We consider trilayer ${\mathrm{F}}_{1}{\mathrm{F}}_{2}{\mathrm{F}}_{3}$ Josephson junctions that are finite in two dimensions and have arbitrary magnetizations each ferromagnet ${\mathrm{F}}_{i}\phantom{\rule{0.28em}{0ex}}(i=1,2,3)$. The trilayers sandwiched between $s$-wave superconductors with a macroscopic phase difference $\mathrm{\ensuremath{\Delta}}\ensuremath{\varphi}$. Our results revea...

Let G be a finite group and $$\varphi (G)=|\{a\in \mid o(a)=\exp (G)\}|$$ , where o(a) denotes the order of in $$\exp (G)$$ exponent G. Under natural hypothesis, this note we determine groups such that $$\forall \, H,K\le G$$ $$H\subseteq K$$ implies (H)\mid \varphi (K)$$ . This partially answers Problem 5.4 [6].

‎In this paper, based on [A. Razani, V. Rako$check{c}$evi$acute{c}$ and Z. Goodarzi, Nonself mappings in modular spaces and common fixed point theorems, Cent. Eur. J. Math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $T$ in the modular space $X_rho$ is presented. Moreover, we study a new version of Krasnoseleskii's fixed point theorem for $S+T$, where $T$ is a cont...

We obtain two fixed point theorems for a kind of $varphi $-contractions incomplete fuzzy metric spaces, which are applied to easily deduceintuitionistic versions that improve and simplify the recent results of X.Huang, C. Zhu and X. Wen.

Abstract Let $$\mathbb {D}$$ D denote the unit disk of complex plane and let $$\mathcal {A}^2(\mathbb {D})$$ A 2 ( ) be Bergman space that consists those analytic functions on are integrable squar...

Let $\mathcal{X}$ be a separable Hilbert space with norm $\|\cdot\|$ and let $T>0$. $Q$ linear, self-adjoint, positive, trace class operator on $\mathcal{X}$, $F:\mathcal{X}\rightarrow \mathcal{X}$ (smooth enough) function $W(t)$ $\mathcal{X}$-valued cylindrical Wiener process. For $\alpha\in [0,1/2]$ we consider the $A:=-(1/2)Q^{2\alpha-1}:Q^{1-2\alpha}(\mathcal{X})\subseteq \mathcal{X}\righta...