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Historically, the notion of entropy emerged in conceptually very distinct contexts. This book deals with the connection between entropy, probability, and fractional dynamics as they appeared, for example, in solar neutrino astrophysics since the 1970's (Mathai and Rathie 1975, Mathai and Pederzoli 1977, Mathai and Saxena 1978, Mathai, Saxena, and Haubold 2010).The original solar neutrino problem, experimentally and theoretically, was resolved through the discovery of neutrino oscillations and was recently enriched by neutrino entanglement entropy. To reconsider possible new physics of solar neutrinos, diffusion entropy analysis, utilizing Boltzmann entropy, and standard deviation analysis was undertaken with SuperKamiokande solar neutrino data. This analysis revealed a nonGaussian signal with harmonic content. The Hurst exponent is different from the scaling exponent of the probability density function and both Hurst exponent and scaling exponent of the SuperKamiokande data deviate considerably from the value of ½, which indicates that the statistics of the underlying phenomenon is anomalous. Here experiment may provide guidance about the generalization of theory of Boltzmann statistical mechanics. Arguments in the socalled BoltzmannPlanckEinstein discussion related to Planck's discovery of the blackbody radiation law are recapitulated mathematically and statistically and emphasize from this discussion is pursued that a meaningful implementation of the complex ‘entropyprobabilitydynamics’ may offer two ways for explaining the results of diffusion entropy analysis and standard deviation analysis. One way is to consider an anomalous diffusion process that needs to use the fractional spacetime diffusion equation (Gorenflo and Mainardi) and the other way is to consider a generalized Boltzmann entropy by assuming a power law probability density function. Here new mathematical framework, invented by sheer thought, may provide guidance for the generalization of Boltzmann statistical mechanics. In this book Boltzmann entropy, generalized by Tsallis and Mathai, is considered. The second one contains a varying parameter that is used to construct an entropic pathway covering generalized type1 beta, type2 beta, and gamma families of densities. Similarly, pathways for respective distributions and differential equations can be developed. Mathai's entropy is optimized under various conditions reproducing the wellknown Boltzmann distribution, Raleigh distribution, and other distributions used in physics. Properties of the entropy measure for the generalized entropy are examined. In this process the role of special functions of mathematical physics, particularly the Hfunction, is highlighted.
special functions  fractional calculus  entropic functional  mathematical physics  applied analysis  statistical distributions  geometrical probabilities  multivariate analysis
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This book summarizes the found insights of grain growth behavior, of multidimensional decomposition for regular grids to efficiently parallelize computing and how to simulate recrystallization by coupling the finite element method with the phasefield method for microstructure texture analysis. The frame of the book is created by the phasefield method, which is the tool used in this work, to investigate microstructure phenomena.
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The causes and consequences of differences in microbial community structure, defined here as the relative proportions of rare and abundant organisms within a community, are poorly understood. Articles in "The Causes and Consequences of Microbial Community Structure", use empirical or modeling approaches as well as literature reviews to enrich our mechanistic understanding of the controls over the relationship between community structure and ecosystem processes. Specifically, authors address the role of trait distributions and tradeoffs, speciesspecies interactions, evolutionary dynamics, community assembly processes and physical controls in affecting ‘who’s there’ and ‘what they are doing’.
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Discontinuous fiberreinforced polymers have gained importance in the transportation industries due to their outstanding material properties, lower manufacturing costs and superior lightweight characteristics. One of the most attractive attributes of discontinuous fiber reinforced composites is the ease with which they can be manufactured in large numbers, using injection and compression molding processes.Typical processes involving discontinuous fiber reinforced thermoplastic composite materials include injection and compression molding processes as well as extrusion. Furthermore, the automotive and appliance industries also use thermosets reinforced with chopped fibers in the form of sheet molding compound and bulk molding compound, for compression and injectioncompression molding processes, respectively.A big disadvantage of discontinuous fiber composites is that the configuration of the reinforcing fibers is significantly changed throughout production process, reflected in the form of fiber attrition, excessive fiber orientation, fiber jamming and fiber matrix separation. This processinduced variation of the microstructural fiber properties within the molded part introduces heterogeneity and anisotropies to the mechanical properties, which can limit the potential of discontinuous fiber reinforced composites for lightweight applications.The main aim of this Special Issue is to collect various investigations focused on the processing of discontinuous fiber reinforced composites and the effect processing has on fiber orientation, fiber length and fiber density distributions throughout the final part. Papers presenting investigations on the effect fiber configurations have on the mechanical properties of the final composite products and materials are welcome in the Special Issue. Researchers who are modeling and simulating processes involving discontinuous fiber composites as well as those performing experimental studies involving these composites are welcomed to submit papers. Authors are encouraged to present new models, constitutive laws and measuring and monitoring techniques to provide a complete framework on these groundbreaking materials and facilitate their use in different engineering applications.
