This paper studies the asymptotic stability of shock profiles and rarefaction waves under space-periodic perturbations for one-dimensional convex scalar viscous conservation laws. For profile, we show that solution approaches background profile with a constant shift in $ L^\infty(\mathbb{R}) norm at exponential rates. The new phenomena contrasting to case localized is cannot be determined by in...

We prove a continuity inheritance property for super- and sub-additive transformations of non-negative continuous multivariate functions defined on the domain of all non-negative points and vanishing at the origin. As a corollary of this result we obtain that super- and sub-additive transformations of continuous aggregation functions are again continuous aggregation functions.

Suppose q is a prime power and f ∈ Fq[x] is a univariate polynomial with exactly t nonzero terms and degree <q−1. To establish a finite field analogue of Descartes’ Rule, Bi, Cheng and Rojas (2013) proved an upper bound of 2(q − 1) t−2 t−1 on the number of cosets in F∗ q needed to cover the roots of f in F∗ q . Here, we give explicit f with root structure approaching this bound: For q a t power...

Eye movements are crucial in understanding complex scenes. By predicting where humans look in natural scenes, we can understand how they percieve scenes and priotriaze information for further high-level processing. Here, we study the effect of a particular type of scene structural information known as vanishing point and show that human gaze is attracted to vanishing point regions. We then buil...

We prove the instability of $d$-dimensional conformal field theories (CFTs) having in operator-product expansion two fundamental fields a primary operator scaling dimension $h=d/2+i r$, with non-vanishing $ r\in\mathbb{R}$. From an AdS/CFT point view, this corresponds to well-known tachyonic instability, associated violation Breitenlohner-Freedman bound AdS${}_{d+1}$; we derive it here directly...

In this paper, we consider how to formulate semiclassical problems in the context of AdS/CFT correspondence, based on proposal Compere and Marolf. Our prescription involves effective action with self-action term for boundary dynamical fields, which can be viewed as imposing mixed conditions gravity dual. We derive Einstein equations sourced by CFT stress-energy tensor. Analyzing perturbations h...

Aim of this paper is to review some basic ideas and recent developments in the theory of strictly hyperbolic systems of conservation laws in one space dimension. The main focus will be on the uniqueness and stability of entropy weak solutions and on the convergence of vanishing viscosity approximations. 2000 Mathematics Subject Classification: 35L60, 35L65.