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Статті в журналах з теми "Retard fractionnel":

1

Pskhu, A. V., and S. Sh Rekhviashvili. "Retarded Potentials in Fractional Electrodynamics." Moscow University Physics Bulletin 75, no. 4 (July 2020): 316–19. http://dx.doi.org/10.3103/s0027134920040098.

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2

Schiavone, S. E. "Fractional powers of the retarded potential." Applicable Analysis 42, no. 1-4 (December 1991): 145–55. http://dx.doi.org/10.1080/00036819108840038.

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3

Sikora, Beata. "Controllability criteria for time–delay fractional systems with a retarded state." International Journal of Applied Mathematics and Computer Science 26, no. 3 (September 1, 2016): 521–31. http://dx.doi.org/10.1515/amcs-2016-0036.

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Abstract The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative U-controllability are established and proved. Numerical examples illustrate the obtained theoretical results.
4

Jiang, Wei, and Zheng Xia Wang. "Image Denoising New Method Based on Fractional Partial Differential Equation." Advanced Materials Research 532-533 (June 2012): 797–802. http://dx.doi.org/10.4028/www.scientific.net/amr.532-533.797.

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Current total variation method excels at denoising and keeping the characteristics of image edges. However, its ability to retain texture details of smoothing region of image is poor. By combining fractional-order differential theory with total variation method, a new image denoising method is proposed. The new method, while effectively inheriting these advantages, uses the fractional-order differential amplitude-frequency and effectively. Simulation results which we have got show that the new method, on the one hand, can better suppress noise, keep the characteristics of image edges, and retain more texture details than integer-order partial differential methods. On the other hand, the method, above mentioned, is more effective and practical on image denoising than results of PSNR.
5

Nguyen, Van Quang, and Suchin Arunsawatwong. "Stability and Stabilization of Retarded Fractional Delay Differential Systems." IFAC Proceedings Volumes 41, no. 2 (2008): 3928–33. http://dx.doi.org/10.3182/20080706-5-kr-1001.00661.

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6

Dhandapani, Prasantha Bharathi, Jayakumar Thippan, Dumitru Baleanu, and Vinoth Sivakumar. "On a novel fuzzy fractional retarded delay epidemic model." AIMS Mathematics 7, no. 6 (2022): 10122–42. http://dx.doi.org/10.3934/math.2022563.

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<abstract><p>The traditional compartmental epidemic models such as SIR, SIRS, SEIR consider mortality rate as a parameter to evaluate the population changes in susceptible, infected, recovered, and exposed. We present a modern model where population changes in mortality are also considered as the parameter. The existing models in epidemiology always construct a system of the closed medium in which they assume that new birth, as well as new death, will not be possible. But in real life, such a concept will not be assumed to not exist. From our wide observation, we find that the changing rate in every population case is notably negligible, That's why we are preferring to calculate them fractionally using FFDE. Using Lofti's fuzzy concept we are picturing the models after that we are estimating their non-integer values using three distinct methodologies LADM-4, DTM-4 for arbitrary fractional-order $ \alpha_i $, and RKM-4. At $ \alpha_{i} = 1, $ comparison of the estimations will be done. In addition to the simulation, works of numerical estimations, the existence of steady states, equilibrium points, and stability analysis are all done.</p></abstract>
7

Tafesse, Simegne, and Nagarajan Sukavanam. "Approximate Controllability of Fractional Order Retarded Semilinear Control Systems." International Journal of Modern Nonlinear Theory and Application 02, no. 03 (2013): 153–60. http://dx.doi.org/10.4236/ijmnta.2013.23020.

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8

Subramanian, Shivaram, and Hanif D. Sherali. "A fractional programming approach for retail category price optimization." Journal of Global Optimization 48, no. 2 (November 21, 2009): 263–77. http://dx.doi.org/10.1007/s10898-009-9491-2.

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9

Kim, Daewook, and Jin-Mun Jeong. "Controllability for Retarded Semilinear Neutral Control Systems of Fractional Order in Hilbert Spaces." Mathematics 9, no. 6 (March 21, 2021): 671. http://dx.doi.org/10.3390/math9060671.

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In this paper, we discuss the approximate controllability for a class of retarded semilinear neutral control systems of fractional order by investigating the relations between the reachable set of the semilinear retarded neutral system of fractional order and that of its corresponding linear system. The research direction used here is to find the conditions for nonlinear terms so that controllability is maintained even in perturbations. Finally, we will show a simple example to which the main result can be applied.
10

Wang, Ying, Jingxiao Jiang, Zhi Cai, and Kaifeng Zhang. "Fractional Prospect Theory-Based Bidding Strategy of Power Retail Company in the Uniform Pricing Electricity Market under Price Uncertainty." Fractal and Fractional 7, no. 3 (February 23, 2023): 210. http://dx.doi.org/10.3390/fractalfract7030210.

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This paper first proposes a fractional prospect theory-based method for modeling the bidding strategy of a power retail company in the uniform pricing electricity market under price uncertainty. Different from the traditional methods which assume that the retail company always bids completely rationally to maximize its individual payoffs, this paper introduces the prospect theory (PT) into the bidding model to reflect the impacts of psychological factors and subjective perceptions. To address the partial uncertainties brought by the continuous probability distribution in the value function, this paper modifies the classical PT into the fractional prospect theory (FPT) and builds up the FPT-based bidding strategy model under 1-segment and 3-segment bidding rules. The simulation results show that the proposed method can effectively model the psychological factors in the bidding strategy of a power retail company in the uniform pricing electricity market under price uncertainty, which can help to further study the competition and equilibrium of the uniform pricing market considering the psychological factors of the participants.

Дисертації з теми "Retard fractionnel":

1

Bouldja, Nacera. "Slow Light in a SPS Photorefractive Crystal." Electronic Thesis or Diss., CentraleSupélec, 2020. http://www.theses.fr/2020CSUP0005.

