We describe the emergence of topological singularities in periodic media within Ginzburg-Landau model and core-radius approach. The energy functionals both models are denoted by $E_{\varepsilon,\delta}$, where $\varepsilon$ represent coherence length (in model) or size approach) $\delta$ denotes periodicity scale. carry out $\Gamma$-convergence analysis $E_{\varepsilon,\delta}$ as $\varepsilon\...

We establish uniform error bounds of an exponential wave integrator Fourier pseudospectral (EWI-FP) method for the long-time dynamics nonlinear Klein--Gordon equation (NKGE) with a cubic nonlinearity whose strength is characterized by $\varepsilon^2$ $\varepsilon \in (0, 1]$ dimensionless parameter. When $0 < \varepsilon \ll 1$, problem equivalent to NKGE small initial data (and $O(1)$ nonlinea...

In this paper, we prove some results on characterization of $varepsilon$-simultaneous approximations of downward sets in vector lattice Banach spaces. Also, we give some results about simultaneous approximations of normal sets.

In $L_2(\mathbb{R}^d;\mathbb{C}^n)$, we consider a selfadjoint matrix strongly elliptic second order differential operator $\mathcal{A}_\varepsilon$, $\varepsilon >0$. The coefficients of the $\mathcal{A}_\varepsilon$ are periodic and depend on $\mathbf{x}/\varepsilon$. We study behavior $\mathcal{A}_\varepsilon ^{-1/2}\sin (\tau \mathcal{A}_\varepsilon ^{1/2})$, $\tau\in\mathbb{R}$, in small p...

Abstract We deal with Dirichlet problems of the form { ? ? u + f ( stretchy="false">)</m:mo...

Cockcroft S. Monomeric IgE stimulates NFAT translocation into the nucleus, a rise in cytosol Ca2+, degranulation, and membrane ruffling in the cultured rat basophilic leukemia-2H3 mast cell line. J Immunol 2004; 172: 4048–4058. 5 Nunomura S, Gon Y, Yoshimaru T, et al. Role of the Fc (varepsilon) RI (b)-chain ITAM as a signal regulator for mast cell activation with monomeric IgE. Int Immunol 200...

We establish Ramanujan-style congruences modulo certain primes $$\ell $$ between an Eisenstein series of weight k, prime level p and a cuspidal newform in the $$\varepsilon -eigenspace Atkin–Lehner operator inside space cusp forms k for $$\Gamma _0(p)$$ . Under mild assumption, this refines result Gaba–Popa. use these recent work Ciolan, Languasco third author on Euler–Kronecker constants, to q...

In this article, we investigate effective sketching schemes via sparsification for high dimensional multilinear arrays or tensors. More specifically, propose a novel tensor algorithm that retains subset of the entries in judicious way, and prove it can attain given level approximation accuracy terms spectral norm with much smaller sample complexity when compared existing approaches. particular,...