Browsing Faculty Works, Department of Mathematics by Title
Now showing items 136155 of 226

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 ... 
On the diagonal subalgebra of an Ext algebra
(201704)Let R be a Koszul algebra over a field k and M be a linear Rmodule. We study a graded subalgebra Delta(M) of the Extalgebra Ext(R)*(M, M) called the diagonal subalgebra and its properties. Applications to the Hochschild ... 
On the efficiency of Hamiltonianbased quantum computation for lowrank matrices
(AIP Publishing, 201203)We present an extension of adiabatic quantum computing (AQC) algorithm for the unstructured search to the case when the number of marked items is unknown. The algorithm maintains the optimal Grover speedup and includes a ... 
On the eigenfunctions for Hookean and FENE dumbbell models
(AIP Publishing, 201309)We study the linear eigenvalue problem for the distribution function associated with Hookean and FENE dumbbell models. For Hookean dumbbells, the eigenfunctions can be expressed by generalized Laguerre polynomials. The ... 
on the Levinson theorem for Dirac operators
(AIP Publishing, 199001)For the Dirac equation with potential V(r) obeying ∫∞ 0(1+r)‖V(r)‖d r<∞ we prove a relativistic version of Levinson’s theorem that relates the number of bound states in the spectral gap [−m,m] to the variation of an ... 
on the number of bound states for the onedimensional Schrodinger equation
(AIP Publishing, 199809)The number of bound states of the onedimensional Schrodinger equation is analyzed in terms of the number of bound states corresponding to ''fragments'' of the potential. When the potential is integrable and has a finite ... 
On the number of zeros of iterated operators on analytic Legendre expansions
(Hindawi, 20010101)Let L=(1−z2)D2−2zD, D=d/dz and f(z)=∑n=0∞cnpn(z), with Pn being the nth Legendre polynomialand f analytic in an ellipse with foci ±1. Set Lk=L(Lk−1), k≥2. Then the number of zeros of Lkf(z) in this ellipse is O(klnk). 
on the RiemannHilbert problem for the onedimensional Schrodingerequation
(AIP Publishing, 199307)A matrix RiemannHilbert problem associated with the onedimensional Schrodinger equation is considered, and the existence and uniqueness of its solutions are studied. The solution of this RiemannHilbert problem yields ... 
Optimal Control of Drug Therapy in a Hepatitis B Model
(MDPI, 20160803)Combination antiviral drug therapy improves the survival rates of patients chronically infected with hepatitis B virus by controlling viral replication and enhancing immune responses. Some of these drugs have side effects ... 
Optimization and model reduction in the high dimensional parameter space of a budding yeast cell cycle model
(Biomed Central Ltd, 20130628)Background 'Parameter estimation from experimental data is critical for mathematical modeling of protein regulatory networks. For realistic networks with dozens of species and reactions, parameter estimation is an especially ...