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La lumière lente est le domaine scientifique qui s’intéresse aux processus non linéaires quipeuvent réduire la vitesse du groupe d’une impulsion lumineuse lorsqu’elle se propage dansun milieu. Cette technologie a récemment suscité un grand intérêt pour ses larges domainesd’application tels que le router optique, la photonique non linéaire et la spectroscopie.L’efficacité des systèmes à lumière lente est généralement mesurée par deux paramètresclés : le retard ou la vitesse du groupe et la bande passante de l’impulsion lumineuse desortie. Ce dernier est défini par le retard dit fractionnel qui est le rapport entre le retardet la largeur de l’impulsion de sortie. Un système de lumière lente dit efficace lorsqu’ilest capable de ralentir les courtes impulsions lumineuses, tout en maintenant une valeurimportante du retard fractionnel (FD).Au cours des dernières années, de nombreuses études du ralentissement de la lumière ontété réalisées dans plusieurs matériaux dispersifs à différentes longueurs d’onde. En fait, desvitesses de groupe inférieures à 17 m/s[1] ont été mesurées expérimentalement par Hau etal. dans un gaz atomique en utilisant la Transparence Induite Electromagnétiquement.Plus récemment, la décélération de la vitesse de groupe a été également observée avec succèsdans des matériaux à l’état solide tels que les fibres optiques [2], les cristaux photoniques[3]. D’autre part, plusieurs études ont montré que les cristaux photoréfractifs peuventégalement réduire la vitesse de propagation de la lumière à température ambiante. En effet,la plus petite vitesse du groupe de 0, 025 cm/s a été obtenue en utilisant l’enregistrementdes réseaux d’indice de réfraction dans le cristal photoréfractif BaTiO3[4]. Cette méthodeconsiste à coupler un faisceau pompe continu et une sonde pour augmenter la dispersionde l’indice de réfraction et générer un gain photoréfractif ainsi le ralentissement de lasonde à la sortie du cristal. Cependant, cette petite vitesse est souvent accompagnéed’une distorsion de l’impulsion de sortie, ce qui réduit la valeur du retard fractionnel (parexemple, un FD de l’ordre de 0, 4 a été mesuré dans [4]).Cette thèse porte sur l’étude de différentes méthodes qui permettent, en plus du ralentissementde la lumière, de limiter la distorsion de l’impulsion dans les milieux photoréfractifs.Tout d’abord, en utilisant la méthode TWM, le cristal SPS avec un temps de réponse de10 ms peut ralentir les impulsions lumineuses ou sombres de l’ordre de ms. Il est démontréque la valeur du retard et la largeur de l’impulsion transmise peuvent être contrôlées parle gain photoréfractif et la durée de l’impulsion d’entrée. En améliorant la configurationdu TWM, nous mesurons un retard fractionnaire de 0, 79 et 1 respectivement pour lesimpulsions lumineuses et sombres de durées proches du temps de réponse du cristal. Lecoma photoréfractive ou le « beam fanning » a également été utilisé pour ralentir lalumière dans le cristal photoréfractif. Le couplage du fanning avec l’impulsion d’entréeentraîne à la fois la modulation des réseaux d’indice de réfraction et le ralentissement del’impulsion de sortie à différentes longueurs d’onde.La lumière lente avec le TWM et le fanning peut être observée pour des impulsions longues,typiquement pour des impulsions de l’ordre de la ms à la seconde. En d’autres termes,seules les impulsions dont les durées sont proches du temps de réponse du cristal qui sontralenties. Dans cette thèse, nous montrons pour la première fois que l’utilisation du TWMen régime impulsionnel et un laser à haute intensité peut réduire le temps de réponsephotoréfractif du cristal et le ralentissement d’une impulsion plus courte (d’une largeur dens). Les résultats obtenus dans un cristal PR d’épaisseur 1 cm sont comparables à ceuxréalisés dans un 1 km de fibre optique pour les mêmes durées d’impulsions
Slow light is the science domain that focuses on the physical nonlinear processes that canreduce the group velocity of a light pulse as it propagates in the medium. This discoveryhas been a great deal of recent interest for a wide range of applications such as opticalbuffering, nonlinear photonics and various types of spectroscopic.The slow light performance is typically measured through two key parameters: the valueof the delay or the group delay and the bandwidth of the output light pulse. This lastone is generally defined by the so-called fractional delay, which is the ratio between theoptical delay and the width of the output pulse. It is important to know that the opticaltelecommunication needs a slow light system that is able to slowdown short input lightpulses with therefore a large value of the fractional delay (FD).In the last years, numerous studies of slow light have been performed in several dispersivematerials at different wavelengths. In 1999, group velocities smaller than 17 m/s [1] havebeen experimentally measured by Hau et al. in an ultra-cold gas using ElectromagneticallyInduced Transparency. More recently, the deceleration of the light pulses has been alsosuccessfully observed in solid-state materials such as in optical fibers [2] and in photoniccrystals [3]. On the other hand, several studies have shown that photorefractive (PR)crystals can also be used to reduce the light propagation velocity at room temperature.As a matter of fact, the smallest group velocity of 0.025 cm/s has been achieved using therecording of refractive index gratings in a BaTiO3 photorefractive crystal [4]. This methodconsists of the coupling of a continuous pump beam and a probe signal to increase therefractive index dispersion and leads the generation of a photorefractive gain. However,this small group velocity is often accompanied by the output pulse distortion which reducesthe value of the fractional delay (FD of the order of 0.4 in [4]).This thesis focuses on the study of the methods which allow in addition to the decelerationgroup velocity, the limitation of the distortion of the pulse in a photorefractive (PR) media.First, using the two-wave mixing (TWM) method, the PR crystal with a response time of10 ms can slow down bright or dark pulses with duration of the order of ms. It is shownthat the value of the time delay and the width of the transmitted pulse can be controlledby the photorefractive gain and the input pulse duration. By improving the TWM setup,we measure a fractional delay of 0.79 and 1 respectively, for the bright and the dark pulseswith a duration close to the response time of the crystal. The beam fanning in a PRcrystal has also been used to slow down a single light pulse. The coupling between thebeam fanning and the input beam leads both to the modulation of the noisy refractiveindex gratings and to the slowing down of the output pulse. The use of beam fanning forlight slow down is new and significantly simplifies the slow light setup.Slow light with the TWM and the beam fanning can be observed for long pulses, typicallyfor a pulse of the order of the milliseconds and the seconds. In other words, only pulseswith durations around the crystal response time are slowed down. In this thesis, we showfor the first time that the use of the TWM at the nanosecond regime and a high laserintensity can reduce the photorefractive response time of the crystal and the slowdown ofa shorter pulse (with a width of ns). The results achieved in a PR crystal with a thicknessof 1 cm are similar to those achieved in slow light systems using a km-long optical fiberand for the same pulse durations
2

Myung, Young-soo, and Dong-wan Tcha. "Return on Investment Analysis for Facility Location." Massachusetts Institute of Technology, Operations Research Center, 1991. http://hdl.handle.net/1721.1/5306.

