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Applied Mathematics

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Old Dominion University

1992

Articles 1 - 7 of 7

Full-Text Articles in Physical Sciences and Mathematics

Solution Uniqueness And Stability Criteria For A Model Of Growth Factor Production, J. A. Adam Jan 1992

Solution Uniqueness And Stability Criteria For A Model Of Growth Factor Production, J. A. Adam

Mathematics & Statistics Faculty Publications

Uniqueness and stability criteria are established for the steady states of a nonlinear model of growth factor production. A specific expression for the nonlinearity is chosen, containing three parameters which can be adjusted to fit a specific biological context, but much of the analysis applies to a general class of source terms that exhibit the same qualitative behavior.

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Temperature And Suction Effects On The Instability Of An Infinite Swept Attachment Line, D. G. Lasseigne, T. L. Jackson, F. Q. Hu Jan 1992

Temperature And Suction Effects On The Instability Of An Infinite Swept Attachment Line, D. G. Lasseigne, T. L. Jackson, F. Q. Hu

Mathematics & Statistics Faculty Publications

It is known that the incompressible, infinite swept attachment line flow is unstable to streamwise disturbances that originate in the boundary layer when the cross-flow exceeds a critical magnitude. Furthermore, a small degree of suction at the surface has a significant stabilizing influence while a small degree of blowing has a considerable destabilizing influence. This paper investigates the stabilizing and destabilizing effects of, respectively, cooling or heating the plate and the competing or enhancing effects of suction or blowing. A nonorthogonal flow with respect to the attachment line is also considered by adding a component of shear to the mean …

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Numerical Solutions For Weakly Singular Hammerstein Equations And Their Superconvergence, Hideaki Kaneko, Richard D. Noren, Yuesheng Xu Jan 1992

Numerical Solutions For Weakly Singular Hammerstein Equations And Their Superconvergence, Hideaki Kaneko, Richard D. Noren, Yuesheng Xu

Mathematics & Statistics Faculty Publications

In the recent paper [7], it was shown that the solutions of weakly singular Hammerstein equations satisfy certain regularity properties. Using this result, the optimal convergence rate of a standard piecewise polynomial collocation method and that of the recently proposed collocationtype method of Kumar and Sloan [10] are obtained. Superconvergence of both of these methods are also presented. In the final section, we discuss briefly a standard productintegration method for weakly singular Hammerstein equations and indicate its superconvergence property. © 1992 Rocky Mountain Mathematics Consortium.

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A Tree Representation For P4-Sparse Graphs, B. Jamison, Stephan Olariu Jan 1992

A Tree Representation For P4-Sparse Graphs, B. Jamison, Stephan Olariu

Computer Science Faculty Publications

A graph G is P4-sparse if no set of five vertices in G induces more than one chordless path of length three. P4-sparse graphs generalize both the class of cographs and the class of P4-reducible graphs. We give several characterizations for P4-sparse graphs and show that they can be constructed from single-vertex graphs by a finite sequence of operations. Our characterization implies that the P4-sparse graphs admit a tree representation unique up to isomorphism. Furthermore, this tree representation can be obtained in polynomial time.

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The Morphology Of Convex Polygons, Stephan Olariu Jan 1992

The Morphology Of Convex Polygons, Stephan Olariu

Computer Science Faculty Publications

A simple polygon P is said to be unimodal if for every vertex of P, the Euclidian distance function to the other vertices of P is unimodal. The study of unimodal polygons has emerged as a fruitful area of computational and discrete geometry. We study unimodality properties of a number of special convex polygons from the morphological point of view. In particular, we establish a hierarchy among three classes of convex polygons in terms of their unimodality properties.

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On Sources In Comparability Graphs, With Applications, Stephan Olariu Jan 1992

On Sources In Comparability Graphs, With Applications, Stephan Olariu

Computer Science Faculty Publications

We characterize sources in comparability graphs and show that our result provides a unifying look at two recent results about interval graphs.

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A Charming Class Of Perfectly Orderable Graphs, Chinh T. Hoang, Frederic Maffray, Stephan Olariu, Myriam Preissmann Jan 1992

A Charming Class Of Perfectly Orderable Graphs, Chinh T. Hoang, Frederic Maffray, Stephan Olariu, Myriam Preissmann

Computer Science Faculty Publications

We investigate the following conjecture of Vašek Chvátal: any weakly triangulated graph containing no induced path on five vertices is perfectly orderable. In the process we define a new polynomially recognizable class of perfectly orderable graphs called charming. We show that every weakly triangulated graph not containing as an induced subgraph a path on five vertices or the complement of a path on six vertices is charming.

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