LEADER 05248nam 22006255 450 001 9910300132803321 005 20200630064634.0 010 $a3-319-92586-5 024 7 $a10.1007/978-3-319-92586-8 035 $a(CKB)4100000005471833 035 $a(DE-He213)978-3-319-92586-8 035 $a(MiAaPQ)EBC6225979 035 $a(PPN)229915175 035 $a(EXLCZ)994100000005471833 100 $a20180803d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDistributions in the Physical and Engineering Sciences, Volume 3 $eRandom and Anomalous Fractional Dynamics in Continuous Media /$fby Alexander I. Saichev, Wojbor A. woyczy?ski 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2018. 215 $a1 online resource (XX, 403 p. 61 illus., 6 illus. in color.) 225 1 $aApplied and Numerical Harmonic Analysis,$x2296-5009 311 $a3-319-92584-9 327 $aIntroduction to Volume 3 -- Notation -- Basic Distributional Tools for Probability Theory -- Random Distributions: Generalized Stochastic Processes -- Dynamical and Statistical Characteristics of Random Fields and Waves -- Forced Burgers Turbulence and Passive Tracer Transport in Burgers Flows -- Probability Distributions of Passive Tracers in Randomly Moving Media -- Levy Processes and Their Generalized Derivatives -- Linear Anomalous Fractional Dynamics in Continuous Media -- Nonlinear and Multiscale Anomalous Fractional Dynamics in Continuous Media -- Appendix A: Basic Facts About Distributions -- Bibliography -- Index. 330 $aContinuing the authors? multivolume project, this text considers the theory of distributions from an applied perspective, demonstrating how effective a combination of analytic and probabilistic methods can be for solving problems in the physical and engineering sciences. Volume 1 covered foundational topics such as distributional and fractional calculus, the integral transform, and wavelets, and Volume 2 explored linear and nonlinear dynamics in continuous media. With this volume, the scope is extended to the use of distributional tools in the theory of generalized stochastic processes and fields, and in anomalous fractional random dynamics. Chapters cover topics such as probability distributions; generalized stochastic processes, Brownian motion, and the white noise; stochastic differential equations and generalized random fields; Burgers turbulence and passive tracer transport in Burgers flows; and linear, nonlinear, and multiscale anomalous fractional dynamics in continuous media. The needs of the applied-sciences audience are addressed by a careful and rich selection of examples arising in real-life industrial and scientific labs and a thorough discussion of their physical significance. Numerous illustrations generate a better understanding of the core concepts discussed in the text, and a large number of exercises at the end of each chapter expand on these concepts. Distributions in the Physical and Engineering Sciences is intended to fill a gap in the typical undergraduate engineering/physical sciences curricula, and as such it will be a valuable resource for researchers and graduate students working in these areas. The only prerequisites are a three-four semester calculus sequence (including ordinary differential equations, Fourier series, complex variables, and linear algebra), and some probability theory, but basic definitions and facts are covered as needed. An appendix also provides background material concerning the Dirac-delta and other distributions. 410 0$aApplied and Numerical Harmonic Analysis,$x2296-5009 606 $aProbabilities 606 $aEngineering mathematics 606 $aFunctional analysis 606 $aStatistics 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aEngineering Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/T11030 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/S17020 615 0$aProbabilities. 615 0$aEngineering mathematics. 615 0$aFunctional analysis. 615 0$aStatistics. 615 14$aProbability Theory and Stochastic Processes. 615 24$aEngineering Mathematics. 615 24$aFunctional Analysis. 615 24$aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. 676 $a515.782 700 $aSaichev$b Alexander I$4aut$4http://id.loc.gov/vocabulary/relators/aut$0344910 702 $awoyczy?ski$b Wojbor A$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300132803321 996 $aDistributions in the Physical and Engineering Sciences, Volume 3$92022342 997 $aUNINA