discontinuous fibers  chopped fibers  short fiber reinforced thermoplastics (SFT)  long fiber reinforced thermoplastics (LFT)  sheet molding compound (SMC)  bulk Molding Compound (BMC)  fiber orientation distributions  fiber length distributions  fiber density distributions  fiber attrition  micro computed tomography  compression molding  injection molding  compounding
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Financial econometrics has developed into a very fruitful and vibrant research area in the last two decades. The availability of good data promotes research in this area, specially aided by online data and highfrequency data. These two characteristics of financial data also create challenges for researchers that are different from classical macroeconometric and microeconometric problems. This Special Issue is dedicated to research topics that are relevant for analyzing financial data. We have gathered six articles under this theme.
asset price bubbles  explosive regimes  multivariate nonlinear time series  steady state distributions  TVAR models  bond risk premia  affine term structure models  risk prices  stochastic conditional duration  threshold  Bayesian inference  MarkovChain Monte Carlo  probability integral transform  deviance information criterion  Mallows criterion  model averaging  model selection  shrinkage  tuning parameter choice  threshold autoregression  Markov process  stationarity  volatility forecasting  realized volatility  linear programming estimator  Tukey’s power transformation  nonlinear nonnegative autoregression  forecast comparisons  n/a
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The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.
time fractional differential equations  mixedindex problems  analytical solution  asymptotic stability  conservative problems  Hamiltonian problems  energyconserving methods  Poisson problems  Hamiltonian Boundary Value Methods  HBVMs  line integral methods  constrained Hamiltonian problems  Hamiltonian PDEs  highly oscillatory problems  boundary element method  finite difference method  floating strike Asian options  continuous geometric average  barrier options  isogeometric analysis  adaptive methods  hierarchical splines  THBsplines  local refinement  linear systems  preconditioners  Cholesky factorization  limited memory  Volterra integral equations  Volterra integro–differential equations  collocation methods  multistep methods  convergence  Bspline  optimal basis  fractional derivative  Galerkin method  collocation method  spectral (eigenvalue) and singular value distributions  generalized locally Toeplitz sequences  discretization of systems of differential equations  higherorder finite element methods  discontinuous Galerkin methods  finite difference methods  isogeometric analysis  Bsplines  curl–curl operator  time harmonic Maxwell’s equations and magnetostatic problems  low rank completion  matrix ODEs  gradient system  ordinary differential equations  Runge–Kutta  tree  stump  order  elementary differential  edgehistogram  edgepreserving smoothing  histogram specification  initial value problems  onestep methods  Hermite–Obreshkov methods  symplecticity  Bsplines  BS methods  hyperbolic partial differential equations  high order discontinuous Galerkin finite element schemes  shock waves and discontinuities  vectorization and parallelization  high performance computing  generalized Schur algorithm  nullspace  displacement rank  structured matrices  stochastic differential equations  stochastic multistep methods  stochastic Volterra integral equations  meansquare stability  asymptotic stability  numerical analysis  numerical methods  scientific computing  initial value problems  onestep methods  Hermite–Obreshkov methods  symplecticity  Bsplines  BS methods
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Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous realworld 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.
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)  continuoustime Markov chains  catastrophes  bounds  birthdeath process  rate of convergence  doubleended queues  timenonhomogeneous birthdeath processes  catastrophes  repairs  transient probabilities  periodic intensity functions  timenonhomogeneous jumpdiffusion processes  transition densities  firstpassagetime  lognormal diffusion process  exogenous factors  growth curves  maximum likelihood estimation  asymptotic distribution  firstpassage time  inverse firstpassage problem  diffusion  mixture of Gaussian laws  rate of convergence  total variation distance  Wasserstein distance  weighted quadratic variation  nonMarkovian queue  general bulk service  multiple vacation  breakdown and repair  standby server  reservice  discrete time stochastic model  firstpassage time  time between inspections  hostparasite interaction  nematode infection  nonhomogeneous Poisson process  seasonal environment  Strang–Marchuk splitting approach  Cohen and Grossberg neural networks  random impulses  mean square stability  fractional differentialdifference equations  fractional queues  fractional birthdeath processes  busy period  twodimensional signature  multistate 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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Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences.
