A problem of great interest in optimization is to minimize a sum of two closed, proper, and convex functions where one is smooth and the other has a …

Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear const…

Calibration parameters in deterministic computer experiments are those attributes that cannot be measured or available in physical experiments. Kenne…

Multivariate problems are typically governed by anisotropic features such as edges in images. A common bracket of most of the various directional rep…

A weak turbulence theory is derived for magnetohydrodynamics under rapid rotation and in the presence of a large-scale magnetic field. The angular ve…

We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimension…

Coherence lengths of one particle states described by quantum wave functions are studied. We show that one particle states in various situations are …

The theory of confinement and deconfinement is discussed as based on the properties of the QCD vacuum. The latter are described by field correlators …

Heterogeneity is often natural in many contemporary applications involving massive data. While posing new challenges to effective learning, it can pl…

In this paper two types of multgrid methods, i.e., the Rayleigh quotient iteration and the inverse iteration with fixed shift, are developed for solv…

Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given mat…

The hierarchical triple body approximation has useful applications to a variety of systems from planetary and stellar scales to supermassive black ho…

The present paper develops an optimal linear quadratic boundary controller for $2\times2$ linear hyperbolic partial differential equations (PDEs) wit…

We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide gen…

We study locking of the modulation frequency of a relative periodic orbit in a general $S^1$-equivariant system of ordinary differential equations un…

There has been an increase in the use of resilient control algorithms based on the graph theoretic properties of $r$- and $(r,s)$-robustness. These a…

The Nambu bracket was first proposed as a generalization of the Poisson bracket for the canonical formulation of physical systems. In particular, the Nambu bracket and its generalizations found its natural applications to systems involving extended …

Nambu proposed an extension of dynamical system through the introduction of a new bracket (Nambu bracket) in 1973. This article is a short review of …

Let (fλ)λ∈Λ be a holomorphic family of rational maps of degree d≥2 on P1 with dim(Λ)=m. Let ωΛ be a Kähler form on Λ. Assume that c1,…,ck are marked critical points and let T1,…,Tk be their respective bifurcation currents (see Section 2.1).

In the moduli space of degree d polynomials, we prove the equidistribution of postcritically finite polynomials toward the bifurcation measure. More …

Inspired by the construction of the Gribov-Zwanziger action in the Landau gauge, we introduce a quark model exhibiting both confinement and chiral sy…

In this paper, a new approach based on convex analysis is introduced to solve the $H_\infty$ problem for discrete-time nonlinear stochastic systems. …

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