Related papers: Quantization coefficients for uniform distribution…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish criteria…
The polygonal distributions are a class of distributions that can be defined via the mixture of triangular distributions over the unit interval. The class includes the uniform and trapezoidal distributions, and is an alternative to the beta…
We study a random polynomial of degree $n$ over the finite field $\mathbb{F}_q$, where the coefficients are independent and identically distributed and uniformly chosen from the squares in $\mathbb{F}_q$. Our main result demonstrates that…
Quantum coherence is the outcome of the superposition principle. Recently, it has been theorized as a quantum resource, and is the premise of quantum correlations in multipartite systems. It is therefore interesting to study the coherence…
We obtain an estimate for uniform approximation rate of bounded analytic in the unit disk functions by logarithmic derivatives of $C$-polynomials, i.e., polynomials, all of whose zeros lie on the unit circle $C:|z|=1$.
The diffusion coefficient of a circular shaped inclusion in a liquid membrane is investigated by taking into account the interaction between membranes and bulk solvents of arbitrary thickness. As illustrative examples, the diffusion…
We study the characteristic polynomial of random permutation matrices following some measures which are invariant by conjugation, including Ewens' measures which are one-parameter deformations of the uniform distribution on the permutation…
Differentiability of semigroups is useful for many applications. Here we focus on stochastic differential equations whose diffusion coefficient is the square root of a differentiable function but not differentiable itself. For every…
We prove that there is a universal measure on the unit circle such that any probability measure on the unit disk is the limit distribution of some subsequence of the corresponding orthogonal polynomials. This follows from an extension of a…
In this paper we implement the holonomic gradient method to exactly compute the normalising constant of Bingham distributions. This idea is originally applied for general Fisher-Bingham distributions in Nakayama et al. (2011). In this paper…
In this work we provide a novel approach for computing the coefficients of the characteristic polynomial of a square matrix. We demonstrate that each coefficient can be efficiently represented by a set of circle graphs. Thus, one can employ…
We study the rational approximation properties of special manifolds defined by a set of polynomials with rational coefficients. Mostly we will assume the case of all polynomials to depend on only one variable. In this case the manifold can…
Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite set. In this article, we consider a probability distribution generated by an infinite system of…
This work describes a novel image analysis approach to characterize the uniformity of objects in agglomerates by using the propagation of normal wavefronts. The problem of width uniformity is discussed and its importance for the…
Restrictions to diffusion result in the dispersion of the bulk diffusion coefficient. We derive the exact universal high-frequency behavior of the diffusion coefficient in terms of the surface-to-volume ratio of the restrictions. This…
This paper develops a systematic and geometric theory of optimal quantization on the unit sphere $\mathbb S^2$, focusing on finite uniform probability distributions supported on the spherical surface - rather than on lower-dimensional…
We describe the boundary behaviors of the squeezing functions for all bounded convex domains in $\mathbb{C}^n$ and bounded domains with a $C^2$ strongly convex boundary point.
For $d\geq 2$, we discuss $d$-dimensional complex manifolds $M$ that are the increasing union of bounded open sets $M_n$'s of $\mathbb{C}^d$ with a common uniform squeezing constant. The description of $M$ is given in terms of the corank of…
A simple model for addition spectra in quantum dots is proposed and studied. It is an extension of the standard charging model which assumes that the charge spreads uniformely over the entire dot. The proposed model attempts to account for…