Wyniki wyszukiwania - BazTech

1

Comparison between two approaches to modeling microsatellite DNA repeats: infinite dimensional model and its n-dimensional

Białka M.

Archives of Control Sciences

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2011

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Vol. 21, no. 4

419-441

EN

Two approaches to modeling microsatellite DNA repeats are considered. The former is an infinite dimensional system based on the theory of branching random walks which dynamic properties are characterized using Laplace transforms and Laplace asymptotic techniques. The latter is an n-dimensional approximation where microsatellite DNA repeats model is the example of a chain system. Both models were the subject of many numerical calculations using the MATLAB software. The results allow us to evaluate the asymptotic behavior and determine the effect of the system parameters on the run of the solution and the state variables.

2

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.

3

Exact Observability of Diagonal Systems With a One-Dimensional Output Operator

Jacob B., Zwart H.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 6

1277-1283

EN

In this paper equivalent conditions for exact observability of diagonal systems with a one-dimensional output operator are given. One of these equivalent conditions is the conjecture of Russell and Weiss (1994). The other conditions are given in terms of the eigenvalues and the Fourier coefficients of the system data.

4

Constrained Controllability of Dynamic Systems

Klamka J.

International Journal of Applied Mathematics and Computer Science

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1999

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Vol. 9, no 2

231-244

EN

The present paper is devoted to a study of constrained controllability and controllability for linear dynamic systems if the controls are taken to be non-negative. By analogy to the usual definition of controllability it is possible to introduce the concept of positive controllability. Weshall concentrate on approximate positive controllability for linear infinite-dimensional dynamic systems when the values of controls are taken from a positive closed convex cone and the operator of the system is normal and has pure discrete point spectrum. Special attention is paid to positive infinite-dimensional linear dynamic systems. General approximate constrained controllability results are then applied to distributed-parameter dynamic systems described by linear partial-differential equations of parabolic type with various kinds of boundary conditions. Several remarks and comments on the relationships between different concepts of controllability are given. Finally, a simple illustrative example is also presented.

5

Unit sliding mode control in infinite dimensional systems

Orlov Y., Utkin V. I.

Applied Mathematics and Computer Science

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1998

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Vol. 8, no 1

7-20

EN

In contrast to the conventional component-wise design of sliding mode controI, a new approach is developed for infinite-dimensional systems. The conventional approach is not applicable since, generally speaking, the infinite-dimensional controI may not be represented in the component form as well as a sliding manifold. The concept of "unit controI", previously introduced for finite-dimensional systems, does not depend on the dimension of controI and is generalized for the dynamic processes governed by differential equations in Banach and Hilbert spaces. The design methods for heat and mechanical distributed processes are given.

6

Controllability of second-order semilinear infinite-dimensional dynamical systems

Klamka J.

Applied Mathematics and Computer Science

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1998

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Vol. 8, no 3

459-470

EN

In the paper, the approximate controllability of semilinear abstract second-order infinite-dimensional dynamical systems is considered. It is proved by using the frequency-domain and functional-analysis methods that the approximate controllability of second-order semilinear dynamical system can be verified by the approximate controllability conditions for a simplified suitably-defined firstorder linear dynamical system. General results are then applied to a semilinear mechanical flexible-structure vibratory dynamical system. Some special cases are also considered. Moreover, remarks and comments on the relationships between different concepts of controllability are given. The paper extends the results presented in (Klamka, 1992; Triggiani, 1978) to a more generaI class of second-order abstract dynamical systems.