We consider the homogenization of compressible Navier-Stokes-Fourier equations in a randomly perforated domain $\mathbb{R}^3$. Assuming that particle size scales like $\varepsilon^\alpha$, where $\varepsilon>0$ is their mutual distance and $\alpha>3$, we show limit $\varepsilon\to 0$, velocity, density, temperature converge to solution same system. follow methods Lu Pokorn\'{y} [https://doi.org...

in this paper,  we provide two different kinds of fixed pointtheorems in  fuzzy metric spaces. the first kind is for the fuzzy$varepsilon$-contractive type mappings and  the second kind is forthe fuzzy order $psi$-contractive type mappings. they improve thecorresponding  conclusions in the literature.

In this paper, we determine the $L^p(\mathbb{R})\times L^q(\mathbb{R})\rightarrow L^r(\mathbb{R})$ boundedness of bilinear Hilbert transform $H_{\gamma}(f,g)$ along a convex curve $\gamma$ $$H_{\gamma}(f,g)(x):=\mathrm{p.\,v.}\int_{-\infty}^{\infty}f(x-t)g(x-\gamma(t)) \,\frac{\textrm{d}t}{t},$$ where $p$, $q$, and $r$ satisfy $\frac{1}{p}+\frac{1}{q}=\frac{1}{r}$, $r>\frac{1}{2}$, $p>1$, $q>1$...

In this paper we study connections between Besov spaces of functions on a compact metric space $Z$, equipped with doubling measure, and the Newton--Sobolev uniform domain $X_\varepsilon$. This is obtained as uniformization (Gromov) hyperbolic filling $Z$. To do so, construct family fillings in style work Bonk Kleiner Bourdon Pajot. Then for each parameter $\beta>0$ lift $\mu_\beta$ measure $\nu...

We consider the question introduced by [16] of identifying all $$\varepsilon $$ -optimal arms in a finite stochastic multi-armed bandit with Gaussian rewards. give two lower bounds on sample complexity any algorithm solving problem confidence at least $$1-\delta . The first, unimprovable asymptotic regime, motivates design Track-and-Stop strategy whose average is asymptotically optimal when ris...

In this paper, we shall study the convergence of Taylor approximations for backward Loewner differential equation (driven by Brownian motion) near origin. More concretely, whenever initial condition (which lies in upper half plane) is small and has form $Z_{0} = \varepsilon i$, show these exhibit an $O(\varepsilon)$ error provided time horizon $\varepsilon^{2+\delta}$ $\delta > 0$. Statements t...

The response of a semi-infinite ocean to slowly travelling atmospheric perturbation crossing the coast provides simple example breakdown nearly geostrophic balance induced by boundary. We examine this in linear shallow-water model at small Rossby number $\varepsilon \ll 1$. Using matched asymptotics we show that long Kelvin wave, with $O(\varepsilon^{-1})$ length scale and $O(\varepsilon)$ ampl...

In this paper we study stationary incompressible Newtonian fluid flow in a thin porous media. The media under consideration is bounded perforated 3D domain confined between two parallel plates. description of the includes small parameters: ε representing distance plates and $a_\varepsilon$ connected to microstructure such that ≪ $a_\varepsilon \ll \varepsilon$ . We consider classical setting me...

We present the best known separation between tree-like and general resolution, improving on the recent $exp(n^{\varepsilon}$ separation of [BEGJ98]. This is done by constructing a natural family of contradictions, of size $n$, that have $O(n)$-size resolution refutations, but only $exp(\Omega(n / log n))$size tree-like refutations. This result implies that the most commonly used automated theor...