Browsing Faculty Works, Department of Mathematics by Title
Now showing items 127146 of 226

multiplescales spacetime analysis of a randomly perturbed onedimensional waveequation
(AIP Publishing, 197710)An initial value problem for one_dimensional wave propagation is considered; the medium is assumed to be randomly perturbed as a function of both space and time. The stochastic perturbation theory of Papanicolaou and Keller ... 
Multiscale Coupling of Transcranial Direct Current Stimulation to Neuron Electrodynamics: Modeling the Influence of the Transcranial Electric Field on Neuronal Depolarization
(Hindawi Publishing Corporation, 20141023)Transcranial direct current stimulation (tDCS) continues to demonstrate success as a medical intervention for neurodegenerative diseases, psychological conditions, and traumatic brain injury recovery. One aspect of tDCS ... 
Multistate Model Builder (MSMB): a flexible editor for compact biochemical models
(Biomed Central Ltd, 20140404)Background Building models of molecular regulatory networks is challenging not just because of the intrinsic difficulty of describing complex biological processes. Writing a model is a creative effort that calls for more ... 
A Network of SCOP Hidden Markov Models and Its Analysis
(20110523)Background The Structural Classification of Proteins (SCOP) database uses a large number of hidden Markov models (HMMs) to represent families and superfamilies composed of proteins that presumably share the same evolutionary ... 
A New Topological Degree Theory for Perturbations of Demicontinuous Operators and Applications to Nonlinear Equations with Nonmonotone Nonlinearities
(Hindawi, 20161018)Let 𝑋 be a real reflexive locally uniformly convex Banach space with locally uniformly convex dual space 𝑋∗. Let 𝑇 : 𝑋 ⊇ 𝐷(𝑇)→ 2𝑋∗ be maximal monotone of type 𝚪𝜙 𝑑 (i.e., there exist 𝑑 ≥ 0 and a nondecreasing ... 
Noncoercive Perturbed Densely Defined Operators and Application to Parabolic Problems
(Hindawi, 20150809)Let 𝑋 be a real locally uniformly convex reflexive separable Banach space with locally uniformly convex dual space 𝑋∗. Let 𝑇: 𝑋 ⊇ 𝐷(𝑇) → 2𝑋∗ be maximal monotone and 𝑆 : 𝑋 ⊇ 𝐷(𝑆) → 𝑋∗ quasibounded generalized ... 
Nonlinear Integral Inequalities in Two Independent Variables and Their Applications
(Hindawi Publishing Corporation, 20071105)This paper generalizes results of Cheung and Ma (2005) to more general inequalities with more than one distinct nonlinear term. From our results, some results of Cheung and Ma ( 2005) can be deduced as some special cases. ... 
Nonlinear integral inequalities with delay for discontinuous functions and their applications
(20130911)This paper investigates integral inequalities with delay for discontinuous functions involving two nonlinear terms. We do not require the classes ℘ and ȷ in Gallo and Piccirillo’s paper (Bound. Value Probl. 2009:808124, ... 
NONLINEAR PARAMETRIC INVERSION USING INTERPOLATORY MODEL REDUCTION
(Siam Publications, 20150101) 
Note on a role for entire functions of the classes and
(Hindawi, 19810101)We use the B and B* operators of Levin on the Classes P and P* and a comparison principle to prove a GaussLucas Theorem for differential operators. The connection with the determination of final sets for differential ... 
A note on best approximation and invertibility of operators on uniformly convex Banach spaces
(Hindawi Publishing Corp, 19910101)It is shown that if X is a uniformly convex Banach space and S a bounded linear operator onX for which ?IS?=1, then S is invertible if and only if ?I12S? <1. From this it follows thatif S is invertible on X then either ... 
Nucleation of superconductivity in finite anisotropic superconductors and the evolution of surface superconductivity toward the bulk mixed state
(American Physical Society, 20020214)In anisotropic superconductors having an arbitrary orientation of the sample surface relative to the crystal principal axes, the surface critical field Hc3 is less than 1.695H(c2) unless the field is situated along one ... 
Numerical Approximations of the Dynamical System Generated by Burgers' Equation with NeumannDirichlet Boundary Conditions
(EDP Sciences, 201309)Using Burgers' equation with mixed NeumannDirichlet boundary conditions, we highlight a problem that can arise in the numerical approximation of nonlinear dynamical systems on computers with a finite precision floating ... 
Numerical investigation of elongated drops in a microfluidic Tjunction
(American Institute of Physics, 201102)We present a combined numerical and asymptotic approach for modeling droplets in microchannels. The magnitude of viscous forces relative to the surface tension force is characterized by a capillary number, Ca, which is ... 
Numerical simulation of breakup of a viscous drop in simple shear flow through a volumeoffluid method
(American Institute of Physics, 200002)A spherical drop, placed in a second liquid of the same density, is subjected to shearing between parallel plates. The subsequent flow is investigated numerically with a volumeoffluid (VOF) method. The scheme incorporates ... 
Numerical simulation of drop retraction after a strain jump
(American Physical Society, 200904)A spherical drop of one liquid suspended in another is subjected to an instantaneous initial shear. We simulate the retraction of the drop to its spherical equilibrium and compare the results with recent experiments. In ... 
An ObjectOriented Framework for Versatile Finite Element Based Simulations of Neurostimulation
(Hindawi, 20151021)Computational simulations of transcranial electrical stimulation (TES) are commonly utilized by the neurostimulation community, and while vastly different TES application areas can be investigated, the mathematical equations ... 
Obtaining reliable transient rheological data on concentrated short fiber suspensions using a rotational rheometer
(AIP Publishing, 20090901)The conventional method for obtaining transient rheological data on short glass fiberfilled polymeric fluids is to use the parallel disk (PP) geometry in a rotational rheometer. Using the PP geometry large transient stress ... 
On a stochastic hyperbolic system in linear elasticity
(Siam Publications, 200008)In this paper we discuss the Cauchy problem for linear elasticity with a spacetime white noise forcing term. We show that the solution can be represented by a formula analogous to the Riesz formula for solutions of a wave ... 
On a wave equation with a boundary condition associated with capillary waves
(Siam Publications, 199809)This paper discusses an initialboundary value problem for a wave equation with a nonstandard boundary condition associated with linear capillary waves on the surface of a compressible liquid. We prove the wellposedness ...