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We consider how the optimal decision can be made if the optimality criterion of maximizing profit changes to that of maximizing return on investment for the general uncapacitated facility location problem. We show that the inherent structure of the proposed model can be exploited to make a significant computational reduction.
3

Nguyen, Le Ha Vy. "Stability and stabilization of several classes of fractional systems with delays." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112387/document.

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Nous considérons deux classes de systèmes fractionnaires linéaires invariants dans le temps avec des ordres commensurables et des retards discrets. La première est composée de systèmes fractionnaires à entrées multiples et à une sortie avec des retards en entrées ou en sortie. La seconde se compose de systèmes fractionnaires de type neutre avec retards commensurables. Nous étudions la stabilisation de la première classe de systèmes à l'aide de l'approche de factorisation. Nous obtenons des factorisations copremières à gauche et à droite et les facteurs de Bézout associés: ils permettent de constituer l'ensemble des contrôleurs stabilisants. Pour la deuxième classe de systèmes, nous nous sommes intéressés au cas critique où certaines chaînes de pôles sont asymptotiques à l'axe imaginaire. Tout d'abord, nous réalisons une approximation des pôles asymptotiques afin de déterminer leur emplacement par rapport à l'axe. Le cas échéant, des conditions nécessaires et suffisantes de stabilité H-infini sont données. Cette analyse de stabilité est ensuite étendue aux systèmes à retard classiques ayant la même forme. Enfin, nous proposons une approche unifiée pour les deux classes de systèmes à retards commensurables de type neutre (standards et fractionnaires). Ensuite, la stabilisation d'une sous-classe de systèmes neutres fractionnaires est étudiée. Premièrement, l'ensemble de tous les contrôleurs stabilisants est obtenu. Deuxièmement, nous prouvons que pour une grande classe de contrôleurs fractionnaires à retards il est impossible d'éliminer dans la boucle fermée les chaînes de pôles asymptotiques à l'axe imaginaire si de telles chaînes sont présentes dans les systèmes à contrôler
We consider two classes of linear time-invariant fractional systems with commensurate orders and discrete delays. The first one consists of multi-input single-output fractional systems with output or input delays. The second one consists of single-input single-output fractional neutral systems with commensurate delays. We study the stabilization of the first class of systems using the factorization approach. We derive left and right coprime factorizations and Bézout factors, which are the elements to constitute the set of all stabilizing controllers. For the second class of systems, we are interested in the critical case where some chains of poles are asymptotic to the imaginary axis. First, we approximate asymptotic poles in order to determine their location relative to the axis. Then, when appropriate, necessary and sufficient conditions for H-infinity-stability are derived. This stability analysis is then extended to classical delay systems of the same form and finally a unified approach for both classes of neutral delay systems with commensurate delays (standard and fractional) is proposed. Next, the stabilization of a subclass of fractional neutral systems is studied. First, the set of all stabilizing controllers is derived. Second, we prove that a large class of fractional controllers with delays cannot eliminate in the closed loop chains of poles asymptotic to the imaginary axis if such chains are present in the controlled systems
4

Fioravanti, André. "H∞ analysis and control of time-delay systems by methods in frequency domain." Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00627352.

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This thesis addresses the H∞ analysis and control of continuous commensurate time-delay systems by frequential methods. First, the asymptotic behavior of the chains of poles are studied, and the conditions of stability for neutral systems with poles approaching the imaginary axis are given. The same analysis is done for fractional systems. In the sequel, a numerical method able to locate all the stability windows as well as the unstable root-locus for classical and fractional system is given. We conclude the analysis part by providing the stability crossing curves of a class of distributed delay system. Starting the synthesis part, we design PID controllers for unstable fractional systems using a small-gain theorem approach. Finally, using the Rekasius substitution, we construct a linear time invariant comparison system that allows us to get information about stability and H∞-norm for classical time-delay systems. Using this approach it is possible to design state and output feedback controllers, as well as linear filters for this class of systems.
5

Tenoutit, Mammar. "Définition et réglage de correcteurs robustes d'ordre fractionnaire." Thesis, Poitiers, 2013. http://www.theses.fr/2013POIT2268.

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Les applications du calcul fractionnaire en automatique se sont considérablement développées ces dernières années, surtout en commande robuste. Ce mémoire est une contribution à la commande robuste des systèmes d'ordre entier à l'aide d'un correcteur PID d'ordre fractionnaire.Le conventionnel régulateur PID, unanimement apprécié pour le contrôle des processus industriels, a été adapté au cas fractionnaire sous la forme PInDf grâce à l'introduction d'un modèle de référence d'ordre non entier, réputé pour sa robustesse vis-à-vis des variations du gain statique.Cette nouvelle structure a été étendue aux systèmes à retard sous la forme d'un Prédicteur de SMITH fractionnaire. Dans leur forme standard, ces correcteurs sont adaptés à la commande des systèmes du premier et du second ordre, avec ou sans retard pur.Pour des systèmes plus complexes, deux méthodologies de synthèse du correcteur ont été proposées, grâce à la méthode des moments et à l'approche retour de sortie.Pour les systèmes dont le modèle est obtenu à partir d'une identification, la boucle fermée doit en outre être robuste aux erreurs d'estimation. Un modèle pire-cas, déduit de la matrice de covariance de l'estimateur et des domaines d'incertitudes fréquentielles, a été proposé pour la synthèse du correcteur.Les différentes simulations numériques montrent l'efficacité de cette méthodologie pour l'obtention d'une boucle fermée robuste aux variations du gain statique et aux incertitudes d'identification
The application of fractional calculus in automatic control have received much attention these last years, mainly in robust control. This PhD dissertation is a contribution to the control of integer order systems using a fractional order PID controller.The classical PID, well known for its applications to industrial plants, has been adapted to the fractional case as a PInDf controller, thanks to a fractional order reference model, characterized by its robustness to static gain variations.This new controller has been generalized to time delay systems as a fractional SMITH Predictor. In standard case, these controllers are adapted to first and second order systems, with or without a time delay. For more complex systems, two design methodologies have been proposed, based on the method of moments and on output feedback approach.For systems whose model is obtained by an identification procedure, the closed loop has to be robust to estimation errors. So, a worst-case model, derived from the covariance matrix of the estimator and the frequency uncertainty domains, has been proposed for the design of the controller.The different numerical simulations demonstrate that this methodology is able to provide robustness to static gain variations and to identification uncertainties
6

Bai, Jing. "Commande des Systèmes Multi-agent d'Ordre Fractionnaire." Thesis, Ecole centrale de Lille, 2015. http://www.theses.fr/2015ECLI0019/document.

