Related papers: Core-based criterion for extreme supermodular func…
We establish the essential normality of a large new class of homogeneous submodules of the finite rank d-shift Hilbert module. The main idea is a notion of essential decomposability that determines when an arbitrary submodule can be…
In the work, the property of the second-order subdifferential is studied and second-order optimality conditions are obtained for the minimization problem. We also obtained necessary and sufficient conditions for an extremum for the extremal…
In graph theory, the Szemer\'edi regularity lemma gives a decomposition of the indicator function for any graph $G$ into a structured component, a uniform part, and a small error. This result, in conjunction with a counting lemma that…
We prove that a set of finite perimeter is indecomposable if and only if it is, up to a choice of suitable representative, connected in the 1-fine topology. This gives a topological characterization of indecomposability which is new even in…
We give a parametrization for crystal bases of Demazure modules as a set of lattice points in some convex polytope and we also describe explicitly the extremal vectors as solutions of some system of linear equations.
All extremal solutions of the truncated $L$-problem of moments in two real variables , with support contained in a given compact set, are described as characteristic functions of semi-algebraic sets given by a single polynomial inequality.…
A polytope is called indecomposable if it cannot be expressed nontrivially as a Minkowski sum of other polytopes. Since Gale introduced the concept in 1954, several increasingly strong criteria have been developed to characterize…
The core of an ideal is defined as the intersection of all of its reductions. In this paper we provide an explicit description for the core of a monomial ideal $I$ satisfying certain residual conditions, showing that ${\rm core}(I)$…
An unconstrained optimization problem is formulated in terms of tropical mathematics to minimize a functional that is defined on a vector set by a matrix and calculated through multiplicative conjugate transposition. For some particular…
Let M be a matrix whose entries are power series in several variables and determinant det(M) does not vanish identically. The equation det(M)=0 defines a hypersurface singularity and the (co)-kernel of M is a maximally Cohen-Macaulay module…
The aim of this paper is to generalize the Core Inverse to arbitrary vector spaces using finite potent endomorphisms. As an application, the core partial order is studied in the set of finite potent endomorphisms (of index lesser or equal…
We show that there is a largely unexplored class of functions (positive polymatroids) that can define proper discrete metrics over pairs of binary vectors and that are fairly tractable to optimize over. By exploiting submodularity, we are…
Functor morphing provides a method to translate complex representations of automorphism groups of finite modules over finite rings to representations of automorphism groups of functors in some abelian category. In this paper we give an…
The present paper is a continuation of the author's previous works, in which necessary and sufficient local extrema at a stationary point of a polynomial or a power series (and thus of an analytic function) are given. It is known that for…
A relational structure is a core, if all its endomorphisms are embeddings. This notion is important for computational complexity classification of constraint satisfaction problems. It is a fundamental fact that every finite structure has a…
The {\em hypermetric cone} is defined as the cone of semimetrics satisfying the {\em hypermetric inequalities}. Every {\em Delaunay polytope} corresponds to a ray of this polyhedral cone. The Delaunay polytopes, which correspond to extreme…
We give a new sufficient condition for the normal extensions in an admissible Galois structure to be reflective. We then show that this condition is indeed fulfilled when X is the (protomodular) reflective subcategory of S-special objects…
We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…
Submodular set functions are undoubtedly among the most important building blocks of combinatorial optimization. Somewhat surprisingly, continuous counterparts of such functions have also appeared in an analytic line of research where they…
The conventional definition of extremality of a finite collection of sets is extended by replacing a fixed point (extremal point) in the intersection of the sets by a collection of sequences of points in the individual sets with the…