The paper deals with the homogenization of a magneto-elastodynamics equation satisfied by displacement $$u_\varepsilon $$ an elastic body which is subjected to oscillating magnetic field $$B_\varepsilon generating Lorentz force $$\partial _t u_\varepsilon \times B_\varepsilon . When only depends on time or space, oscillations induce increase mass in homogenized equation. More generally, when ti...

Let $$\pi :M\rightarrow B$$ be a Riemannian submersion of two compact smooth manifolds, B is connected. $$M(\varepsilon )$$ denote the manifold M equipped with new metric which obtained from original one by multiplying $$\varepsilon $$ along vertical subspaces (i.e. fibers) and keeping unchanged (orthogonal to them) horizontal subspaces. $$V_i(M(\varepsilon ))$$ ith intrinsic volume. The main r...

We consider a conservation law model of traffic flow, where the velocity each car depends on weighted average density $\rho$ ahead. The averaging kernel is exponential type: $w_\varepsilon (s)=\varepsilon^{-1} e^{-s / \varepsilon}$. For any decreasing function $v$, we prove that, as $\varepsilon \to 0$, limit solutions to nonlocal equation coincides with unique entropy-admissible solution scala...

In 1991 De Giorgi conjectured that, given $\lambda >0$, if $\mu_\varepsilon$ stands for the density of Allen-Cahn energy and $v_\varepsilon$ represents its first variation, then $\int [v_\varepsilon^2 + \lambda] d\mu_\varepsilon$ should $\Gamma$-converge to $c\lambda \mathrm{Per}(E) k \mathcal{W}(\Sigma)$ some real constant $k$, where $\mathrm{Per}(E)$ is perimeter set $E$, $\Sigma=\partial E$,...

This paper investigates the propreties of persistence diagrams stemming from almost surely continuous random processes on [0, t]. We focus our study two variables which together characterize barcode: number points diagram inside a rectangle $$]\!-\!\infty ,x]\times [x+\varepsilon ,\infty [$$ , $$N^{x,x+\varepsilon }$$ and bars length $$\ge \varepsilon $$ $$N^\varepsilon . For with strong Markov...

List-decodability of Reed–Solomon codes has received a lot attention, but the best-possible dependence between parameters is still not well-understood. In this work, we focus on case where list-decoding radius form $r=1-\varepsilon $ ...

In this note, we consider the homogenization of compressible Navier-Stokes equations in a periodically perforated domain $\mathbb{R}^3$. Assuming that particle size scales like $\varepsilon^3$, where $\varepsilon>0$ is their mutual distance, and Mach number decreases fast enough, show limit $\varepsilon\to 0$, velocity density converge to solution incompressible with Brinkman term. We strongly ...

Let $u^\varepsilon$ and $u$ be viscosity solutions of the oscillatory Hamilton-Jacobi equation its corresponding effective equation. Given bounded, Lipschitz initial data, we present a simple proof to obtain optimal rate convergence $\mathcal{O}(\varepsilon)$ $u^\varepsilon \rightarrow u$ as $\varepsilon 0^+$ for large class convex Hamiltonians $H(x,y,p)$ in one dimension. This includes from cl...

We consider the following Schr\"odinger-Bopp-Podolsky system in $\mathbb R^{3}$ $$\left\{ \begin{array}{c} -\varepsilon^{2} \Delta u + V(x)u \phi = f(u)\\ \varepsilon^{4} \Delta^{2}\phi 4\pi\varepsilon u^{2}\\ \end{array} \right.$$ where $\varepsilon > 0$ with $ V:\mathbb{R}^{3} \rightarrow \mathbb{R}, f:\mathbb{R} \mathbb{R}$ satisfy suitable assumptions. By using variational methods, we pr...