Browsing Faculty Works, Department of Mathematics by Title
Now showing items 198217 of 226

Stabilizing gene regulatory networks through feedforward loops
(American Institute of Physics, 201306)The global dynamics of gene regulatory networks are known to show robustness to perturbations in the form of intrinsic and extrinsic noise, as well as mutations of individual genes. One molecular mechanism underlying this ... 
Stochastic dynamics of GinzburgLandau vortices in superconductors
(American Physical Society, 20010801)Thermal fluctuations and randomly distributed defects in superconductors are modeled by stochastic variants of the timedependent GinzburgLandau equations. Numerical simulations are used to compare the effects of additive ... 
A structural equation model looking at student’s participatory behavior and their success in Calculus I
(20171110)Abstract Background Government projections in the USA indicate that the country will need a million more science, technology, engineering, and mathematics (STEM) graduates ... 
Structured noncommutative multidimensional linear systems
(Siam Publications, 2005)We introduce a class of multidimensional linear systems with evolution along a free semigroup. The transfer function for such a system is a formal power series in noncommuting indeterminates. Standard systemtheoretic ... 
Sufficient conditions and perfect duality in nonconvex minimization with inequality constraints
(American Institute of Mathematical Sciences, 200502)The paper studies forced surface waves on an incompressible, inviscid fluid in a twodimensional channel with a small negative or oscillatory bump on a rigid flat bottom. Such wave motions are determined by a nondimensional ... 
The effect of insoluble surfactant at dilute concentration on drop breakup under shear with inertia
(American Institute of Physics, 200401)Direct numerical simulations are conducted with a volumeoffluid continuous surface stress algorithm. The linear equation of state is used to characterize the effects of an insoluble surfactant at low concentration on a ... 
The effect of negative feedback loops on the dynamics of Boolean networks
(CELL PRESS, 200807)Feedback loops play an important role in determining the dynamics of biological networks. To study the role of negative feedback loops, this article introduces the notion of distancetopositivefeedback which, in essence, ... 
the effect of nonzero viscosity ratio on the stability of fingers and bubbles in a HeleShaw cell
(AIP Publishing, 198811)The linear stability of a steadily moving bubble or a finger in a Hele–Shaw cell is considered in the case when gravity and the ratio between the viscosities of the less and more viscous fluids are nonzero. The effect of ... 
the effect of surface tension on the shape of a HeleShaw cell bubble
(AIP Publishing, 198611)Numerical and asymptotic solutions are found for the steady motion of a symmetrical bubble through a parallel‐sided channel in a Hele–Shaw cell containing a viscous liquid. The degeneracy of the Taylor–Saffman zero ... 
The PMU placement problem
(Siam Publications, 2005)PMU placement problem is an optimization problem abstracted from an approach to supervising an electrical power system. The power system is modeled as a graph, and adequate supervision of the system requires that the voltage ... 
the RiemannHilbert problem for nonsymmetric systems
(AIP Publishing, 199112)A comparison of the RiemannHilbert problem and the WienerHopf factorization problem arising in the solution of halfspace singular integral equations is presented. Emphasis is on the factorization of functions lacking ... 
the semiclassical limit of quantum dynamics. I. time evolution
(AIP Publishing, 198802)The ℏ→0 limit of the quantum dynamics determined by the Hamiltonian H(ℏ) =−(ℏ2/2m)Δ+V on L 2(R n ) is studied for a large class of potentials. By convolving with certain Gaussian states, classically determined asymptotic ... 
The thinlayer effect and interfacial stability in a twolayer Couette flow with similar liquids
(AIP Publishing, 198706)The linear stability of Couette flow composed of two layers of immiscible fluids, one lying on top of the other, is considered for the special case when the two fluids have similar mechanical properties. The interfacial ... 
Topologies between compact and uniform convergence on function spaces
(Hindawi, 19930101)This paper studies two topologies on the set of all continuous realvalued functionson a Tychonoff space which lie between the topologies of compact convergence and uniformconvergence. 
Transfer function approach to output specification in certain linear distributed parameter systems
(American Institute of Mathematical Sciences, 2003)We carry out error estimation of a class of immersed finite element (IFE) methods for elliptic interface problems with both perfect and imperfect interface jump conditions. A key feature of these methods is that their ... 
transverse plasma oscillations
(AIP Publishing, 1979)An operator theoretic approach is used to solve the linearized Vlasov–Maxwell equations for transverse plasma oscillations. In particular, the special cases of simple and second‐order real zeros of the plasma dispersion ... 
Understanding the complex patterns observed during hepatitis B Virus therapy
(MDPI, 20170519)Data from human clinical trials have shown that the hepatitis B virus (HBV) follows complex profiles, such as biphasic, triphasic, stepwise decay and rebound. We utilized a deterministic model of HBV kinetics following ... 
uniqueness of solutions to linearized Boltzmann equation
(AIP Publishing, 197801)Uniqueness theorems are proved for the linearized Boltzmann equation for both the ’’exterior’’ and ’’interior’’ problems under generalized Maxwellboundary conditions. The solution space is a weighted L p space, and agrees ...