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Wyświetlanie 1-15 z 16
Tytuł:
Gradient Observability for Diffusion Systems
Autorzy:
Zerrik, E. H.
Bourray, H.
Powiązania:
https://bibliotekanauki.pl/articles/908195.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
informatyka
diffusion system
observability
regional gradient observability
gradient strategic sensor
gradient reconstruction
Opis:
The aim of this paper is to study regional gradient observability for a diffusion system and the reconstruction of the state gradient without the knowledge of the state. First, we give definitions and characterizations of these new concepts and establish necessary conditions for the sensor structure in order to obtain regional gradient observability. We also explore an approach which allows for a regional gradient reconstruction. The developed method is original and leads to a numerical algorithm illustrated by simulations.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2003, 13, 2; 139-150
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Applications of the fractional Sturm-Liouville difference problem to the fractional diffusion difference equation
Autorzy:
Malinowska, Agnieszka B.
Odzijewicz, Tatiana
Poskrobko, Anna
Powiązania:
https://bibliotekanauki.pl/articles/24200687.pdf
Data publikacji:
2023
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
anomalous diffusion
fractional diffusion equation
fractional calculus
difference equation
dyfuzja anomalna
równanie dyfuzji ułamkowe
rachunek ułamkowy
równanie różnicowe
Opis:
This paper deals with homogeneous and non-homogeneous fractional diffusion difference equations. The fractional operators in space and time are defined in the sense of Grünwald and Letnikov. Applying results on the existence of eigenvalues and corresponding eigenfunctions of the Sturm-Liouville problem, we show that solutions of fractional diffusion difference equations exist and are given by a finite series.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2023, 33, 3; 349--359
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A numerical solution for a class of time fractional diffusion equations with delay
Autorzy:
Pimenov, V. G.
Hendy, A. S.
Powiązania:
https://bibliotekanauki.pl/articles/330624.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
fractional diffusion equation
difference scheme
convergence analysis
równanie dyfuzji ułamkowe
schemat różnicowy
analiza zbieżności
Opis:
This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ 2−α + h4) in L ∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2017, 27, 3; 477-488
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Global behavior of a multi-group SEIR epidemic model with spatial diffusion in a heterogeneous environment
Autorzy:
Liu, Pengyan
Li, Hong-Xu
Powiązania:
https://bibliotekanauki.pl/articles/2134056.pdf
Data publikacji:
2022
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
global stability
multigroup epidemic model
spatial heterogeneity
spatial diffusion
globalna stabilność
wielogrupowy model epidemii
różnorodność przestrzenna
dyfuzja przestrzenna
Opis:
In this paper, we propose a multi-group SEIR epidemic model with spatial diffusion, where the model parameters are spatially heterogeneous. The positivity and ultimate boundedness of the solution, as well as the existence of a global attractor of the associated solution semiflow, are established. The definition of the basic reproduction number is given by utilizing the next generation operator approach, whereby threshold-type results on the global dynamics in terms of this number are established. That is, when the basic reproduction number is less than one, the disease-free steady state is globally asymptotically stable, while if it is greater than one, uniform persistence of this model is proved. Finally, the feasibility of the main theoretical results is shown with the aid of numerical examples for a model with two groups.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2022, 32, 2; 271--283
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A mathematical model for file fragment diffusion and a neural predictor to manage priority queues over BitTorrent
Autorzy:
Napoli, C.
Pappalardo, G.
Tramontana, E.
