Related papers: Regularity stabilization for the powers of graded …
Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…
In this article we extend a previous definition of Castelnuovo-Mumford regularity for modules over an algebra graded by a finitely generated abelian group. Our notion of regularity is based on Maclagan and Smith's definition, and is…
Let $F$ be a non-negatively graded free module over a polynomial ring $\mathbb{K}[x_1,\dots,x_n]$ generated by $m$ basis elements. Let $M$ be a submodule of $F$ generated by elements in $F$ with degrees bounded by $D$ and dim $F/M$=$r$. We…
Let $x$ be an eigenvector for an element of a finite irreducible reflection group $W$. Let $W_x$ denote the subgroup of $W$ which stabilises $x$. We provide an upper bound for the number of roots in the root system of $W_x$ . This…
We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around…
In this paper, we introduce a new class of monomial ideals, called $d$-fixed ideals, which generalize the class of $p$-Borel ideals and show how some results for $p$-Borel ideals can be transfered to this new class. In particular, we give…
The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its…
In this paper, we study the $F$-rationality of the Rees algebra and the extended Rees algebra of $\mathfrak{m}$-primary ideals in excellent local rings $(R, \mathfrak{m})$ of prime characteristic. We partially answer some conjectures and…
We classify all graphs for which the Rees algebras of their edge ideals are normal and have regularity equal to their matching numbers.
We illustrate how to extend the concept of structural stability through applying it to the front propagation speed selection problem. This consideration leads us to a renormalization group study of the problem. The study illustrates two…
We prove that the regularity of edge ideals of powers of forests is weakly decreasing. We then compute the regularity of edge ideals of powers of cycles.
We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated by toric geometry, we work with modules over a polynomial ring graded by a finitely generated abelian group. As in the standard graded case, our definition of…
In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave…
Given a local Cohen-Macaulay ring $(R, {\mathfrak m})$, we study the interplay between the integral closedness -- or even the normality -- of an ${\mathfrak m}$-primary $R$-ideal $I$ and conditions on the Hilbert coefficients of $I$. We…
This paper derives two stabilizability theorems for a basic class of discrete-time nonlinear systems with multiple unknown parameters. First, we claim that a discrete-time multi-parameter system is stabilizable if its nonlinear growth rate…
An ideal $I$ of a ring $R$ is square stable if $aR+bR=R$ with $a\in I$ and $b\in R$ implies that $a^2+by$ is invertible in $I$ for some $y\in I$. We prove that an exchange ideal $I$ of a ring $R$ is square stable if and only if for any…
In this paper, we propose a globally hyperbolic regularization to the general Grad's moment system in multi-dimensional spaces. Systems with moments up to an arbitrary order are studied. The characteristic speeds of the regularized moment…
We study $F$-graded systems of ideals in $R$, which are sequences of ideals giving rise to Cartier algebras on $R$. We identify how properties of these systems (or modifications of these systems) affect the singularity properties of the…
In this paper, we present the asymptotic distribution of M-estimators for parameters in non-stationary AR(p) processes. The innovations are assumed to be in the domain of attraction of a stable law with index $0<\alpha\le2$. In particular,…
We establish strong relationships between the Castelnuovo-Mumford regularity and the Ratliff-Rush closure of an ideal. Our results have several interesting consequences on the computation of the Ratliff-Rush closure, the stability of the…