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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:
A quantitative management support model for a certain production supply system in non-extreme states
Autorzy:
Galanc, T.
Kołwzan, W.
Pieronek, J.
Powiązania:
https://bibliotekanauki.pl/articles/406677.pdf
Data publikacji:
2012
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
production supply system
process
non-extreme state
system of differential equations
Opis:
The paper is devoted to building a probabilistic method of analyzing the operation of a certain production supply system. The analysis is carried out for non-extreme states of the level in store, into which two separate streams of production (the product) are directed. A system of partial differential equations describing this case was derived which is satisfied by the joint density function defining the probabilities of states of the three-dimensional process characterizing the system’s functioning.
Źródło:
Operations Research and Decisions; 2012, 22, 1; 5-12
2081-8858
2391-6060
Pojawia się w:
Operations Research and Decisions
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A quantitative management support model of a certain production - supply system : boundary conditions
Autorzy:
Galanc, T.
Kołwzan, W.
Pieronek, J.
Powiązania:
https://bibliotekanauki.pl/articles/406454.pdf
Data publikacji:
2012
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
production-supply system
process
boundary state
system of differential equations
Opis:
The paper is dedicated to constructing a method for the probabilistic analysis of the functioning a certain production-supply system. Previously a set of partial differential equations has been derived satisfied by the joint density function of the state of a three-dimensional process characterizing the functioning of the system. The operation of the system at the boundaries of the stock levels is analyzed. Two sets of differential equations have been derived, one describing the operation of the system when the stock level is zero and one describing the operation of the system when the stocks are full.
Źródło:
Operations Research and Decisions; 2012, 22, 2; 5-13
2081-8858
2391-6060
Pojawia się w:
Operations Research and Decisions
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Algebraic forms of solutions of linear state equations for determined control vectors
Autorzy:
Porada, Ryszard
Mielczarek, Norbert
Powiązania:
https://bibliotekanauki.pl/articles/376440.pdf
Data publikacji:
2020
Wydawca:
Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Tematy:
state equation
solutions of state equations
algebraic forms
Opis:
Despite intensive development of numerical methods of resolution of ordinary differential equations, we still seek analytical solutions of these equations in the algebraic form. The analytical solution in an algebraic form, is very convenient in case of investigation of the course of solution in a large interval of changes of parameters, it also gives more qualitative informations. This concerns first of all linear equations which are the most often met models of physical objects. Important advantage of these solutions is also their open form regarding established state of the system. The paper proves existence of algebraic forms of solutions of control vectors with components: exponential, sinusoidal with different circular frequencies and sinusoidal multiple. Also solutions for other kind of control vectors which are mentioned in the literature are presented.
Źródło:
Poznan University of Technology Academic Journals. Electrical Engineering; 2020, 104; 75-86
1897-0737
Pojawia się w:
Poznan University of Technology Academic Journals. Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of the classical implicit function theorem in sensitivity analysis of parametric optimal control
Autorzy:
Malanowski, K.
Powiązania:
https://bibliotekanauki.pl/articles/206654.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
równania różniczkowe nieliniowe
różniczkowalność rozwiązań
sterowanie optymalne parametryczne
differentiability of solutions
implicit function theorem
nonlinear ordinary differential equations
parametric optimal control
state constraints
Opis:
A family {(O[sub h])} of parametric optimal control problems for nonlinear ODEs is considered. The problems are subject to pointwise inequality type state constraints. It is assumed that the reference solution is regular. The original problems (O[sub h]) are substituted by problems [...] subject to equality type constraints with the sets of activity depending on the parameter. Using the classical implicit function theorem, conditions are derived under which stationary points of [...] are Frechet differentiable functions of the parameter. It is shown that, under additional conditions, the stationary points of [...] correspond to the solutions and Lagrange multipliers of (O[sub h]9).
Źródło:
Control and Cybernetics; 1998, 27, 3; 335-352
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximate state-space and transfer function models for 2x2 linear hyperbolic systems with collocated boundary inputs
Autorzy:
Bartecki, Krzysztof
Powiązania:
https://bibliotekanauki.pl/articles/330464.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
distributed parameter system
hyperbolic equations
approximation model
state space
transfer function
układ o parametrach rozłożonych
równanie hiperboliczne
model aproksymacyjny
przestrzeń stanu
funkcja przesyłowa
Opis:
Two approximate representations are proposed for distributed parameter systems described by two linear hyperbolic PDEs with two time- and space-dependent state variables and two collocated boundary inputs. Using the method of lines with the backward difference scheme, the original PDEs are transformed into a set of ODEs and expressed in the form of a finite number of dynamical subsystems (sections). Each section of the approximation model is described by state-space equations with matrix-valued state, input and output operators, or, equivalently, by a rational transfer function matrix. The cascade interconnection of a number of sections results in the overall approximation model expressed in finite-dimensional state-space or rational transfer function domains, respectively. The discussion is illustrated with a practical example of a parallel-flow double-pipe heat exchanger. Its steady-state, frequency and impulse responses obtained from the original infinite-dimensional representation are compared with those resulting from its approximate models of different orders. The results show better approximation quality for the “crossover” input–output channels where the in-domain effects prevail as compared with the “straightforward” channels, where the time-delay phenomena are dominating.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2020, 30, 3; 475-491
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Charakterystyki detonacyjne FOX-7 i równania stanu jego produktów detonacji
Detonation characteristics of FOX-7 and equations of state for its detonation products
Autorzy:
Trzciński, W. A.