Powiązania:
https://bibliotekanauki.pl/articles/331212.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
P2P model
neural network
wavelet
diffusion
file sharing
model P2P
sieć neuronowa
falka
dyfuzja
wymiana plików
Opis:
BitTorrent splits the files that are shared on a P2P network into fragments and then spreads these by giving the highest priority to the rarest fragment. We propose a mathematical model that takes into account several factors such as the peer distance, communication delays, and file fragment availability in a future period also by using a neural network module designed to model the behaviour of the peers. The ensemble comprising the proposed mathematical model and a neural network provides a solution for choosing the file fragments that have to be spread first, in order to ensure their continuous availability, taking into account that some peers will disconnect.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2016, 26, 1; 147-160
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Response of Lyapunov exponents to diffusion state of biological networks
Autorzy:
Altuntas, Volkan
Gok, Murat
Kocal, Osman Hilmi
Powiązania:
https://bibliotekanauki.pl/articles/1838156.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
synthetic network
biological network
Lyapunov exponents
sieć syntetyczna
sieć biologiczna
wykładniki Lapunova
Opis:
The topologies of protein-protein interaction networks are uncertain and noisy. The network topology determines the reliability of computational knowledge acquired from noisy networks and can impose the deterministic and non-deterministic character of the resulting data. In this study, we analyze the effect of the network topology on Lyapunov exponents and its relationship with network stability. We define the methodology to convert the network data into signal data and obtain the Lyapunov exponents for a variety of networks. We then compare the Lyapunov exponent response and the stability results. Our technique can be applied to all types of network topologies as demonstrated with our experiments, conducted on both synthetic and real networks from public databases. For the first time, this article presents findings where Lyapunov exponents are evaluated under topological mutations and used for network analysis. Experimental results show that Lyapunov exponents have a strong correlation with network stability and both are correlatively affected by the network model. Hence we develop a novel coefficient, termed LEC, to measure the robustness of biological networks. LEC can be applied to real or synthetic biological networks rapidly. Results are a striking indication that the Lyapunov exponent is a potential candidate measure for network analysis.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2020, 30, 4; 689-702
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical solutions to integral equations equivalent to differential equations with fractional time
Autorzy:
Bandrowski, B.
Karczewska, A.
Rozmej, P.
Powiązania:
https://bibliotekanauki.pl/articles/907763.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
równanie ułamkowe
metoda Galerkina
dyfuzja anomalna
fractional equations
Galerkin method
anomalous diffusion
Opis:
This paper presents an approximate method of solving the fractional (in the time variable) equation which describes the processes lying between heat and wave behavior. The approximation consists in the application of a finite subspace of an infinite basis in the time variable (Galerkin method) and discretization in space variables. In the final step, a large-scale system of linear equations with a non-symmetric matrix is solved with the use of the iterative GMRES method.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2010, 20, 2; 261-269
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Logistic Equations in Tumour Growth Modelling
Autorzy:
Foryś, U.
Marciniak-Czochra, A.
Powiązania:
https://bibliotekanauki.pl/articles/908165.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
matematyka
medycyna
logistic equation
delay differential equation
reaction-diffusion equation
stability
global stability
Hopf bifurcation
spatial pattern
Ehrlich ascities tumour
Opis:
The aim of this paper is to present some approaches to tumour growth modelling using the logistic equation. As the first approach the well-known ordinary differential equation is used to model the EAT in mice. For the same kind of tumour, a logistic equation with time delay is also used. As the second approach, a logistic equation with diffusion is proposed. In this case a delay argument in the reaction term is also considered. Some mathematical properties of the presented models are studied in the paper. The results are illustrated using computer simulations.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2003, 13, 3; 317-325
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:
A robust computational technique for a system of singularly perturbed reaction–diffusion equations
Autorzy:
Kumar, V.
Bawa, R. K.
Lal, A. K.
Powiązania:
https://bibliotekanauki.pl/articles/330202.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
asymptotic expansion approximation
backward difference operator
trapezoidal method
piecewise uniform Shishkin mesh
rozwinięcie asymptotyczne
operator różnicowy
metoda trapezowa
Opis:
In this paper, a singularly perturbed system of reaction–diffusion Boundary Value Problems (BVPs) is examined. To solve such a type of problems, a Modified Initial Value Technique (MIVT) is proposed on an appropriate piecewise uniform Shishkin mesh. The MIVT is shown to be of second order convergent (up to a logarithmic factor). Numerical results are presented which are in agreement with the theoretical results.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2014, 24, 2; 387-395
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Finite-Dimensional Control of Nonlinear Parabolic Pde Systems With Time-Dependent Spatial Domains Using Empirical Eigenfunctions
Autorzy:
Armaou, A.
