Related papers: Groebner-Shirshov Bases: Some New Results

We introduce the theory of monoidal Groebner bases, a concept which generalizes the familiar notion in a polynomial ring and allows for a description of Groebner bases of ideals that are stable under the action of a monoid. The main…

D. Bayer and M. Stillman showed that Grobner bases can be used to compute the Castelnuovo-Mumford regularity, which is a measure for the vanishing of graded local cohomology modules. The aim of this paper is to show that the same method can…

Let $R$ be a ring with identity $1$. Jacobson's lemma states that for any $a,b\in R$, if $1-ab$ is invertible then so is $1-ba$. Jacobson's lemma has suitable analogues for several types of generalized inverses, e.g., Drazin inverse,…

Extensions of the $Stirling$ numbers of the second kind and $Dobinski$ -like formulas are proposed in a series of exercises for graduates. Some of these new formulas recently discovered by me are to be found in the source paper $ [1]$.…

Substantial developments have been achieved in the synthesis of chemical vapour deposition (CVD) diamond in recent years, providing engineers and designers with access to a large range of new diamond materials. CVD diamond has a number of…

We prove a compactness result in GBD which also provides a new proof of the compactness theorem in GSBD, due to Chambolle and Crismale [5, Theorem 1.1]. Our proof is based on a Fr\'echet-Kolmogorov compactness criterion and does not rely on…

This paper significantly strengthens directed low-diameter decompositions in several ways. We define and give the first results for separated low-diameter decompositions in directed graphs, tighten and generalize probabilistic guarantees,…

We provide a new short proof for the Birman--Solomyak theorem for Hilbert--Schmidt operators and give an application to a Schr\"odinger--Poisson system.

An algebra $\cal{R}$ is called an extension of the algebra $M$ by $B$ if $M^2=0$, $M$ is an ideal of $\cal{R}$ and $\cal{R}$$/M\cong B$ as algebras. In this paper, by using the Gr\"{o}bner-Shirshov bases, we characterize completely the…

While the charmonium model has been effective in describing ccbar bound mesons, there have been many recently discovered charmonium-like states it cannot accommodate. Here I provide a review of recent results from the B-factories including…

In this note we obtain a new convergence result for the Adomian decomposition method.

Using powerful tools of harmonic maps and integrable systems, all the Gribov copies in the Coulomb gauge in 3D Chern-Simons theory are constructed. Some issues about the Gribov and the modular re- gions are shortly discussed. The Gribov…

We establish the Gr\"obner-Shirshov bases theory for differential Lie $\Omega$-algebras. As an application, we give a linear basis of a free differential Lie Rota-Baxter algebra on a set.

We carried out a first principles investigation on the microscopic properties of nickel-related defect centers in diamond. Several configurations, involving substitutional and interstitial nickel impurities, have been considered either in…

We prove new characterizations based on Gr\"obner bases for the Cohen-Macaulay property of a projective monomial curve.

The authors of the letter "Test of the Brink-Axel Hypothesis for the Pygmy Dipole Resonance" [Phys. Rev. Lett. 119, 182503 (2017)] claim a violation of the Brink-Axel hypothesis by (gamma,gamma') data from gELBE for 96Mo [Phys. Rev. C 79,…

We obtain some new inequalities of Chebyshev Type.

We establish a poset structure on combinatorial bases of multivariate polynomials defined by positive expansions, and study properties common to bases in this poset. Included are the well-studied bases of Schubert polynomials, Demazure…

We develop methods for studying the smooth closing lemma for Reeb flows in any dimension using contact homology. As an application, we prove a conjecture of Irie, stating that the strong closing lemma holds for Reeb flows on ellipsoids. Our…

This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.