Let $A(G)$ and $D(G)$ be the adjacency matrix degree of $G$, respectively. For any real $\alpha \in [0,1]$, Nikiforov defined $A_{\alpha}(G)$ as \[ A_{\alpha}(G) = \alpha D(G) + (1-\alpha) A(G). \] In this paper, we generalize some previous results about $A_{1/2}$-spectral radius bicyclic graphs with a given sequence. Furthermore, characterize all extremal which have largest $A_{\alpha}$-spectr...

Let G $G$ be a finite group admitting coprime automorphism α $\alpha$ . J ( ) $J_G(\alpha )$ denote the set of all commutators [ x , ] $[x,\alpha ]$ where $x$ belongs to an -invariant Sylow subgroup We show that $[G,\alpha is soluble or nilpotent if and only any generated by pair elements orders from nilpotent, respectively.

for all $a,b>0$, the following two optimal inequalities are presented: $h^{alpha}(a,b)l^{1-alpha}(a,b)geq m_{frac{1-4alpha}{3}}(a,b)$ for $alphain[frac{1}{4},1)$, and $ h^{alpha}(a,b)l^{1-alpha}(a,b)leq m_{frac{1-4alpha}{3}}(a,b)$ for $alphain(0,frac{3sqrt{5}-5}{40}]$. here, $h(a,b)$, $l(a,b)$, and $m_p(a,b)$ denote the harmonic, logarithmic, and power means of order $p$ of two positive numbers...

Abstract So-called respectively readings have posed serious challenges for theories of syntax and semantics. Sentences like George and Martha respectively denounced and were denounced by the governor (McCawley 1998) show that although the conjoined verbal expressions share the same syntactic subject, they do not predicate that subject in the same way; George (not Martha) denounced the governor,...

We have measured plasma volume and cardiac index in rats after 50% isovolemic exchange transfusion with human hemoglobin cross-linked between the alpha-chains with bis(3,5-dibromosalicyl)fumarate (alpha alpha Hb) and with bovine hemoglobin modified with polyethylene glycol (PEGHb). alpha alpha Hb and PEGHb differ in colloid osmotic pressure (23.4 and 118.0 Torr, respectively), oxygen affinity (...

The shape of a sessile drop on horizontal substrate depends upon the Bond number $Bo$ and contact angle $\alpha$ . Inspired by puddle approximations at large (Quéré, Rep. Prog. Phys. , vol. 68, 2005, p. 2495), we address here limit small angles fixed volume arbitrary It readily leads to pancake approximation, where height radius scale as $\alpha ^{-1/2}$ respectively, with capillary forces bein...