相关论文: About the Characteristic Function of a Set
In this paper we investigate the properties of function spaces using the selection principles.
A general formulation of optimization problems in which various candidate solutions may use different feature-sets is presented, encompassing supervised classification, automated program learning and other cases. A novel characterization of…
This paper presents a detailed symbolic approach to the study of self-similar tilings. It uses properties of addresses associated with graph-directed iterated function systems to establish conjugacy properties of tiling spaces. Tiles may be…
We study the sets of the infinite sentences constructible with a dictionary over a finite alphabet, from the viewpoint of descriptive set theory. Among other things, this gives some true co-analytic sets. The case where the dictionary is…
Aspects of the theory of characteristic modes, based on their variational formulation, are presented and an explicit form of a related functional, involving only currents in a spatial domain, is derived. The new formulation leads to deeper…
A relationship between the Riemann zeta function and a density on integer sets is explored. Several properties of the examined density are derived.
In classification, it is usual to observe that models trained on a given set of classes can generalize to previously unseen ones, suggesting the ability to learn beyond the initial task. This ability is often leveraged in the context of…
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
A method for selecting solution constructors in narrowing is presented. The method is based on a sort discipline that describes regular sets of ground constructor terms as sorts. It is extended to cope with regular sets of ground…
Set function optimization is essential in AI and machine learning. We focus on a subadditive set function that generalizes submodularity, and examine the subadditivity of non-submodular functions. We also deal with a minimax subadditive…
The statistical methods derived and described in this thesis provide new ways to elucidate the structural properties of text and other symbolic sequences. Generically, these methods allow detection of a difference in the frequency of a…
We study the arity gap of functions of several variables defined on an arbitrary set A and valued in another set B. The arity gap of such a function is the minimum decrease in the number of essential variables when variables are identified.…
Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical…
We give an elementary characterization of rational functions among meromorphic functions in the complex plane.
In the framework of the generalized measure theory the decomposable probabilistic-valued set functions are introduced with triangle functions $\tau$ in an appropriate probabilistic metric space as natural candidates for the "addition",…
We give a complete characterization of closed sets $F \subset \mathbb{R}^2$ whose distance function $d_F:= \mathrm{dist}(\cdot,F)$ is DC (i.e., is the difference of two convex functions on $\mathbb{R}^2$). Using this characterization, a…
The aim of this work is to show how we can decompose a module (if decomposable) into an indecomposable module with the help of the minimization process.
We present some results on character degree sums in connection with certain characteristics of finite groups such as p-solvability, solvability, supersolvability, and nilpotency. Some of them strengthen known results in the literature.
Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.
We develop the concept of character level for the complex irreducible characters of finite, general or special, linear and unitary groups. We give characterizations of the level of a character in terms of its Lusztig's label and in terms of…