Christofides, P. D.
Powiązania:
https://bibliotekanauki.pl/articles/908332.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
sterowanie nieliniowe
sterowanie skończenie wymiarowe
Karhunen-Loeve expansion
Galerkin's method
nonlinear control
diffusion-reaction processes with moving boundaries
Opis:
This article presents a methodology for the synthesis of finite-dimensional nonlinear output feedback controllers for nonlinear parabolic partial differential equation (PDE) systems with time-dependent spatial domains. Initially, the nonlinear parabolic PDE system is expressed with respect to an appropriate time-invariant spatial coordinate, and a representative (with respect to different initial conditions and input perturbations) ensemble of solutions of the resulting time-varying PDE system is constructed by computing and solving a high-order discretization of the PDE. Then, the Karhunen-Loeve expansion is directly applied to the ensemble of solutions to derive a small set of empirical eigenfunctions (dominant spatial patterns) that capture almost all the energy of the ensemble of solutions. The empirical eigenfunctions are subsequently used as basis functions within a Galerkin model reduction framework to derive low-order ordinary differential equation (ODE) systems that accurately describe the dominant dynamics of the PDE system. The ODE systems are subsequently used for the synthesis of nonlinear output feedback controllers using geometric control methods. The proposed control method is used to stabilize an unstable steady-state of a diffusion-reaction process with nonlinearities, spatially-varying coefficients and time-dependent spatial domain, and is shown to lead to the construction of accurate low-order models and the synthesis of low-order controllers. The performance of the low-order models and controllers is successfully tested through computer simulations.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2001, 11, 2; 287-317
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Path planning for an autonomous underwater vehicle in a cluttered underwater environment based on the heat method
Autorzy:
Sun, Kaiyue
Liu, Xiangyang
Powiązania:
https://bibliotekanauki.pl/articles/1838198.pdf
Data publikacji:
2021
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
autonomous underwater vehicle
path planning
heat method
heat diffusion
cost function
pojazd podwodny autonomiczny
planowanie trasy
dyfuzja ciepła
funkcja kosztu
Opis:
This paper proposes a novel autonomous underwater vehicle path planning algorithm in a cluttered underwater environment based on the heat method. The algorithm calculates the isotropic and anisotropic geodesic distances by adding the direction and magnitude of the currents to the heat method, which is named the anisotropy-based heat method. Taking account of the relevant influence of the environment on the cost functions, such as currents, obstacles and turn of the vehicle, an efficient collision-free and energy-optimized path solution can be obtained. Simulation results show that the anisotropy-based heat method is able to find a good trajectory in both static and dynamic clutter fields (including uncertain obstacles and changing currents). Compared with the fast marching (FM) algorithm, the anisotropy-based heat method is not only robust, flexible, and simple to implement, but it also greatly saves time consumption and memory footprint in a time-variant environment. Finally, the evaluation criteria of paths are proposed in terms of length, arrival time, energy consumption, and smoothness.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2021, 31, 2; 289-301
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Integrated region-based segmentation using color components and texture features with prior shape knowledge
Autorzy:
Emambakhsh, M.
Ebrahimnezhad, H.
Sedaaghi, M. H.
