Browsing Scholarly Works, Department of Mathematics by Title
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Calibrated Filtered Reduced Order Modeling
We propose a calibrated filtered reduced order model (CFROM) framework for the numerical simulation of general nonlinear PDEs that are amenable to reduced order modeling. The novel CFROM framework consists of two steps: ... 
Canonical dual approach to solving 01 quadratic programming problems
(American Institute of Mathematical Sciences, 200802)This paper presents a canonical duality theory for solving nonconvex polynomial programming problems subjected to box constraints. It is proved that under certain conditions, the constrained nonconvex problems can be ... 
Capillarygravity wave drag
(AIP Publishing, 200108)Drag due to the production of capillarygravity waves is calculated for an object moving along the surface of a liquid. Both two and three dimensional objects, moving at large Froude and Weber numbers, are treated. (C) ... 
Case eigenfunction expansion for a conservative medium
(AIP Publishing, 197602)By using the resolvent integration technique introduced by Larsen and Habetler, the one‐speed, isotropic scattering,neutron transport equation is treated in the infinite and semi‐infinite media. It is seen that the results ... 
Cauchyproblem for the linearized version of the Generalized Polynomial KdV equation
(AIP Publishing, 199206)In the present paper results about the "Generalized Polynomial Kortewegde Vries equation" (GPKdV) are obtained, extending the ones by Sachs [SIAM J. Math. Anal. 14, 674 (1983)] for the Kortewegde Vries (KdV) equation. ... 
ChernSchwartzMacPherson classes for Schubert cells in flag manifolds
We obtain an algorithm computing the ChernSchwartzMacPherson (CSM) classes of Schubert cells in a generalized flag manifold G/B. In analogy to how the ordinary divided difference operators act on Schubert classes, each ... 
Closure Learning for Nonlinear Model Reduction Using Deep Residual Neural Network
(MDPI, 20200323)Developing accurate, efficient, and robust closure models is essential in the construction of reduced order models (ROMs) for realistic nonlinear systems, which generally require drastic ROM mode truncations. We propose a ... 
Cohomology of Finite Groups
(University of Essen, 1992)This is a short lecture course on the cohomology of finite groups. Topics include Künneth formula, cup products and cohomology ring, differential graded algebras, Evens norm map and the Steenrod operations. 
Comment on "A numerical study of periodic disturbances on twolayer Couette flow" [Phys. Fluids 10, 3056 (1998)]
(AIP Publishing, 199910) 
Commutative rings with homomorphic power functions
(Hindawi, 19920101)A (commutative) ring R (with identity) is called mlinear (for an integer m≥2) if (a+b)m=am+bm for all a and b in R. The mlinear reduced rings are characterized, with special attention to the finite case. A structure ... 
Complete function spaces
(Hindawi, 19830101)A study is made of certain completeness properties of the space of allcontinuous realvalued functions on a space, where this function space has the compactopen topology. 
Computational simulation of typeII superconductivity including pinning phenomena
(American Physical Society, 19950615)A flexible tool, based on the finiteelement method, for the computational simulation of vortex phenomena in typeII superconductors has been developed. These simulations use refined or newly developed phenomenological ... 
Computing Reduced Order Models via InnerOuter Krylov Recycling in Diffuse Optical Tomography
(Siam Publications, 20170101) 
Continuity of the S matrix for the perturbed Hill's equation
(AIP Publishing, 199407)The behavior of the scattering matrix associated with the perturbed Hill's equation as the spectral parameter approaches an endpoint of a spectral band is studied. In particular, the continuity of the scattering matrix at ... 
Convergence theorems for intermediate problems. II
(Cambridge University Press, 2002)Convergence theorems for the practical eigenvector free methods of Gay and Goerisch are obtained under a variety of hypotheses, so that our theorems apply to both traditional boundaryvalue problems and atomic problems. ... 
Couette flow of a binary gas mixture
(AIP Publishing, 198803)The linearized binary model described by Hamel [Phys. Fluids 8, 418 (1964)] is used to obtain a set of kinetic equations and boundary conditions for the Couette flow problem. The derived set of two coupled integrodifferential ... 
Coupling constant behavior of eigenvalues of ZakharovShabat systems
(AIP Publishing, 200712)We consider the eigenvalues of the nonselfadjoint ZakharovShabat systems as the coupling constant of the potential is varied. In particular, we are interested in eigenvalue collisions and eigenvalue trajectories in the ... 
Coupling constant thresholds of perturbed periodic Hamiltonians
(AIP Publishing, 199809)We consider Schrodinger operators of the form Hlambda= Delta + V + lambda W on L2(Rv) (v=1, 2, or 3) with V periodic, W short range, and lambda a real nonnegative parameter. Then the continuous spectrum of Hlambda ... 
Damping optimization of parameter dependent mechanical systems by rational interpolation
We consider an optimization problem related to semiactive damping of vibrating systems. The main problem is to determine the best damping matrix able to minimize influence of the input on the output of the system. We use ...