We investigate the nonequilibrium dynamics following a quench to zero temperature of nonconserved Ising model with power-law decaying long-range interactions $\ensuremath{\propto}1/{r}^{d+\ensuremath{\sigma}}$ in $d=2$ spatial dimensions. The zero-temperature coarsening is always special interest among processes, because often peculiar behavior observed. provide estimates exponents, viz., growt...

Abstract For a bounded 2D planar domain Ω, we investigate the impact of geometry on oscillatory translational instabilities N -spot equilibrium solutions for singularly perturbed Schnakenberg reaction-diffusion system with activator-inhibitor diffusivity ratio. An is characterized by an activator concentration that exponentially small ev...

In this paper, we introduce the notion of (?,F)-contractive multi-valued mappings in setting uniform spaces. Some fixed point and common theorems for endowed with spaces are established. The existence uniqueness points by using structure is discussed detail. We set up a non-trivial example elaboration these novel results. eventually, an application also provided to elaborate applicability our

It is shown that if $\gamma: [a,b] \to S^2$ $C^3$ with $\det(\gamma, \gamma', \gamma'') \neq 0$, and $A \subseteq \mathbb{R}^3$ a Borel set, then $\dim \pi_{\theta} (A) \geq \min\left\{ 2,\dim A, \frac{ \dim A}{2} + \frac{3}{4} \right\}$ for a.e. $\theta \in [a,b]$, where $\pi_{\theta}$ denotes projection onto the orthogonal complement of $\gamma(\theta)$ ``$\dim$'' refers to Hausdorff dimensio...

Let $G$ be a locally compact abelian metric group with Haar measure $\lambda $ and $\hat{G}$ its dual $\mu ,$ ( G) is finite. Assume that$~1<p_{i}<\infty $, $p_{i}^{\prime }=\frac{ p_{i}}{p_{i}-1}$, $( i=1,2,3) $\theta \geq 0$. L^{(p_{i}^{\prime },\theta }( small Lebesgue spaces. A bounded measurable function $m( \xi ,\eta ) defined on $\hat{G}\times \hat{G}$ said to bilinear multiplier of type...

‎‎A natural generalization of two dimensional cyclic code ($T{TDC}$) is two dimensional skew cyclic code‎. ‎It is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $R_n:=F[x,y;rho,theta]/_l$‎. ‎In this paper we characterize the left ideals of the ring $R_n$ with two methods and find the generator matrix for two dimensional s...

The main purpose of this article is to improve, generalize and complement some recently established results for Perov’s type F-contractions. In our approach, we use only the property (F1) Wardowski while other authors employed all three conditions. Working with fact that function F strictly increasing on 0,+∞m, obtain as a consequence new families contractive conditions in realm vector-valued m...

Motivated by the discovery that the eighth root of the theta series of the E 8 lattice and the 24th root of the theta series of the Leech lattice both have integer coefficients, we investigate the question of when an arbitrary element f ∈ Z[[x]]

Objective: This study aimed to evaluate the effect of neurofeedback training on improving&nbsp;sustained attention of veterans with posttraumatic stress disorder (PTSD). Methods: The research design is quasi-experimental with pretest-posttest and control group.&nbsp;The study population consisted of the veterans with PTSD who were hospitalized in psychiatric&nbsp;wards. Purposeful sampling met...