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This book gathers a number of selected contributions aimed at providing a balanced picture of the main research lines in the realm of delay differential equations and their applications to mathematical modelling. The contributions have been carefully selected so that they cover interesting theoretical and practical analysis performed in the deterministic and the stochastic settings. The reader will find a complete overview of recent advances in ordinary and partial delay differential equations with applications in other multidisciplinary areas such as Finance, Epidemiology or Engineering

delay systems --- nonstandard numerical methods --- dynamic consistency --- semilinear problems with delay --- hyperbolic equations --- difference scheme --- stability --- Hilbert space --- SEIRS model --- age structure --- time delay --- traveling wave solution --- local asymptotic stability --- Hopf bifurcation --- spot freight rates --- freight options --- stochastic diffusion process --- stochastic delay differential equation --- risk-neutral measure --- arbitration arguments --- partial differential equations --- second-order dual phase lag equation --- laser heating --- thin metal films --- melting and resolidification --- finite difference method --- random linear delay differential equation --- stochastic forcing term --- random Lp-calculus --- uncertainty quantification --- delay random differential equation --- non-standard finite difference method --- mean square convergence --- size-structured population --- consumer-resource model --- delay differential equation --- numerical methods --- characteristics method --- convergence analysis --- implementation delay --- information delay --- stability switching curve --- Cournot oligopoly --- growth rate dynamics --- fractional convection diffusion-wave equations --- compact difference scheme --- nonlinear delay --- spatial variable coefficients --- convergence and stability --- Gerasimov–Caputo fractional derivative --- differential equation with delay --- degenerate evolution equation --- fixed point theorem --- relaxation mode --- large parameter --- asymptotics --- HIV infection --- mathematical delay model --- eclipse phase --- NSFD --- numerical simulation

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Delay, difference, functional, fractional, and partial differential equations have many applications in science and engineering. In this Special Issue, 29 experts co-authored 10 papers dealing with these subjects. A summary of the main points of these papers follows:Several oscillation conditions for a first-order linear differential equation with non-monotone delay are established in Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays, whereas a sharp oscillation criterion using the notion of slowly varying functions is established in A Sharp Oscillation Criterion for a Linear Differential Equation with Variable Delay. The approximation of a linear autonomous differential equation with a small delay is considered in Approximation of a Linear Autonomous Differential Equation with Small Delay; the model of infection diseases by Marchuk is studied in Around the Model of Infection Disease: The Cauchy Matrix and Its Properties. Exact solutions to fractional-order Fokker–Planck equations are presented in New Exact Solutions and Conservation Laws to the Fractional-Order Fokker–Planck Equations, and a spectral collocation approach to solving a class of time-fractional stochastic heat equations driven by Brownian motion is constructed in A Collocation Approach for Solving Time-Fractional Stochastic Heat Equation Driven by an Additive Noise. A finite difference approximation method for a space fractional convection-diffusion model with variable coefficients is proposed in Finite Difference Approximation Method for a Space Fractional Convection–Diffusion Equation with Variable Coefficients; existence results for a nonlinear fractional difference equation with delay and impulses are established in On Nonlinear Fractional Difference Equation with Delay and Impulses. A complete Noether symmetry analysis of a generalized coupled Lane–Emden–Klein–Gordon–Fock system with central symmetry is provided in Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays, and new soliton solutions of a fractional Jaulent soliton Miodek system via symmetry analysis are presented in New Soliton Solutions of Fractional Jaulent-Miodek System with Symmetry Analysis.

integro–differential systems --- Cauchy matrix --- exponential stability --- distributed control --- delay differential equation --- ordinary differential equation --- asymptotic equivalence --- approximation --- eigenvalue --- oscillation --- variable delay --- deviating argument --- non-monotone argument --- slowly varying function --- Crank–Nicolson scheme --- Shifted Grünwald–Letnikov approximation --- space fractional convection-diffusion model --- variable coefficients --- stability analysis --- Lane-Emden-Klein-Gordon-Fock system with central symmetry --- Noether symmetries --- conservation laws --- differential equations --- non-monotone delays --- fractional calculus --- stochastic heat equation --- additive noise --- chebyshev polynomials of sixth kind --- error estimate --- fractional difference equations --- delay --- impulses --- existence --- fractional Jaulent-Miodek (JM) system --- fractional logistic function method --- symmetry analysis --- lie point symmetry analysis --- approximate conservation laws --- approximate nonlinear self-adjointness --- perturbed fractional differential equations

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"How is consciousness possible? What biological purpose does it serve? And why do we value it so highly? In Soul Dust, the psychologist Nicholas Humphrey, a leading figure in consciousness research, proposes a startling new theory. Consciousness, he argues, is nothing less than a magical-mystery show that we stage for ourselves inside our own heads. This self-made show lights up the world for us and makes us feel special and transcendent. Thus consciousness paves the way for spirituality, and allows us, as human beings, to reap the rewards, and anxieties, of living in what Humphrey calls the "soul niche." Tightly argued, intellectually gripping, and a joy to read, Soul Dust provides answers to the deepest questions. It shows how the problem of consciousness merges with questions that obsess us all--how life should be lived and the fear of death. Resting firmly on neuroscience and evolutionary theory, and drawing a wealth of insights from philosophy and literature ..."--Jacket.

Consciousness. --- Bewusstsein. --- Evolution. --- Theorie. --- Consciousness --- Apperception --- Mind and body --- Perception --- Philosophy --- Psychology --- Spirit --- Self --- Aldous Huxley. --- Analogy. --- Anthony Marcel. --- Anthropologist. --- Behavior. --- Buddhism. --- Cheating death. --- Childlessness. --- Chimpanzee. --- Christopher Isherwood. --- Concept. --- Culture. --- Daniel Dennett. --- Death anxiety (psychology). --- Decision-making. --- Delay differential equation. --- Developmental psychology. --- Douglas Hofstadter. --- Dualism (philosophy of mind). --- Dylan Evans. --- Emergence. --- Enthusiasm. --- Existence. --- Explanation. --- Faber and Faber. --- Feeling. --- George Santayana. --- God. --- Hard problem of consciousness. --- Heat death of the universe. --- Human. --- Illustration. --- Incorruptibility. --- Indication (medicine). --- Individualism. --- Individuation. --- Ineffability. --- Instance (computer science). --- Instant. --- Intentionality. --- Johansson. --- Lecture. --- Literary agent. --- Ludwig Wittgenstein. --- Matt Ridley. --- Mental representation. --- Mescaline. --- Midwife. --- Mortality salience. --- Narrative. --- Niche construction. --- Penguin Books. --- Perception. --- Personhood. --- Pessimism. --- Phenomenon. --- Philosopher. --- Philosophical zombie. --- Philosophy. --- Pity. --- Precognition. --- Principle. --- Probability. --- Psychology. --- Qualia. --- Reality. --- Reason. --- Religion. --- Requirement. --- Ross Anderson. --- Rupert Sheldrake. --- Ruth Brandon. --- Science. --- Scientist. --- Self-concept. --- Self-consciousness. --- Self-image. --- Seminar. --- Sense. --- Special Period. --- Spirituality. --- Stimulation. --- Strange loop. --- Suffering. --- Suggestion. --- Termite. --- Terror management theory. --- The Dog Beneath the Skin. --- The Philosopher. --- The Various. --- Theory. --- Thomas Kuhn. --- Thought experiment. --- Thought. --- Uncertainty. --- Uniqueness. --- Visual system. --- W. H. Auden. --- What Is Your Dangerous Idea?.