes…
This brief note concerns the invertibility of certain alternant matrices. In particular those that consisting of polynomials and products of polynomials and logarithms are shown to be invertible under appropriate conditions on the degrees…
We provide a concise introduction to the symmetry approach to integrability. Some results on integrable evolution and systems of evolution equations are reviewed. Quasi-local recursion and Hamiltonian operators are discussed. We further…
This brief note corrects some errors in the paper quoted in the title, highlights a combinatorial result which may have been overlooked, and points to further improvements in recent literature.
In this paper we consider an algorithmic technique more general than that proposed by Zharkov and Blinkov for the involutive analysis of polynomial ideals. It is based on a new concept of involutive monomial division which is defined for a…
The so called generalized down-up algebras are revisited from a viewpoint of Gr\"obner basis theory. Particularly it is shown explicitly that generalized down-up algebras are solvable polynomial algebras (provided $\lambda\omega\ne 0$), and…
The purpose of this article is to present, in a simple way, an analytic approach to special numbers and polynomials. The approach is based on the derivative polynomials. The paper is, to some extent, a review article, although it contains…
These notes deal with algebras equipped with an involution and related matters.
Ihe first author presented an efficient algorithm for computing involutive (and reduced Groebner) bases. In this paper, we consider a modification of this algorithm which simplifies matters to understand it and to implement. We prove…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…