Related papers: Self-Inverse and Exchangeable Random Variables
Using direct numerical simulations, we study the statistical properties of reversals in two-dimensional Rayleigh-B\'enard convection for infinite Prandtl number. We find that the large-scale circulation reverses irregularly, with the…
In some of the problems, complicated functions of the Z-transform variable, $z$, appear which either cannot be inverted analytically or the required calculations are quite tedious. In such cases numerical methods should be used to find the…
It is shown that the exponential is the only distribution which satisfies a certain regression equation. This characterization equation involves the conditional expectation (regression function) of a record value given a pair of record…
We define here the notion of a {\it weakly reversible ring} $R$ saying that a non-zero element $a\in R$ is weakly reversible if there exists an integer $m>0$ depending on $a$ such that $a^m\neq 0$ is reversible, that is,…
A new version of a strong law of large numbers for a ``good'' pairwise independent sequence of random variables (r.v.'s) with a small part of ``bad'' dependent r.v.'s is proposed. The main goal is to relax the assumption on the existence of…
For two independent, almost surely finite random variables, independence of their minimum (time) and the event that one of them is either greater, equal or less than the other (cause) is completely characterized. It is shown that, other…
Our paper introduces a novel method for calculating the inverse $\mathcal{Z}$-transform of rational functions. Unlike some existing approaches that rely on partial fraction expansion and involve dividing by $z$, our method allows for the…
Under certain conditions, a symmetric unimodal continuous random variable $\xi$ can be represented as a scale mixture of the standard Normal distribution $Z$, i.e., $\xi = \sqrt{W} Z$, where the mixing distribution $W$ is independent of…
We consider a square random matrix of size N of the form A + Y where A is deterministic and Y has iid entries with variance 1/N. Under mild assumptions, as N grows, the empirical distribution of the eigenvalues of A+Y converges weakly to a…
An element $g$ of a group is called {\em reversible} if it is conjugate in the group to its inverse. This paper is about reversibles in the group $G$ of formally-invertible pairs of formal power series in two variables, with complex…
The Schinzel Hypothesis is a conjecture about irreducible polynomials in one variable over the integers: under some standard condition, they should assume infinitely many prime values at integers. We consider a relative version: if the…
The purpose of this paper is to study the generalization of inverse semigroups (without order). An ordered semigroup S is called an inverse ordered semigroup if for every a 2 S, any two inverses of a are H-related. We prove that an ordered…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
When the weak value of a projector is 1, a quantum system behaves as in that eigenstate with probability 1. By definition, however, the weak value may take an anomalous value lying outside the range of probability like -1. From the…
This paper has solved the inverse eigenvalue problem for "fixed-free" mass-chain systems with inerters. It is well known that for a spring-mass system wherein the adjacent masses are linked through a spring, the natural frequency assignment…
We investigate the strength of a randomness notion $\mathcal R$ as a set-existence principle in second-order arithmetic: for each $Z$ there is an $X$ that is $\mathcal R$-random relative to $Z$. We show that the equivalence between…
We study an information analogue of infinitely divisible probability distributions, where the i.i.d. sum is replaced by the joint distribution of an i.i.d. sequence. A random variable $X$ is called informationally infinitely divisible if,…
Thanks to works by M. Kontsevich and A. Zorich followed by C. Boissy, we have a classification of all Rauzy Classes of any given genus. It follows from these works that Rauzy Classes are closed under the operation of inverting the…
We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…
The goal of this paper is to understand the set $\mathrm{End}(W)$ of endomorphisms of an irreducible spherical reflection group $W$. We do this in two ways: numerically, by deriving an explicit formula for $|\mathrm{End}(W)|$; and…