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Optimal TimeDependent Lower Bound On Density For Classical Solutions of 1D Compressible Euler Equations
(Indiana University Mathematics Journal, 2017)For the compressible Euler equations, even when the initial data are uniformly away from vacuum, solution can approach vacuum in infinite time. Achieving sharp lower bounds of density is crucial in the study of Euler ... 
Periodic Traveling Waves of the Regularized Short Pulse and Ostrovsky Equations: Existence and Stability
(Society for Industrial and Applied Mathematics, 2017)We construct various periodic traveling wave solutions of the Ostrovsky/HunterSaxton/short pulse equation and its KdV regularized version. For the regularized short pulse model with small Coriolis parameter, we describe ... 
Accounting for Model Error from Unresolved Scales in Ensemble Kalman Filters by Stochastic Parameterization
(American Meteorological Society, 20170823)The use of discretetime stochastic parameterization to account for model error due to unresolved scales in ensemble Kalman filters is investigated by numerical experiments. The parameterization quantifies the model error ... 
Noncentral limit theorem for the generalized Rosenblatt process
(Institute of Mathematical Statistics, 2017)We use techniques of Malliavin calculus to study the convergence in law of a family of generalized Rosenblatt processes Zγ with kernels defined by parameters γ taking values in a tetrahedral region Δ of $\RR^q$. We prove ... 
The determinant of the iterated Malliavin matrix and the density of a pair of multiple integrals
(Institute of Mathematical Statistics, 2017)The aim of this paper is to show an estimate for the determinant of the covariance of a twodimensional vector of multiple stochastic integrals of the same order in terms of a linear combination of the expectation of the ... 
Formation enthalpies for transition metal alloys using machine learning
(Formation enthalpies for transition metal alloys using machine learning, 201706)The enthalpy of formation is an important thermodynamic property. Developing fast and accurate methods for its prediction is of practical interest in a variety of applications. Material informatics techniques based on ... 
Oscillation estimates of eigenfunctions via the combinatorics of noncrossing partitions
(Diamond Open Access Journals, 201709)We study oscillations in the eigenfunctions for a fractional Schrödinger operator on the real line. An argument in the spirit of Courant's nodal domain theorem applies to an associated local problem in the upper half plane ... 
Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions
(American Meteorological Society, 20160322)For a stochastic differential equation(SDE) driven by a fractional Brownian motion(fBm) with Hurst parameter H>12, it is known that the existing (naive) Euler scheme has the rate of convergence n1−2H. Since the limit H→12 ... 
Fluctuations of TASEP and LPP with general initial data
(Institute of Mathematical Statistics, 20150813)We prove Airy process variational formulas for the onepoint probability distribution of (discrete time parallel update) TASEP with general initial data, as well as last passage percolation from a general lattice path to ... 
A monotone Sinai theorem
(Institute of Mathematical Statistics, 20160202)Sinai proved that a nonatomic ergodic measurepreserving system has any Bernoulli shift of no greater entropy as a factor. Given a Bernoulli shift, we show that any other Bernoulli shift that is of strictly less entropy ... 
Quantitative stable limit theorems on the Wiener space
(Institute of Mathematical Statistics, 2016)We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener space, where the target distribution is given by a possibly multidimensional mixture of Gaussian distributions. Our findings ... 
On the intermittency front of stochastic heat equation driven by colored noises
(Institute of Mathematical Statistics, 20160301)We study the propagation of high peaks (intermittency fronts) of the solution to a stochastic heat equation driven by multiplicative centered Gaussian noise in RdRd. The noise is assumed to have a general homogeneous ... 
Stability of Explicit OneStep Methods for P1Finite Element Approximation of Linear Diffusion Equations on Anisotropic Meshes
(Society for Industrial and Applied Mathematics, 20160526)We study the stability of explicit onestep integration schemes for the linear finite element approximation of linear parabolic equations. The derived bound on the largest permissible time step is tight for any mesh and ... 
The Partitionability Conjecture
(American Mathematical Society, 201702)In 1979 Richard Stanley made the following conjecture: Every CohenMacaulay simplicial complex is partitionable. Motivated by questions in the theory of face numbers of simplicial complexes, the Partitionability Conjecture ... 
Certain plane configurations
(University of Kansas, 1930) 
Multiplicities in Commutative Algebra
(University of Kansas, 20160831)This dissertation explores the notion of multiplicity and its generalizations within the theory of commutative algebra. Chapter 2 is dedicated to calculating the limits which give rise to BuchsbaumRim multiplicities. We ... 
Composing Scalable Nonlinear Algebraic Solvers
(Society for Industrial and Applied Mathematics (SIAM), 20151105)Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of concepts may be used for ... 
A FETIDP TYPE DOMAIN DECOMPOSITION ALGORITHM FOR THREEDIMENSIONAL INCOMPRESSIBLE STOKES EQUATIONS
(Society for Industrial and Applied Mathematics, 20150303)The FETIDP (dualprimal finite element tearing and interconnecting) algorithms, proposed by the authors in [SIAM J. Numer. Anal., 51 (2013), pp. 1235–1253] and [Internat. J. Numer. Methods Engrg., 94 (2013), pp. 128–149] ... 
Nonexistence of solitonlike solutions for defocusing generalized KdV equations
(Texas State University, Department of Mathematics, 20150224)We consider the global dynamics of the defocusing generalized KdV equation $$ \partial_t u + \partial_x^3 u = \partial_x(u^{p1}u). $$ We use Tao's theorem [5] that the energy moves faster than the mass to prove a ... 
On L2 modulus of continuity of Brownian local times and Riesz potentials
(Institute of Mathematical Statistics, 20150505)This article is concerned with modulus of continuity of Brownian local times. Specifically, we focus on three closely related problems: (a) Limit theorem for a Brownian modulus of continuity involving Riesz potentials, ...