The influence of the geometry domain on behavior generalized solutions Dirichlet problems for elliptic partial differential equations has been an important subject over a century. We investigate boundary variational $f$ prescribed mean curvature in $\Omega \subset \mathbb{R}^{2}$ near point $\mathcal{O} \in \partial \Omega$ under different assumptions about $\partial each side $\mathcal{O}$. pr...

This paper is about the homogenization of linear elliptic operators in divergence form with stationary random coefficients that have only slowly decaying correlations. It deduces optimal estimates error from growth (extended) corrector. In line heuristics, there are transitions at dimension $d=2$, and for a correlation-decay exponent $\beta=2$; we capture correct power logarithms coming these t...

By exploiting an old idea first used by Pizzetti for the classical Laplacian, we introduce a notion of asymptotic average solutions making pointwise solvable every Poisson equation ${\mathcal {L}} u(x)=-f(x)$ with continuous data f, where {L}}$ is hypoelliptic linear partial differential operator positive semidefinite characteristic form.

is said to be universal in X with respect to rearrangements, if for any f ∈ X the members of (1.1) can be rearranged so that the obtained series ∑∞ k=1 fσ(k) converges to f by norm of X . Definition 1.2. The series (1.1) is said to be universal (in X) in the usual sense, if for any f ∈ X there exists a growing sequence of natural numbers nk such that the sequence of partial sums with numbers nk...

Algebraic attacks are relatively new and interesting subject in cryptanalysis. The algebraic attacks where introduced in [1], where several possible attack’s scenarios where given. The big attention was paid to deterministic scenarios of those. In this paper, probabilistic scenarios are studied. Conception of conditional correlation and partial higher order nonlinearity of Boolean function wher...

BACKGROUND Acyl-COA:cholesterol acyltransferase (ACAT) converts cholesterol to cholesteryl esters. The form of ACAT in macrophages, ACAT1, contributes to foam cell formation in the arterial wall and the development of atherosclerosis. Recent studies in a mouse model of atherosclerosis (the apolipoprotein E [apoE]-deficient mouse), however, have suggested that complete deficiency of ACAT1 activi...

We show that the main properties of fracton quasiparticles can be derived from a generalized covariant Maxwell-like action. Starting rank-2 symmetric tensor field ${A}_{\ensuremath{\mu}\ensuremath{\nu}}(x)$, we build partially rank-3 strength ${F}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}}(x)$ which obeys kind Bianchi identity. The most general action invariant under ``fracton'' transf...

"This work studies the initial boundary value problem for Petrovsky equation with nonlinear damping \begin{equation*} \frac{\partial ^{2}u}{\partial t^{2}}+\Delta ^{2}u-\Delta u^{\prime} +\left\vert u\right\vert ^{p-2}u+\alpha g\left( u^{\prime }\right) =\beta f\left( u\right) \text{ in }\Omega \times \left[ 0,+\infty \right[, \end{equation*} where $\Omega $ is open and bounded domain $\mathbb{...

— For a regular twistor D-module and for a given function f , we compare the nearby cycles at f =∞ and the nearby or vanishing cycles at τ = 0 for its partial Fourier-Laplace transform relative to the kernel e−τf .

The concept of slice regular function over the real algebra $$\mathbb {H}$$ quaternions is a generalization notion holomorphic complex variable. Let $$\varOmega \subset \mathbb be domain, i.e., non-empty connected open subset {H}=\mathbb {R}^4$$ . Suppose that $$\varOmega$$ intersects {R}$$ and invariant under rotations around A $$f:\varOmega \rightarrow if it class $$\mathcal {C}^1$$ and, for ...