Related papers: Which are the Maximal Ideals ?
We investigate strong maximum (and minimum) principles for fully nonlinear second order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of…
In optimal control problems, there exist different kinds of extremals, that is, curves candidates to be solution: abnormal, normal and strictly abnormal. The key point for this classification is how those extremals depend on the cost…
We determine the set of catenary degrees, the set of distances, and the unions of sets of lengths of the monoid of nonzero ideals and of the monoid of invertible ideals of orders in quadratic number fields.
The paper is devoted to obtain first and second order necessary optimality conditions for continuous-time optimization problems with equality and inequality constraints. A full rank type regularity condition along with an uniform implicit…
In this article, we set up the continuous maximal regularity theory for a class of linear differential operators on manifolds with singularities. These operators exhibit degenerate or singular behaviors while approaching the singular ends.…
Necessary optimality conditions in the form of the maximum principle for control problems with infinite time horizon are considered. Both finite and infinite values of objective functional are allowed since the concept of overtaking or…
Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying a special property must be prime. We present a "Prime Ideal Principle" that gives a uniform method of proving such facts, generalizing the…
We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
New form of sufficient optimality condition is obtained in comparison with the Mangasarian sufficiency theorem. Both finite and infinite values of objective functional are allowed since concepts of overtaking and weakly overtaking…
The classical "generalized principal ideal theorems" of Macaulay, Eagon-Northcott, and others give sharp bounds on the heights of determinantal ideals in arbitrary rings. But in regular local rings (or graded polynomial rings) these are far…
This paper is concerned with necessary and sufficient second-order conditions for finite-dimensional and infinite-dimensional constrained optimization problems. Using a suitably defined directional curvature functional for the admissible…
Among the several types of closures of an ideal $I$ that have been defined and studied in the past decades, the integral closure $\bar{I}$ has a central place being one of the earliest and most relevant. Despite this role, it is often a…
Ideals generated by adjacent 2-minors are studied. First, the problem when such an ideal is a prime ideal as well as the problem when such an ideal possesses a quadratic Gr\"obner basis is solved. Second, we describe explicitly a primary…
The aim of this paper is to investigate the dynamics of a higher order system of rational difference equations. Our concentration is on boundedness character, the oscillatory, the existence of unbounded solutions and the global behavior of…
We introduce and explore the concept of positive ideals for both linear and multilinear operators between Banach lattices. This paper delineates the fundamental principles of these new classes and provides techniques for constructing…
In this article we investigate when a homogeneous ideal in a graded ring is normal, that is, when all positive powers of the ideal are integrally closed. We are particularly interested in homogeneous ideals in an N-graded ring generated by…
In dimension two, we study complete monomial ideals combinatorially, their Rees algebras and develop effective means to find their defining equations.
We develop a theory of boundary functions for ideals in trivially analytic subalgebras of simple AF C*-algebras with an injective 0-cocycle, a class which includes all full nest algebras. Boundary functions are maps from the spectrum of the…
This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…