Wyniki wyszukiwania - BazTech

1

Are infinite dimensional models applicable in modelling and analysis of cancer chemotherapy?

Świerniak A., Kimmel M., Śmieja J., Rzeszowska-Wolny J.

Journal of Medical Informatics & Technologies

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2004

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Vol. 8

MM3--10

EN

Drug resistance and phase dependence have been regarded by many authors as the main obstacles against successful cancer chemotherapy. We propose a model which takes into account both these phenomena and give a tool to use phase specificity as an advantage rather than a fault and make it resistant of drug resistance. It combines models that so far have been studied separately, taking into account both the phenomenon of gene amplification and drug specificity in chemotherapy, in their different aspects. The mathematical description is given by an infinite dimensional state equation with a system matrix, the form of which enables decomposition of the model into two interacting subsystems. While the first one, of finite dimension, can have any form, the second one is infinite dimensional and tridiagonal.

2

Optimal multidrug treatment in the presence of drug resistance stemming from gene amplification

Śmieja J., Świerniak A.

Journal of Medical Informatics & Technologies

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2002

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Vol. 3

MI13--19

EN

The paper is concerned with development of optimal treatment protocols that take into account both action of several drugs and the evolution of drug resistance. It is a result of analysis of evolution of drug resistance in cancer population but presented methodology can be applied in any case involving drug resistance stemming from gene amplification. First, a biological background is given. In subsequent sections of the paper, the developed technique is presented and some early analytical results, which form a basis for more precise modeling, are shown. Afterwards, the model description is transformed into a vector integro-differential equation, which makes it possible to define necessary conditions of optimal solution to the minimization problem arising from the search for the optimal treatment. Finally, some remarks on the model applicability are presented.

3

Obserbability of infinite-dimensional finitely presented discrete-time linear systems

Bartosiewicz Z., Mozyrska D.

Zeszyty Naukowe Politechniki Białostockiej. Matematyka, Fizyka, Chemia

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2001

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Z. 20

5--14

EN

Discrete-time infinite-dimensional linear dynamic systems, with one-dimensional output, are studied. They are described by infinite matrices that are row-finite. Observability of such systems is investigated. It may be described as the property that one can calculate the value of each state variable using only finitely many rows of observability matrix. Different conditions of observability of such systems are given.

PL

Badane są nieskończenie wymiarowe liniowe układy dynamiczne z dyskretnym czasem i z jednowymiarowym wyjściem. Układy te opisane są przez nieskończone macierze o skończonych wierszach". Zbadano obserwowalność takich układów. Własność ta została scharakteryzowana następująco: wartość zmiennej stanu może być wyliczona na podstawie skończenie wielu wierszy macierzy obserwowalności. Pokazano kilka innych warunków na obserwowalność.

4

Controllability of discrete-time infinite-dimensional linear systems

Żebrowska-Suchodolska D.

Zeszyty Naukowe Politechniki Białostockiej. Matematyka, Fizyka, Chemia

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2001

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Z. 20

99--106

EN

Discrete-time infinite-dimensional linear control systems, with one-dimensional output, are studie 1. They are described by infinite matrices with finite columns i.e. columns whh finitely many nonzero elements. Conditions of controllability of such systems are given.

PL

Zbadano nieskończenie wymiarowe liniowe układy sterowania z dyskretnym czasem i jednowymiarowym wyjściem. Opisane są one przez nieskończone macierze ze "skończonymi kolumnami", tzn. kolumnami mającymi skończenie wiele niezerowyrh elementów. Warunki na sterowalność takich układów zostały podane.