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Tytuł:
Low-thrust chaotic based transfer from the earth to a halo orbit
Nisko-energetyczny, chaotyczny transfer sztucznego satelity z Ziemi na orbitę typu halo
Autorzy:
Macau, E. E. N.
Powiązania:
https://bibliotekanauki.pl/articles/280911.pdf
Data publikacji:
2008
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
chaos
kontrola chaosu
wynoszenie na orbitę
control of chaos
orbital transfer
Opis:
Halo orbits around the Lagrange points serve as excellent platforms for scientific missions involving the Sun as well as planetary explorations. The satellites ISEE-3, GGS WIND, SOHO and ACE have exploited these orbits to accomplish their missions. The trajectory design in support of such missions is increasingly challenging as more complex missions, like the case of the Next Generation Space Telescope, are envisioned in the near future. The purpose of this paper is to introduce a new chaotic-based transfer strategy that can be used to transfer a spacecraft from the vicinity of the Earth to a halo orbit around the equilibrium point L1 of the Earth-Sun system. The strategy exploits the inherent exponential sensitivity of chaotic time evolutions to perturbations to guide a spacecraft from its starting position to an invariant stable manifold of the chosen halo orbit. As just judiciously chosen perturbations are used, the transfer operation requires very small amounts of fuel. As an example, we applied the method in context of the restricted three-body problem, which gives a good insight into the strategies to be used in a real situation.
Orbity typu halo wokół punktów Lagrange’a są doskonałymi platformami dla stacji kosmicznych wypełniających misje naukowe w pobliżu Słońca i planet. Przykładem są satelity ISEE-3, GGS-WIND, SOHO i ACE. Projektowanie orbit dla takich misji stanowi ogromne wyzwanie, zwłaszcza że one same stają się coraz bardziej wyszukanymi i złożonymi zadaniami, tak jak np. w przypadku teleskopu kosmicznego następnej generacji. Konieczność ich eksploracji łatwo przewidzieć w przyszłych badaniach. W tej pracy zajęto się zagadnieniem wynoszenia statku kosmicznego z sąsiedztwa Ziemi na orbitę halo wokół punktu Lagrange’a L1 w układzie Ziemia-Słońce, opartym na nowej strategii zawierającej ruch chaotyczny statku. Strategia bazuje na wykładniczej wrażliwości trajektorii chaotycznej na zakłócenia warunków początkowych, co ma bezpośrednie przełożenie na sposób przeniesienia statku kosmicznego z orbity wyjściowej na stabilną rozmaitość orbity halo. Przy odpowiednio dobranych perturbacjach, transfer statku wymaga minimalnego zapotrzebowania na paliwo.W pracy rozważono taki transfer w odniesieniu do zagadnienia trzech ciał, co pozwoliło uzyskać bardzo dobry wgląd do problemu projektowania zmiany orbity w realnych warunkach.
Źródło:
Journal of Theoretical and Applied Mechanics; 2008, 46, 3; 551-564
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Control and chaos for vibro-impact and non-ideal oscillators
Sterowanie i chaos w układach drgających z uderzeniami oraz nieidealnych oscylatorów
Autorzy:
de Souza, S. L. T.
Caldas, I. L.
Viana, R. L.
Balthazar, J. M.
Powiązania:
https://bibliotekanauki.pl/articles/280889.pdf
Data publikacji:
2008
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
chaos
kontrola chaosu
wibracje z uderzeniem
vibro-impact
control of chaos
non-ideal oscillators
Opis:
In the paper, we discuss dynamics of two kinds of mechanical systems. Initially, we consider vibro-impact systems which have many implemen- tations in applied mechanics, ranging from drilling machinery and metal cutting processes to gear boxes. Moreover, from the point of view of dynamical systems, vibro-impact systems exhibit a rich variety of phe- nomena, particularly chaotic motion. In this paper, we review recent works on the dynamics of vibro-impact systems, focusing on chaotic mo- tion and its control. The considered systems are a gear-rattling model and a smart damper to suppress chaotic motion. Furthermore, we inve- stigate systems with non-ideal energy source, represented by a limited power supply. As an example of a non-ideal system, we analyse chaotic dynamics of the damped Duffing oscillator coupled to a rotor. Then, we show how to use a tuned liquid damper to control the attractors of this non-ideal oscillator.
