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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: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 11:49:15
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Abstract

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

Stochastic Processes with Applications

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ISBN: 9783039217281 / 9783039217298 Year: Pages: 284 DOI: 10.3390/books978-3-03921-729-8 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 16:10:12
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Abstract

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

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