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Physical Sciences and Mathematics Commons™

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1988

Mathematics

Articles 1 - 5 of 5

Full-Text Articles in Physical Sciences and Mathematics

Two Discrete Forms Of The Jordan Curve Theorem, Lawrence N. Stout Mar 1988

Two Discrete Forms Of The Jordan Curve Theorem, Lawrence N. Stout

Lawrence N. Stout

The Jordan curve theorem is one of those frustrating results in topology: it is intuitively clear but quite hard to prove. In this note we will look at two discrete analogs of the Jordan curve theorem that are easy to prove by an induction argument coupled with some geometric intuition. One of the surprises is that when we discretize the plane we get two Jordan curve theorems rather than one, a consequence of the interplay between two natural products in the category of graphs. Topology in this context has been studied by Farmer in [2]. To state the discrete versions, …

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Toeplitz Systems Associated With The Product Of A Formal Laurent Series And A Laurent Polynomial, William F. Trench Mar 1988

Toeplitz Systems Associated With The Product Of A Formal Laurent Series And A Laurent Polynomial, William F. Trench

William F. Trench

No abstract provided.

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Numerical Solution Of The Eigenvalue Problem For Symmetric Rationally Generated Toeplitz Matrices, William F. Trench Mar 1988

Numerical Solution Of The Eigenvalue Problem For Symmetric Rationally Generated Toeplitz Matrices, William F. Trench

William F. Trench

No abstract provided.

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Asymptotic Integration Of A Perturbed Constant Coefficient Differential Equation Under Mild Integral Smallness Conditions, William F. Trench Feb 1988

Asymptotic Integration Of A Perturbed Constant Coefficient Differential Equation Under Mild Integral Smallness Conditions, William F. Trench

William F. Trench

No abstract provided.

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Efficient Application Of The Schauder-Tychonoff Theorem To Functional Perturbations Of $X^(N)=0$, William F. Trench Dec 1987

Efficient Application Of The Schauder-Tychonoff Theorem To Functional Perturbations Of $X^(N)=0$, William F. Trench

William F. Trench

No abstract provided.

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