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Ce travail concerne la commande des systèmes multi-agent d’ordre fractionnaire utilisant une topologie de communication fixe. Premièrement, la production en formation avec atténuation absolue et retard de communication est étudiée. Pour cela, une loi de commande et des conditions suffisantes sont proposées. Toutefois, dans certains scénarios, il est souhaitable que tous les agents atteignent la formation souhaitée tout en se déplacent en groupe, au lieu d’un rendez-vous à un point fixe. Ce cas sera traité en étudiant la production en formation avec atténuation relative et retard de communication. Troisièmement, la poursuite par consensus des systèmes avec un état de référence variable dans le temps est étudiée. Une loi de commande commune et une seconde basée sur la prédiction d’erreur sont proposées, et le problème du consensus est résolu quand le graphe de communication contient un arbre dirigé. Il a été prouvé que la convergence du système est plus rapide en utilisant la loi basée sur la prédiction d’erreur plutôt que celle de commande commune. Enfin, les lois de commande ci-dessus sont étendues au cas de la poursuite en formation. En effet, dans de nombreux cas, l'information peut être envoyée à partir d'un état de référence vers les agents voisins uniquement et non pas à l’ensemble des agents. Afin de résoudre ce problème, une loi de commande est proposée afin de résoudre le problème du consensus avec un état de référence constant. Puis, deux lois de commande sont proposées afin de résoudre le problème du consensus avec un état de référence variant dans le temps. Ces lois sont étendues pour résoudre le problème de la poursuite en formation
This thesis focuses on the distributed coordination of fractional-order multi-agent systems under fixed directed communication graph. Firstly, formation producing with absolute damping and communication delay of fractional-order multi-agent systems is studied. A control law is proposed and some sufficient conditions are derived for achieving formation producing. However, in some scenarios, it might be desirable that all agents achieve formation and move as a group, instead of rendezvous at a stationary point. Therefore, secondly, formation producing with relative damping and communication delay is considered. Thirdly, consensus tracking of fractional-order multi-agent systems with a time-varying reference state is studied. A common control law and a control law based on error predictor are proposed, and it is shown that the control laws are effective when a communication graph has directed spanning trees. Meanwhile, it is proved that the convergence of systems is faster using the control law based on error predictor than by the common one. Finally, the above control laws are extended to achieve formation-tracking problems. In fact, in many cases information can be sent from a reference state to only its neighbor agents not to all the agents. In order to solve the above problem, an effective control law is given to achieve consensus with a constant reference state. Then, an effective general control law and an effective particular one are proposed to achieve consensus with a time-varying reference state. Furthermore, the above control laws are extended to achieve the formation tracking problems
7

Karangwa, Innocent. "Comparing South African financial markets behaviour to the geometric Brownian Motion Process." Thesis, University of the Western Cape, 2008. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_4787_1363778247.

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This study examines the behaviour of the South African financial markets with regards to the Geometric Brownian motion process. It uses the daily, weekly, and monthly stock returns time series of some major securities trading in the South African financial market, more specifically the US dollar/Euro, JSE ALSI Total Returns Index, South African All Bond Index, Anglo American Corporation, Standard Bank, Sasol, US dollar Gold Price , Brent spot oil price, and South African white maize near future. The assumptions underlying the 
Geometric Brownian motion in finance, namely the stationarity, the normality and the independence of stock returns, are tested using both graphical (histograms and normal plots) 
and statistical test (Kolmogorov-Simirnov test, Box-Ljung statistic and Augmented Dickey-Fuller test) methods to check whether or not the Brownian motion as a model for South 
African financial markets holds. The Hurst exponent or independence index is also applied to support the results from the previous test. Theoretically, the independent or Geometric 
Brownian motion time series should be characterised by the Hurst exponent of ½
. A value of a Hurst exponent different from that would indicate the presence of long memory or 
fractional Brownian motion in a time series. The study shows that at least one assumption is violated when the Geometric Brownian motion process is examined assumption by 
assumption. It also reveals the presence of both long memory and random walk or Geometric Brownian motion in the South African financial markets returns when the Hurst index analysis is used and finds that the Currency market is the most efficient of the South African financial markets. The study concludes that although some assumptions underlying the 
rocess are violated, the Brownian motion as a model in South African financial markets can not be rejected. It can be accepted in some instances if some parameters such as the Hurst exponent are added.

8

Monteghetti, Florian. "Analysis and Discretization of Time-Domain Impedance Boundary Conditions in Aeroacoustics." Thesis, Toulouse, ISAE, 2018. http://www.theses.fr/2018ESAE0019.

