In this paper we impose distinct restrictions on the moduli of zeros p(z)=n∑v=0avzvp(z)=∑v=0navzv and investigate dependence ∥p(Rz)−p(σz)∥‖p(Rz)−p(σz)‖, R>σ≥1R>σ≥1 MαMα Mα+πMα+π, where Mα=max1≤k≤n|p(ei(α+2kπ)/n)|Mα=max1≤k≤n|p(ei(α+2kπ)/n)| certain coefficients p(z)p(z). This comprises several results, which in particular yields some classical polynomial inequalities as special cas...

In this article, we study the existence of solutions a parabolic-elliptic system partial differential equations describing behaviour biological species “ u $$ ” and chemical stimulus v in bounded regular domain ? \Omega ? N {\mathbb{R}}^N . The equation for is parabolic with nonlinear second order term chemotaxis type flux limitation as ? ? div ( | ? p 2 ) , -\chi \operatorname{div}\lef...

The dipolar cycloaddition reactivity of N-(1-naphthy1)-1,4- benzoquinoneimine N-oxide and N-phenyl-1,4- naphthoquinoneimine Noxide are investigated, The latter gives the expected adducts with common dipolarophiles such as acrylonitryle, methyl methacrylate, dimethylacetylene dicarboxylate and N-phenylmaleimide. The reactivity of the former nitrone is found to be minimal. It undergoes, how...

This paper deals with the following degenerate fractional Kirchhoff-type system magnetic fields and critical growth: $$\begin{aligned} \left\{ \begin{array}{lll} -\mathfrak {M}(\Vert u\Vert _{s,A}^2)[(-\Delta )^s_Au+u] = G_u(|x|,|u|^2,|v|^2) \\ \quad +\left( \mathcal {I}_\mu *|u|^{p^*}\right) |u|^{p^*-2}u \ &{}\text{ in }\,\,\mathbb {R}^N,\\ \mathfrak v\Vert _{s,A})[(-\Delta )^s_Av+v] G_v(|x|,|...

Let P (N, V) denote the vector space of polynomials of maximal degree less than or equal to N in V independent variables. This space is preserved by the enveloping algebra generated by a set of linear, differential operators representing the Lie algebra gl(V + 1). We establish the counterpart of this property for the vector space P (M, V) ⊕ P (N, V) for any values of the integers M, N, V. We sh...

Se zvy??uj?­c?­m se pod?­lem st??rnouc?­ populace p??ib??v?? star???­ch osob s poruchami pamÄ?ti. Poruchy pamÄ?ti ve st?????­ mohou b??t prvn?­m p???­znakem Alzheimerovy nemoci, ale tak?Š ??ady jin??ch onemocnÄ?n?­. K rychl?Šmu a snadn?Šmu vy??et??en?­ slou?ž?­ dva inovativn?­ p??vodn?­ česk?Š testy - Amnesia Light and Brief Assessment (ALBA) Pojmenov??n?­ obr??zk?? jejich vybaven?­ (POBAV), k...