begin{abstract} the relations between the spectrum of the matrix $q+r$ and the spectra of the matrices $(gamma + delta)q+(alpha + beta)r-qr-rq$, $qr-rq$, $alpha beta r-qrq$, $alpha rqr-(qr)^{2}$, and $beta r-qr$ have been given on condition that the matrix $q+r$ is diagonalizable, where $q$, $r$ are ${alpha, beta}$-quadratic matrix and ${gamma, delta}$-quadratic matrix, respectively, of order $...

Let $\Omega\subset\mathbb{R}^2$ be a smooth bounded domain with $0\in\partial\Omega$. In this paper, we prove that for any $\beta\in(0,1)$, the supremum $$\sup_{u\in W^{1,2}(\Omega), \int_\Omega u dx=0, \int_\Omega|\nabla u|^2dx\leq1}\int_\Omega \frac{e^{2\pi(1-\beta) u^2}}{|x|^{2\beta}}dx$$ is finite and can attained. This partially generalizes well-known work of Alice Chang Paul Yang (J. Diff...

In this paper, covalent immobilization of beta amylase enzyme on the surface of modified magnetic nano particles (ZnFe2O4@SiO2-NH2) is reported. For doing so, at first, the magnetic nanoparticles of ZnFe2O4 were synthesized by chemical co-precipitation method and then tetraethyl orthosilicate (TEOS) and 3-aminopropyltriethoxy sil...

We study the elliptic system \begin{equation*} \begin{cases} -\Delta u_1 - \kappa_1u_1 = \mu_1|u_1|^{p-2}u_1 + \lambda\alpha|u_1|^{\alpha-2}|u_2|^\beta u_1, \\ u_2 \kappa_2u_2 \mu_2|u_2|^{p-2}u_2 \lambda\beta|u_1|^\alpha|u_2|^{\beta-2}u_2, u_1,u_2\in D^{1,2}_0(\Omega), \end{cases} \end{equation*} where $\Omega$ is a bounded domain in $\mathbb R^N$, $N\geq 3$, $\kappa_1,\kappa_2\in\mathbb R$, $\...

Introduction: In order to study the alterations of beta 1 and 2 integrins mRNA level in rat lumbar spinal cord following the induction of chronic pain and its effect on the development of tolerance to morphine analgesia, we examined the level of expression of these genes in the presence of chronic pain, which is an inhibitor of morphine tolerance. We used induction of chronic pain alone 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...