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En aéroacoustique numérique, la condition aux limites d’impédance temporelle (TDIBC) peutêtre utilisée pour modéliser un matériau absorbant acoustique localement réactif. Elle permetde calculer l’effet d’un matériau sur le champ acoustique après une distance d’homogénéisation,ce qui s’avère suffisamment précis pour la prédiction de niveaux sonores. L’objectif général decette thèse est d’étudier les aspects physiques, mathématiques, et numériques des TDIBC, enpartant de la littérature physique.La première partie de cette thèse définit des conditions d’admissibilité pour une TDIBCnon-linéaire dans la formulation impédance, admittance, et scattering. Il est ensuite montréque les modèles physiques linéaires ont des transformées de Laplace irrationnelle et admettentdans le domaine temporel une représentation oscillante-diffusive à retard, dont l’interprétationphysique est donnée. L’analyse permet d’obtenir la TDIBC discrète la mieux adaptée à chaquemodèle physique, par opposition à une approche universelle qui consiste à postuler un modèlediscret a priori, et suggère des manières élémentaires de calculer les pôles et les poids. La formulationtemporelle proposée se réduit à la composition d’un ensemble d’équations différentiellesordinaires avec une équation de transport.La principale contribution de la seconde partie est la preuve de la stabilité asymptotiqued’une équation des ondes multidimensionnelle couplée à diverses classes de TDIBC admissibles,dont la transformée de Laplace est une fonction positive-réelle. La démonstration repose surla formulation d’un problème de Cauchy abstrait sur un espace d’état étendu en utilisant uneréalisation de l’impédance, qui peut être de dimension finie ou infinie. La stabilité asymptotiquedu semi-groupe de contraction correspondant est ensuite obtenue en vérifiant les conditionsspectrales du théorème de Arendt-Batty-Lyubich-V˜u.La troisième et dernière partie de cette thèse s’intéresse à la discrétisation des équationsd’Euler linéarisées avec une TDIBC. Elle démontre l’avantage numérique à utiliser l’opérateurde scattering plutôt que les opérateurs d’impédance et d’admittance, y compris pour les TDIBCnon-linéaires. Cela est effectué par une analyse d’énergie semi-discrète de l’imposition faibled’une TDIBC générique et non-linéaire dans une méthode des éléments finis de type Galerkindiscontinu. En particulier, l’analyse met en évidence que la seule définition d’un modèle discretn’est pas suffisante pour complètement définir une TDIBC. Pour appuyer l’analyse, un modèlephysique non-linéaire élémentaire est obtenu et ses propriétés numériques sont étudiées dans untube à impédance. Ensuite, l’obtention d’une TDIBC retardée large bande depuis les modèlesphysiques de coefficients de réflexion est démontrée pour les liners acoustique à un degré deliberté.Une discrétisation d’ordre élevée de la formulation temporelle proposée, qui consiste à composerun ensemble d’équations différentielles ordinaires avec une équation de transport, estappliquée à l’étude numérique de deux conduits aéroacoustiques
In computational aeroacoustics, time-domain impedance boundary conditions (TDIBCs) canbe employed to model a locally reacting sound absorbing material. They enable to computethe effect of a material on the sound field after a homogenization distance and have proveneffective in noise level predictions. The broad objective of this work is to study the physical,mathematical, and computational aspects of TDIBCs, starting from the physical literature.The first part of this dissertation defines admissibility conditions for nonlinear TDIBCs underthe impedance, admittance, and scattering formulations. It then shows that linear physicalmodels, whose Laplace transforms are irrational, admit in the time domain a time-delayedoscillatory-diffusive representation and gives its physical interpretation. This analysis enablesto derive the discrete TDIBC best suited to a particular physical model, by contrast with a onesize-fits-all approach, and suggests elementary ways of computing the poles and weights. Theproposed time-local formulation consists in composing a set of ordinary differential equationswith a transport equation.The main contribution of the second part is the proof of the asymptotic stability of the multidimensionalwave equation coupled with various classes of admissible TDIBCs, whose Laplacetransforms are positive-real functions. The method of proof consists in formulating an abstractCauchy problem on an extended state space using a realization of the impedance, be it finiteor infinite-dimensional. The asymptotic stability of the corresponding strongly continuoussemigroup of contractions is then obtained by verifying the sufficient spectral conditions of theArendt-Batty-Lyubich-V˜u theorem.The third and last part of the dissertation tackles the discretization of the linearized Eulerequations with TDIBCs. It demonstrates the computational advantage of using the scatteringoperator over the impedance and admittance operators, even for nonlinear TDIBCs. This isachieved by a systematic semi-discrete energy analysis of the weak enforcement of a genericnonlinear TDIBC in a discontinuous Galerkin finite element method. In particular, the analysishighlights that the sole definition of a discrete model is not enough to fully define a TDIBC.To support the analysis, an elementary physical nonlinear scattering operator is derived andits computational properties are investigated in an impedance tube. Then, the derivation oftime-delayed broadband TDIBCs from physical reflection coefficient models is carried out forsingle degree of freedom acoustical liners. A high-order discretization of the derived time-localformulation, which consists in composing a set of ordinary differential equations with a transportequation, is applied to two flow ducts
9

Zamoum, Redouane. "Etude théorique des fluctuations de courant de l'admittance et de la densité d'états d'un nano-système en interaction." Phd thesis, Aix-Marseille Université, 2013. http://tel.archives-ouvertes.fr/tel-00881571.

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Dans notre thèse nous nous sommes intéressés à l'étude des fluctuations de courant, de l'admittance quantique ainsi que la densité d'états pour un nano système en interaction. Notre travail se divise en deux parties. Dans la première partie, nous avons étudié les fluctuations de courant et l'admittance pour un conducteur unidimensionnel, en décrivant le système par un liquide de Tomonaga-Luttinger. Nous avons utilisé les techniques de bosonisation et de refermionisation afin d'aboutir à des résultats exacts pour tous les régimes de température, toutes les valeurs de la tension appliquée et toute la gamme des fréquences. Les résultats obtenus sont appliqués à un conducteur cohérent couplé à un quantum de résistance, et aux états de bord dans le régime de l'effet Hall quantique fractionnaire. Dans le cas d'un conducteur cohérent, le bruit non symétrisé à fréquence finie exhibe un profil différent de celui de la théorie de la diffusion, et la conductance à fréquence finie est directement liée au courant. Dans le cas du régime de l'effet Hall quantique fractionnaire, nous avons pu établir que dans certaines limites, il existe une relation entre les corrélations de courant à l'admittance quantique. En particulier, les singularités qui apparaissent dans les corrélations de courant sont celles de l'admittance. Dans la deuxième partie, nous avons étudié un fil quantique connecté à deux réservoirs qui sont représentés par deux impuretés. Le système est décrit par un liquide de Tomonaga-Luttinger. Nous avons établi et résolu l'équation de Dyson pour la fonction de Green retardée. Ce qui permet de calculer la densité d'états pour un fil quantique homogène puis inhomogène. Dans le cas d'un paramètre d'interaction homogène, l'effet des impuretés modifie le profil de la densité d'états. Dans le cas d'un paramètre d'interaction inhomogène, le calcul de la densité d'états est plus difficile et une approche numérique est indispensable.
10

De, Brito Cardeliquio Caetano. "Contributions to the Theory of Time-Delay Systems : Stability and Stabilisation." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLC080/document.