W pracy przedyskutowano zagadnienie dynamiki mechanizmów dwóch rodzajów. Najpierw rozważono układ drgający z uderzeniami, który znajduje liczne aplikacje praktyczne w mechanice stosowanej, począwszy od urządzeń wiertniczych przez procesy cięcia metalu do skrzyń biegów włącznie. Z punktu widzenia dynamiki maszyn układy wibro-uderzeniowe wykazują bogactwo interesujących zjawisk, wliczając w to chaos. W pracy zaprezentowano przegląd ostatnich prac dotyczących dynamiki układów wibro-uderzeniowych, w których zajęto się problemem chaosu i możliwości jego sterowania. Przeanalizowano układy mechaniczne na przykładzie modelu kół zębatych z systemem ”inteligentnego” tłumika do eliminacji ruchu chaotycznego. Zajęto się, po drugie, mechanizmami z nieidealnym źródłem energii odwzorowanym poprzez układ ograniczonego poboru mocy. Jako przykład zbadano dynamikę chaotyczną tłumionego oscylatora Duffinga połączonego z wirnikiem. Pokazano sposób zastosowania płynnego tłumika do sterowania formą atraktorów obserwowanych w nieidealnym oscylatorze.
Źródło:
Journal of Theoretical and Applied Mechanics; 2008, 46, 3; 641-664
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Control of optical chaos spectrum in semiconductor laser for secure RoF communication
Autorzy:
Mazhar, Danish Ali
Ali, Syed Zafar
Islam, Muhammad Khawar
Powiązania:
https://bibliotekanauki.pl/articles/2172849.pdf
Data publikacji:
2022
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
chaos
radio over fiber
secure optical communication
Opis:
A critical requirement in optical chaos based secure radio over fiber (RoF) system design is the ability to control center frequency, spectral bandwidth, power level and signature of chaos to submerge message with sufficient horizontal and vertical margins both in time and frequency domains. Once frequency domain masking is completely achieved, time domain masking is met automatically, the former being more stringent. In a direct modulated semiconductor laser, the three control parameters are bias current (Ibias), modulation current (Imod) and modulation frequency (ωa). It is found that Imod increases bandwidth and amplitude dynamic range of chaotic pulses. Ibias increases the cavity power and hence average peak amplitude of laser chaotic pulses. The modulation frequency increases the speed of overall cavity dynamics and hence is used to increase the bandwidth of chaos but a corresponding increase in bias and modulation currents is required to support high repetition pulses. The results show relationship between three control parameters (bias current, modulation current and modulation frequency) in a direct modulated semiconductor laser and optical chaos bandwidth using regression.
Źródło:
Optica Applicata; 2022, 52, 4; 485--495
0078-5466
1899-7015
Pojawia się w:
Optica Applicata
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Compound-combination synchronization of chaos in identical and different orders chaotic systems
Autorzy:
Ojo, K. S.
Njah, A. N.
Olusola, O. I.
Powiązania:
https://bibliotekanauki.pl/articles/229175.pdf
Data publikacji:
2015
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
control and applications of chaos
low- and high-dimensional chaos
numerical simulations of chaotic models
synchronization
coupled oscillators
Opis:
This paper proposes a new synchronization scheme called compound-combination synchronization. The scheme is investigated using six chaotic Josephson junctions evolving from different initial conditions based on the drive-response configuration via the active backstepping technique. The technique is applied to achieve compound-combination synchronization of: (i) six identical third order resistive-capacitive-inductive-shunted Josepshon junctions (RCLSJJs) (with three as drive and three as response systems); (ii) three third order RCLSJJs (as drive systems) and three second order resistive-capacitive-shunted Josepshon junctions (RCSJJs (as response systems). In each case, sufficient conditions for global asymptotic stability for compound-combination synchronization to any desired scaling factors are achieved. Numerical simulations are employed to verify the feasibility and effectiveness of the compound-combination synchronization scheme. The result shows that this scheme could be used to vary the junction signal to any desired level and also give a better insight into synchronization in biological systems wherein different organs of different dynamical structures and orders are involved. The scheme could also provide high security in information transmission due to the complexity of its dynamical formulation.
