We construct the ($\beta$-deformed) partition function hierarchies with $W$-representations. Based on $W$-representations, we analyze superintegrability property and derive their character expansions respect to Schur functions Jack polynomials, respectively. Some well known superintegrable matrix models such as Gaussian hermitian one-matrix model (in external field), $N\times N$ complex model, ...

Binary neutron star mergers are expected to produce fast dynamical ejecta, with mildly relativistic velocities extending $\beta=v/c>0.6$. We consider the radio X-ray synchrotron emission produced by collisionless shocks driven such ejecta into interstellar medium. Analytic expressions given for spherical broken power-law mass (or energy) distributions, $M(>\gamma\beta)\propto(\gamma\beta)^{-s}$...

The trimeric extracellular matrix molecule laminin-5 and its constituent chains (alpha 3, beta 3, gamma 2) are normally not detectable intracellularly in intestinal epithelial cells but the laminin gamma 2 chain can be detected in cancer cells at the invasive front of a subset of colon carcinomas. These cells are subjected to cytokines such as transforming growth factor beta 1 (TGF-beta 1) and ...

Background: &beta-glucans are glucose polymers with a variety of stimulatory effects on the immune system. The objective of this study was to evaluate the immune-enhancing activities of low molecular weight gamma irradiated &beta-glucan (I&beta-g) extracted from Pleurotus ostreatus in response to Pseudomonas aeruginosa infection in rats. Materials and Methods: &beta-glucan (&beta-g) powder was ...

UNLABELLED In this paper, we propose a five-parameter lifetime model called the McDonald exponentiated gamma distribution to extend beta exponentiated gamma, Kumaraswamy exponentiated gamma and exponentiated gamma, among several other models. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the rth moment. We discuss estimation...

Normal modes have been used to explore the inherent flexibility of the alpha, beta and gamma subunits of F(1)-ATPase in isolation and as part of the alpha(3)beta(3)gamma complex. It was found that the structural plasticity of the gamma and beta subunits, in particular, correlates with their functions. The N and C-terminal helices forming the coiled-coil domain of the gamma subunit are highly fl...

Let $f$ be a locally univalent function on the unit disk $U$. We consider the normalized extensions of $f$ to the Euclidean unit ball $B^nsubseteqmathbb{C}^n$ given by $$Phi_{n,gamma}(f)(z)=left(f(z_1),(f'(z_1))^gammahat{z}right),$$  where $gammain[0,1/2]$, $z=(z_1,hat{z})in B^n$ and $$Psi_{n,beta}(f)(z)=left(f(z_1),(frac{f(z_1)}{z_1})^betahat{z}right),$$ in which $betain[0,1]$, $f(z_1)neq 0$ a...

Given a system of linear equations ℓ i ( x ) = β $$ {\ell}_i(x)={\beta}_i in an n -vector 0–1 variables, we compute the expectation exp − ∑ γ 2 \exp \left\{-{\sum}_i{\gamma}_i{\left({\ell}_i(x)-{\beta}_i\right)}^2\right\} , where is vector independent Bernoulli random variables and > 0 {\gamma}_i>0 are constants. The algorithm runs quasi-polynomial O ln {n}^{O\left(\ln n\right)} time under some...