Powiązania:
https://bibliotekanauki.pl/articles/908141.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
segmentacja obrazów
zbiór poziomicowy
dyfuzja nieliniowa
minimalizacja energii
image segmentation
prior shape knowledge
level set
nonlinear diffusion
energy minimization
Opis:
Segmentation is the art of partitioning an image into different regions where each one has some degree of uniformity in its feature space. A number of methods have been proposed and blind segmentation is one of them. It uses intrinsic image features, such as pixel intensity, color components and texture. However, some virtues, like poor contrast, noise and occlusion, can weaken the procedure. To overcome them, prior knowledge of the object of interest has to be incorporated in a top-down procedure for segmentation. Consequently, in this work, a novel integrated algorithm is proposed combining bottom-up (blind) and top-down (including shape prior) techniques. First, a color space transformation is performed. Then, an energy function (based on nonlinear diffusion of color components and directional derivatives) is defined. Next, signeddistance functions are generated from different shapes of the object of interest. Finally, a variational framework (based on the level set) is employed to minimize the energy function. The experimental results demonstrate a good performance of the proposed method compared with others and show its robustness in the presence of noise and occlusion. The proposed algorithm is applicable in outdoor and medical image segmentation and also in optical character recognition (OCR).
Źródło:
International Journal of Applied Mathematics and Computer Science; 2010, 20, 4; 711-726
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Path planning for an autonomous underwater vehicle in a cluttered underwater environment based on the heat method
Autorzy:
Sun, Kaiyue
Liu, Xiangyang
Powiązania:
https://bibliotekanauki.pl/articles/1838202.pdf
Data publikacji:
2021
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
autonomous underwater vehicle
path planning
heat method
heat diffusion
cost function
autonomiczny pojazd podwodny
planowanie trasy
dyfuzja ciepła
funkcja kosztu
Opis:
This paper proposes a novel autonomous underwater vehicle path planning algorithm in a cluttered underwater environment based on the heat method. The algorithm calculates the isotropic and anisotropic geodesic distances by adding the direction and magnitude of the currents to the heat method, which is named the anisotropy-based heat method. Taking account of the relevant influence of the environment on the cost functions, such as currents, obstacles and turn of the vehicle, an efficient collision-free and energy-optimized path solution can be obtained. Simulation results show that the anisotropy-based heat method is able to find a good trajectory in both static and dynamic clutter fields (including uncertain obstacles and changing currents). Compared with the fast marching (FM) algorithm, the anisotropy-based heat method is not only robust, flexible, and simple to implement, but it also greatly saves time consumption and memory footprint in a time-variant environment. Finally, the evaluation criteria of paths are proposed in terms of length, arrival time, energy consumption, and smoothness.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2021, 31, 2; 289-301
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Evolving morphogenetic fields in the zebra skin pattern based on Turings morphogen hypothesis
Autorzy:
Gravan, C. P.
Lahoz-Beltra, R.
Powiązania:
https://bibliotekanauki.pl/articles/907636.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
pole morfogenetyczne
model reakcji-dyfuzji
automat komórkowy
mammalian coat pattern
morphogenetic field
Turing reaction-diffusion
evolving cellular automata
developmental models
modeling biological structures
Opis:
One of the classical problems of morphogenesis is to explain how patterns of different animals evolved resulting in a consolidated and stable pattern generation after generation. In this paper we simulated the evolution of two hypothetical morphogens, or proteins, that diffuse across a grid modeling the zebra skin pattern in an embryonic state, composed of pigmented and nonpigmented cells. The simulation experiments were carried out applying a genetic algorithm to the Young cellular automaton: a discrete version of the reaction-diffusion equations proposed by Turing in 1952. In the simulation experiments we searched for proper parameter values of two hypothetical proteins playing the role of activator and inhibitor morphogens. Our results show that on molecular and cellular levels recombination is the genetic mechanism that plays the key role in morphogen evolution, obtaining similar results in the presence or absence of mutation. However, spot patterns appear more often than stripe patterns on the simulated skin of zebras. Even when simulation results are consistent with the general picture of pattern modeling and simulation based on the Turing reaction-diffusion, we conclude that the stripe pattern of zebras may be a result of other biological features (i.e., genetic interactions, the Kipling hypothesis) not included in the present model.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2004, 14, 3; 351-361
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 16

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