In recent years, two different multigraded variants of Castelnuovo-Mumford regularity have been developed, namely multigraded regularity, defined by the vanishing of multigraded pieces of local cohomology modules, and the resolution regularity vector, defined by the multi-degrees in a minimal free resolution. In this paper, we study the relationship between multigraded regularity and the resolu...

it is shown that when a special vertex stretching is applied to a graph, the cochordal cover number of the graph increases exactly by one, as it happens to its induced matching number and (castelnuovo-mumford) regularity. as a consequence, it is shown that the induced matching number and cochordal cover number of a special vertex stretching of a graph g are equal provided g is well-covered bipa...

let $r=k[x_1,x_2,cdots, x_n]$ be a polynomial ring over a field $k$. we prove that for any positive integers $m, n$, $text{reg}(i^mj^nk)leq mtext{reg}(i)+ntext{reg}(j)+text{reg}(k)$ if $i, j, ksubseteq r$ are three monomial complete intersections ($i$, $j$, $k$ are not necessarily proper ideals of the polynomial ring $r$), and $i, j$ are of the form $(x_{i_1}^{a_1}, x_{i_2}^{a_2}, cdots, x_{i_l...

This note establishes regularity estimates for the solution of the Maxwell equations in Lipschitz domains with non-smooth coefficients and minimal regularity assumptions. The argumentation relies on elliptic regularity estimates for the Poisson problem with non-smooth coefficients.

The coupled Navier-Stokes and Q-Tensor system is one of the models used to describe the behavior of the nematic liquid crystals. The existence of weak solutions and a uniqueness criteria have been already studied (see [11] for a Cauchy problem in the whole R3 and [7] for a initial-boundary problem in a bounded domain Ω). Nevertheless, results on strong regularity have only been treated in [11] ...

We shall continue to discuss further properties of null-additive fuzzy measure on metric spaces following the previous results. Under the null-additivity condition, some properties of the inner/outer regularity and the regularity of fuzzy measure are shown. Also the strong regularity of fuzzy measure is discussed on complete separable metric spaces. As an application of strong regularity, we pr...

By the linear algebraic representation of Petri nets, Desel introduced regularity property (Desel, 1992). Regularity implies a sufficient condition for a Petri net to be live and bounded. All the conditions checking the regularity of a Petri net are decidable in polynomial time in the size of a net (Desel and Esparza, 1995). This paper proves that regularity, liveness and boundedness can be pre...

Let k be a field and S = k[x1, . . . , xn] be a polynomial ring over k. We consider finite sequences of homogeneous polynomials of positive degrees and their operation on non-trivial finitely generated graded S-modules (with grading in Z). Here and in the following, by a polynomial, we always mean an element of S. Moreover, by an S-module we mean in the following a graded S-module with grading ...

The paper investigates the problem of analyzing regularity multidimensional matrices based on repetition significant (non-empty) characters in matrix cells. Such a means that when is shifted along one or more its coordinates, some are preserved. For each shift repeated r times, number entered as product rs, where s symbols persist for all repetitions shift. Two numerical characteristics introdu...