Źródło:
Archives of Control Sciences; 2015, 25, 4; 463-490
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A method of suppressing chaos in a chemical reactor and the use of chaos for identifying the reactor model
Autorzy:
Berezowski, Marek
Powiązania:
https://bibliotekanauki.pl/articles/185736.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chemical reactor
recycle
chaos
control
fractals
identification
reaktor chemiczny
recykling
kontrola
fraktale
identyfikacja
Opis:
A method of suppressing chaotic oscillations in a tubular reactor with mass recycle is discussed. The method involves intervention in the temperature of the input flow by the recirculation flow and the temperature set from the exterior. The most advantageous solution was proved to be heat coupling elimination and maintenance of the reactor input temperature on the set level. Moreover, the reactor modelwas identified on the basis of a chaotic solution, as it provides the biggest entropy of information.
Źródło:
Chemical and Process Engineering; 2019, 40, 3; 265--272
0208-6425
2300-1925
Pojawia się w:
Chemical and Process Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities
Autorzy:
Vaidyanathan, S.
Volos, C.
Pham, V.-T.
Madhavan, K.
Idowu, B. A.
Powiązania:
https://bibliotekanauki.pl/articles/230036.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
jerk system
novel system
adaptive control
backstepping control
chaos synchronization
Opis:
In this research work, a six-term 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel jerk system are obtained as L1 = 0.07765,L2 = 0, and L3 = −0.87912. The Kaplan-Yorke dimension of the novel jerk system is obtained as DKY = 2.08833. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel jerk chaotic systems with two unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using Spice is presented in detail to confirm the feasibility of the theoretical model.
Źródło:
Archives of Control Sciences; 2014, 24, 3; 375-403
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Synchronization of neuronal bursting using backstepping control with recursive feedback
Autorzy:
Rasappan, Suresh
Powiązania:
https://bibliotekanauki.pl/articles/229893.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Hindmarsh-Rose neuronal bursting system
chaos
synchronization
backstepping control
Lyapunov
stability
Opis:
J. L. Hindmarsh, R. M. Rose introduced the concept of neuronal burst. In this paper, synchronization is investigated for the construction of a model of neuronal burst using backstepping control with recursive feedback. Synchronization for a model of neuronal bursting system is established using Lyapunov stability theory. The backstepping scheme is a recursive procedure that links the choice of a Lyapunov function with the design of a controller. The backstepping control method is effective and convenient to synchronize identical systems. Numerical simulations are furnished to illustrate and validate the synchronization result derived in this paper.
Źródło:
Archives of Control Sciences; 2019, 29, 4; 617-642
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hyperchaos, adaptive control and synchronization of a novel 4-D hyperchaotic system with two quadratic nonlinearities
Autorzy:
Vaidyanathan, S.
Powiązania:
https://bibliotekanauki.pl/articles/229724.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
hyperchaos
control
synchronization
Lyapunov exponents
Opis:
This research work announces an eleven-term novel 4-D hyperchaotic system with two quadratic nonlinearities. We describe the qualitative properties of the novel 4-D hyperchaotic system and illustrate their phase portraits. We show that the novel 4-D hyperchaotic system has two unstable equilibrium points. The novel 4-D hyperchaotic system has the Lyapunov exponents L1 = 3.1575, L2 = 0.3035, L3 = 0 and L4 = −33.4180. The Kaplan-Yorke dimension of this novel hyperchaotic system is found as DKY = 3.1026. Since the sum of the Lyapunov exponents of the novel hyperchaotic system is negative, we deduce that the novel hyperchaotic system is dissipative. Next, an adaptive controller is designed to stabilize the novel 4-D hyperchaotic system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global hyperchaos synchronization of the identical novel 4-D hyperchaotic systems with unknown system parameters. The adaptive control results are established using Lyapunov stability theory. MATLAB simulations are depicted to illustrate all the main results derived in this research work
Źródło:
Archives of Control Sciences; 2016, 26, 4; 471-495
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system
Autorzy:
Vaidyanathan, S.
