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This book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis. For one variable, the topic is classical and rather well understood. In several variables, the necessary understanding of holomorphic functions via partial differential equations has a recent origin, and Professor Stein's book, which emphasizes the potential-theoretic aspects of the boundary value problem, should become the standard work in the field.Originally published in 1972.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Mathematical potential theory --- Holomorphic functions --- Harmonic functions --- Holomorphic functions. --- Harmonic functions. --- Fonctions de plusieurs variables complexes. --- Functions of several complex variables --- Functions, Harmonic --- Laplace's equations --- Bessel functions --- Differential equations, Partial --- Fourier series --- Harmonic analysis --- Lamé's functions --- Spherical harmonics --- Toroidal harmonics --- Functions, Holomorphic --- Absolute continuity. --- Absolute value. --- Addition. --- Ambient space. --- Analytic function. --- Arbitrarily large. --- Bergman metric. --- Borel measure. --- Boundary (topology). --- Boundary value problem. --- Bounded set (topological vector space). --- Boundedness. --- Brownian motion. --- Calculation. --- Change of variables. --- Characteristic function (probability theory). --- Combination. --- Compact space. --- Complex analysis. --- Complex conjugate. --- Computation. --- Conformal map. --- Constant term. --- Continuous function. --- Coordinate system. --- Corollary. --- Cramer's rule. --- Determinant. --- Diameter. --- Dimension. --- Elliptic operator. --- Estimation. --- Existential quantification. --- Explicit formulae (L-function). --- Exterior (topology). --- Fatou's theorem. --- Function space. --- Green's function. --- Green's theorem. --- Haar measure. --- Half-space (geometry). --- Harmonic function. --- Hilbert space. --- Holomorphic function. --- Hyperbolic space. --- Hypersurface. --- Hölder's inequality. --- Invariant measure. --- Invertible matrix. --- Jacobian matrix and determinant. --- Line segment. --- Linear map. --- Lipschitz continuity. --- Local coordinates. --- Logarithm. --- Majorization. --- Matrix (mathematics). --- Maximal function. --- Measure (mathematics). --- Minimum distance. --- Natural number. --- Normal (geometry). --- Open set. --- Order of magnitude. --- Orthogonal complement. --- Orthonormal basis. --- Parameter. --- Poisson kernel. --- Positive-definite matrix. --- Potential theory. --- Projection (linear algebra). --- Quadratic form. --- Quantity. --- Real structure. --- Requirement. --- Scientific notation. --- Sesquilinear form. --- Several complex variables. --- Sign (mathematics). --- Smoothness. --- Subgroup. --- Subharmonic function. --- Subsequence. --- Subset. --- Summation. --- Tangent space. --- Theorem. --- Theory. --- Total variation. --- Transitive relation. --- Transitivity. --- Transpose. --- Two-form. --- Unit sphere. --- Unitary matrix. --- Vector field. --- Vector space. --- Volume element. --- Weak topology.

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Mesoscopic physics deals with systems larger than single atoms but small enough to retain their quantum properties. The possibility to create and manipulate conductors of the nanometer scale has given birth to a set of phenomena that have revolutionized physics: quantum Hall effects, persistent currents, weak localization, Coulomb blockade, etc. This Special Issue tackles the latest developments in the field. Contributors discuss time-dependent transport, quantum pumping, nanoscale heat engines and motors, molecular junctions, electron–electron correlations in confined systems, quantum thermo-electrics and current fluctuations. The works included herein represent an up-to-date account of exciting research with a broad impact in both fundamental and applied topics.

Technology: general issues --- quantum transport --- quantum interference --- shot noise --- persistent current --- mesoscale and nanoscale physics --- Complementary Metal Oxide Semiconductor (CMOS) technology --- electron quantum optics --- photo-assisted noise --- charge and heat fluctuations --- time-dependent transport --- electron–photon coupling --- open quantum systems --- phonon transport --- nanostructured materials --- green’s functions --- density-functional tight binding --- Landauer approach, time-dependent transport --- graphene nanoribbons --- nonequilibrium Green’s function --- electronic transport --- thermal transport --- strongly correlated systems --- Landauer-Büttiker formalism --- Boltzmann transport equation --- time-dependent density functional theory --- electron–phonon coupling --- molecular junctions --- thermoelectric properties --- electron–vibration interactions --- electron–electron interactions --- thermoelectricity --- heat engines --- mesoscopic physics --- fluctuations --- thermodynamic uncertainty relations --- quantum thermodynamics --- steady-state dynamics --- nonlinear transport --- adiabatic quantum motors --- adiabatic quantum pumps --- quantum heat engines --- quantum refrigerators --- transport through quantum dots --- spin pump --- spin-orbit interaction --- quantum adiabatic pump --- interferometer --- geometric phase --- nonadiabaticity --- quantum heat pumping --- spin pumping --- relaxation --- time evolution --- quantum information --- entropy production --- Renyi entropy --- superconducting proximity effect --- Kondo effect --- spin polarization --- Anreev reflection --- conditional states --- conditional wavefunction --- Markovian and Non-Markovian dynamics --- stochastic Schrödinger equation --- quantum electron transport --- quantum dots --- fluctuation–dissipation theorem --- Onsager relations --- dynamics of strongly correlated quantum systems --- quantum capacitor --- local fermi liquids --- kondo effect --- coulomb blockade --- mesoscopic systems --- nanophysics --- quantum noise --- quantum pumping --- thermoelectrics --- heat transport

