相关论文: Maximal divisorial sets in arc spaces

We present filling as a new type of spatial subdivision problem that is related to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most…

In this paper, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on…

We give conditions for a maximal divisorial ideal to be t-maximal and show with examples that, even in a completely integrally closed domain, maximal divisorial ideals need not be t-maximal.

Some new necessary conditions for the existence of vector space partitions are derived. They are applied to the problem of finding the maximum number of spaces of dimension t in a vector space partition of V(2t,q) that contains m_d spaces…

A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…

A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of…

In this paper, we study maximal antipodal sets in simply connected exceptional compact symmetric spaces. Combining our results with the existing literature, we obtain a complete classification of maximal antipodal sets in all such spaces.…

Let X be a smooth projective complex variety, and L a line bundle on X . We say that the linear system |L| has maximal variation if its elements have the maximum number dim|L| of moduli. We discuss some cases where this situation is…

An annulus is, informally, a ring-shaped region, often described by two concentric circles. The maximum-width empty annulus problem asks to find an annulus of a certain shape with the maximum possible width that avoids a given set of $n$…

We consider set covering problems where the underlying set system satisfies a particular replacement property w.r.t. a given partial order on the elements: Whenever a set is in the set system then a set stemming from it via the replacement…

Let $\mathcal{X}$ be a set of $(h-1)$-dimensional subspaces of $\mathrm{PG}(kh-1,q)$ with the property that every hyperplane contains at most $t$ elements of $\mathcal{X}$. We prove the upper bound $|\mathcal{X}| \leq (t-k+2)q^h + t$, and…

This work introduces a multidimensional generalization of the maximum bisection problem. A mixed integer linear programming formulation is proposed with the proof of its correctness. The numerical tests, made on the randomly generated…

Let $A$ be a set of $n$ positive integers. We say that a subset $B$ of $A$ is a divisor of $A$, if the sum of the elements in $B$ divides the sum of the elements in $A$. We are interested in the following extremal problem. For each $n$,…

We use vector bundles to study the locus of totally mixed Nash equilibria of an $n$-player game in normal form, which we call the Nash equilibrium scheme. When the payoff tensor format is balanced, we study the Nash discriminant variety,…

This paper is devoted to variational problems on the set of probability measures which involve optimal transport between unequal dimensional spaces. In particular, we study the minimization of a functional consisting of the sum of a term…

An optimal mesh size of the sampling region can help to reduce computational burden in practical applications. In this work, we investigate optimal choices of mesh sizes for the identifications of medium obstacles from either the far-field…

In this paper we present some new results on the existence of solutions of generalized variational inequalities in real reflexive Banach spaces with Fr\'echet differentiable norms. Moreover, we also give some theorems about the structure of…

In this letter, we study distributed optimization and Nash equilibrium-seeking dynamics from a contraction theoretic perspective. Our first result is a novel bound on the logarithmic norm of saddle matrices. Second, for distributed gradient…

Variational relation problems allow a general approach for variational inequalities, equilibrium problems, optimization problems, variational inclusions. In this paper we consider a system of quasi-variational relations and determine some…

We study Nash valuations on 3-fold terminal singularities, especially in type cAx/2. We find that, in type cAx/2, exceptional prime divisors computing the minimal discrepancy (which is 1/2 in this case) induce Nash valuations. We conjecture…