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Le but de cette thèse est de présenter de nouveaux résultats sur l'analyse et la synthèse de systèmes à retard. Dans la première partie, nous étendons l'utilisation du système invariant d'ordre fini, appelé "système de comparaison", à la conception d'un contrôleur qui dépend non seulement de la sortie à l'heure actuelle et du délai maximum, mais également d'un nombre arbitraire de valeurs entre celles-ci. Cette approche nous permet d'augmenter le délai maximal stable sans exiger d'informations supplémentaires. Les méthodes présentées ici concernent la conception de systèmes de contrôle avec des retards en utilisant des routines numériques classiques basées sur la théorie Hoo. La deuxième partie de ce travail traite d'une nouvelle approche pour développer une enveloppe englobant tous les pôles d'un système à retard. Grâce aux LMIs, nous sommes en mesure de déterminer les enveloppes pour les systèmes à retard du type retardé et du type neutre. Les enveloppes proposées sont non seulement plus étroites que celles de la littérature, mais, avec notre procédure, elles peuvent également être appliquées pour vérifier la stabilité du système et pour projeter contrôleurs de retour d'état qui répondent aux exigences de conception relatives à alpha-stabilité et sont robustes face aux incertitudes paramétriques. Les systèmes fractionnaires sont également discutés dans les deux chapitres mentionnés ci-dessus. La troisième et dernière partie étudie les systèmes stochastiques avec des retards. Nous discutons d'abord des systèmes à temps continu soumis à des sauts de Markov. Nous définissons la stabilité et obtenons des LMIs pour le contrôle par retour d'état de telle sorte que la relation entre les taux de transition entre les modes soit affine, ce qui permet donc de traiter le cas dans lequel les taux sont incertains. Nous discutons ensuite des systèmes positifs avec retards, tant pour le cas continu que pour le cas discret. Des systèmes équivalents sont obtenus et la stabilité dépendante du retard est abordée. De nombreux exemples sont illustrés tout au long de la thèse
The aim of this dissertation is to present new results on analysis and control design of time-delay systems. On the first part, we extend the use of a finite order LTI system, called 'comparison system', to design a controller which depends not only on the output at the present time and maximum delay, but also on an arbitrary number of values between those. This approach allows us to increase the maximum stable delay without requiring any additional information. The methods presented here consider time-delay systems control design with classical numeric routines based on Hoo theory. The second part of this work deals with a new approach to develop an envelope that engulfs all poles of a time-delay system. Through LMIs, we are able to determine envelopes for retarded and neutral time-delay systems. The envelopes proposed are not only tighter than the ones in the literature but, with our procedure, they can also be applied to verify the stability of the system and design state-feedback controllers which cope with design requirements regarding alpha-stability and are robust in face of parametric uncertainties. Fractional systems are also discussed for both chapters mentioned above. The third and last part studies stochastic time-delay systems.First we discuss continuous-time systems that are subjected to Markov jumps. We define stability and obtain LMIs for the state-feedback control in such a way that the relation with the transition rates between the modes is affine, allowing, therefore, to treat the case in which the rates are uncertain. We then discuss positive systems with delays, both for the continuous case as for the discrete case. Equivalent systems are obtained and delay dependent stability is addressed. A fair amount of examples are presented throughout the dissertation

Книги з теми "Retard fractionnel":

1

Lameire, Norbert, Raymond Vanholder, and Wim Van Biesen. Clinical approach to the patient with acute kidney injury. Edited by Norbert Lameire. Oxford University Press, 2018. http://dx.doi.org/10.1093/med/9780199592548.003.0222_update_001.

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The prognosis of acute kidney injury (AKI) depends on early diagnosis and therapy. A multitude of causes are classified according to their origin as prerenal, intrinsic (intrarenal), and post-renal.Prerenal AKI means a loss of renal function despite intact nephrons, for example, because of volume depletion and/or hypotension.There is a broad spectrum of intrinsic causes of AKI including acute tubular necrosis (ATN), interstitial nephritis, glomerulonephritis, and vasculitis. Evaluation includes careful review of the patient’s history, physical examination, urinalysis, selected urine chemistries, imaging of the urinary tree, and eventual kidney biopsy. The history should focus on the tempo of loss of function (if known), associated systemic diseases, and symptoms related to the urinary tract (especially those that suggest obstruction). In addition, a review of the medications looking for potentially nephrotoxic drugs is essential. The physical examination is directed towards the identification of findings of a systemic disease and a detailed assessment of the patient’s haemodynamic status. This latter goal may require invasive monitoring, especially in the oliguric patient with conflicting clinical findings, where the physical examination has limited accuracy.Excluding urinary tract obstruction is necessary in all cases and may be established easily by renal ultrasound.Distinction between the two most common causes of AKI (prerenal AKI and ATN) is sometimes difficult, especially because the clinical examination is often misleading in the setting of mild volume depletion or overload. Urinary chemistries, like calculation of the fractional excretion of sodium (FENa), may be used to help in this distinction. In contrast to FENa, the fractional excretion of urea has the advantage of being rather independent of diuretic therapy. Response to fluid repletion is still regarded as the gold standard in the differentiation between prerenal and intrinsic AKI. Return of renal function to baseline or resuming of diuresis within 24 to 72 hours is considered to indicate ‘transient, mostly prerenal AKI’, whereas persistent renal failure usually indicates intrinsic disease. Transient AKI may, however, also occur in short-lived ATN. Furthermore, rapid fluid application is contraindicated in a substantial number of patients, such as those with congestive heart failure.‘Muddy brown’ casts and/or tubular epithelial cell casts in the urine sediment are typically seen in patients with ATN. Their presence is an important tool in the distinction between ATN and prerenal AKI, which is characterized by a normal sediment, or by occasional hyaline casts. There is a possible role for new serum and/or urinary biomarkers in the diagnosis and prognosis of the patient with AKI, including the differential diagnosis between pre-renal AKI and ATN. Further studies are needed before their routine determination can be recommended.When a diagnosis cannot be made with reasonable certainty through this evaluation, renal biopsy should be considered; when intrarenal causes such as crescentic glomerulonephritis or vasculitis are suspected, immediate biopsy to avoid delay in the initiation of therapy is mandatory.

Частини книг з теми "Retard fractionnel":

1

Matušů, Radek, Bilal Senol, Baris Baykant Alagoz, and Abdullah Ates. "Value Set-Based Numerical Analysis of Robust Stability for Fractional-Order Retarded Quasi-Polynomials with Uncertain Parameters and Uncertain Fractional Orders." In Lecture Notes in Networks and Systems, 18–23. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-90321-3_3.

