Related papers: The slope of v-function and Waldschmidt constant

Let $K_n$ be the convex hull of i.i.d. random variables distributed according to the standard normal distribution on $\R^d$. We establish variance asymptotics as $n \to \infty$ for the re-scaled intrinsic volumes and $k$-face functionals of…

Motivated by the extensive application of approximate gradients in machine learning and optimization, we investigate inexact subgradient methods subject to persistent additive errors. Within a nonconvex semialgebraic framework, assuming…

We study the Floquet Hamiltonian: -i omega d/dt + H + V(t) as depending on the parameter omega. We assume that the spectrum of H is discrete, {h_m (m = 1..infinity)}, with h_m of multiplicity M_m. and that V is an Hermitian operator,…

Let $K$ be a field, $I\subset R=K[x_1,\dots,x_n]$ and $J\subset T=K[y_1,\dots,y_m]$ be graded ideals. Set $S=R\otimes_KT$ and let $L=IS+JS$. The behaviour of the $\text{v}$-function $\text{v}(L^k)$ in terms of the $\text{v}$-functions…

Using time-series of stereoscopic particle image velocimetry data, we study the response of a turbulent von K\'{a}rm\'{a}n swirling flow to a continuous breaking of its forcing symmetry. Experiments are carried over a wide Reynolds number…

In this paper, we study the asymptotic behavior of BV functions in complete metric measure spaces equipped with a doubling measure supporting a $1$-Poincar\'e inequality. We show that at almost every point $x$ outside the Cantor and jump…

This paper derives non-asymptotic error bounds for nonlinear stochastic approximation algorithms in the Wasserstein-$p$ distance. To obtain explicit finite-sample guarantees for the last iterate, we develop a coupling argument that compares…

We shall study the following initial value problem: \begin{equation}{\bf i}\partial_t u - \Delta u + V(x) u=0, \hbox{} (t, x) \in {\mathbf R} \times {\mathbf R}^n, \end{equation} $$u(0)=f,$$ where $V(x)$ is a real short--range potential,…

We study the stability and nonlinear local dynamics of spectrally stable periodic wave trains of the Korteweg-de Vries / Kuramoto-Sivashinsky equation when subjected to classes of periodic perturbations. It is known that for each…

This note provides an effective bound in the Gauss-Kuzmin-L\'evy problem for some Gauss type shifts associated with nearest integer continued fractions, acting on the interval $I_0=[0,\frac{1}{2}]$ or $I_0=[-\frac{1}{2},\frac{1}{2}]$. We…

We formulate a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain setting in the Kelvin's-Voigt's rheology where the viscosity stress tensor complies with the principle of time-continuous frame-indifference.…

Suppose that $\{S_n,\ n\geq0\}$ is an asymptotically stable random walk. Let $g$ be a positive function and $T_g$ be the first time when $S_n$ leaves $[-g(n),\infty)$. In this paper we study asymptotic behaviour of $T_g$. We provide…

Based on the nonlinear steepest descent method of Deift and Zhou for oscillatory Riemann--Hilbert problems and the Dbar approach, the long-time asymptotic behavior of solutions to the fifth-order modified Korteweg-de Vries equation on the…

Let $X=\{X_n: n\in\mathbb{N}\}$ be a long memory linear process in which the coefficients are regularly varying and innovations are independent and identically distributed and belong to the domain of attraction of an $\alpha$-stable law…

Let $(A,\mathfrak{m})$ be an analytically unramified formally equidimensional Noetherian local ring with $\ depth \ A \geq 2$. Let $I$ be an $\mathfrak{m}$-primary ideal and set $I^*$ to be the integral closure of $I$. Set $G^*(I) =…

We investigate the asymptotic behavior of a perturbation around a spatially non homogeneous stable stationary state of a one-dimensional Vlasov equation. Under general hypotheses, after transient exponential Landau damping, a perturbation…

In this paper, we study the following fully nonlinear elliptic equations \begin{equation*} \left\{\begin{array}{rl} \left(S_{k}(D^{2}u)\right)^{\frac1k}=\lambda f(-u) & in\quad\Omega \\ u=0 & on\quad \partial\Omega\\ \end{array} \right.…

In this paper, we are interested in the nonlinear Rayleigh-Taylor instability for the gravity-driven incompressible Navier-Stokes equations with Navier-slip boundary conditions around a smooth increasing density profile $\rho_0(x_2)$ in a…

This article is concerned with the metric study of a construction of G\'erardin of the action of the boundary at infinity of the space of norms on a non-Archimedean vector space, and its generalisation to graded algebras. Namely, given…

In this paper we continue the work that we began in arXiv:1912.07537. Given $1<p<N$, two measurable functions $V\left(r \right)\geq 0$ and $K\left(r\right)> 0$, and a continuous function $A(r) >0\ (r>0)$, we consider the quasilinear…