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In this book, we aim to address the ever-advancing progress in microelectronic device scaling. Complementary Metal-Oxide-Semiconductor (CMOS) devices continue to endure miniaturization, irrespective of the seeming physical limitations, helped by advancing fabrication techniques. We observe that miniaturization does not always refer to the latest technology node for digital transistors. Rather, by applying novel materials and device geometries, a significant reduction in the size of microelectronic devices for a broad set of applications can be achieved. The achievements made in the scaling of devices for applications beyond digital logic (e.g., high power, optoelectronics, and sensors) are taking the forefront in microelectronic miniaturization. Furthermore, all these achievements are assisted by improvements in the simulation and modeling of the involved materials and device structures. In particular, process and device technology computer-aided design (TCAD) has become indispensable in the design cycle of novel devices and technologies. It is our sincere hope that the results provided in this Special Issue prove useful to scientists and engineers who find themselves at the forefront of this rapidly evolving and broadening field. Now, more than ever, it is essential to look for solutions to find the next disrupting technologies which will allow for transistor miniaturization well beyond silicon’s physical limits and the current state-of-the-art. This requires a broad attack, including studies of novel and innovative designs as well as emerging materials which are becoming more application-specific than ever before.

Research & information: general --- Mathematics & science --- FinFETs --- CMOS --- device processing --- integrated circuits --- silicon carbide (SiC) metal-oxide-semiconductor field-effect transistors (MOSFETs) --- solid state circuit breaker (SSCB) --- prototype --- circuit design --- GaN --- HEMT --- high gate --- multi-recessed buffer --- power density --- power-added efficiency --- 4H-SiC --- MESFET --- IMRD structure --- power added efficiency --- 1200 V SiC MOSFET --- body diode --- surge reliability --- silvaco simulation --- floating gate transistor --- control gate --- CMOS device --- active noise control --- vacuum channel --- mean free path --- vertical air-channel diode --- vertical transistor --- field emission --- particle trajectory model --- F-N plot --- space-charge-limited currents --- 4H-SiC MESFET --- simulation --- power added efficiency (PAE) --- new device --- three-input transistor --- T-channel --- compact circuit style --- CMOS compatible technology --- avalanche photodiode --- SPICE model --- bandwidth --- high responsivity --- silicon photodiode --- AlGaN/GaN HEMTs --- thermal simulation --- transient channel temperature --- pulse width --- gate structures --- band-to-band tunnelling (BTBT) --- tunnelling field-effect transistor (TFET) --- germanium-around-source gate-all-around TFET (GAS GAA TFET) --- average subthreshold swing --- direct source-to-drain tunneling --- transport effective mass --- confinement effective mass --- multi-subband ensemble Monte Carlo --- non-equilibrium Green's function --- DGSOI --- FinFET --- core-insulator --- gate-all-around --- field effect transistor --- GAA --- nanowire --- one-transistor dynamic random-access memory (1T-DRAM) --- polysilicon --- grain boundary --- electron trapping --- flexible transistors --- polymers --- metal oxides --- nanocomposites --- dielectrics --- active layers --- nanotransistor --- quantum transport --- Landauer-Büttiker formalism --- R-matrix method --- nanoscale --- mosfet --- quantum current --- surface transfer doping --- 2D hole gas (2DHG) --- diamond --- MoO3 --- V2O5 --- MOSFET --- reliability --- random telegraph noise --- oxide defects --- SiO2 --- split-gate trench power MOSFET --- multiple epitaxial layers --- specific on-resistance --- device reliability --- nanoscale transistor --- bias temperature instabilities (BTI) --- defects --- single-defect spectroscopy --- non-radiative multiphonon (NMP) model --- time-dependent defect spectroscopy --- FinFETs --- CMOS --- device processing --- integrated circuits --- silicon carbide (SiC) metal-oxide-semiconductor field-effect transistors (MOSFETs) --- solid state circuit breaker (SSCB) --- prototype --- circuit design --- GaN --- HEMT --- high gate --- multi-recessed buffer --- power density --- power-added efficiency --- 4H-SiC --- MESFET --- IMRD structure --- power added efficiency --- 1200 V SiC MOSFET --- body diode --- surge reliability --- silvaco simulation --- floating gate transistor --- control gate --- CMOS device --- active noise control --- vacuum channel --- mean free path --- vertical air-channel diode --- vertical transistor --- field emission --- particle trajectory model --- F-N plot --- space-charge-limited currents --- 4H-SiC MESFET --- simulation --- power added efficiency (PAE) --- new device --- three-input transistor --- T-channel --- compact circuit style --- CMOS compatible technology --- avalanche photodiode --- SPICE model --- bandwidth --- high responsivity --- silicon photodiode --- AlGaN/GaN HEMTs --- thermal simulation --- transient channel temperature --- pulse width --- gate structures --- band-to-band tunnelling (BTBT) --- tunnelling field-effect transistor (TFET) --- germanium-around-source gate-all-around TFET (GAS GAA TFET) --- average subthreshold swing --- direct source-to-drain tunneling --- transport effective mass --- confinement effective mass --- multi-subband ensemble Monte Carlo --- non-equilibrium Green's function --- DGSOI --- FinFET --- core-insulator --- gate-all-around --- field effect transistor --- GAA --- nanowire --- one-transistor dynamic random-access memory (1T-DRAM) --- polysilicon --- grain boundary --- electron trapping --- flexible transistors --- polymers --- metal oxides --- nanocomposites --- dielectrics --- active layers --- nanotransistor --- quantum transport --- Landauer-Büttiker formalism --- R-matrix method --- nanoscale --- mosfet --- quantum current --- surface transfer doping --- 2D hole gas (2DHG) --- diamond --- MoO3 --- V2O5 --- MOSFET --- reliability --- random telegraph noise --- oxide defects --- SiO2 --- split-gate trench power MOSFET --- multiple epitaxial layers --- specific on-resistance --- device reliability --- nanoscale transistor --- bias temperature instabilities (BTI) --- defects --- single-defect spectroscopy --- non-radiative multiphonon (NMP) model --- time-dependent defect spectroscopy

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The present volume reflects both the diversity of Bochner's pursuits in pure mathematics and the influence his example and thought have had upon contemporary researchers.Originally published in 1971.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Mathematical analysis --- -Advanced calculus --- Analysis (Mathematics) --- Algebra --- Addresses, essays, lectures --- Mathematical analysis. --- -517.1 Mathematical analysis --- -Addresses, essays, lectures --- 517.1 Mathematical analysis --- 517.1. --- Approximation theory. --- System analysis. --- 517.1 --- Network analysis --- Network science --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Absolute continuity. --- Analytic continuation. --- Analytic function. --- Asymptotic expansion. --- Automorphism. --- Banach algebra. --- Banach space. --- Bessel function. --- Big O notation. --- Bounded operator. --- Branch point. --- Cauchy's integral formula. --- Cauchy's integral theorem. --- Characterization (mathematics). --- Cohomology. --- Commutative property. --- Compact operator. --- Compact space. --- Complex analysis. --- Complex number. --- Complex plane. --- Continuous function (set theory). --- Continuous function. --- Convolution. --- Coset. --- Covariance operator. --- Differentiable function. --- Differentiable manifold. --- Differential form. --- Dimension (vector space). --- Discrete group. --- Dominated convergence theorem. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Equation. --- Equivalence class. --- Even and odd functions. --- Existential quantification. --- First variation. --- Formal power series. --- Fréchet derivative. --- Fubini's theorem. --- Function space. --- Functional analysis. --- Fundamental group. --- Green's function. --- Haar measure. --- Hermite polynomials. --- Hermitian symmetric space. --- Holomorphic function. --- Hyperbolic partial differential equation. --- Infimum and supremum. --- Infinite product. --- Integral equation. --- Lebesgue measure. --- Lie algebra. --- Lie group. --- Linear map. --- Markov chain. --- Meromorphic function. --- Metric space. --- Monotonic function. --- Natural number. --- Norm (mathematics). --- Normal subgroup. --- Null set. --- Partition of unity. --- Pointwise. --- Polynomial. --- Power series. --- Pseudogroup. --- Riemann surface. --- Riemannian manifold. --- Schrödinger equation. --- Self-adjoint operator. --- Self-adjoint. --- Semigroup. --- Semisimple algebra. --- Sesquilinear form. --- Sign (mathematics). --- Singular perturbation. --- Special case. --- Spectral theory. --- Stokes' theorem. --- Subgroup. --- Submanifold. --- Subset. --- Support (mathematics). --- Symplectic geometry. --- Symplectic manifold. --- Theorem. --- Uniform convergence. --- Unitary operator. --- Unitary representation. --- Upper and lower bounds. --- Vector bundle. --- Vector field. --- Volterra's function. --- Weierstrass theorem. --- Zorn's lemma.

