相关论文: Wild sets in global function fields

The escaping set of an entire function consists of the points in the complex plane that tend to infinity under iteration. This set plays a central role in the dynamics of transcendental entire functions. The goal of this survey is to…

In this paper we study mean field games with possibly multiple mean field equilibria. Instead of focusing on the individual equilibria, we propose to study the set of values over all possible equilibria, which we call the set value of the…

Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.

We give a criterion of tameness and wildness for a finite-dimensional Lie algebra over an algebraically closed field.

Except for a limited number of cases, a complete classification of the Diophantine sets of polynomial rings and fields of rational functions seems out of reach at present. We contribute to this problem by proving that several natural sets…

Tree sets are posets with additional structure that generalize tree-like objects in graphs, matroids, or other combinatorial structures. They are a special class of abstract separation systems. We study infinite tree sets and how they…

In this note, we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover any vector space V over any field. If V is a finite set, this is related to the problem of…

This paper deals with properties of the algebraic variety defined as the set of zeros of a "deficient" sequence of multivariate polynomials. We consider two types of varieties: ideal-theoretic complete intersections and absolutely…

It is pointed out that the universality might seriously be violated by models with several fixed points.

An involution on a finite set is a bijection such as I(I(e))=e for all the element of the set. A fixed-point free involution on a finite set is an involution such as I(e)=e for none element of the set. In this article, the fixed-point free…

In this paper the set of value functions of all-possible zero-sum differential games with terminal payoff is characterized. The necessary and sufficient condition for a given function to be a value of some differential game with terminal…

We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…

Constructible complexes have the same characteristic cycle if they have the same wild ramification, even if the characteristics of the coefficients fields are different.

We write down the functional equation of the zeta function of a global field. This equation is implicit in Weil's ``Basic Number Theory''.

We introduce the notion of the definable rank of an ordered field, ordered abelian group and ordered set, respectively. We study the relation between the definable rank of an ordered field and the definable rank of the value group of its…

Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal…

The schematic finite spaces are those finite ringed spaces where a theory of quasi-coherent modules can be developed with minimal natural conditions. We give various characterizations of these spaces and their natural morphisms. We show…

This paper introduces semiopen and semiclosed soft sets in soft topological spaces. The notions of interior and closure are generalized using these sets. A detail study is carried out on properties of semiopen, semiclosed soft sets, semi…

It is shown that the physical states of a source free gauge field form pre-Hilbert spaces already on the classical level. These spaces may be closed in such a way that the determining characteristics remain. One type of free fields has a…

A function is boundedly finite-to-one if there is a natural number $k$ such that each point has at most $k$ inverse images. In this paper, we prove in $\mathsf{ZF}$ (i.e., the Zermelo--Fraenkel set theory without the axiom of choice)…