Let $G$ be a finite group. The prime graph of $G$ is a graph $Gamma(G)$ with vertex set $pi(G)$, the set of all prime divisors of $|G|$, and two distinct vertices $p$ and $q$ are adjacent by an edge if $G$ has an element of order $pq$. In this paper we prove that if $Gamma(G)=Gamma(G_2(5))$, then $G$ has a normal subgroup $N$ such that $pi(N)subseteq{2,3,5}$ and $G/Nequiv G_2(5)$.

by the method of weight coefficients, techniques of real analysis andhermite-hadamard's inequality, a half-discrete hardy-hilbert-type inequalityrelated to the kernel of the hyperbolic cosecant function with the best possibleconstant factor expressed in terms of the extended riemann-zeta function is proved.the more accurate equivalent forms, the operator expressions with the norm,the reverses a...

The prime graph $Gamma(G)$ of a group $G$ is a graph with vertex set $pi(G)$, the set of primes dividing the order of $G$, and two distinct vertices $p$ and $q$ are adjacent by an edge written $psim q$ if there is an element in $G$ of order $pq$. Let $pi(G)={p_{1},p_{2},...,p_{k}}$. For $pinpi(G)$, set $deg(p):=|{q inpi(G)| psim q}|$, which is called the degree of $p$. We also set $D(G):...

We investigate the local existence, finite time blow-up and global existence of sign-changing solutions to inhomogeneous parabolic system with space-time forcing terms $$ u_t-\Delta u =|v|^{p}+t^\sigma w_1(x),\,\, v_t-\Delta v =|u|^{q}+t^\gamma w_2(x),\,\, (u(0,x),v(0,x))=(u_0(x),v_0(x)), where $t>0$, $x\in \mathbb{R}^N$, $N\geq 1$, $p,q>1$, $\sigma,\gamma>-1$, $\sigma,\gamma\neq0$, $w_1,w_2\no...

purpose post exercise proteinuria and increased urinary gamma-glutamyl transferase (ggt) levels can be indicative of exercise-induced renal damage. the aim of this investigation is to study the effect of one session of intensive training on renal damage markers and compare their values to those 6 hours after training. methods in this cross-sectional study with pre- and post-test design, 10 elit...

We introduce a fast algorithm to compute the Ramanujan-Deninger gamma function and its logarithmic derivative at positive values. Such an allows us greatly extend numerical investigations about Euler-Kronecker constants $\mathfrak{G}_q$, $\mathfrak{G}_q^+$ $M_q=\max_{\chi\ne \chi_0} \vert L^\prime/L(1,\chi)\vert$, where $q$ is odd prime, $\chi$ runs over primitive Dirichlet characters $\bmod\ q...

Motivated by Harish-Chandra theory, we construct, starting from a simple CDD-pole S-matrix, a hierarchy of new S-matrices involving ever “higher” (in the sense of Barnes) gamma functions. These new S-matrices correspond to scattering of excitations in ever more complex integrable models. From each of these models, new ones are obtained either by “q-deformation”, or by considering the Selberg-ty...

Components of nonlinear capacitance, or charge movement, were localized in the membranes of frog skeletal muscle fibers by studying the effect of 'detubulation' resulting from sudden withdrawal of glycerol from a glycerol-hypertonic solution in which the muscles had been immersed. Linear capacitance was evaluated from the integral of the transient current elicited by imposed voltage clamp steps...

In orbifold vacua containing an $S^q/\Gamma$ factor, we compute the relative order of scale separation, $r$, defined as ratio eigenvalue lowest-lying $\Gamma$-invariant state scalar Laplacian on $S^q$, to state. For $q=2$ and $\Gamma$ finite subgroup $SO(3)$, or $q=5$ $SU(3)$, maximal separation that can be achieved is $r=21$ $r=12$, respectively. smooth $S^5$ orbifolds, $r=4.2$. Methods from i...