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  • Optimal Time-Dependent Lower Bound On Density For Classical Solutions of 1-D Compressible Euler Equations 

    Chen, Geng (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 ...
  • Accounting for Model Error from Unresolved Scales in Ensemble Kalman Filters by Stochastic Parameterization 

    Lu, Fei; Tu, Xuemin; Chorin, Alexandre J. (American Meteorological Society, 2017-08-23)
    The use of discrete-time 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 

    Bell, Denis; Nualart, David (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 

    Nualart, David; Tudor, Ciprian A. (Institute of Mathematical Statistics, 2017)
    The aim of this paper is to show an estimate for the determinant of the covariance of a two-dimensional 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 

    Ubaru, Shashanka; Międlar, Agnieszka; Saad, Yousef; Chelikowsky, James R. (Formation enthalpies for transition metal alloys using machine learning, 2017-06)
    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 

    Hur, Vera Mikyoung; Johnson, Mathew A.; Martin, Jeremy L. (Diamond Open Access Journals, 2017-09)
    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 

    Hu, Yaozhong; Liu, Yanghui; Nualart, David (American Meteorological Society, 2016-03-22)
    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 

    Corwin, Ivan; Liu, Zhipeng; Wang, Dong (Institute of Mathematical Statistics, 2015-08-13)
    We prove Airy process variational formulas for the one-point 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 

    Quas, Anthony; Soo, Terry (Institute of Mathematical Statistics, 2016-02-02)
    Sinai proved that a nonatomic ergodic measure-preserving 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 

    Nourdin, Ivan; Nualart, David; Peccati, Giovanni (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 

    Hu, Yaozhong; Huang, Jingyu; Nualart, David (Institute of Mathematical Statistics, 2016-03-01)
    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 One-Step Methods for P1-Finite Element Approximation of Linear Diffusion Equations on Anisotropic Meshes 

    Huang, Weizhang; Kamenski, Lennard; Lang, Jens (Society for Industrial and Applied Mathematics, 2016-05-26)
    We study the stability of explicit one-step 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 

    Duval, Art M.; Klivans, Caroline J.; Martin, Jeremy L. (American Mathematical Society, 2017-02)
    In 1979 Richard Stanley made the following conjecture: Every Cohen-Macaulay simplicial complex is partitionable. Motivated by questions in the theory of face numbers of simplicial complexes, the Partitionability Conjecture ...
  • Certain plane configurations 

    Cook, George Stafford (University of Kansas, 1930)
  • Multiplicities in Commutative Algebra 

    Serio, Jared Grant (University of Kansas, 2016-08-31)
    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 Buchsbaum-Rim multiplicities. We ...
  • Composing Scalable Nonlinear Algebraic Solvers 

    Brune, Peter R.; Knepley, Matthew G.; Smith, Barry F.; Tu, Xuemin (Society for Industrial and Applied Mathematics (SIAM), 2015-11-05)
    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 FETI-DP TYPE DOMAIN DECOMPOSITION ALGORITHM FOR THREE-DIMENSIONAL INCOMPRESSIBLE STOKES EQUATIONS 

    Tu, Xuemin; Li, Jing (Society for Industrial and Applied Mathematics, 2015-03-03)
    The FETI-DP (dual-primal 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 soliton-like solutions for defocusing generalized KdV equations 

    Kwon, Soonsik; Shao, Shuanglin (Texas State University, Department of Mathematics, 2015-02-24)
    We consider the global dynamics of the defocusing generalized KdV equation $$ \partial_t u + \partial_x^3 u = \partial_x(|u|^{p-1}u). $$ 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 

    Deya, Aurelien; Nualart, David; Tindel, Samy (Institute of Mathematical Statistics, 2015-05-05)
    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, ...
  • Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency 

    Hu, Yaozhong; Huang, Jingyu; Nualart, David; Tindel, Samy (Institute of Mathematical Statistics, 2016-06-04)
    This paper studies the stochastic heat equation with multiplicative noises of the form uW, where W is a mean zero Gaussian noise and the differential element uW is interpreted both in the sense of Skorohod and Stratonovich. ...

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