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2

Avanessoff, David, André R. Fioravanti, Catherine Bonnet, and Le Ha Vy Nguyen. "H ∞ -Stability Analysis of (Fractional) Delay Systems of Retarded and Neutral Type with the Matlab Toolbox YALTA." In Delay Systems, 285–97. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-01695-5_21.

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3

El-Sayed, Ahmed M. A. "Nonlinear retarded functional differential equations of arbitrary (fractional) orders." In Equadiff 99, 1393–95. World Scientific Publishing Company, 2000. http://dx.doi.org/10.1142/9789812792617_0258.

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4

Jayananda Singh, Samom, Rajesh Kumar, and M. M. Dixit. "Study Analysis of Printed Monopole Antenna for C and X Band Application." In Frontiers in Artificial Intelligence and Applications. IOS Press, 2022. http://dx.doi.org/10.3233/faia220525.

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In this design, dimension of the proposed antenna is 20 × 25 × 1.6 mm3 with FR4 substrate having circular patch fed with co-planar waveguide (CPW) that operates at numerous resonance frequencies between 5 and 10 GHz. The proposed antenna can be used well for low range communication transceivers in the C and X bands, according to simulation results. The optimal parameters for UWB antenna are the fractional bandwidth, which should be greater than 85%, and VSWR, which is another parameter. For the best and most efficient technique of using printed monopole antenna, the range of Ultra wideband (UWB) bandwidth should be lower than 2. Simulate data suggest that the proposed antenna has outstanding impedance matching capabilities, achieving a peak gain of 8 dBi. Results indicate that the ground plane’s dimensions of 15.9 mm and 11.4 mm are the most suitable for UWB due to its return loss of -41.86 dB, fractional bandwidth of about 89%, and Voltage standing wave ratio(VSWR) of less than 2 within the frequency spectrum. This modified prototype antenna has a decent, omnidirectional radiation pattern.
5

Bora, Onur, M. Sedat Kabdaşlı, Nuray Gedik, and Emel İrtem. "Floating Object Induced Hydro-morphological Effects in Approach Channel." In Fractional Calculus: New Applications in Understanding Nonlinear Phenomena, 232–50. BENTHAM SCIENCE PUBLISHERS, 2022. http://dx.doi.org/10.2174/9789815051933122030013.

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Transversal and diverging waves, return flows, propeller induced jet flows, and other hydrodynamic effects induced by a floating object may cause significant movement and/or suspension of bottom and bank sediments in the marine environment, especially in approach channels. Using the CFD (Computational Fluid Dynamics) process, the hydro-morphodynamic effects induced by a non-powered floating object navigating in an approach channel are investigated in this study. The approach channel dimensions depth, width, and channel slope are determined according to PIANC (2014) [1]. The floating object locations and velocities are used in nine different scenarios. In these cases, the floating object is 0.90, 1.10, and 1.30 meters from the bottom of the approach channel, respectively. According to the findings, when the floating object is located nearest to the bottom and its speed is fastest, there is a significant amount of sediment suspension and sediment movement in the channel slope, which is mostly attributed to super-critical return flows. When the floating object is farthest from the channel bottom and the floating object speed is lowest, however, there is a noticeable reduction in the acceleration and suspension of the sediment. As a result, the velocity and location of the floating object, channel slope, the kinematics of ship-generated waves, and particularly the return flows are found to have a significant impact on sediment movement and suspension.
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Nwajana, Augustine O., Emenike Raymond Obi, Gerald Kelechi Ijemaru, Emmanuel U. Oleka, and Destiny Chidi Anthony. "Fundamentals of RF/Microwave Bandpass Filter Design." In Handbook of Research on 5G Networks and Advancements in Computing, Electronics, and Electrical Engineering, 149–64. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-6992-4.ch005.

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This chapter presents the basic approach of microwave bandpass filter design for 5G network applications. The chapter serves as a reference source to microwave stakeholders with little or no filter design experience. It should help them to design and implement their first filter device using microstrip technology. A three-pole Chebyshev bandpass filter with centre frequency of 2.6 GHz, fractional bandwidth of 3%, passband ripple of 0.04321 dB, and return loss of 20 dB has been designed. The designed filter implementation is based on the Rogers RT/Duroid 6010LM substrate with a 10.7 dielectric constant and 1.27 mm thickness. The circuit model and microstrip layout results of the BPF are presented and show good agreement. The microstrip layout simulation results show that a less than 1.8 dB minimum insertion loss and a greater than 25 dB in-band return loss were achieved. The overall device size of the BPF is 18.0 mm by 10.7 mm, which is equivalent to 0.16λg x 0.09λg, where λg is the guided wavelength of the 50 Ohm microstrip line at the filter centre frequency.
7

Pestovska, Zoia, and Mariia Rahulina. "MANAGEMENT OF THE INVESTMENT PORTFOLIO OF INDIVIDUALS DURING INFLATION." In The scientific paradigm in the context of technological development and social change. Publishing House “Baltija Publishing”, 2023. http://dx.doi.org/10.30525/978-9934-26-297-5-10.

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Inflation is usually defined as a constant increase in the average prices of goods and services in a certain region. Searching for ways to take inflation into account when choosing investment areas and developing an investment portfolio is an urgent problem today. The purpose of the study is to develop a methodology for choosing and improving an investment portfolio in the period of inflation. The following research methods are used in the work: analysis – when considering existing strategies for forming an investment portfolio and increasing its profitability, synthesis – when formulating the definition of an investment portfolio, comparison – when considering the impact of inflationary processes on the profitability of financial instruments in Ukraine and the world, financial analysis – during selection shares in the recommended investment portfolio. Results. It has been established that an investment portfolio is a set of financial investments: shares, bonds, goods, cash. Five of its most widespread types can be identified: aggressive; protective; income portfolio; speculative; hybrid. It has also been established that there are six common investment strategies in the world: Warren Buffett, Paul Merriman (buy and hold, Ivy League universities, Bill Schultheiss (coffee shop portfolio), Bill Bernstein, Harry Brown. The procedure for registering a brokerage account in the USA for an individual resident of Ukraine is summarized: obtain an EIN, submit an SS-4 form, register a US LLC, open a brokerage account for the purchase of fractional shares of American companies included in the S&P 500 index. Practical implications. In terms of the impact of inflation on the return on investment, US companies were chosen as the most appropriate for investment, because their economy is characterized by the dominance of the service sector and the knowledge economy, and the manufacturing sector is the second largest in the world. When selecting stocks for the portfolio, their Performance, P/E Ratio, DPR and other indicators were taken into account, as well as the graphs of stocks during the crisis of 2007–2008 and during the pandemic and inflation of 2021–2022 were analyzed in order to compare the behavior of quotations during crisis even now. 25 shares of the S&P 500 index were selected for the recommended investment portfolio. Value/originality. The most stable and profitable investments in the period of inflation are investments in companies engaged in the retail trade of food products, the production and sale of snacks and semi-finished products, fast food, beverages, as well as restaurant chains, biopharmaceuticals companies, companies in the field of health care, agricultural products, insurance and energy companies engaged in exploration, development and production of oil and gas.

