Browsing Faculty Works, Department of Mathematics by Title
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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 ... 
Outlier Detection for Sensor Systems (ODSS): A MATLAB Macro for Evaluating Microphone Sensor Data Quality
(MDPI, 20171013)Microphone sensor systems provide information that may be used for a variety of applications. Such systems generate large amounts of data. One concern is with microphone failure and unusual values that may be generated as ... 
Peano compactifications and property metric spaces
(Hindawi, 19800101)Let (X,d) denote a locally connected, connected separable metric space. We say the X is Smetrizable provided there is a topologically equivalent metric ρ on X such that (X,ρ) has Property S, i.e. for any ϵ>0, X is the ... 
Phaselocked loops, demodulation, and averaging approximation timescale extensions
(Siam Publications, 2013)Among the many applications of the phaselocked loop (PLL), a device used extensively in telecommunications and electronics, is the demodulation of modulated carrier signals. The PLL contains a voltage controlled oscillator ... 
power statistics for wave propagation in onedimension and comparison with radiative transporttheory. II.
(AIP Publishing, 197412)We consider the one_dimensional problem of a slab having a random index of refraction and illuminated from within by a point source. We compute the expected value and the fluctuations of both the total power and power flux. ... 
Preconditioners for generalized saddlepoint problems
(Siam Publications, 2006)We propose and examine blockdiagonal preconditioners and variants of indefinite preconditioners for block twobytwo generalized saddlepoint problems. That is, we consider the nonsymmetric, nonsingular case where the ( ... 
Preconditioning Parametrized Linear Systems
Preconditioners are generally essential for fast convergence in the iterative solution of linear systems of equations. However, the computation of a good preconditioner can be expensive. So, while solving a sequence of ...