Let $mathcal {A} $ and $mathcal {B} $ be C$^*$-algebras. Assume that $mathcal {A}$ is of real rank zero and unital with unit $I$ and $k>0$ is a real number. It is shown that if $Phi:mathcal{A} tomathcal{B}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $Phi(|A|^k)=|Phi(A)|^k $ for all normal elements $Ainmathcal A$, $Phi(I)$ is a projection, and there exists a posit...

Let X be a Spin manifold with boundary, such that the Spin structure is defined near the boundary by an almost complex structure, which is either strictly pseudoconvex or pseudoconcave (and hence contact). Using generalized Szego projectors, we define modified partial differential-Neumann boundary conditions, Reo, for spinors, which lead to subelliptic Fredholm boundary value problems for the S...

A system of polynomial ordinary differential equations (ode's) is specified via a vector of multivariate polynomials, or vector field, F. A safety assertion psi->[F]phi means that the system's trajectory will lie in a subset phi (the postcondition) of the state-space, whenever the initial state belongs to a subset psi (the precondition). We consider the case when phi and psi are algebraic varie...

let $mathcal {a} $ and $mathcal {b} $ be c$^*$-algebras. assume that $mathcal {a}$ is of real rank zero and unital with unit $i$ and $k>0$ is a real number. it is shown that if $phi:mathcal{a} tomathcal{b}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $phi(|a|^k)=|phi(a)|^k $ for all normal elements $ainmathcal a$, $phi(i)$ is a projection, and there exists a posit...

We discuss vacuum static, spherically symmetric asymptotically flat solutions of the generalized hybrid metric-Palatini theory gravity (generalized HMPG) suggested by Böhmer and Tamanini, involving both a metric $$g_{\mu\nu}$$ an independent connection $$\hat{\Gamma}_{\mu\nu}^{\alpha}$$ ; gravitational field Lagrangian is arbitrary function $$f(R,P)$$ two Ricci scalars, $$R$$ obtained from $$P$...

Let G be a noncompact semisimple Lie group with finite centre. $$X=G/K$$ the associated Riemannian symmetric space and assume that X is of rank one. The generalized spectral projections to Laplace-Beltrami operator are given by $$P_{\lambda }f =f*\Phi _{\lambda }$$ , where $$\Phi elementary spherical functions on X. In this paper, we prove an Ingham type uncertainty principle for }f$$ . Moreove...

A generalized tanh method has been proposed and discussed. This method has been employed for solving two well-known models of nonlinear equations, namely the Drinfeld-Sokolov (DS) system and PHI-four equation. The exact solutions of these models are obtained. Finally, some wave solutions are exhibited.