Тези доповідей конференцій з теми "Retard fractionnel":

1

Lorenzo, Carl F., and Tom T. Hartley. "Energy Considerations for Fractional Elements." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13247.

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This paper considers the energy aspects of fractional elements defined by the equation Ft=kλDtλ0xt. In contrast to the typically conservative assumption of classical physics that lead to the potential and kinetic energy expressions, a number of important non-conservative differences are exposed. Firstly, the considerations must be time-based rather than displacement or momentum based variables. Time based equations for energy behavior of fractional elements are presented and example applications are considered. The effect of fractional order on the energy requirements and energy return of these systems is shown. Importantly, it is shown that the history, or initialization, has a strong effect on energy requirements. Finally, compact expressions for the work or energy, are developed.
2

Harrington, Mark W., Nicolas Fontaine, Mikael Mazur, and Daniel J. Blumenthal. "Optical Frequency Transfer Stability of 1E-15 at 1 Second Over Correlated Core Pairs in a 40 km 7-core Fiber Link." In Optical Fiber Communication Conference. Washington, D.C.: Optica Publishing Group, 2023. http://dx.doi.org/10.1364/ofc.2023.m3j.3.

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We demonstrate a 40km stabilized optical frequency transfer system with fractional frequency stability of 1e-15 at 1s without single-core bidirectional propagation. Highly correlated cores of a 7-core fiber are used for signal transmission and return, mitigating uncorrelated phase fluctuations found in duplex approaches.
3

Busher, Victor, Vasily Horoshko, Anatoly Shestaka, and Lubov Melnikova. "Fractional Integrated Dual Electromagnetic Retarder Controller for Tuning Internal Combustion Engines." In 2020 IEEE Problems of Automated Electrodrive. Theory and Practice (PAEP). IEEE, 2020. http://dx.doi.org/10.1109/paep49887.2020.9240785.

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4

Hristova, Snezhana, and Cemil Tunc. "On the stability properties of retarded Volterra integro-fractional differential equations with Caputo derivative." In SEVENTH INTERNATIONAL CONFERENCE ON NEW TRENDS IN THE APPLICATIONS OF DIFFERENTIAL EQUATIONS IN SCIENCES (NTADES 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0040076.

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5

Papoulia, Katerina D., Vassilis P. Panoskaltsis, and Igor Korovajchuk. "Some Equivalences in the Theory of Linear Viscoelasticity and Their Implications in Modeling and Simulation." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-1191.

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Abstract A class of linear viscoelastic models is examined which accurately represent the response of many materials in a wide frequency range. These include power law and logarithmic type models, such as those of fractional order, the Kuhn model of linear viscoelasticity and generalizations thereof. An equivalence between the fractional element and the generalized Kuhn model is established. A continuous representation of these models is naturally available. It is shown that a discrete rheological representation, in the form of series of springs and dashpots, is also possible. This allows an internal variable formulation, which establishes the thermodynamic admissibility of this class of models, in the sense that they satisfy the dissipation inequality. Introduction of appropriate state variables leads to convolution type equations, which, in the finite deformation case, retain much of the structure of linear viscoelasticity. Numerical implementation of the models is enhanced by the equivalence principles. It is shown that the accuracy expected of a long chain of classical structural units is achieved with a greatly reduced number of model parameters.
6

Yaşar, Aysu, and Kenan Terzioğlu. "Long Memory in Exchange Rate Volatility." In International Conference on Eurasian Economies. Eurasian Economists Association, 2021. http://dx.doi.org/10.36880/c13.02560.

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Considering rapidly evolving technology and effective markets, wherein information and news are quickly and effectively reflected in financial asset prices, the positions of investors trading in financial markets regarding financial asset prices vary according to the continuous stream of information coming to the market. However, markets are not fully efficient in terms of maintaining a long memory that enables future pricing estimates based on the past market price of the financial asset. Revealing the existence of a long memory structure is essential to the development of monetary policies since exchange rates that tend to return to average exert high resistance. In this study, the exchange rate’s long-range dependence is determined in the scope of the log-periodogram estimator and using a fractional model structure, the average model, and the variance model structure related to the exchange rate between February 22, 2001–March 16, 2020 are examined. In this context, the parameters in the model allow an examination of the long memory process. According to the fractionally integrated exponential generalized autoregressive conditional heteroskedasticity model, it is determined that the effects of shocks in the exchange rate market continue and persist for a long period. Policy suggestions within the scope of exchange rates are evaluated within model outputs.

Звіти організацій з теми "Retard fractionnel":

1

Picciotto, Sol. The Contested Shaping of International Tax Rules: The Growth of Services and the Revival of Fractional Apportionment. Institute of Development Studies (IDS), July 2021. http://dx.doi.org/10.19088/ictd.2021.014.

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The digitalisation of the economy has spotlighted fundamental flaws in international tax rules, which have been exacerbated since the 1970s with the wider shift to the services economy and the growth of international services. These systemic flaws have been more evident from the perspective of countries that are mainly importers of services that have tried to retain rights to tax profits at the source from which they derive. While they succeeded in retaining a wider scope for source taxation, key provisions have been subject to continuing conflicts and contestation over their formulation and interpretation, leaving a legacy of ambiguity and confusion. Digitalisation has now sparked a dramatic reversal of perspective by more developed countries and an acceptance of principles they have long resisted: that taxation of transnational corporations can be based on apportionment of an appropriate fraction of their global income and can be by countries from where they derive income, regardless of physical presence. This paper outlines the contested process that has shaped the formulation of key provisions on taxation of international services, discusses the recent moves to reshape these rules and evaluates some policy options for capital-importing countries to strengthen their taxing rights in the current context.

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