Cudziło, S.
Chyłek, Z.
Szymańczyk, L.
Powiązania:
https://bibliotekanauki.pl/articles/210215.pdf
Data publikacji:
2007
Wydawca:
Wojskowa Akademia Techniczna im. Jarosława Dąbrowskiego
Tematy:
materiały wybuchowe
detonacja
równania stanu produktów detonacji
explosives
detonation
equations of state of detonation products
Opis:
Dokonano optymalizacji metody rekrystalizacji nowego materiału wybuchowego DADNE (FOX-7) pod kątem uzyskania drobnoziarnistego produktu o obniżonej wrażliwości na bodźce mechaniczne. Zbadano wrażliwość otrzymanego produktu na falę uderzeniową. Natomiast ciśnienie detonacji oraz równania stanu dla produktów detonacji wyznaczono dla gruboziarnistego FOX-7.
Optimization of the recrystallization method of the new explosive FOX-7 has been done to obtain a fine-grained product of low-sensitivity to the mechanical stimuli. The sensitivity to shock wave has been investigated for the obtained product. The detonation pressure and equations of state for the detonation products of coarse-grained FOX-7 have been determined, as well.
Źródło:
Biuletyn Wojskowej Akademii Technicznej; 2007, 56, 2; 283-296
1234-5865
Pojawia się w:
Biuletyn Wojskowej Akademii Technicznej
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Classes of relativistic stars with quadratic equation of state
Autorzy:
Malaver, Manuel
Powiązania:
https://bibliotekanauki.pl/articles/1194131.pdf
Data publikacji:
2016
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Charge anisotropic matter distribution
Charge density
Field equations
Gravitational potential
Radial pressure
quadratic equation of state
Opis:
In this paper, we found new exact solutions to the Einstein-Maxwell system of equations with charged anisotropic matter distribution considering quadratic equation of state. We specify the gravitational potential Z(x) that depends of a adjustable parameter n and that allow integrate analytical the field equations in order to calculate the energy density, the radial pressure, the anisotropy, charge density and the mass function for different values of n. The obtained solutions can be written in terms of elementary and polynomial functions.
Źródło:
World Scientific News; 2016, 57; 58-68
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Complementary analysis of the initial value problem for a system of o.d.e. modelling the immune system after vaccinations
Autorzy:
Foryś, Urszula
Żołek, Norbert
Powiązania:
https://bibliotekanauki.pl/articles/1208222.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
VT-complex
antibody
antigen
B-cell
plasma cell
stationary state
stability
ordinary differential equations
lymphocyte
phase space
Opis:
Complementary analysis of a model of the human immune system after a series of vaccinations, proposed in [7] and studied in [6], is presented. It is shown that all coordinates of every solution have at most two extremal values. The theoretical results are compared with experimental data.
Źródło:
Applicationes Mathematicae; 2000, 27, 1; 103-111
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Delay differential equations: theory and applications
Autorzy:
Bodnar, Marek
Piotrowska, Monika Joanna
Powiązania:
https://bibliotekanauki.pl/articles/748670.pdf
Data publikacji:
2010
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
delay differential equations, uniqueness of solutions, stability of s steady state, Hopf bifurcation, mathematical models
Opis:
 Równania różniczkowe z opóźnionym argumentem pojawiają się w modelach matematycznych dotyczących zagadnień biologicznych, biochemicznych czy medycznych. Chociaż sama struktura równań jest podobna do równań różniczkowych zwyczajnych, to jednak istnieje zasadnicza różnica: równanie czy układ równań z opóźnieniem jest problemem nieskończeniewymiarowym z odpowiadającą mu przestrzenią fazową będącą przestrzenią funkcyjną — zwykle rozważamy przestrzeń funkcji ciągłych. W tej pracy przestawiamy podstawową teorię dotyczącą tej klasy równań, jak również kilka przykładów zastosowań równań z opóźnieniem do opisu zagadnień biologicznych, medycznych i biochemicznych.Słowa kluczowe: równania różniczkowe z opóźnieniem, jednoznaczność rozwiązań, stabilność stanu stacjonarnego, bifurkacja Hopfa, modele matematyczne
Delay differential equations are used in mathematical models of biological, biochemical or medical phenomenons. Although the structure of these equations is similar to ordinary differential equations, the crucial difference is that a delay differential equation (or a system of equations) is an infinite dimensional problem and the corresponding phase space is a functional space — usually the space of continuous functions is considered.In this paper we present the basic theory of delay differential equations as well as some example of applications to models of biological, medical and biochemical systems.
