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One might say that ordinary differential equations (notably, in Isaac Newton’s analysis of the motion of celestial bodies) had a central role in the development of modern applied mathematics. This book is devoted to research articles which build upon this spirit: combining analysis with the applications of ordinary differential equations (ODEs). ODEs arise across a spectrum of applications in physics, engineering, geophysics, biology, chemistry, economics, etc., because the rules governing the time-variation of relevant fields is often naturally expressed in terms of relationships between rates of change. ODEs also emerge in stochastic models—for example, when considering the evolution of a probability density function—and in large networks of interconnected agents. The increasing ease of numerically simulating large systems of ODEs has resulted in a plethora of publications in this area; nevertheless, the difficulty of parametrizing models means that the computational results by themselves are sometimes questionable. Therefore, analysis cannot be ignored. This book comprises articles that possess both interesting applications and the mathematical analysis driven by such applications.

heteroclinic tangle --- n/a --- coupled system --- integral boundary conditions --- EADs --- transport --- bifurcation analysis --- SIR epidemic model --- ion current interactions --- green’s function --- surface of section --- endemic equilibrium --- age structure --- MATCONT --- Ulam’s stability --- nonlinear dynamics --- stability --- basic reproduction number --- green's function --- Ulam's stability

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What is the future of CMOS? Sustaining increased transistor densities along the path of Moore's Law has become increasingly challenging with limited power budgets, interconnect bandwidths, and fabrication capabilities. In the last decade alone, transistors have undergone significant design makeovers; from planar transistors of ten years ago, technological advancements have accelerated to today's FinFETs, which hardly resemble their bulky ancestors. FinFETs could potentially take us to the 5-nm node, but what comes after it? From gate-all-around devices to single electron transistors and two-dimensional semiconductors, a torrent of research is being carried out in order to design the next transistor generation, engineer the optimal materials, improve the fabrication technology, and properly model future devices. We invite insight from investigators and scientists in the field to showcase their work in this Special Issue with research papers, short communications, and review articles that focus on trends in micro- and nanotechnology from fundamental research to applications.

MOSFET --- n/a --- total ionizing dose (TID) --- low power consumption --- process simulation --- two-dimensional material --- negative-capacitance --- power consumption --- technology computer aided design (TCAD) --- thin-film transistors (TFTs) --- band-to-band tunneling (BTBT) --- nanowires --- inversion channel --- metal oxide semiconductor field effect transistor (MOSFET) --- spike-timing-dependent plasticity (STDP) --- field effect transistor --- segregation --- systematic variations --- Sentaurus TCAD --- indium selenide --- nanosheets --- technology computer-aided design (TCAD) --- high-? dielectric --- subthreshold bias range --- statistical variations --- fin field effect transistor (FinFET) --- compact models --- non-equilibrium Green’s function --- etching simulation --- highly miniaturized transistor structure --- compact model --- silicon nanowire --- surface potential --- Silicon-Germanium source/drain (SiGe S/D) --- nanowire --- plasma-aided molecular beam epitaxy (MBE) --- phonon scattering --- mobility --- silicon-on-insulator --- drain engineered --- device simulation --- variability --- semi-floating gate --- synaptic transistor --- neuromorphic system --- theoretical model --- CMOS --- ferroelectrics --- tunnel field-effect transistor (TFET) --- SiGe --- metal gate granularity --- buried channel --- ON-state --- bulk NMOS devices --- ambipolar --- piezoelectrics --- tunnel field effect transistor (TFET) --- FinFETs --- polarization --- field-effect transistor --- line edge roughness --- random discrete dopants --- radiation hardened by design (RHBD) --- low energy --- flux calculation --- doping incorporation --- low voltage --- topography simulation --- MOS devices --- low-frequency noise --- high-k --- layout --- level set --- process variations --- subthreshold --- metal gate stack --- electrostatic discharge (ESD) --- non-equilibrium Green's function

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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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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.