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Tytuł:
A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis
Autorzy:
Cherniha, R.
Stachowska-Piętka, J.
Waniewski, J.
Powiązania:
https://bibliotekanauki.pl/articles/907934.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
fluid transport
transport in peritoneal dialysis
nonlinear partial differential equations
ordinary differential equation
steady-state solution
transport płynu
dializa otrzewnowa
nieliniowe równanie różniczkowe
równanie różniczkowe zwyczajne
Opis:
A mathematical model for fluid and solute transport in peritoneal dialysis is constructed. The model is based on a three-component nonlinear system of two-dimensional partial differential equations for fluid, glucose and albumin transport with the relevant boundary and initial conditions. Our aim is to model ultrafiltration of water combined with inflow of glucose to the tissue and removal of albumin from the body during dialysis, by finding the spatial distributions of glucose and albumin concentrations as well as hydrostatic pressure. The model is developed in one spatial dimension approximation, and a governing equation for each of the variables is derived from physical principles. Under some assumptions the model can be simplified to obtain exact formulae for spatially non-uniform steady-state solutions. As a result, the exact formulae for fluid fluxes from blood to the tissue and across the tissue are constructed, together with two linear autonomous ODEs for glucose and albumin concentrations in the tissue. The obtained analytical results are checked for their applicability for the description of fluid-glucose-albumin transport during peritoneal dialysis.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2014, 24, 4; 837-851
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework
Autorzy:
Chaturantabut, Saifon
Powiązania:
https://bibliotekanauki.pl/articles/1838159.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
model order reduction
ordinary differential equation
partial differential equation
proper orthogonal decomposition
discrete empirical interpolation method
redukcja rzędu modelu
równanie różniczkowe zwyczajne
równanie różniczkowe cząstkowe
rozkład ortogonalny
Opis:
This work develops a technique for constructing a reduced-order system that not only has low computational complexity, but also maintains the stability of the original nonlinear dynamical system. The proposed framework is designed to preserve the contractivity of the vector field in the original system, which can further guarantee stability preservation, as well as provide an error bound for the approximated equilibrium solution of the resulting reduced system. This technique employs a low-dimensional basis from proper orthogonal decomposition to optimally capture the dominant dynamics of the original system, and modifies the discrete empirical interpolation method by enforcing certain structure for the nonlinear approximation. The efficiency and accuracy of the proposed method are illustrated through numerical tests on a nonlinear reaction diffusion problem.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2020, 30, 4; 615-628
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the controllability of fractional dynamical systems
Autorzy:
Balachandran, K.
Kokila, J.
Powiązania:
https://bibliotekanauki.pl/articles/330108.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
sterowalność
równanie różniczkowe ułamkowe
funkcja Mittag-Lefflera
controllability
fractional differential equations
Mittag-Leffler function
Opis:
This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder's fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2012, 22, 3; 523-531
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Controllability of nonlinear implicit fractional integrodifferential systems
Autorzy:
Balachandran, K.
Divya, S.
Powiązania:
https://bibliotekanauki.pl/articles/329784.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
controllability
fractional derivative
integrodifferential equations
fixed point theorem
sterowalność
pochodna ułamkowa
równanie różniczkowe
punkty stałe
Opis:
In this paper, we study the controllability of nonlinear fractional integrodifferential systems with implicit fractional derivative. Sufficient conditions for controllability results are obtained through the notion of the measure of noncompactness of a set and Darbo’s fixed point theorem. Examples are included to verify the result.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2014, 24, 4; 713-722
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Fast State-Space Algorithms for Predictive Control
Autorzy:
Błachuta, M. J.
Powiązania:
https://bibliotekanauki.pl/articles/908313.pdf
Data publikacji:
1999
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
równanie różniczkowe Riccatiego
równanie Chandrasekhara
sterowanie predykcyjne
Riccati equation
Chandrasekhar equation
LQG control
predictive control
Opis:
A Riccati-equation-based solution to a class of receding-horizon predictive control problems for an explicit-delay state-space model of an ARMAX system is found and the corresponding vector Chandrasekhar-type equations are derived for both filter and controller gains to improve the computational efficiency.
Źródło:
International Journal of Applied Mathematics and Computer Science; 1999, 9, 1; 149-160
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A modified filter SQP method as a tool for optimal control of nonlinear systems with spatio-temporal dynamics
Autorzy:
Rafajłowicz, E.
Styczeń, K.
Rafajłowicz, W.
