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  • The Partitionability Conjecture 

    Duval, Art; Klivans, Caroline; 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 ...
  • 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 ...

    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. ...
  • Density convergence in the Breuer-Major theorem for Gaussian stationary sequences 

    Hu, Yaozhong; Nualart, David; Tindel, Samy; Xu, Fangjun (Bernoulli Society for Mathematical Statistics and Probability, 2015)
    Consider a Gaussian stationary sequence with unit variance X={Xk;k∈N∪{0}}. Assume that the central limit theorem holds for a weighted sum of the form Vn=n−1/2∑n−1k=0f(Xk), where f designates a finite sum of Hermite ...
  • Effects of (Small) Permanent Charge and Channel Geometry on Ionic Flows via Classical Poisson--Nernst--Planck Models 

    Ji, Shuguan; Liu, Weishi; Zhang, Mingji (Society for Industrial and Applied Mathematics, 2015-01-15)
    In this work, we examine effects of permanent charges on ionic flows through ion channels via a quasi-one-dimensional classical Poisson--Nernst--Planck (PNP) model. The geometry of the three-dimensional channel is presented ...
  • Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations 

    Hur, Vera Mikyoung; Johnson, Mathew A. (Society for Industrial and Applied Mathematics, 2015-09-17)
    We study the stability and instability of periodic traveling waves for Korteweg--de Vries-type equations with fractional dispersion and related, nonlinear dispersive equations. We show that a local constrained minimizer ...
  • Simplicial and Cellular Trees 

    Duval, Art M.; Klivans, Caroline J.; Martin, Jeremy L. (Springer International Publishing, 2016-04-16)
    Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question of developing a theory of trees in higher ...
  • A Non-Partitionable Cohen-Macaulay Simplicial Complex 

    Duval, Art M.; Bennet, Goeckner; Klivans, Caroline J.; Martin, Jeremy L. (Elsevier, 2016-08-20)
    A long-standing conjecture of Stanley states that every Cohen–Macaulay simplicial complex is partitionable. We disprove the conjecture by constructing an explicit counterexample. Due to a result of Herzog, Jahan and Yassemi, ...
  • Cuts and flows of cell complexes 

    Duval, Art M.; Klivans, Caroline J.; Martin, Jeremy L. (Springer Verlag, 2014-10-15)
    We study the vector spaces and integer lattices of cuts and flows associated with an arbitrary finite CW complex, and their relationships to group invariants including the critical group of a complex. Our results extend ...
  • Enumerating Colorings, Tensions and Flows in Cell Complexes 

    Beck, Matthias; Breuer, Felix; Godkin, Logan; Martin, Jeremy L. (Elsevier, 2014-02)
    We study quasipolynomials enumerating proper colorings, nowhere-zero tensions, and nowhere-zero flows in an arbitrary CW-complex X, generalizing the chromatic, tension and flow polynomials of a graph. Our colorings, tensions ...
  • Pseudodeterminants and Perfect Square Spanning Tree Counts 

    Martin, Jeremy L.; Maxwell, Molly; Reiner, Victor; Wilson, Scott O. (International Press, 2015-06)
    The pseudodeterminant pdet(M) of a square matrix is the last nonzero coe cient in its characteristic polynomial; for a nonsingular matrix, this is just the determinant. If @ is a symmetric or skewsymmetric matrix then ...
  • Projective normality and higher syzygies for algebraic surfaces 

    Gallego, F. J.; Purnaprajna, Bangere P. (De Gruyter Open, 1999-03-05)
    In this work we develop new techniques to compute Koszul cohomology groups for several classes of varieties. As applications we prove results on projective normality and syzygies for algebraic surfaces. From more general ...
  • Erratum to Projective normality and higher syzygies for algebraic surfaces 

    Gallego, F. J.; Purnaprajna, Bangere P. (De Gruyter Open, 1999-06-05)
  • On the Stochastic Burgers’ Equation in the Real Line 

    Gyöngy, István; Nualart, David (Institute of Mathematical Statistics, 1999-01-01)
    In this paper we establish the existence and uniqueness of an L2(R) -valued solution for a one-dimensional Burgers’ equation perturbed by a space–time white noise on the real line. We show that the solution is continuous ...
  • Some results on rational surfaces and Fano varieties 

    Gallego, F. J.; Purnaprajna, Bangere P. (De Gruyter, 2001-01-23)
  • Nucleation and propagation of phase mixtures in a bistable chain 

    Vainchtein, Anna; Van Vleck, Erik (American Physical Society, 2009-04-29)
    We consider a prototypical discrete model of phase transitions. The model consists of a chain of particles, each interacting with its nearest and next-to-nearest neighbors. The long-range interaction between next-to-nearest ...
  • Spectral Stability for Subsonic Traveling Pulses of the Boussinesq “abc" System 

    Hakkaev, Sevdzhan; Stanislavova, Milena; Stefanov, Atanas (Society for Industrial and Applied Mathematics, 2013-09-01)
    See article for abstract.

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