We look for solutions to the Schr\"{o}dinger-Poisson-Slater equation $$- \Delta u + \lambda - \gamma (|x|^{-1} * |u|^2) a |u|^{p-2}u = 0 \quad \text{in} \mathbb{R}^3, $$ which satisfy \begin{equation*} \int_{\mathbb{R}^3}|u|^2 \, dx c \end{equation*} some prescribed $c>0$. Here $ \in H^1(\mathbb{R}^3)$, $\gamma \mathbb{R},$ \mathbb{R}$ and $p (\frac{10}{3}, 6]$. When >0$ $a > 0$, both in Sobole...

Abstract We consider a one-dimensional integral inequality of Moser type: set $$\begin{aligned} \quad J_c(v) = \int _{0}^1 {\textrm{e}}^{c(s) v^2(s)} ds \hbox { and } \sup _{ \{\int _0^1 |v'|^2 1, v(0) 0\}} \end{aligned}$$ J c </mml:ms...

Let $[\, \cdot\,]$ be the floor function. In this paper, we prove that when $1<c<\frac{16559}{15276}$, then every sufficiently large positive integer $N$ can represented in form \begin{equation*} N=[p^c_1]+[p^c_2]+[p^c_3]\,, \end{equation*} where $p_1,p_2,p_3$ are primes, such $p_1=x^2 + y^2 +1$.

We consider a 2D model of an autophoretic particle in which the has circular shape and emits/absorbs solute that diffuses is advected by suspending fluid. Beyond certain emission/absorption rate (characterized dimensionless P\'eclet number, $Pe$) known to undergo bifurcation from non motile state, with different trajectories, going straight chaotic motion progressively increasing $Pe$. From ful...

the average distance of a vertex $v$ of a connected graph $g$is the arithmetic mean of the distances from $v$ to allother vertices of $g$. the proximity $pi(g)$ and the remoteness $rho(g)$of $g$ are defined as the minimum and maximum averagedistance of the vertices of $g$. in this paper we investigate the difference between proximity or remoteness and the classical distanceparameters diameter a...

This note investigates modules having quasi-injective and duo submodules. We introduce a new generalization of C_1-module. The main method that was adopted in this is how to obtain submodule N M the characteristic Quasi-injective. investigate relationship between pseudo-injective module Quasi-injective property Finally, we anti-hopfian module.

The nonlocal chiral effective theory is applied to investigate the electromagnetic and strange form factors of nucleon. bubble tadpole diagrams are included in calculation. With contributions from diagrams, obtained close results without these as long low energy constants $c_1$ $c_2$ properly chosen, while magnitudes become larger. Both still good agreement with experimental data.