We prove that many of beta, beta prime, gamma, inverse gamma, Student tand ultraspherical distributions are freely infinitely divisible, but some of them are not. The latter negative result follows from a local property of probability density functions. Moreover, we show that the Gaussian, many of ultraspherical and Student t-distributions have free divisibility indicator 1.

The retina responds to a wide range of light stimuli by adaptation of retinal signaling to background light intensity and the use of two different photoreceptors: rods that sense dim light and cones that sense bright light. Rods signal to rod bipolar cells that receive significant inhibition from amacrine cells in the dark, especially from a rod bipolar cell-activated GABAergic amacrine cell. T...

in this paper, we introduce and study a mixed variational inclusion problem involving infinite family of fuzzy mappings. an iterative algorithm is constructed for solving a mixed variational inclusion problem involving infinite family of fuzzy mappings and the convergence of iterative sequences generated by the proposed algorithm is proved. some illustrative examples are also given.

a normed space $mathfrak{x}$ is said to have the fixed point property, if for each nonexpansive mapping $t : e longrightarrow e $ on a nonempty bounded closed convex subset $ e $ of $ mathfrak{x} $ has a fixed point. in this paper, we first show that if $ x $ is a locally compact hausdorff space then the following are equivalent: (i) $x$ is infinite set, (ii) $c_0(x)$ is infinite dimensional, (...

Let $R$ be an infinite ring. Here we prove that if $0_R$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin X}$ for every infinite subset $X$ of $R$, then $R$ satisfies the polynomial identity $x^n=0$. Also we prove that if $0_R$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in X}$ for every infinite subset $X$ of $R$, then $x^n=x$ for all $xin R$.

This study is concerned with the formulation of three dimensional mapped infinite elements with 1/r and 1/ decay types. These infinite elements are coupled with conventional finite elements and their application to some problems of soil structure interaction are discussed. The effeciency of the coupled finite-infinite elements formulation with respect to computational effort, data preparation a...

Because the mouse retina has become an important model system, we have begun to identify its specific neuron types and their synaptic connections. Here, based on electron micrographs of serial sections, we report that the wild-type mouse retina expresses the standard rod pathways known in other mammals: (1) rod --> cone (via gap junctions) to inject rod signals into the cone bipolar circuit; an...

The paper is concerned with algebras whose elements can be used to represent runs of a system from a state to a state. These algebras, called multiplicative transition systems, are categories with respect to a partial binary operation called composition. They can be characterized by axioms such that their elements and operations can be represented by partially ordered multisets of a certain typ...

We prove that the q-Gaussian distribution is freely infinitely divisible for all q ∈ [0, 1].