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This book appeals to scientists, teachers and graduate students in mathematics, and will be of interest for scholars in applied sciences as well, in particular in medicine, biology and social sciences. The models in this connection apply, in particular, to the study of the immune system response and to the predator–prey dynamic. The efficiency of public transport is also considered and blast waves in explosions are studied. Other contributions concern pure mathematics, in particular Pythagorean means, sequences of matrices and Markov chains, and these give evidence of deep links with Symmetry.

Research & information: general --- Mathematics & science --- paradox of enrichment --- prey–predator system --- persistence of predators --- extinction of predators --- blast waves --- non-ideal gas --- Rankine–Hugoniot conditions --- magnetogasdynamics --- dynamic model --- immune system response --- immune cells --- abnormal cells --- nonlinear ordinary differential equations --- stability --- diet --- Aggregation dynamic system --- Discrete system --- Epidemic model --- Cauchy’s interlacing theorem --- Output-feedback control --- Stability --- Antistable/Stable matrix --- onboard comfort level --- Markow chain --- bus passenger occupancy prediction --- Chebyshev inequality --- Tracy-Singh product --- continuous field of operators --- Bochner integral --- weighted Pythagorean mean

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This book appeals to scientists, teachers and graduate students in mathematics, and will be of interest for scholars in applied sciences as well, in particular in medicine, biology and social sciences. The models in this connection apply, in particular, to the study of the immune system response and to the predator–prey dynamic. The efficiency of public transport is also considered and blast waves in explosions are studied. Other contributions concern pure mathematics, in particular Pythagorean means, sequences of matrices and Markov chains, and these give evidence of deep links with Symmetry.

paradox of enrichment --- prey–predator system --- persistence of predators --- extinction of predators --- blast waves --- non-ideal gas --- Rankine–Hugoniot conditions --- magnetogasdynamics --- dynamic model --- immune system response --- immune cells --- abnormal cells --- nonlinear ordinary differential equations --- stability --- diet --- Aggregation dynamic system --- Discrete system --- Epidemic model --- Cauchy’s interlacing theorem --- Output-feedback control --- Stability --- Antistable/Stable matrix --- onboard comfort level --- Markow chain --- bus passenger occupancy prediction --- Chebyshev inequality --- Tracy-Singh product --- continuous field of operators --- Bochner integral --- weighted Pythagorean mean

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This Special Issue collects the latest results on differential/difference equations, the mathematics of networks, and their applications to engineering and physical phenomena. It features nine high-quality papers that were published with original research results. The Special Issue brings together mathematicians with physicists, engineers, as well as other scientists.

History of engineering & technology --- fractional discrete calculus --- discrete chaos --- Tinkerbell map --- bifurcation --- stabilization --- communication networks --- maximum flow --- network policies --- algorithms --- gas flow --- stress-sensitive porous media --- multiple hydraulic fractures --- vertical fractured well --- Output-feedback --- centralized control --- decentralized control --- closed-loop stabilization --- Hardy Cross method --- pipe networks --- piping systems --- hydraulic networks --- gas distribution --- multi-switching combination synchronization --- time-delay --- fractional-order --- stability --- Shehu transformation --- Adomian decomposition --- analytical solution --- Caputo derivatives --- (2+time fractional-order) dimensional physical models --- homotopy perturbation method --- variational iteration method --- Laplace transform method --- acoustic wave equations --- n/a

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The dynamics of systems have proven to be very powerful tools in understanding the behavior of different natural phenomena throughout the last two centuries. However, the attributes of natural systems are observed to deviate from their classical states due to the effect of different types of uncertainties. Actually, randomness and impreciseness are the two major sources of uncertainties in natural systems. Randomness is modeled by different stochastic processes and impreciseness could be modeled by fuzzy sets, rough sets, Dempster–Shafer theory, etc.

Research & information: general --- Mathematics & science --- Fuzzy MARCOS --- Fuzzy PIPRECIA --- traffic risk --- TFN --- MCDM --- dual-rotor --- multi-frequency excitation --- non-intrusive calculation --- metamodel --- NDSL model --- AHP --- criteria weights --- pairwise comparisons --- AES --- PC --- MIMO discrete-time system --- state feedback and output feedback --- parameter dependence --- D numbers --- fuzzy sets --- DEMATEL --- multi-criteria decision-making --- multi-criteria optimization --- RAFSI method --- performance comparison --- rank reversal --- Magnetic Resonance Imaging (MRI) --- wavelet transform --- GARCH --- LLA --- LDA --- KNN --- BWM --- BWM-I --- multi-criteria --- renewable energy --- the CCSD method --- the ITARA method --- the MARCOS method --- stackers --- logistics --- ensemble techniques --- data mining --- classification and discrimination --- linear regression --- applied mathematics general --- prediction theory --- theory of mathematical modeling --- medical applications --- empathic building --- fuzzy grey cognitive maps --- Thayer’s emotion model --- artificial emotions --- affective computing --- n/a --- Thayer's emotion model

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It is very well known that differential equations are related with the rise of physical science in the last several decades and they are used successfully for models of real-world problems in a variety of fields from several disciplines. Additionally, difference equations represent the discrete analogues of differential equations. These types of equations started to be used intensively during the last several years for their multiple applications, particularly in complex chaotic behavior. A certain class of differential and related difference equations is represented by their respective fractional forms, which have been utilized to better describe non-local phenomena appearing in all branches of science and engineering. The purpose of this book is to present some common results given by mathematicians together with physicists, engineers, as well as other scientists, for whom differential and difference equations are valuable research tools. The reported results can be used by researchers and academics working in both pure and applied differential equations.

Research & information: general --- Mathematics & science --- dynamic equations --- time scales --- classification --- existence --- necessary and sufficient conditions --- fractional calculus --- triangular fuzzy number --- double-parametric form --- FRDTM --- fractional dynamical model of marriage --- approximate controllability --- degenerate evolution equation --- fractional Caputo derivative --- sectorial operator --- fractional symmetric Hahn integral --- fractional symmetric Hahn difference operator --- Arrhenius activation energy --- rotating disk --- Darcy–Forchheimer flow --- binary chemical reaction --- nanoparticles --- numerical solution --- fractional differential equations --- two-dimensional wavelets --- finite differences --- fractional diffusion-wave equation --- fractional derivative --- ill-posed problem --- Tikhonov regularization method --- non-linear differential equation --- cubic B-spline --- central finite difference approximations --- absolute errors --- second order differential equations --- mild solution --- non-instantaneous impulses --- Kuratowski measure of noncompactness --- Darbo fixed point --- multi-stage method --- multi-step method --- Runge–Kutta method --- backward difference formula --- stiff system --- numerical solutions --- Riemann-Liouville fractional integral --- Caputo fractional derivative --- fractional Taylor vector --- kerosene oil-based fluid --- stagnation point --- carbon nanotubes --- variable thicker surface --- thermal radiation --- differential equations --- symmetric identities --- degenerate Hermite polynomials --- complex zeros --- oscillation --- third order --- mixed neutral differential equations --- powers of stochastic Gompertz diffusion models --- powers of stochastic lognormal diffusion models --- estimation in diffusion process --- stationary distribution and ergodicity --- trend function --- application to simulated data --- n-th order linear differential equation --- two-point boundary value problem --- Green function --- linear differential equation --- exponential stability --- linear output feedback --- stabilization --- uncertain system --- nonlocal effects --- linear control system --- Hilbert space --- state feedback control --- exact controllability --- upper Bohl exponent