highly oscillatory  convolution quadrature rule  volterra integral equation  Bessel kernel  convergence  higher order Schwarzian derivatives  Janowski starlike function  Janowski convex function  bound on derivatives  tangent numbers  tangent polynomials  Carlitztype qtangent numbers  Carlitztype qtangent polynomials  (p,q)analogue of tangent numbers and polynomials  (p,q)analogue of tangent zeta function  symmetric identities  zeros  Lommel functions  univalent functions  starlike functions  convex functions  inclusion relationships  analytic function  Hankel determinant  exponential function  upper bound  nonlinear boundary value problems  fractionalorder differential equations  RiemannStieltjes functional integral  LiouvilleCaputo fractional derivative  infinitepoint boundary conditions  advanced and deviated arguments  existence of at least one solution  Fredholm integral equation  Schauder fixed point theorem  Hölder condition  generalized Kuramoto–Sivashinsky equation  modified Kudryashov method  exact solutions  Maple graphs  analytic function  Hadamard product (convolution)  partial sum  Srivastava–Tomovski generalization of Mittag–Leffler function  subordination  differential equation  differential inclusion  Liouville–Caputotype fractional derivative  fractional integral  existence  fixed point  Bernoulli spiral  Grandi curves  Chebyshev polynomials  pseudoChebyshev polynomials  orthogonality property  symmetric  encryption  password  hash  cryptography  PBKDF  q–Bleimann–Butzer–Hahn operators  (p,q)integers  (p,q)Bernstein operators  (p,q)Bleimann–Butzer–Hahn operators  modulus of continuity  rate of approximation  Kfunctional  HurwitzLerch zeta function  generalized functions  analytic number theory  ?generalized HurwitzLerch zeta functions  derivative properties  series representation  basic hypergeometric functions  generating functions  qpolynomials  analytic functions  Mittag–Leffler functions  starlike functions  convex functions  Hardy space  vibrating string equation  initial conditions  spectral decomposition  regular solution  the uniqueness of the solution  the existence of a solution  analytic  ?convex function  starlike function  stronglystarlike function  subordination  q Sheffer–Appell polynomials  generating relations  determinant definition  recurrence relation  q Hermite–Bernoulli polynomials  q Hermite–Euler polynomials  q Hermite–Genocchi polynomials  Volterra integral equations  highly oscillatory Bessel kernel  Hermite interpolation  direct Hermite collocation method  piecewise Hermite collocation method  differential operator  qhypergeometric functions  meromorphic function  Mittag–Leffler function  Hadamard product  differential subordination  starlike functions  Bell numbers  radius estimate  (p, q)integers  Dunkl analogue  generating functions  generalization of exponential function  Szász operator  modulus of continuity  function spaces and their duals  distributions  tempered distributions  Schwartz testing function space  generalized functions  distribution space  wavelet transform of generalized functions  Fourier transform  analytic function  subordination  Dziok–Srivastava operator  nonlinear boundary value problem  nonlocal  multipoint  multistrip  existence  Ulam stability  functions of bounded boundary and bounded radius rotations  subordination  functions with positive real part  uniformly starlike and convex functions  analytic functions  univalent functions  starlike and qstarlike functions  qderivative (or qdifference) operator  sufficient conditions  distortion theorems  Janowski functions  analytic number theory  ?generalized Hurwitz–Lerch zeta functions  derivative properties  recurrence relations  integral representations  Mellin transform  natural transform  Adomian decomposition method  Caputo fractional derivative  generalized mittagleffler function  analytic functions  Hadamard product  starlike functions  qderivative (or qdifference) operator  Hankel determinant  qstarlike functions  fuzzy volterra integrodifferential equations  fuzzy general linear method  fuzzy differential equations  generalized Hukuhara differentiability  spectrum symmetry  DCT  MFCC  audio features  anuran calls  analytic functions  convex functions  starlike functions  strongly convex functions  strongly starlike functions  uniformly convex functions  Struve functions  truncatedexponential polynomials  monomiality principle  generating functions  Apostoltype polynomials and Apostoltype numbers  Bernoulli, Euler and Genocchi polynomials  Bernoulli, Euler, and Genocchi numbers  operational methods  summation formulas  symmetric identities  Euler numbers and polynomials  qEuler numbers and polynomials  HurwitzEuler eta function  multiple HurwitzEuler eta function  higher order qEuler numbers and polynomials  (p, q)Euler numbers and polynomials of higher order  symmetric identities  symmetry of the zero
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Image analysis is a fundamental task for extracting information from images acquired across a range of different devices. Since reliable quantitative results are requested, image analysis requires highly sophisticated numerical and analytical methods—particularly for applications in medicine, security, and remote sensing, where the results of the processing may consist of vitally important data. The contributions to this book provide a good overview of the most important demands and solutions concerning this research area. In particular, the reader will find image analysis applied for feature extraction, encryption and decryption of data, color segmentation, and in the support new technologies. In all the contributions, entropy plays a pivotal role.
