Simple measure of similarity for the market graph construction

A simple measure of similarity for the construction of the market graph is proposed. The measure is based on the probability of the coincidence of the signs of the stock returns. This measure is robust, has a simple interpretation, is easy to calculate and can be used as measure of similarity between any number of random variables. For the case of pairwise similarity the connection of this measure with the sign correlation of Fechner is noted. The properties of the proposed measure of pairwise similarity in comparison with the classic Pearson correlation are studied. The simple measure of pairwise similarity is applied (in parallel with the classic correlation) for the study of Russian and Swedish market graphs. The new measure of similarity for more than two random variables is introduced and applied to the additional deeper analysis of Russian and Swedish markets. Some interesting phenomena for the cliques and independent sets of the obtained market graphs are observed.     

Geometric interpretation of the optimality conditions in multifacility location and applications

Geometrical optimality conditions are developed for the minisum multifacility location problem involving any norm. These conditions are then used to derive sufficient conditions for coincidence of facilities at optimality; an example is given to show that these coincidence conditions seem difficult to generalize.     

The finiteness of the Reidemeister number of morphisms between almost-crystallographic groups

We give a practical criterion to determine whether a given pair of morphisms between almost-crystallographic groups has a finite Reidemeister coincidence number. As an application, we determine all two- and three-dimensional almost-crystallographic groups that have the R _∞ property. We also show that for a pair of continuous maps between oriented infra-nilmanifolds of equal dimension, the Nielsen coincidence number equals the Reidemeister coincidence number when the latter is finite.     

Finitely purely atomic measures: Coincidence and rigidity properties

This paper is a natural continuation of the paper [2] by the same author. We shall prove that several coincidence and rigidity phenomena which usually do not appear are possible only in case the underlying measure space is trivial (i.e. is a finite union of atoms). Examples: coincidence of twoL ^p spaces, reflexivity ofL ¹, Radon—Nikodym property ofL ^∞, coincidence of Dunford, Pettis or Bochner integrability, coincidence of theL ^p space and of the weakL ^p space.     

Common coupled fixed point theorems in cone metric spaces for w-compatible mappings

In this paper we introduce the concept of a w-compatible mappings to obtain coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in cone metric space with a cone having non-empty interior. Coupled common fixed point theorems for such mappings are also proved. Our results generalize, extend and unify several well known comparable results in the literature. Results are supported by three examples.     

On the uniqueness of the coincidence index on orientable differentiable manifolds

The fixed point index of topological fixed point theory is a well studied integer-valued algebraic invariant of a mapping which can be characterized by a small set of axioms. The coincidence index is an extension of the concept to topological (Nielsen) coincidence theory. We demonstrate that three natural axioms are sufficient to characterize the coincidence index in the setting of continuous mappings on oriented differentiable manifolds, the most common setting for Nielsen coincidence theory.     

Computing Modular Coincidences for Substitution Tilings and Point Sets

Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice inR^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the number of iterations needed. The main tool is a simple algorithm for computing modular coincidences, which is essentially a generalization of the Dekking coincidence to more than one dimension, and the proof of equivalence of this generalized Dekking coincidence and modular coincidence. As a consequence, we also obtain some conditions for the existence of modular coincidences. In a separate section, and throughout the article, a number of examples are given.     

A constructive proof of Ky Fan’s coincidence theorem

We present a constructive proof for the well-known Ky Fan’s coincidence theorem through a simplicial algorithm. In a finite number of steps the algorithm generates a simplex containing an approximate coincidence point. In the limit, when the mesh size converges to zero, the sequence of approximations converges to a coincidence point. This research was carried out while the second author was visiting the CentER for Economic Research, Tilburg University. He would like to thank both CentER and the Netherlands Organization for Scientific Research (NWO) for their financial support.     

Relative preimage problem

We pose the problem of minimization for the relative preimage problem and prove a minimization theorem. The relative common preimage problem for a finite system of maps, whose particular cases are the relative coincidence and common root problems for finitely many maps, is reduced to the relative preimage problem. As corollaries, results concerning the relative coincidence problems for two maps, problems of fixed points and roots are obtained; these results, with certain distinctions, can be found in known papers by other authors.     

Random coincidence theorems and applications

In this article we state conditions under which the existence of deterministic coincidence points of two multivalued random functions implies the existence of random coincidence points. Moreover, two existence results of measurable selections are obtained for the intersection of the multivalued function evaluated at the random coincidence point. Our results extend or improve some theorems in the literature.     

