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Applied Mathematics Commons™

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1995

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Articles 61 - 68 of 68

Full-Text Articles in Applied Mathematics

A Convergent Reconstruction Method For An Elliptic Operator In Potential Form, Lester Caudill Jan 1995

A Convergent Reconstruction Method For An Elliptic Operator In Potential Form, Lester Caudill

Department of Math & Statistics Faculty Publications

We investigate the problem of recovering a potential q(x) in the equation -∆u + q(x)u = 0 from overspecified boundary data on the unit square in R2. The potential is characterized as a fixed point of a nonlinear operator, which is shown to be a contraction on a ball in C∝. Uniqueness of q(x) follows, as does convergence of the resulting recovery scheme. Numerical examples, demonstrating the performance of the algorithm, are presented.

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Metode De Calcul În Analiza Matematică, Florentin Smarandache, C. Dumitrescu Jan 1995

Metode De Calcul În Analiza Matematică, Florentin Smarandache, C. Dumitrescu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

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Generalized Geynman Integrals: The 𝓛(L2, L2) Theory, Chull Park, David Skough Jan 1995

Generalized Geynman Integrals: The 𝓛(L2, L2) Theory, Chull Park, David Skough

Department of Mathematics: Faculty Publications

In this paper we develop an 𝓛(L2(R), L2(R)) theory for the Feynman integral of functionals of general stochastic processes.

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Fixed Points Of Generalized Contractive Multi-Valued Mappings, Peter Z. Daffer, Hideaki Kaneko Jan 1995

Fixed Points Of Generalized Contractive Multi-Valued Mappings, Peter Z. Daffer, Hideaki Kaneko

Mathematics & Statistics Faculty Publications

In a recent paper N. Mizoguchi and W. Takahashi gave a positive answer to the conjecture of S. Reich concerning the existence of fixed points of multi-valued mappings that satisfy a certain contractive condition. In this paper, we provide an alternative and somewhat more straightforward proof for the theorem of Mizoguchi and Takahashi. Also the problems associated with fixed points of weakly contractive multi-valued mappings are studied. Finally, we make a few comments that improve other results from their paper (J. Math. Anal. Appl. 141 (1989), 177-188).

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A Logistic Model Of Periodic Chemotherapy, J. C. Panetta Jan 1995

A Logistic Model Of Periodic Chemotherapy, J. C. Panetta

Mathematics & Statistics Faculty Publications

A logistic differential equation with a time-varying periodic parameter is used to model the growth of cells, in particular cancer cells, in the presences of chemotherapeutic drugs. The chemotherapeutic effects are modeled by a periodic parameter that modifies the growth rate of the cell tissue. A negative growth rate represents the detrimental effects of the drugs. A simple criterion is obtained for the behavior of the chemotherapy.

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Error Estimates And Lipschitz Constants For Best Approximation In Continuous Function Spaces, M. Bartelt, W. Li Jan 1995

Error Estimates And Lipschitz Constants For Best Approximation In Continuous Function Spaces, M. Bartelt, W. Li

Mathematics & Statistics Faculty Publications

We use a structural characterization of the metric projection PG(f), from the continuous function space to its one-dimensional subspace G, to derive a lower bound of the Hausdorff strong unicity constant (or weak sharp minimum constant) for PG and then show this lower bound can be attained. Then the exact value of Lipschitz constant for PG is computed. The process is a quantitative analysis based on the Gâteaux derivative of PG, a representation of local Lipschitz constants, the equivalence of local and global Lipschitz constants for lower semicontinuous mappings, and construction …

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Optimality Conditions For Systems Driven By Nonlinear Evolution Equations, Nikolaos S. Papageorgiou Jan 1995

Optimality Conditions For Systems Driven By Nonlinear Evolution Equations, Nikolaos S. Papageorgiou

Mathematics and System Engineering Faculty Publications

Using the Dubovitskii-Milyutin theory we derive necessary and sufficient conditions for optimality for a class of Lagrange optimal control problems monitored by a nonlinear evolution equation and involving initial and/or terminal constraints. An example of a parabolic control system is also included.

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Modelling And Risk Analysis Of The Western Rock Lobster (Panulirus Cygnus) Fishery Of Western Australia, C. S. Yap Jan 1995

Modelling And Risk Analysis Of The Western Rock Lobster (Panulirus Cygnus) Fishery Of Western Australia, C. S. Yap

Theses: Doctorates and Masters

The predictive power for short-term forecasting of selected biomass dynamic models was examined using the standardised catch and effort data from the 1944/45 to 1990/91 season of the western rock lobster. Risk analysis of the fishery based on the predicted fishing efforts with the Deriso-Schnute delay-difference model indicates a high probability of recruitment failure. Some hypothetical management strategies of reducing fishing effort were evaluated by taking into consideration the total catch and biological risk to the fishery.

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