image retrieval  multifeature fusion  entropy  relevance feedback  chaotic system  image encryption  permutationdiffusion  SHA256 hash value  dynamic index  entropy  keyframes  Shannon’s entropy  sign languages  video summarization  video skimming  image encryption  multipleimage encryption  twodimensional chaotic economic map  security analysis  image encryption  chaotic cryptography  cryptanalysis  chosenplaintext attack  image information entropy  blind image quality assessment (BIQA)  information entropy, natural scene statistics (NSS)  Weibull statistics  discrete cosine transform (DCT)  ultrasound  hepatic steatosis  Shannon entropy  fatty liver  metabolic syndrome  multiexposure image fusion  texture information entropy  adaptive selection  patch structure decomposition  image encryption  timedelay  random insertion  information entropy  chaotic map  uncertainty assessment  deep neural network  random forest  Shannon entropy  positron emission tomography  reconstruction  field of experts  additive manufacturing  3D prints  3D scanning  image entropy  depth maps  surface quality assessment  machine vision  image analysis  Arimoto entropy  freeform deformations  normalized divergence measure  gradient distributions  nonextensive entropy  nonrigid registration  pavement  macrotexture  3D digital imaging  entropy  decay trend  discrete entropy  infrared images  low contrast  multiscale tophat transform  image encryption  DNA encoding  chaotic cryptography  cryptanalysis  image privacy  computer aided diagnostics  colonoscopy  Rényi entropies  structural entropy  spatial filling factor  binary image  Cantor set  Hénon map  Minkowski island  primeindexed primes  Ramanujan primes  Kapur’s entropy  color image segmentation  whale optimization algorithm  differential evolution  hybrid algorithm  Otsu method  image encryption  dynamic filtering  DNA computing  3D Latin cube  permutation  diffusion  fuzzy entropy  electromagnetic field optimization  chaotic strategy  color image segmentation  multilevel thresholding  contrast enhancement  sigmoid  Tsallis statistics  qexponential  qsigmoid  qGaussian  ultrasound images  person reidentification  image analysis  hash layer  quantization loss  Hamming distance  crossentropy loss  image entropy  Shannon entropy  generalized entropies  image processing  image segmentation  medical imaging  remote sensing  security
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Unconventional reservoirs are usually complex and highly heterogeneous, such as shale, coal, and tight sandstone reservoirs. The strong physical and chemical interactions between fluids and pore surfaces lead to the inapplicability of conventional approaches for characterizing fluid flow in these lowporosity and ultralowpermeability reservoir systems. Therefore, new theories and techniques are urgently needed to characterize petrophysical properties, fluid transport, and their relationships at multiple scales for improving production efficiency from unconventional reservoirs. This book presents fundamental innovations gathered from 21 recent works on novel applications of new techniques and theories in unconventional reservoirs, covering the fields of petrophysical characterization, hydraulic fracturing, fluid transport physics, enhanced oil recovery, and geothermal energy. Clearly, the research covered in this book is helpful to understand and master the latest techniques and theories for unconventional reservoirs, which have important practical significance for the economic and effective development of unconventional oil and gas resources.
fracturing fluid  rheology  chelating agent  viscosity  polymer  fluidsolid interaction  velocity profile  the average flow velocity  flow resistance  pore network model  shale gas  volume fracturing  finite volume method  production simulation  multiscale flow  multiscale fracture  shale gas reservoir  fractured well transient productivity  succession pseudosteady state (SPSS) method  complex fracture network  multiscale flow  analysis of influencing factors  tight sandstones  spontaneous imbibition  remaining oil distributions  imbibition front  imbibition recovery  NMR  slip length  large density ratio  contact angle  pseudopotential model  lattice Boltzmann method  microfracture  dissolved gas  experimental evaluation  reservoir depletion  recovery factor  tight oil  Lucaogou Formation  tight oil  pore structure  prediction by NMR logs  tight oil reservoir  SRVfractured horizontal well  multiporosity and multiscale  flow regimes  productivity contribution degree of multimedium  equilibrium permeability  nonequilibrium permeability  matrix–fracture interaction  effective stress  coal deformation  porous media  nonlinear flow  conformable derivative  fractal  hydraulic fracturing  tight reservoirs  fracture diversion  extended finite element method  fracture network  gas adsorption capacity  shale reservoirs  influential factors  integrated methods  sulfonate gemini surfactant  thickener  temperatureresistance  clean fracturing fluid  lowsalinity water flooding  clay mineral composition  enhanced oil recovery  wetting angle  pH of formation water  fractional diffusion  fractal geometry  analytical model  shale gas reservoir  carbonate reservoir  petrophysical characterization  pore types  pore structure  permeability  fractal dimension  reservoir classifications  deep circulation groundwater  groundwater flow  geothermal water  faults  isotopes  shale permeability  local effect  global effect  matrixfracture interactions  nanopore  pore structure  shale  tight sandstone  mudstone  nitrogen adsorption  fractal  enhanced geothermal system  wellplacement optimization  fracture continuum method  01 programming  unconventional reservoirs  petrophysical characterization  fluid transport physics
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