Volos, C.
Powiązania:
https://bibliotekanauki.pl/articles/229285.pdf
Data publikacji:
2015
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
chaotic system
conservative chaotic system
adaptive control
synchronization
Opis:
First, this paper announces a seven-term novel 3-D conservative chaotic system with four quadratic nonlinearities. The conservative chaotic systems are characterized by the important property that they are volume conserving. The phase portraits of the novel conservative chaotic system are displayed and the mathematical properties are discussed. An important property of the proposed novel chaotic system is that it has no equilibrium point. Hence, it displays hidden chaotic attractors. The Lyapunov exponents of the novel conservative chaotic system are obtained as L1 = 0.0395, L2 = 0 and L3 = −0.0395. The Kaplan-Yorke dimension of the novel conservative chaotic system is DKY =3. Next, an adaptive controller is designed to globally stabilize the novel conservative chaotic system with unknown parameters. Moreover, an adaptive controller is also designed to achieve global chaos synchronization of the identical conservative chaotic systems with unknown parameters. MATLAB simulations have been depicted to illustrate the phase portraits of the novel conservative chaotic system and also the adaptive control results.
Źródło:
Archives of Control Sciences; 2015, 25, 3; 333-353
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Motion direction control of a robot based on chaotic synchronization phenomena
Autorzy:
Volos, C. K.
Powiązania:
https://bibliotekanauki.pl/articles/384720.pdf
Data publikacji:
2013
Wydawca:
Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
Tematy:
humanoid robot
motion direction control
nonlinear circuit
chaos
true random bits generator
complete synchronization
inverse π-lag synchronization
Opis:
This work presents chaotic motion direction control of a robot and especially of a humanoid robot, in order to achieve complete coverage of the entire work terrain with unpredictable way. The method, which is used, is based on a chaotic true random bits generator. The coexistence of two different synchronization phenomena between mutually coupled identical nonlinear circuits, the well-known complete chaotic synchronization and the recently new proposed inverse π-lag synchronization, is the main feature of the proposed chaotic generator. Computer simulations confirm that the proposed method can obtain very satisfactory results in regard to the fast scan of the entire robot’s work terrain.
Źródło:
Journal of Automation Mobile Robotics and Intelligent Systems; 2013, 7, 2; 64-69
1897-8649
2080-2145
Pojawia się w:
Journal of Automation Mobile Robotics and Intelligent Systems
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hybrid synchronization of n-scroll Chua and Lur’e chaotic systems via backstepping control with novel feedback
Autorzy:
Suresh, R.
Sundarapandian, V.
Powiązania:
https://bibliotekanauki.pl/articles/229485.pdf
Data publikacji:
2012
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
hybrid synchronization
n-scroll Chua system
Lur'e system
backstepping control
Opis:
This paper investigates the backstepping control design with novel feedback input approach for controlling chaotic systems to guarantee the complete synchronization as well as the anti-synchronization of chaotic systems, viz. n-scroll Chua (K. Wallace et.al. 2001) and Lur’e chaotic systems. Our theorems on hybrid synchronization for n-scroll Chua and Lur’e (J.Suyken et.al. 1997) chaotic systems is established using Lyapunov stability theory. Based on the Lyapunov function, the backstepping control is determined to tune the controller gain based on the precalculated feedback control inputs. The backstepping scheme is recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global stability performance of strict-feedback chaotic systems. Since the Lyapunov exponents are not required for these calculations, the backstepping control method is effective and convenient to synchronize the chaotic systems. Mainly this technique gives the flexibility to construct a control law. Numerical simulations are also given to illustrate and validate the hybrid synchronization results derived in this paper.
Źródło:
Archives of Control Sciences; 2012, 22, 3; 343-365
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Chaos synchronization of uncertain coronary artery systems through sliding mode
Autorzy:
Qian, D. W.
