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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
On A Convex Set With Nondifferentiable Metric Projection, Shyan S. Akmal, Nguyen Mau Nam, J. J. P. Veerman
On A Convex Set With Nondifferentiable Metric Projection, Shyan S. Akmal, Nguyen Mau Nam, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a convex set with smooth boundary which possesses the same property.
A Posteriori Eigenvalue Error Estimation For The Schrödinger Operator With The Inverse Square Potential, Hengguang Li, Jeffrey S. Ovall
A Posteriori Eigenvalue Error Estimation For The Schrödinger Operator With The Inverse Square Potential, Hengguang Li, Jeffrey S. Ovall
Mathematics and Statistics Faculty Publications and Presentations
We develop an a posteriori error estimate of hierarchical type for Dirichlet eigenvalue problems of the form (−∆ + (c/r) 2 )ψ = λψ on bounded domains Ω, where r is the distance to the origin, which is assumed to be in Ω. This error estimate is proven to be asymptotically identical to the eigenvalue approximation error on a family of geometrically-graded meshes. Numerical experiments demonstrate this asymptotic exactness in practice.
Stochastic Comparisons Of Weighted Sums Of Arrangement Increasing Random Variables, Xiaoqing Pan, Min Yuan, Subhash C. Kochar
Stochastic Comparisons Of Weighted Sums Of Arrangement Increasing Random Variables, Xiaoqing Pan, Min Yuan, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
Assuming that the joint density of random variables X1,X2, . . . ,Xn is arrangement increasing (AI), we obtain some stochastic comparison results on weighted sums of Xi’s under some additional conditions. An application to optimal capital allocation is also given.
Monomials And Basin Cylinders For Network Dynamics, Daniel Austin, Ian H. Dinwoodie
Monomials And Basin Cylinders For Network Dynamics, Daniel Austin, Ian H. Dinwoodie
Mathematics and Statistics Faculty Publications and Presentations
We describe methods to identify cylinder sets inside a basin of attraction for Boolean dynamics of biological networks. Such sets are used for designing regulatory interventions that make the system evolve towards a chosen attractor, for example initiating apoptosis in a cancer cell. We describe two algebraic methods for identifying cylinders inside a basin of attraction, one based on the Groebner fan that finds monomials that define cylinders and the other on primary decomposition. Both methods are applied to current examples of gene networks.
Robust Estimates For Hp-Adaptive Approximations Of Non-Self-Adjoint Eigenvalue Problems, Stefano Giani, Luka Grubišić, Agnieszka Międlar, Jeffrey S. Ovall
Robust Estimates For Hp-Adaptive Approximations Of Non-Self-Adjoint Eigenvalue Problems, Stefano Giani, Luka Grubišić, Agnieszka Międlar, Jeffrey S. Ovall
Mathematics and Statistics Faculty Publications and Presentations
We present new residual estimates based on Kato’s square root theorem for spectral approximations of non-self-adjoint differential operators of convection–diffusion–reaction type. These estimates are incorporated as part of an hp-adaptive finite element algorithm for practical spectral computations, where it is shown that the resulting a posteriori error estimates are reliable. Provided experiments demonstrate the efficiency and reliability of our approach.
Mathematical Model For Bone Mineralization, Svetlana V. Komarova, Lee Safranek, Jay Gopalakrishnan, Miao-Jung Yvonne Ou, Marc D. Mckee, Monzur Murshed, Frank Rauch, Erica Zuhr
Mathematical Model For Bone Mineralization, Svetlana V. Komarova, Lee Safranek, Jay Gopalakrishnan, Miao-Jung Yvonne Ou, Marc D. Mckee, Monzur Murshed, Frank Rauch, Erica Zuhr
Mathematics and Statistics Faculty Publications and Presentations
Defective bone mineralization has serious clinical manifestations, including deformities and fractures, but the regulation of this extracellular process is not fully understood. We have developed a mathematical model consisting of ordinary differential equations that describe collagen maturation, production and degradation of inhibitors, and mineral nucleation and growth. We examined the roles of individual processes in generating normal and abnormal mineralization patterns characterized using two outcome measures: mineralization lag time and degree of mineralization. Model parameters describing the formation of hydroxyapatite mineral on the nucleating centers most potently affected the degree of mineralization, while the parameters describing inhibitor homeostasis most effectively …