Related papers: Points accessible in average by rearrangement of s…

For a stochastic process reset at random times, we discuss to what extent the probabilities of some orderings of observables associated with the intervals of time between resetting events are universal, i.e., independent of the choice of…

We introduce a new type of means. It is new in two ways: its domain consists of sets and its values are sets too. We investigate the properties and behavior of such generalization. We also present many naturally arisen examples for such…

We give a method for taking microscopic limits of normal matrix ensembles. We apply this method to study the behaviour near certain types of singular points on the boundary of the droplet. Our investigation includes ensembles without…

Using a measure of clustering derived from the nearest neighbour distribution and the void probability function we are able to distinguish between regular and clustered structures. With an example we show that regularity is a property of a…

We introduce the abstract notion of a chain, which is a sequence of $n$ points in the plane, ordered by $x$-coordinates, so that the edge between any two consecutive points is unavoidable as far as triangulations are concerned. A general…

We are going to classify sets by a given mean in two ways. Firstly we study small and big sets regarding a given mean. Secondly we study sets that have the same weight according to a mean. We also generalize the notion of roundness and get…

We propose a generalization of small world networks, in which the reconnection of links is governed by a function that depends on the distance between the elements to be linked. An adequate choice of this function lets us control the…

Finding the underlying probability distributions of a set of observed sequences under the constraint that each sequence is generated i.i.d by a distinct distribution is considered. The number of distributions, and hence the number of…

In the space of marked group, we determine the structure of groups which are limit points of the set of all generalized quaternion groups.

Consider n unit intervals, say [1,2], [3,4], ..., [2n-1,2n]. Identify their endpoints in pairs at random, with all (2n-1)!! = (2n-1) (2n-3) ... 3 1 pairings being equally likely. The result is a collection of cycles of various lengths, and…

This paper describes a simple method for estimating lower bounds on the number of classes of equivalence for a special kind of integer sequences, called division sequences. The method is based on adding group structure to classes of…

Recently Sasane defined a notion of evaluating a distribution at a point using delta sequences. In this paper, we explore the relationship between generalizations of his definition and the standard definition of distributional point values.…

We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.

In this paper we formally define the family of sequences know as "Pea Pattern". We then analyse its behaviour and conditions for fixed and periodic points. The paper ends with a list of fixed points and cycles.

We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the…

In the literature, various types of points and meager sets whose complements are connected have been studied, such as colocally connected points, non-weak cut points/sets, non-block points/sets, shore points/sets, etc. We extend that study,…

We introduce smooth sequences of integral domains as well-ordered ascending chains that behave well at limit ordinals. Subsequently, we use this notion to give some conditions on the freeness of kernels of extension maps between groups of…

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…

In this paper, we introduce a convergence notion for ordered selections. Our convergence notion is based on subpermutation densities and convergences of the marginal distributions. A particular case of this convergence is the well-known…

We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…