<p style='text-indent:20px;'>This work considers a pursuit-evasion model</p><p style='text-indent:20px;'><disp-formula><label/><tex-math id="FE1000">\begin{document}$\begin{equation} \left\{ \begin{split} &u_t = \Delta u-\chi\nabla\cdot(u\nabla w)+u(\mu-u+av),\\ &v_t v+\xi\nabla\cdot(v\nabla z)+v(\lambda-v-bu),\\ &w_t w-w+v,\\ &amp...

In this paper, we study the following class of nonlinear equations: $$\begin{aligned} -\Delta u+V(x) u = \left[ |x|^{-\mu }*(Q(x)F(u))\right] Q(x)f(u),\quad x\in \mathbb {R}^2, \end{aligned}$$where V and Q are continuous potentials, which can be unbounded or vanishing at infintiy, f(s) is a function, F(s) primitive f(s), \(*\) convolution operation \(0<\mu <2\). Assuming that nonlinearity has e...

The edge Szeged polynomial of a graph G is defined as Sze(G,x) = ( ) ( ) , u v m e m e e uv x = ∑ where mu(e) is the number of edges of G lying closer to u than to v and mv(e) is the number of edges of G lying closer to v than to u. In this paper the main properties of this newly proposed polynomial are investigated. We also compute this polynomial for some classes of well-known graphs. Finally...

This review provides alternatives to two well established theories regarding membrane energization by H(+) V-ATPases. Firstly, we offer an alternative to the notion that the H(+) V-ATPase establishes a protonmotive force (pmf) across the membrane into which it is inserted. The term pmf, which was introduced by Peter Mitchell in 1961 in his chemiosmotic hypothesis for the synthesis of ATP by H(+...

Quotient sets U/U = {u/u : u, u ∈ U} have been considered several times before in the MONTHLY [4], [5], [9]. We consider more general quotient sets U/V and we apply our results to certain simultaneous Diophantine equations with side constraints. In the following, we let R = (0,∞) denote the set of positive real numbers and N = {1, 2, . . .} the set of natural numbers. A subset S of R is said to...

The new ligand 6-mercapto-2(1H)-pyridone (H(2)PySO) has been prepared in good yield by reaction of 6-chloro-pyridin-2-ol with NaSH. Reaction of the salt K(2)PySO, generated in situ, with the appropriate complex [M(mu-Cl)(diolefin)](2) affords the tetranuclear complexes [M(4)(mu-PySO)(2)(diolefin)(4)] [M = Rh, diolefin = 1,5-cyclooctadiene (cod) (1), tetrafluorobenzobarralene (tfbb) (2); M = Ir,...

Two 14beta-p-nitrocinnamoyl derivatives of dihydrocodeinone, 14beta-(p-nitrocinnamoylamino)-7,8-dihydrocodeinone (CACO) and N-cyclopropylmethylnor-14beta-(p-nitrocinnamoylamino)- 7, 8-dihydrocodeinone (N-CPM-CACO), and the corresponding chlorocinnamoylamino analogs, 14beta-(p-chlorocinnamoylamino)-7, 8-dihydrocodeinone (CAM) and N-cyclopropylmethylnor-14beta-(p-chlorocinnamoylamino) -7, 8-dihyd...

Implications for Cabibbo universality based on progress in the study of semileptonic kaon and pion decays are discussed. Included recent updates experimental input along with improved radiative corrections, form factors, isospin-breaking effects. As a result, we obtain Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix element $|{V}_{us}|=0.22309(56)$ from ${K}_{\ensuremath{\ell}3}$ $(K\ensure...

Let $ {\mathbb {C}}^{n+1}_o$ denote the germ of {C}}^{n+1}$ at origin. $V$ be a hypersurface in and $W$ deformation over {C}}_{o}^{m}$ . Under hypothesis that is Newton non-degenerate deformation, this article we prove $\mu$ -constant if only admits simultaneous embedded resolution. This result gives lot information about , for example, topological triviality family fact natural morphism $(\ope...

This paper deals with a flux-limited chemotaxis-haptotaxis system nonlinear diffusion \begin{document}$ \begin{eqnarray*} \left\{ \begin{split}{} &amp;u_t = \nabla\cdot(D(u)\nabla u)-\chi\nabla\cdot(u|\nabla v|^{p-2}\nabla v)-\xi\nabla\cdot(u\nabla w)+\mu u(1-u-w), \\ &amp;v_t \Delta v-v+u, &amp;w_t -vw, \ \end{split} \right. \end{eqnarray*} $\end{document} in $ \Omega\times(0, \infty) $, where...