Xi, Y. F.
Tong, S. W.
Powiązania:
https://bibliotekanauki.pl/articles/201501.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos synchronization
coronary artery systems
sliding mode control
nonlinear dynamics
synchronizacja chaosu
system tętnic wieńcowych
kontroler trybu przesuwnego
dynamika nieliniowa
Opis:
The chaotic phenomena of coronary artery systems are hazardous to health and may induce illness development. From the perspective of engineering, the potential harm can be eliminated by synchronizing chaotic coronary artery systems with a normal one. This paper investigates the chaos synchronization problem in light of the methodology of sliding mode control (SMC). Firstly, the nonlinear dynamics of coronary artery systems are presented. Since the coronary artery systems suffer from uncertainties, the technique of derivative-integral terminal SMC is employed to achieve the chaos synchronization task. The stability of such a control system is proven in the sense of Lyapunov. To verify the feasibility and effectiveness of the proposed method, some simulation results are illustrated in comparison with a benchmark.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2019, 67, 3; 455-462
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation
Autorzy:
Vaidyanathan, S.
Volos, C.
Pham, V.-T.
Powiązania:
https://bibliotekanauki.pl/articles/229321.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
hyperchaos
control
synchronization
circuit realization
Opis:
In this research work, a twelve-term novel 5-D hyperchaotic Lorenz system with three quadratic nonlinearities has been derived by adding a feedback control to a ten-term 4-D hyperchaotic Lorenz system (Jia, 2007) with three quadratic nonlinearities. The 4-D hyperchaotic Lorenz system (Jia, 2007) has the Lyapunov exponents L1 = 0.3684,L2 = 0.2174,L3 = 0 and L4 =−12.9513, and the Kaplan-Yorke dimension of this 4-D system is found as DKY =3.0452. The 5-D novel hyperchaotic Lorenz system proposed in this work has the Lyapunov exponents L1 = 0.4195,L2 = 0.2430,L3 = 0.0145,L4 = 0 and L5 = −13.0405, and the Kaplan-Yorke dimension of this 5-D system is found as DKY =4.0159. Thus, the novel 5-D hyperchaotic Lorenz system has a maximal Lyapunov exponent (MLE), which is greater than the maximal Lyapunov exponent (MLE) of the 4-D hyperchaotic Lorenz system. The 5-D novel hyperchaotic Lorenz system has a unique equilibrium point at the origin, which is a saddle-point and hence unstable. Next, an adaptive controller is designed to stabilize the novel 5-D hyperchaotic Lorenz system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global hyperchaos synchronization of the identical novel 5-D hyperchaotic Lorenz systems with unknown system parameters. Finally, an electronic circuit realization of the novel 5-D hyperchaotic Lorenz system using SPICE is described in detail to confirm the feasibility of the theoretical model.
Źródło:
Archives of Control Sciences; 2014, 24, 4; 409-446
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dynamics, control, stability, diffusion and synchronization of modified chaotic Colpitts oscillator
Autorzy:
Rasappan, Suresh
Niranjan Kumar, K. A.
Powiązania:
https://bibliotekanauki.pl/articles/1845536.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
Colpitts oscillator
Lyapunov exponent
diffusion
stability
synchronization
Opis:
The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.
Źródło:
Archives of Control Sciences; 2021, 31, 3; 731-759
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Synchronization of an uncertain Duffing oscillator with higher order chaotic systems
Autorzy:
Kabziński, J.
Powiązania:
https://bibliotekanauki.pl/articles/330344.pdf
Data publikacji:
2018
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
chaos synchronization
adaptive control
Duffing oscillator
synchronizacja chaosu
sterowanie adaptacyjne
oscylator Duffinga
Opis:
The problem of practical synchronization of an uncertain Duffing oscillator with a higher order chaotic system is considered. Adaptive control techniques are used to obtain chaos synchronization in the presence of unknown parameters and bounded, unstructured, external disturbances. The features of the proposed controllers are compared by solving Duffing–Arneodo and Duffing–Chua synchronization problems.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2018, 28, 4; 625-634
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł

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