零调复合映象的重合定理和最佳逼近定理

对定义在可缩空间上的零调值复合映象证明了某些新的重合点定理.作为应用某些最佳逼近定理和集值映象的重合点定理被给出.这些定理改进和推广了最近文献中许多已知结果.     

Some remarks on the moment problem and its relation to the theory of extrapolation of spaces

It is well known that that the coincidence of integer moments (nth-power moments, where n is an integer) of two nonnegative random variables does not imply the coincidence of their distributions. Moreover, we show that, given coinciding integer moments, the ratio of half-integer moments may tend to infinity arbitrarily fast. Also, in this paper, we give a new proof of uniqueness in the continuous moment problem and show that, in that problem, it is impossible to replace the condition of coincidence of all moments by a two-sided inequality between them, while preserving the inequality between the distributions. In conclusion, we study the relationship with the theory of extrapolation of spaces.     

Coincidence Points of Two Mappings Acting from a Partially Ordered Space to an Arbitrary Set

A coincidence point of a pair of mappings is an element, at which these mappings take on the same value. Coincidence points of mappings of partially ordered spaces were studied by A.V. Arutyunov, E.S. Zhukovskiy, and S.E. Zhukovskiy (see Topology and its Applications, 2015, V. 179, No. 1, p. 13–33); they proved, in particular, that an orderly covering mapping and a monotone one, both acting from a partially ordered space to a partially ordered one, possess a coincidence point. In this paper, we study the existence of a coincidence point of a pair of mappings that act from a partially ordered space to a set, where no binary relation is defined, and, consequently, it is impossible to define covering and monotonicity properties of mappings. In order to study the mentioned problem, we define the notion of a “quasi-coincidence” point. We understand it as an element, for which there exists another element, which does not exceed the initial one and is such that the value of the first mapping at it equals the value of the second mapping at the initial element. It turns out that the following condition is sufficient for the existence of a coincidence point: any chain of “quasi-coincidence” points is bounded and has a lower bound, which also is a “quasi-coincidence” point. We give an example of mappings that satisfy the above requirements and do not allow the application of results obtained for coincidence points of orderly covering and monotone mappings. In addition, we give an interpretation of the stability notion for coincidence points of mappings that act in partially ordered spaces with respect to their small perturbations and establish the corresponding stability conditions.     

Nielsen coincidence theory on infra-solvmanifolds of Sol

Science China Mathematics - We derive averaging formulas for the Lefschetz coincidence numbers, the Nielsen coincidence numbers and the Reidemeister coincidence numbers of maps on...     

Rearrangement in variational inequalities

Summary We establish some isoperimetric inequalities for the solution of an obstacle problem, when the coincidence set reaches the boundary. Particularly we get an optimal lower bound for the measure of the coincidence set.     

Unconditionally τ-closed and τ-algebraic sets in groups

Families of unconditionally τ-closed and τ-algebraic sets in a group are defined, which are natural generalizations of unconditionally closed and algebraic sets defined by Markov. A sufficient condition for the coincidence of these families is found. In particular, it is proved that these families coincide in any group of cardinality at most τ. This result generalizes both Markov's theorem on the coincidence of unconditionally closed and algebraic sets in a countable group (as is known, they may be different in an uncountable group) and Podewski's theorem on the topologizability of any ungebunden group.     

BOUNDS ON COINCIDENCE INDICES ON NON-ORIENTABLE SURFACES

§ 1 . IntroductionQuestions about bounds for indices ?rst appeared in the ?xed point context. The ?rstresults appeared in studies of surface homeomorphisms (see [13, 18, 19]). In [12, 14] and[15] some results about bounds for Nielsen ?xed point class ind…     

一类高阶中立型泛函微分方程周期解的存在性

该文利用重合度理论研究了一类具有分布时滞的高阶中立型泛函微分方程的周期解问题,得到了周期解存在的简单判别条件.     

On the existence of periodic solutions for a class of p-Laplacian system

By using generalized Borsuk theorem in coincidence degree theory, some criteria to guarantee the existence of ω-periodic solutions for a class of p-Laplacian system are derived.     

Periodic solutions of some fourth-order nonlinear differential equations

Using inequality techniques and coincidence degree theory, new results are provided concerning the existence of T-periodic solutions for fourth-order nonlinear differential equations. Two illustrative examples are provided to demonstrate that the results in this paper hold under weaker conditions than the existing ones, and are more effective.