Related papers: On functions with a unique identification minor

We show that separability and second-countability are first-order properties among topological spaces definable in o-minimal expansions of $(\mathbb{R},<)$. We do so by introducing first-order characterizations -- definable separability and…

We examine dynamical systems with the property that pseudo-orbits can be traced by small diameter sets with bounded cardinality. In particular, we show that mixing sofic subshifts and surjective dynamical systems with the specification…

In this paper, we study classes of subexcedant functions enumerated by the Bell numbers and present bijections on set partitions. We present a set of permutations whose transposition arrays are the restricted growth functions, thus defining…

The aim of this paper is to define a new operator by using the generalized Struve functions. By using this operator we define a subclass of analytic functions. We discuss some properties of this class such as inclusion problems, radius…

A systematic procedure for generating certain identities involving elementary symmetric functions is proposed. These identities, as particular cases, lead to new identities for binomial and q-binomial coefficients.

We consider a class of functions defined on metric spaces which generalizes the concept of piecewise Lipschitz continuous functions on an interval or on polyhedral structures. The study of such functions requires the investigation of their…

For n=1,2,3,... define S(n) as the smallest integer m>1 such that those 2k(k-1) mod m for k=1,...,n are pairwise distinct; we show that S(n) is the least prime greater than 2n-2 and hence the value set of the function S(n) is exactly the…

We describe some "unrestricted" algorithms which are useful for the computation of elementary and special functions when the precision required is not known in advance. Several general classes of algorithms are identified and illustrated by…

This paper is devoted to second-order variational analysis of a rather broad class of extended-real-valued piecewise liner functions and their applications to various issues of optimization and stability. Based on our recent explicit…

We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. The construction involves an iteration procedure on an infinite-dimensional…

The notions and certain fundamental characteristics of the proximal and limiting normal cones with respect to a set are first presented in this paper. We present the ideas of the limiting coderivative and subdifferential with respect to a…

Let F be a class of functions with the uniqueness property: if a function f in F vanishes on a set of positive measure, then f is the zero function. In many instances, we would like to have a quantitative version of this property, e.g. a…

In the present paper a new concept of representability is introduced, which can be applied to not total and also to intransitive relations (semiorders in particular). This idea tries to represent the orderings in the simplest manner,…

Probability functions appear in constraints of many optimization problems in practice and have become quite popular. Understanding their first-order properties has proven useful, not only theoretically but also in implementable algorithms,…

Choice functions accept a set of alternatives as input and produce a preferred subset of these alternatives as output. We study the problem of learning such functions under conditions of context-dependence of preferences, which means that…

In various applications the problem of separation of the original signal and the noise arises. For example, in the identification problem for discrete linear and causal systems, the original signal consists of the values of transfer…

This is a survey paper on rainbow sets (another name for ``choice functions''). The main theme is the distinction between two types of choice functions: those having a large (in the sense of belonging to some specified filter, namely closed…

Planar functions are special functions from a finite field to itself that give rise to finite projective planes and other combinatorial objects. We consider polynomials over a finite field $K$ that induce planar functions on infinitely many…

This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas…

It is known that a minimal teaching set of any threshold function on the twodimensional rectangular grid consists of 3 or 4 points. We derive exact formulae for the numbers of functions corresponding to these values and further refine them…