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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

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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.

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

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This book presents an overview of recent developments in the area of localization for quasi-periodic lattice Schrödinger operators and the theory of quasi-periodicity in Hamiltonian evolution equations. The physical motivation of these models extends back to the works of Rudolph Peierls and Douglas R. Hofstadter, and the models themselves have been a focus of mathematical research for two decades. Jean Bourgain here sets forth the results and techniques that have been discovered in the last few years. He puts special emphasis on so-called "non-perturbative" methods and the important role of subharmonic function theory and semi-algebraic set methods. He describes various applications to the theory of differential equations and dynamical systems, in particular to the quantum kicked rotor and KAM theory for nonlinear Hamiltonian evolution equations. Intended primarily for graduate students and researchers in the general area of dynamical systems and mathematical physics, the book provides a coherent account of a large body of work that is presently scattered in the literature. It does so in a refreshingly contained manner that seeks to convey the present technological "state of the art."

Schrödinger operator. --- Green's functions. --- Hamiltonian systems. --- Evolution equations. --- Evolutionary equations --- Equations, Evolution --- Equations of evolution --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Operator, Schrödinger --- Differential equations --- Differentiable dynamical systems --- Potential theory (Mathematics) --- Differential operators --- Quantum theory --- Schrödinger equation --- Almost Mathieu operator. --- Analytic function. --- Anderson localization. --- Betti number. --- Cartan's theorem. --- Chaos theory. --- Density of states. --- Dimension (vector space). --- Diophantine equation. --- Dynamical system. --- Equation. --- Existential quantification. --- Fundamental matrix (linear differential equation). --- Green's function. --- Hamiltonian system. --- Hermitian adjoint. --- Infimum and supremum. --- Iterative method. --- Jacobi operator. --- Linear equation. --- Linear map. --- Linearization. --- Monodromy matrix. --- Non-perturbative. --- Nonlinear system. --- Normal mode. --- Parameter space. --- Parameter. --- Parametrization. --- Partial differential equation. --- Periodic boundary conditions. --- Phase space. --- Phase transition. --- Polynomial. --- Renormalization. --- Self-adjoint. --- Semialgebraic set. --- Special case. --- Statistical significance. --- Subharmonic function. --- Summation. --- Theorem. --- Theory. --- Transfer matrix. --- Transversality (mathematics). --- Trigonometric functions. --- Trigonometric polynomial. --- Uniformization theorem.

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The development of micro- and nanodevices for blood analysis continues to be a growing interdisciplinary subject that demands the careful integration of different research fields. Following the success of the book “Micro/Nano Devices for Blood Analysis”, we invited more authors from the scientific community to participate in and submit their research for a second volume. Researchers from different areas and backgrounds cooperated actively and submitted high-quality research, focusing on the latest advances and challenges in micro- and nanodevices for diagnostics and blood analysis; micro- and nanofluidics; technologies for flow visualization and diagnosis; biochips, organ-on-a-chip and lab-on-a-chip devices; and their applications to research and industry.

Information technology industries --- blood viscosity --- Erythrocyte sedimentation rate (ESR) --- T-shaped microfluidic channel --- air-compressed syringe (ACS) --- micro-particle image velocimetry --- viscoelasticity --- microfluidic device --- coflowing streams --- interface --- linear differential equation --- two approximate factors --- dielectrophoresis --- electrophysiological properties --- crossover frequency --- wake or recirculation formation --- dielectric spectra --- air compliance effect --- RBC aggregation --- blood viscoelasticity --- blood velocity fields --- interface in co-flowing streams --- blood flow --- particle tracking --- red blood cells --- manual methods --- automatic methods --- image analysis --- biomicrofluidics --- microfluidics --- blood plasma filtration --- chip extract --- blood molecules --- patient-derived organoids --- colorectal cancer --- 3D model --- drug screening --- diagnostics --- malaria --- optical filters --- reflectance --- spectrophotometry --- TFCalc --- small caliber blood vessel --- composite molding --- micro-nano structure --- tissue repair --- 3D printing --- blood cells --- fourier transform infrared (FTIR) spectroscopy --- functional group --- lab-on-a-chip --- n/a

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These two new collections, numbers 28 and 29 respectively in the Annals of Mathematics Studies, continue the high standard set by the earlier Annals Studies 20 and 24 by bringing together important contributions to the theories of games and of nonlinear differential equations.

Oscillations. --- Addition. --- Analytic function. --- Approximation. --- Arc length. --- Asymptotic expansion. --- Big O notation. --- Bijection. --- Calculation. --- Canonical form. --- Cartesian coordinate system. --- Characteristic equation. --- Characteristic exponent. --- Circumference. --- Clockwise. --- Coefficient matrix. --- Coefficient. --- Concentric. --- Continuous function. --- Contradiction. --- Coordinate system. --- Determinant. --- Differential equation. --- Divisor. --- Dynamical system. --- Equation. --- Existential quantification. --- Exterior (topology). --- First variation. --- Geometry. --- Homotopy. --- Initial condition. --- Integer. --- Intersection (set theory). --- Interval (mathematics). --- Isolated point. --- Iteration. --- Limit cycle. --- Limit set. --- Linear differential equation. --- Linear equation. --- Main diagonal. --- Mathematician. --- Matrix (mathematics). --- Matrix coefficient. --- Monotonic function. --- Natural number. --- Nonlinear system. --- Parameter. --- Partial derivative. --- Periodic function. --- Phase plane. --- Phase portrait. --- Polar coordinate system. --- Polynomial. --- Projective plane. --- Quadratic transformation. --- Requirement. --- Saddle point. --- Separatrix (mathematics). --- Sequence. --- Special case. --- Square matrix. --- Statistical hypothesis testing. --- Structural stability. --- Subset. --- Suggestion. --- Theorem. --- Theory. --- Three-dimensional space (mathematics). --- Time derivative. --- Topology. --- Trigonometric polynomial. --- Uniqueness theorem. --- Unit vector. --- Variable (mathematics). --- Vector field. --- Velocity. --- Without loss of generality.