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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, ... 
Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency
(Institute of Mathematical Statistics, 20160604)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 BreuerMajor theorem for Gaussian stationary sequences
(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 PoissonNernstPlanck Models
(Society for Industrial and Applied Mathematics, 20150115)In this work, we examine effects of permanent charges on ionic flows through ion channels via a quasionedimensional classical PoissonNernstPlanck (PNP) model. The geometry of the threedimensional channel is presented ... 
Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations
(Society for Industrial and Applied Mathematics, 20150917)We study the stability and instability of periodic traveling waves for Kortewegde Vriestype equations with fractional dispersion and related, nonlinear dispersive equations. We show that a local constrained minimizer ... 
Simplicial and Cellular Trees
(Springer International Publishing, 20160416)Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1dimensional cell complex, raising the question of developing a theory of trees in higher ... 
A NonPartitionable CohenMacaulay Simplicial Complex
(Elsevier, 20160820)A longstanding 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
(Springer Verlag, 20141015)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
(Elsevier, 201402)We study quasipolynomials enumerating proper colorings, nowherezero tensions, and nowherezero flows in an arbitrary CWcomplex X, generalizing the chromatic, tension and flow polynomials of a graph. Our colorings, tensions ... 
Pseudodeterminants and Perfect Square Spanning Tree Counts
(International Press, 201506)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 ... 
A special Riemann surface with application to the hyperelliptic case
(University of Kansas, 1915) 
The principle of duality in a projective space of N dimensions
(University of Kansas, 1922.) 
Projective normality and higher syzygies for algebraic surfaces
(De Gruyter Open, 19990305)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
(De Gruyter Open, 19990605) 
On the Stochastic Burgers’ Equation in the Real Line
(Institute of Mathematical Statistics, 19990101)In this paper we establish the existence and uniqueness of an L2(R) valued solution for a onedimensional 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
(De Gruyter, 20010123) 
Nucleation and propagation of phase mixtures in a bistable chain
(American Physical Society, 20090429)We consider a prototypical discrete model of phase transitions. The model consists of a chain of particles, each interacting with its nearest and nexttonearest neighbors. The longrange interaction between nexttonearest ...