Powiązania:
https://bibliotekanauki.pl/articles/331421.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
programowanie nieliniowe
sterowanie optymalne
równanie różniczkowe cząstkowe
filter approach
nonlinear programming
optimal control
partial differential equations
Opis:
Our aim is to adapt Fletcher's filter approach to solve optimal control problems for systems described by nonlinear Partial Differential Equations (PDEs) with state constraints. To this end, we propose a number of modifications of the filter approach, which are well suited for our purposes. Then, we discuss possible ways of cooperation between the filter method and a PDE solver, and one of them is selected and tested.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2012, 22, 2; 313-326
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Verified solution method for population epidemiology models with uncertainty
Autorzy:
Enszer, J. A.
Stadtherr, M. A.
Powiązania:
https://bibliotekanauki.pl/articles/930132.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
dynamika nieliniowa
epidemiologia
analiza interwałowa
równanie różniczkowe
nonlinear dynamics
epidemiology
interval analysis
verified computing
ordinary differential equations
Opis:
Epidemiological models can be used to study the impact of an infection within a population. These models often involve parameters that are not known with certainty. Using a method for verified solution of nonlinear dynamic models, we can bound the disease trajectories that are possible for given bounds on the uncertain parameters. The method is based on the use of an interval Taylor series to represent dependence on time and the use of Taylor models to represent dependence on uncertain parameters and/or initial conditions. The use of this method in epidemiology is demonstrated using the SIRS model, and other variations of Kermack-McKendrick models, including the case of time-dependent transmission.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2009, 19, 3; 501-512
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Behaviour of Solutions to Marchuks Model Depending on a Time Delay
Autorzy:
Bodnar, M.
Foryś, U.
Powiązania:
https://bibliotekanauki.pl/articles/929743.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
antygen
przeciwciało
opóźnienie różniczkowe
antigen
antibody
plasma cell
organ-target
delay differential equation
stationary state
stability
bifurcation point
Opis:
Marchuk's model of an immune reaction is a system of differential equations with a time delay. The aim of this paper is to study the behaviour of solutions to Marchuk's model depending upon the delay of immune reaction and the history of an illness. We study Marchuk's model without delays, with aconstant delay and with an infinite delay. A continuous dependence on thedelay is considered. Bifurcation points are found using computer simulations.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2000, 10, 1; 97-112
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Matrix Quadratic Equations, Column/row Reduced Factorizations and an Inertia Theorem for Matrix Polynomials
Autorzy:
Karelin, I.
Lerer, L.
Powiązania:
https://bibliotekanauki.pl/articles/908122.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
macierz
równanie różniczkowe Riccatiego
matrix quadratic equations
Bezoutians
inertia
column (row) reduced polynomials
factorization
algebraic Riccati equation
extremal solutions
Opis:
It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial G(lambda) (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of G(lambda). The proof of these results depends heavily on a new inertia theorem for matrix polynomials which is also one of the main results in this paper.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2001, 11, 6; 1285-1310
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A novel interval arithmetic approach for solving differential-algebraic equations with VALENCIA-IVP
Autorzy:
Rauh, A.
Brill, M.
Günther, C.
Powiązania:
https://bibliotekanauki.pl/articles/930113.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
równanie różniczkowe
symulacja sprawdzona
sterowanie odwrotne
ordinary differential equations
differential algebraic equations
VALENCIA-IVP
verified simulation
inverse control problems
Opis:
The theoretical background and the implementation of a new interval arithmetic approach for solving sets of differential-algebraic equations (DAEs) are presented. The proposed approach computes guaranteed enclosures of all reachable states of dynamical systems described by sets of DAEs with uncertainties in both initial conditions and system parameters. The algorithm is based on VALENCIA-IVP, which has been developed recently for the computation of verified enclosures of the solution sets of initial value problems for ordinary differential equations. For the application to DAEs, VALENCIA-IVP has been extended by an interval Newton technique to solve nonlinear algebraic equations in a guaranteed way. In addition to verified simulation of initial value problems for DAE systems, the developed approach is applicable to the verified solution of the so-called inverse control problems. In this case, guaranteed enclosures for valid input signals of dynamical systems are determined such that their corresponding outputs are consistent with prescribed time-dependent functions. Simulation results demonstrating the potential of VALENCIA-IVP for solving DAEs in technical applications conclude this paper. The selected application scenarios point out relations to other existing verified simulation techniques for dynamical systems as well as directions for future research.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2009, 19, 3; 381-397
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Feedback design of differential equations of reconstruction for second-order distributed parameter systems
Autorzy:
Maksimov, V. I.
Mordukhovich, B. S.
