Related papers: Which are the Maximal Ideals ?
We describe the universal Groebner basis of the ideal of maximal minors and the ideal of $2$-minors of a multigraded matrix of linear forms. Our results imply that the ideals are radical and provide bounds on the regularity. In particular,…
We establish a positivity property for a class of semilinear elliptic problems involving indefinite sublinear nonlinearities. Namely, we show that any nontrivial nonnegative solution is positive for a class of problems the strong maximum…
In this article, we study the monoid of fractional ideals and the ideal class semigroup of an arbitrary given one dimensional normal domain O obtained by an infinite integral extension of a Dedekind domain. We introduce a notion of "upper…
This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…
Let $D$ be a domain and $M$ a maximal ideal of $D$. The ring of integer-valued polynomials on a subset $E$ of $D$, as well as more general rings of functions from $E$ to $D$, can be viewed as subrings of the product $D^E=\prod_{e\in E}D$.…
In this paper the necessary conditions of optimality in the form of maximum principle are derived for a very general class of variational problems. This class includes problems with any optimization criteria and constraints that can be…
We consider relative or subjective optimization problems where the goal function and feasible set are dependent of the current state of the system under consideration. In general, they are formulated as quasi-equilibrium problems, hence…
This paper investigates the behavior of sets and functions at infinity by introducing new concepts, namely directional normal cones at infinity for unbounded sets, along with limiting and singular subdifferentials at infinity in the…
Equilibrium is a rather ideal situation, the exception rather than the rule in Nature. Whenever the external or internal parameters of a physical system are varied its subsequent relaxation to equilibrium may be either impossible or take…
We characterize monomial ideals which are intersections of monomial prime ideals and study classes of ideals with this property, among them polymatroidal ideals.
Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…
We characterize the validity of the Maximum Principle in bounded domains for fully nonlinear degenerate elliptic operators in terms of the sign of a suitably defined generalized principal eigenvalue. Here, maximum principle refers to the…
We give criteria for graded ideals to have the property that all their powers are componentwise linear. Typical examples to which our criteria can be applied include the vertex cover ideals of certain finite graphs.
We obtain sufficient conditions for an exponential type entire function not to have zeros in the open lower half-plane. An exact inequality containing the real and imaginary parts of such functions and their derivatives restricted to the…
The aim of this work is to study duality of fractional ideals with respect to a fixed ideal and to investigate the relationship between value sets of pairs of dual ideals in admissible rings, a class of rings that contains the local rings…
We develop some basic facts on deformations of exterior differential ideals on a smooth complex algebraic variety. With these tools we study deformations of several types of differential ideals, leading to several irreducible components of…
We show that the class of completely m-full ideals coincides with the class of componentwise linear ideals in a polynomial ring over an infinite field.
We investigate, using the notion of linear quotients, significative classes of connected graphs whose monomial edge ideals, not necessarily squarefree, have linear resolution, in order to compute standard algebraic invariants of the…
We investigate exponential ideals within the context of exponential polynomial rings over exponential fields. We establish two distinct notions of maximality for exponential ideals and explore their relationship to primeness. These three…
We introduce a two-parameter modification of the cofinality invariant of ideals. This allows us to include the interaction of a pair of ideals in the study of base-like structures. We find the values (cardinal numbers or well-known cardinal…