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In the last three decades, fractional calculus has broken into the field of mathematical analysis, both at the theoretical level and at the level of its applications. In essence, the fractional calculus theory is a mathematical analysis tool applied to the study of integrals and derivatives of arbitrary order, which unifies and generalizes the classical notions of differentiation and integration. These fractional and derivative integrals, which until not many years ago had been used in purely mathematical contexts, have been revealed as instruments with great potential to model problems in various scientific fields, such as: fluid mechanics, viscoelasticity, physics, biology, chemistry, dynamical systems, signal processing or entropy theory. Since the differential and integral operators of fractional order are nonlinear operators, fractional calculus theory provides a tool for modeling physical processes, which in many cases is more useful than classical formulations. This is why the application of fractional calculus theory has become a focus of international academic research. This Special Issue "Applied Mathematics and Fractional Calculus" has published excellent research studies in the field of applied mathematics and fractional calculus, authored by many well-known mathematicians and scientists from diverse countries worldwide such as China, USA, Canada, Germany, Mexico, Spain, Poland, Portugal, Iran, Tunisia, South Africa, Albania, Thailand, Iraq, Egypt, Italy, India, Russia, Pakistan, Taiwan, Korea, Turkey, and Saudi Arabia.

Research & information: general --- Mathematics & science --- condensing function --- approximate endpoint criterion --- quantum integro-difference BVP --- existence --- fractional Kadomtsev-Petviashvili system --- lie group analysis --- power series solutions --- convergence analysis --- conservation laws --- symmetry --- weighted fractional operators --- convex functions --- HHF type inequality --- fractional calculus --- Euler–Lagrange equation --- natural boundary conditions --- time delay --- MHD equations --- weak solution --- regularity criteria --- anisotropic Lorentz space --- Sonine kernel --- general fractional derivative of arbitrary order --- general fractional integral of arbitrary order --- first fundamental theorem of fractional calculus --- second fundamental theorem of fractional calculus --- ρ-Laplace variational iteration method --- ρ-Laplace decomposition method --- partial differential equation --- caputo operator --- fractional Fornberg–Whitham equation (FWE) --- Riemann–Liouville fractional difference operator --- boundary value problem --- discrete fractional calculus --- existence and uniqueness --- Ulam stability --- elastic beam problem --- tempered fractional derivative --- one-sided tempered fractional derivative --- bilateral tempered fractional derivative --- tempered riesz potential --- collocation method --- hermite cubic spline --- fractional burgers equation --- fractional differential equation --- fractional Dzhrbashyan–Nersesyan derivative --- degenerate evolution equation --- initial value problem --- initial boundary value problem --- partial Riemann–Liouville fractional integral --- Babenko’s approach --- Banach fixed point theorem --- Mittag–Leffler function --- gamma function --- nabla fractional difference --- separated boundary conditions --- Green’s function --- existence of solutions --- Caputo q-derivative --- singular sum fractional q-differential --- fixed point --- equations --- Riemann–Liouville q-integral --- Shehu transform --- Caputo fractional derivative --- Shehu decomposition method --- new iterative transform method --- fractional KdV equation --- approximate solutions --- Riemann–Liouville derivative --- concave operator --- fixed point theorem --- Gelfand problem --- order cone --- integral transform --- Atangana–Baleanu fractional derivative --- Aboodh transform iterative method --- φ-Hilfer fractional system with impulses --- semigroup theory --- nonlocal conditions --- optimal controls --- fractional derivatives --- fractional Prabhakar derivatives --- fractional differential equations --- fractional Sturm–Liouville problems --- eigenfunctions and eigenvalues --- Fredholm–Volterra integral Equations --- fractional derivative --- Bessel polynomials --- Caputo derivative --- collocation points --- Caputo–Fabrizio and Atangana-Baleanu operators --- time-fractional Kaup–Kupershmidt equation --- natural transform --- Adomian decomposition method