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Fractional Order Systems

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ISBN: 9783039216086 9783039216093 Year: Pages: 114 DOI: 10.3390/books978-3-03921-609-3 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 11:49:16
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This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of real-world phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems.

New Trends in Differential and Difference Equations and Applications

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ISBN: 9783039215386 9783039215393 Year: Pages: 198 DOI: 10.3390/books978-3-03921-539-3 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 11:49:15
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This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to real-life phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.

Keywords

Legendre wavelets --- collocation method --- three-step Taylor method --- asymptotic stability --- time-dependent partial differential equations --- non-instantaneous impulses --- Caputo fractional derivative --- differential equations --- state dependent delays --- lipschitz stability --- limit-periodic solutions --- difference equations --- exponential dichotomy --- strong nonlinearities --- effective existence criteria --- population dynamics --- discrete Lyapunov equation --- difference equations --- Hilbert space --- dichotomy --- exponential stability --- ?-Laplacian operator --- mean curvature operator --- heteroclinic solutions --- problems in the real line --- lower and upper solutions --- Nagumo condition on the real line --- fixed point theory --- coupled nonlinear systems --- functional boundary conditions --- Schauder’s fixed point theory --- Arzèla Ascoli theorem --- lower and upper solutions --- first order periodic systems --- SIRS epidemic model --- mathematical modelling --- Navier–Stokes equations --- global solutions --- regular solutions --- a priori estimates --- weak solutions --- kinetic energy --- dissipation --- Bäcklund transformation --- Clairin’s method --- generalized Liouville equation --- Miura transformation --- Korteweg-de Vries equation --- second-order differential/difference/q-difference equation of hypergeometric type --- non-uniform lattices --- divided-difference equations --- polynomial solution --- integro-differentials --- Sumudu decomposition method --- dynamical system

Fractional Differential Equations: Theory, Methods and Applications

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ISBN: 9783039217328 9783039217335 Year: Pages: 172 DOI: 10.3390/books978-3-03921-733-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 11:49:16
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Fractional calculus provides the possibility of introducing integrals and derivatives of an arbitrary order in the mathematical modelling of physical processes, and it has become a relevant subject with applications to various fields, such as anomalous diffusion, propagation in different media, and propogation in relation to materials with different properties. However, many aspects from theoretical and practical points of view have still to be developed in relation to models based on fractional operators. This Special Issue is related to new developments on different aspects of fractional differential equations, both from a theoretical point of view and in terms of applications in different fields such as physics, chemistry, or control theory, for instance. The topics of the Issue include fractional calculus, the mathematical analysis of the properties of the solutions to fractional equations, the extension of classical approaches, or applications of fractional equations to several fields.

Stochastic Processes with Applications

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ISBN: 9783039217281 9783039217298 Year: Pages: 284 DOI: 10.3390/books978-3-03921-729-8 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 16:10:12
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Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included.

Keywords

fusion estimation --- sensor networks --- random parameter matrices --- multiplicative noises --- random delays --- realized volatility --- forecast combinations --- structural breaks --- arithmetic progressions --- first Chebyshev function --- products of primes --- regularly varying functions --- slowly varying functions --- mixed Gaussian process --- small deviations --- exact asymptotics --- loan interest rate regulation --- diffusion model --- first passage time (FPT) --- continuous-time Markov chains --- catastrophes --- bounds --- birth-death process --- rate of convergence --- double-ended queues --- time-non-homogeneous birth-death processes --- catastrophes --- repairs --- transient probabilities --- periodic intensity functions --- time-non-homogeneous jump-diffusion processes --- transition densities --- first-passage-time --- lognormal diffusion process --- exogenous factors --- growth curves --- maximum likelihood estimation --- asymptotic distribution --- first-passage time --- inverse first-passage problem --- diffusion --- mixture of Gaussian laws --- rate of convergence --- total variation distance --- Wasserstein distance --- weighted quadratic variation --- non-Markovian queue --- general bulk service --- multiple vacation --- breakdown and repair --- stand-by server --- re-service --- discrete time stochastic model --- first-passage time --- time between inspections --- host-parasite interaction --- nematode infection --- nonhomogeneous Poisson process --- seasonal environment --- Strang–Marchuk splitting approach --- Cohen and Grossberg neural networks --- random impulses --- mean square stability --- fractional differential-difference equations --- fractional queues --- fractional birth-death processes --- busy period --- two-dimensional signature --- multi-state network --- totally positive of order 2 --- stochastic order --- stochastic process --- reliability --- stochastic orders --- scale family of distributions --- proportional hazard rates --- differential entropy

High Voltage Engineering and Applications

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ISBN: 9783039287161 / 9783039287178 Year: Pages: 304 DOI: 10.3390/books978-3-03928-717-8 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2020-06-09 16:38:57
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This book is a collection of recent publications from researchers all over the globe in the broad area of high-voltage engineering. The presented research papers cover both experimental and simulation studies, with a focus on topics related to insulation monitoring using state-of-the-art sensors and advanced machine learning algorithms. Special attention was given in the Special Issue to partial discharge monitoring as one of the most important techniques in insulation condition assessment. Moreover, this Special Issue contains several articles which focus on different modeling techniques that help researchers to better evaluate the condition of insulation systems. Different power system assets are addressed in this book, including transformers, outdoor insulators, underground cables, and gas-insulated substations.

Keywords

space/interface charge --- electrical field strength --- temperature --- oil-paper insulation --- simulation --- bipolar charge transport model --- earthing systems --- electrode’s geometry --- fast-impulses --- high-magnitude currents and impulse polarity --- grounding --- grounding electrodes --- high impulse conditions --- seasonal --- soil resistivity --- partial discharges (PD) --- partial discharge --- calibrator --- Tettex 9520 --- DDX 8003 --- DDX 9121b --- secondary arc --- short-circuit discharge --- numerical modeling --- plasma discharge --- post insulator --- non-uniform pollution between windward and leeward sides --- residual resistance formulation --- flashover dynamic model --- artificial flashover tests --- flashover characteristics --- feature selection --- insulation health index --- machine learning --- oil/paper insulation --- transformer asset management --- thermal effect --- cable --- XLPE --- laying modes --- Comsol Multiphysics --- thermal parameters --- cable ampacity --- partial discharge --- surface discharge --- UHF sensor --- FDTD simulation --- cavity discharge --- partial discharge --- denoising --- RF signal --- wavelet transform --- artificial neural network --- curve fitting --- saline mechanism --- shoreline --- wind speed --- outdoor insulators --- dry band arcing --- flashover --- tracking --- ageing --- hydrophobicity --- leakage current --- dry band arcing --- degradation --- polymeric insulation --- tracking test setup --- composite insulator --- dry band formation --- heat transfer model --- generalized finite difference time domain --- corona discharge --- electric field analysis --- ion flow field --- space charge density --- UFVM --- partial discharge --- optical-UHF integrated detection --- photoelectric fusion pattern --- GIL --- NSCT --- cable joint --- charge simulation method --- electrical tree --- random walk theory --- finite element analysis --- partial discharge modeling --- high-frequency --- fast-rise square wave voltages --- silicone gel --- wide bandgap power modules --- surface discharge --- flashover --- gas --- modelling --- pressure --- thermal properties

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