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"Scattering theory provides a framework for understanding the scattering of waves and particles. This book presents a simple physical picture of diffractive nuclear scattering in terms of semi-classical trajectories, illustrated throughout with examples and case studies. Trajectories in a complex impact parameter plane are discussed, and it stresses the importance of the analytical properties of the phase shift function in this complex impact plane in the asymptotic limit. Several new rainbow phenomena are also discussed and illustrated. Written by Nobel Prize winner Roy Glauber, and Per Osland an expert in the field of particle physics, it illustrates the transition from quantum to classical scattering, and provides a valuable resource for researchers using scattering theory in nuclear, particle, atomic and molecular physics."--

Scattering (Physics) --- Diffractive scattering --- Particles (Nuclear physics) --- Asymptotic expansions

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Mathematical and computational modeling approaches in biological and medical research are experiencing rapid growth globally. This Special Issue Book intends to scratch the surface of this exciting phenomenon. The subject areas covered involve general mathematical methods and their applications in biology and medicine, with an emphasis on work related to mathematical and computational modeling of the complex dynamics observed in biological and medical research. Fourteen rigorously reviewed papers were included in this Special Issue. These papers cover several timely topics relating to classical population biology, fundamental biology, and modern medicine. While the authors of these papers dealt with very different modeling questions, they were all motivated by specific applications in biology and medicine and employed innovative mathematical and computational methods to study the complex dynamics of their models. We hope that these papers detail case studies that will inspire many additional mathematical modeling efforts in biology and medicine

predator-prey model --- n/a --- uncertainty quantification --- identification of DNA-binding proteins --- chemostat --- numerical characterization --- differential equations --- uniform persistence --- spotting --- 2-combination --- wildfire --- chronic myeloid leukemia --- combination therapy --- liquid-solid-porous media seepage coupling --- dynamic model --- obesity --- epidermis --- articular cartilage --- androgen deprivation therapy --- quorum sensing --- mechano-electrochemical model --- bifurcations --- bacterial competition --- global stability --- cartilage degeneration --- flocculation --- dynamical system --- transport equations --- bootstrapping --- stationary distribution --- algae growth models --- hemodynamic model --- delay --- Raphidocelis subcapitata --- cartilage loading --- Daphnia magna --- cell-based vector --- switched harvest --- hepatitis B --- rich dynamics --- spotting distribution --- asymptotic theory --- tyrosine kinase inhibitors --- phylogenetic analysis --- immune response --- microcirculation load --- graphical representation --- intraguild predation --- numerical simulation --- bacterial inflammation --- data fitting --- immunomodulatory therapies --- drug therapy --- delay differential equations (DDE) --- global asymptotic stability --- model comparison tests --- optimal control --- generalized pseudo amino acid composition --- random perturbations --- limit cycle --- prostate cancer --- mathematical model --- mathematical modeling --- persistence --- equilibrium points

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Continuous casting is an industrial process whereby molten metal is solidified into a semi-finished billet, bloom, or slab for subsequent rolling in finishing mills; it is the most frequently used process to cast not only steel, but also aluminium and copper alloys. Since its widespread introduction for steel in the 1950s, it has evolved to achieve improved yield, quality, productivity and cost efficiency. It allows lower-cost production of metal sections with better quality, due to the inherently lower costs of continuous, standardized production of a product, as well as providing increased control over the process through automation. Nevertheless, challenges remain and new ones appear, as ways are sought to minimize casting defects and to cast alloys that could originally only be cast via other means. This Special Issue of the journal ""Metals"" consists of 14 research articles that cover many aspects of experimental work and theoretical modelling related to the ongoing development of continuous casting processes.

inclusion motion --- n/a --- air mist spray cooling --- empirical mode decomposition --- electromagnetic field --- solidification --- final electromagnetic stirring --- beam blank --- liquid core reduction --- tundish --- thermomechanical coupling --- flow behavior --- steel tundish --- austenite grain coarsening --- pores --- annular argon blowing --- round bloom --- mold --- thin-slab cast direct-rolling --- data stream --- grain growth control --- propagation --- two-phase pinning --- HTC --- prediction --- argon gas distribution --- baffle --- flow field --- bubbles --- heat transfer --- inclusions --- upper nozzle --- swirling flow tundish --- crystal --- hybrid simulation model --- roll gap value --- inclusion entrapment --- fluid flow --- billet continuous casting --- mechanism --- heat flux --- numerical simulation --- secondary cooling --- uneven secondary cooling --- polycrystalline model --- mold level --- continuous casting --- entrainment --- slab continuous casting --- magnetohydrodynamics --- entrapment --- asymptotic analysis --- bulge deformation --- slab mold --- segmented roller --- velocity --- finite element analysis --- multi-source information fusion --- global optimization --- support vector regression --- variational mode decomposition --- multiphase flow --- molten steel flow --- PIV

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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.

structured matrices --- numerical methods --- time fractional differential equations --- hierarchical splines --- finite difference methods --- null-space --- highly oscillatory problems --- stochastic Volterra integral equations --- displacement rank --- constrained Hamiltonian problems --- hyperbolic partial differential equations --- higher-order finite element methods --- continuous geometric average --- spectral (eigenvalue) and singular value distributions --- generalized locally Toeplitz sequences --- Volterra integro–differential equations --- B-spline --- discontinuous Galerkin methods --- adaptive methods --- Cholesky factorization --- energy-conserving methods --- order --- collocation method --- Poisson problems --- time harmonic Maxwell’s equations and magnetostatic problems --- tree --- multistep methods --- stochastic differential equations --- optimal basis --- finite difference method --- elementary differential --- gradient system --- curl–curl operator --- conservative problems --- line integral methods --- stochastic multistep methods --- Hamiltonian Boundary Value Methods --- limited memory --- boundary element method --- convergence --- analytical solution --- preconditioners --- asymptotic stability --- collocation methods --- histogram specification --- local refinement --- Runge–Kutta --- edge-preserving smoothing --- numerical analysis --- THB-splines --- BS methods --- barrier options --- stump --- shock waves and discontinuities --- mean-square stability --- Volterra integral equations --- high order discontinuous Galerkin finite element schemes --- B-splines --- vectorization and parallelization --- initial value problems --- one-step methods --- scientific computing --- fractional derivative --- linear systems --- Hamiltonian problems --- low rank completion --- ordinary differential equations --- mixed-index problems --- edge-histogram --- Hamiltonian PDEs --- matrix ODEs --- HBVMs --- floating strike Asian options --- Hermite–Obreshkov methods --- generalized Schur algorithm --- Galerkin method --- symplecticity --- high performance computing --- isogeometric analysis --- discretization of systems of differential equations

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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.

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