Źródło:
Mathematica Applicanda; 2010, 38, 1
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Error estimates for the finite-element approximation of an elliptic control problem with pointwise state and control constraints
Autorzy:
Meyer, C.
Powiązania:
https://bibliotekanauki.pl/articles/971011.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
równanie eliptyczne
aproksymacja numeryczna
linear quadratic optimal control problems
elliptic equations
state constraints
numerical approximation
Opis:
We consider a linear-quadratic elliptic optimal control problem with pointwise state constraints. The problem is fully discretized using linear ansatz functions for state and control. Based on a Slater-type argument, we investigate the approximation behavior for mesh size tending to zero. The obtained convergence order for the L²-error of the control and for H 1-error of the state is 1 - ε in the two-dimensional case and 1/2 - ε in three dimensions, provided that the domain satisfies certain regularity assumptions. In a second step, a state-constrained problem with additional control constraints is considered. Here, the control is discretized by constant ansatz functions. It is shown that the convergence theory can be adapted to this case yielding the same order of convergence. The theoretical findings are confirmed by numerical examples.
Źródło:
Control and Cybernetics; 2008, 37, 1; 51-83
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Exact penalization of pointwise constraints for optimal control problems
Autorzy:
Casas, E.
Powiązania:
https://bibliotekanauki.pl/articles/970884.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
semilinear elliptic equations
pointwise state constraints
exact penalization
first and second order optimality conditions
Opis:
In this paper we consider a control problem governed by a semilinear elliptic equation with pointwise control and state constraints. We analyze the existence of an exact penalization of the state constraints. In particular, we prove that the first and second order optimality conditions imply the existence of such a penalization. Finally, we prove some extra regularity of the strict local minima of the control problem, assuming the existence of an exact penalization for them.
Źródło:
Control and Cybernetics; 2009, 38, 4A; 1131-1150
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence and controllability results for damped second order impulsive functional differential systems with state-dependent delay
Autorzy:
Arjunan, M. M.
Nadaf, N. Y.
Powiązania:
https://bibliotekanauki.pl/articles/255760.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
damped second order differential equations
impulsive differential equations
controllability
state-dependent delay
cosine function
mild solution
fixed point
Opis:
In this paper, we investigate the existence and controllability of mild solutions for a damped second order impulsive functional differential equation with state-dependent delay in Banach spaces. The results are obtained by using Sadovskii’s fixed point theorem combined with the theories of a strongly continuous cosine family of bounded linear operators. Finally, an example is provided to illustrate the main results.
Źródło:
Opuscula Mathematica; 2014, 34, 3; 503-522
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Finite element error analysis for state-constrained optimal control of the Stokes equations
Autorzy:
Los Reyes, J. C. de
Meyer, C.
Vexler, B.
Powiązania:
https://bibliotekanauki.pl/articles/969607.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
równanie Stokesa
aproksymacja numeryczna
element skończony
linear quadratic optimal control problems
Stokes equations
state constraints
numerical approximation
finite elements
Opis:
An optimal control problem for 2d and 3d Stokes equations is investigated with pointwise inequality constraints on the state and the control. The paper is concerned with the full discretization of the control problem allowing for different types of discretization of both the control and the state. For instance, piecewise linear and continuous approximations of the control are included in the present theory. Under certain assumptions on the L∞-error of the finite element discretization of the state, error estimates for the control are derived which can be seen to be optimal since their order of convergence coincides with the one of the interpolation error. The assumptions of the L∞-finite-eleinent-error can be verified for different numerical settings. Finally the results of two numerical experiments are presented.
Źródło:
Control and Cybernetics; 2008, 37, 2; 251-284
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Finite-time SDRE control of F16 aircraft dynamics
Autorzy:
Chodnicki, Marcin
Pietruszewski, Paweł
Wesołowski, Mariusz
Stępień, Sławomir
Powiązania:
https://bibliotekanauki.pl/articles/2175113.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
aircraft modelling
state-dependent Riccati equations
finite-time optimal control
Opis:
This paper proposes a finite-time horizon suboptimal control strategy based on state-dependent Riccati equation (SDRE) to control of F16 multirole aircraft. Flight stabilizer control of super maneuverable aircraft is modelled and simulated. For aircraft modelling purpose a full 6 DOF model is considered and described by nonlinear state-space approach. Also a stable state-dependent parametrization (SDP) necessary for solution of the SDRE control problem is proposed. Solution of the SDRE control problem with adequate defined weighting matrices in performance index shows possibility of fast and optimal aircraft control in finite-time. The method in this form can be used for stabilization of aircraft flight and aerodynamics.
Źródło:
Archives of Control Sciences; 2022, 32, 3; 557--576
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 27

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