Powiązania:
https://bibliotekanauki.pl/articles/330817.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
partial differential equation
equations of reconstruction
distributed parameter system
równanie różniczkowe cząstkowe
układ o parametrach rozłożonych
równanie drugiego rzędu
Opis:
The paper aims at studying a class of second-order partial differential equations subject to uncertainty involving unknown inputs for which no probabilistic information is available. Developing an approach of feedback control with a model, we derive an efficient reconstruction procedure and thereby design differential equations of reconstruction. A characteristic feature of the obtained equations is that their inputs formed by the feedback control principle constructively approximate unknown inputs of the given second-order distributed parameter system.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2017, 27, 3; 467-475
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The controllability of nonlinear implicit fractional delay dynamical systems
Autorzy:
Joice Nirmala, R.
Balachandran, K.
Powiązania:
https://bibliotekanauki.pl/articles/331001.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
controllability
fractional delay
differential equation
Mittag-Leffler function
fixed point theorem
sterowalność
opóźnienie ułamkowe
równanie różniczkowe
funkcja Mittag-Lefflera
Opis:
This paper is concerned with the controllability of nonlinear fractional delay dynamical systems with implicit fractional derivatives for multiple delays and distributed delays in control variables. Sufficient conditions are obtained by using the Darbo fixed point theorem. Further, examples are given to illustrate the theory.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2017, 27, 3; 501-513
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlinear state observers and extended Kalman filters for battery systems
Autorzy:
Rauh, A.
Butt, S. S.
Aschemann, H.
Powiązania:
https://bibliotekanauki.pl/articles/330696.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
observer
state estimation
Riccati equations
extended Kalman filter
parameter estimation
obserwator
estymacja stanu
równanie różniczkowe Riccatiego
filtr Kalmana
estymacja parametryczna
Opis:
The focus of this paper is to develop reliable observer and filtering techniques for finite-dimensional battery models that adequately describe the charging and discharging behaviors. For this purpose, an experimentally validated battery model taken from the literature is extended by a mathematical description that represents parameter variations caused by aging. The corresponding disturbance models account for the fact that neither the state of charge, nor the above-mentioned parameter variations are directly accessible by measurements. Moreover, this work provides a comparison of the performance of different observer and filtering techniques as well as a development of estimation procedures that guarantee a reliable detection of large parameter variations. For that reason, different charging and discharging current profiles of batteries are investigated by numerical simulations. The estimation procedures considered in this paper are, firstly, a nonlinear Luenberger-type state observer with an offline calculated gain scheduling approach, secondly, a continuous-time extended Kalman filter and, thirdly, a hybrid extended Kalman filter, where the corresponding filter gains are computed online.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2013, 23, 3; 539-556
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlinear filtering for Markov systems with delayed observations
Autorzy:
Calzolari, A.
Florchinger, P.
Nappo, G.
Powiązania:
https://bibliotekanauki.pl/articles/907856.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
filtracja nieliniowa
proces dyfuzji
procesy Markova
stochastyczne równanie różniczkowe
nonlinear filtering
jump processes
diffusion processes
Markov processes
stochastic delay differential equation
Opis:
This paper deals with nonlinear filtering problems with delays, i.e., we consider a system (X,Y ), which can be represented by means of a system [...], in the sense that [...], where a(t) is a delayed time transformation. We start with X being a Markov process, and then study Markovian systems, not necessarily diffusive, with correlated noises. The interest is focused on the existence of explicit representations of the corresponding filters as functionals depending on the observed trajectory. Various assumptions on the function a(t) are considered.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2009, 19, 1; 49-57
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Travelling waves for low-grade glioma growth and response to a chemotherapy model
Autorzy:
Bartłomiejczyk, Agnieszka
Bodnar, Marek
Bogdańska, Magdalena U.
Piotrowska, Monika J.
Powiązania:
https://bibliotekanauki.pl/articles/24202933.pdf
Data publikacji:
2023
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
low grade glioma
generalized model
partial differential equation
wave solution
chemotherapy model
glejak
model uogólniony
równanie różniczkowe cząstkowe
rozwiązanie falowe
model chemioterapii
Opis:
Low-grade gliomas (LGGs) are primary brain tumours which evolve very slowly in time, but inevitably cause patient death. In this paper, we consider a PDE version of the previously proposed ODE model that describes the changes in the densities of functionally alive LGGs cells and cells that are irreversibly damaged by chemotherapy treatment. Besides the basic mathematical properties of the model, we study the possibility of the existence of travelling wave solutions in the framework of Fenichel’s invariant manifold theory. The estimates of the minimum speeds of the travelling wave solutions are provided. The obtained analytical results are illustrated by numerical simulations.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2023, 33, 4; 569--581
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 22

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