Let $G$ be a finite group and $cd^*(G)$ be the set of nonlinear irreducible character degrees of  $G$. Suppose that $rho(G)$ denotes the set of primes dividing some element of $cd^*(G)$. The bipartite divisor graph for the set of character degrees which is denoted by $B(G)$, is a bipartite graph whose vertices are the disjoint union of $rho(G)$ and $cd^*(G)$, and a vertex $p in rho(G)$ is conne...

Abstract Funding Acknowledgements Type of funding sources: Foundation. Main source(s): Swiss National Science Foundation Philips Healthcare. Introduction Intrinsic cardiac elastography in echocardiography estimates myocardial stiffness by measuring the propagation stretch generated atrial contraction. The aims present study were (A) to assess its value differentiating amyloidosis (CA) from hype...

For a positive integer $d$ and unitary representation $\rho:G\rightarrow\mathrm{U}(d)$ of compact group $G$, the twirling channel for this is linear mapping $\Phi: M_d\rightarrow M_d$ defined as $\Phi(X)=\int_{G}\mathrm{d}\mu(g)\,\rho(g)X\rho(g^{-1})$ every $X\in M_d$, where $\mu$ Haar measure on $G$. Such channels are examples mixed-unitary channels, they in convex hull set fixed size. By Cara...

By mapping the molecular fraction of Galactic Center (GC), we quantitatively address question how much and central CMZ (Central Molecular Zone) is. For this purpose analyze CO HI-line archival data, determine column- (surface-) volume-molecular fractions, $f_{\rm mol}^\Sigma$ mol}^\rho$, which are ratio column-mass density H$_2$ projected on sky to that total gas (H$_2$ + HI) from line intensit...

A $Gamma$-so-ring is a structure possessing a natural partial ordering, an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a $Gamma$-so-ring. In this paper we introduce the notions of subdirect product and $(phi,rho)$-product of $Gamma$-so-rings and study $(phi,rho)$-represen...

In the paper we study equiaffine immersions $f\colon (M^n,\nabla) \rightarrow {\mathbb{R}}^{n+2}$ with flat connection $\nabla$ and one-dimensional Weingarten mapping. For such there are two types of transversal distribution frame.We give a parametrization submanifold given properties for both frame. The main result is contained in Theorems 1, 2 Corollary 1: Let ({M}^n,\nabla)\rightarrow({\math...

in this paper, we give some results on the common fixed point of self-mappings defined on complete $b$-metric spaces. our results generalize kannan and chatterjea fixed point theorems on complete $b$-metric spaces. in particular, we show that two self-mappings satisfying a contraction type inequality have a unique common fixed point. we also give some examples to illustrate the given results.