Capillary operators—II
| Autor: | J. M. Bateman |
|---|---|
| Rok vydání: | 1985 |
| Předmět: |
Pharmacology
Pure mathematics Normed algebra General Mathematics General Neuroscience Immunology Mathematical analysis Inverse Models Biological Permeability General Biochemistry Genetics and Molecular Biology Addition theorem Capillaries Operator (computer programming) Computational Theory and Mathematics Banach algebra Filtration (mathematics) Animals Algebraic number General Agricultural and Biological Sciences Commutative property Mathematics General Environmental Science |
| Zdroj: | Bulletin of Mathematical Biology. 47:651-668 |
| ISSN: | 1522-9602 0092-8240 |
| DOI: | 10.1007/bf02460131 |
| Popis: | This work continues with an examination of capillary exchange models as operators, namely the operatorsO k andK αk relating extravascular and intravascular concentration to input for the Krogh cylinder model of a single capillary, a model basic to many organ models. Fundamental algebraic and analytic properties are presented: the operators belong to a commutative Banach algebra; an addition theorem holdsK αk +K βk =K α+β,k ; the operatorK αk has an inverse;K -1 , (as an operator on LebesgueL p space or on the locally integrable functions); partial derivatives are given forK αk [f](t) andO k [f](t) (sensitivity functions); and inequalities are established for the derivatives. Dominance relations between model curves are inferred. Error bound formulas are presented forK andO as bounds on ‖K αk f-K βl f‖ p and ‖O k f-O l f‖ p for allL p . Consequent limitations on relative errors are shown. The implications for operators on a finite time interval are deduced. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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