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This is the first modern calculus book to be organized axiomatically and to survey the subject's applicability to science and engineering. A challenging exposition of calculus in the European style, it is an excellent text for a first-year university honors course or for a third-year analysis course. The calculus is built carefully from the axioms with all the standard results deduced from these axioms. The concise construction, by design, provides maximal flexibility for the instructor and allows the student to see the overall flow of the development. At the same time, the book reveals the origins of the calculus in celestial mechanics and number theory. The book introduces many topics often left to the appendixes in standard calculus textbooks and develops their connections with physics, engineering, and statistics. The author uses applications of derivatives and integrals to show how calculus is applied in these disciplines. Solutions to all exercises (even those involving proofs) are available to instructors upon request, making this book unique among texts in the field. Focuses on single variable calculus Provides a balance of precision and intuition Offers both routine and demanding exercises

Calculus --- Accumulation point. --- Analytic function. --- Bisection, the method. --- Central limit theorem, Conditional convergence. --- Countably infinite. --- Darboux sums. --- Escape velocity. --- Extrema. --- Fluid resistance. --- Graph of a function. --- Heine-Borel lemma. --- Inertial force. --- Infinite series. --- Integrable. --- Lindelof principle. --- Linear approximation. --- Logarithm. --- Mean value theorem. --- Midpoint rule. --- Objective function. --- Observed fact. --- Osculating circle. --- Partial derivative. --- Partial fractions. --- Poisson flow. --- Ratio test. --- Reactor scram. --- Scientific method. --- Secant lines. --- Tangent lines. --- Uniformly continuous.

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This book studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q. In general, these varieties are not compact. The intersection cohomology of the Shimura variety associated to a reductive group G carries commuting actions of the absolute Galois group of the reflex field and of the group G(Af) of finite adelic points of G. The second action can be studied on the set of complex points of the Shimura variety. In this book, Sophie Morel identifies the Galois action--at good places--on the G(Af)-isotypical components of the cohomology. Morel uses the method developed by Langlands, Ihara, and Kottwitz, which is to compare the Grothendieck-Lefschetz fixed point formula and the Arthur-Selberg trace formula. The first problem, that of applying the fixed point formula to the intersection cohomology, is geometric in nature and is the object of the first chapter, which builds on Morel's previous work. She then turns to the group-theoretical problem of comparing these results with the trace formula, when G is a unitary group over Q. Applications are then given. In particular, the Galois representation on a G(Af)-isotypical component of the cohomology is identified at almost all places, modulo a non-explicit multiplicity. Morel also gives some results on base change from unitary groups to general linear groups.

Shimura varieties. --- Homology theory. --- Cohomology theory --- Contrahomology theory --- Algebraic topology --- Varieties, Shimura --- Arithmetical algebraic geometry --- Accuracy and precision. --- Adjoint. --- Algebraic closure. --- Archimedean property. --- Automorphism. --- Base change map. --- Base change. --- Calculation. --- Clay Mathematics Institute. --- Coefficient. --- Compact element. --- Compact space. --- Comparison theorem. --- Conjecture. --- Connected space. --- Connectedness. --- Constant term. --- Corollary. --- Duality (mathematics). --- Existential quantification. --- Exterior algebra. --- Finite field. --- Finite set. --- Fundamental lemma (Langlands program). --- Galois group. --- General linear group. --- Haar measure. --- Hecke algebra. --- Homomorphism. --- L-function. --- Logarithm. --- Mathematical induction. --- Mathematician. --- Maximal compact subgroup. --- Maximal ideal. --- Morphism. --- Neighbourhood (mathematics). --- Open set. --- Parabolic induction. --- Permutation. --- Prime number. --- Ramanujan–Petersson conjecture. --- Reductive group. --- Ring (mathematics). --- Scientific notation. --- Shimura variety. --- Simply connected space. --- Special case. --- Sub"ient. --- Subalgebra. --- Subgroup. --- Symplectic group. --- Theorem. --- Trace formula. --- Unitary group. --- Weyl group.

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Despite our deep interest in mortality, little is known about why some individuals live to middle age and others to extreme old age. Life span, mortality, and aging present some of the most profound mysteries in biology. In Longevity, James Carey draws on unprecedented data to develop a biological and demographic framework for identifying the key factors that govern aging, life span, and mortality in humans and other animals. Carey presents the results of a monumental, twelve-year, National Institute on Aging-funded research project on the determinants of longevity using data from the life tables of five million Mediterranean fruit flies, the most comprehensive set of life table studies ever on the mortality dynamics of a single species. He interprets the fruit fly data within the context of human aging and the aging process in general to identify the determinants of mortality. Three key themes emerge: the absence of species-specific life span limits, the context-specific nature of the mortality rate, and biodemographic linkages between longevity and reproduction. A powerful foundation for the emerging field of biodemography and a rich framework for considering the future of human life span, Longevity will be an indispensable resource for readers from a range of fields including population biology, demography, gerontology, ecology, evolutionary biology, and medical research.

Longevity. --- Ageing. --- Amphibian. --- Bacteria. --- Baseline Study. --- Behavior. --- Biodemography. --- Biological system. --- Biologist. --- Biology. --- Biomedicine. --- Brain size. --- Centenarian. --- Ceratitis capitata. --- Ceteris paribus. --- Coevolution. --- Confidence interval. --- Correlation coefficient. --- Degenerative disease. --- Demographic dividend. --- Demography. --- Disease. --- Drosophila melanogaster. --- Drosophila. --- Ecology. --- Egg as food. --- Emergence. --- Environmental factor. --- Estimation. --- Eusociality. --- Evolution. --- Evolutionary biology. --- Extrapolation. --- Fecundity. --- Female. --- Fertility. --- Germ cell. --- Gerontology. --- Grandparent. --- Heritability. --- Hibernation. --- Hominidae. --- Homo erectus. --- Homo habilis. --- Homo sapiens. --- Housefly. --- Hydrolysate. --- Insect. --- Invertebrate. --- James Vaupel. --- Jeanne Calment. --- Kin selection. --- Larva. --- Late-life mortality deceleration. --- Leveling (philosophy). --- Life expectancy. --- Life history theory. --- Life table. --- Logarithm. --- Macronucleus. --- Mammal. --- Mating. --- Maximum life span. --- Menopause. --- Middle age. --- Model organism. --- Mortality rate. --- Multicellular organism. --- Natural selection. --- Nematode. --- Nutrient. --- Nutrition. --- Offspring. --- Old age. --- Opportunity cost. --- Organism. --- Oviparity. --- Parental investment. --- Probability. --- Protein. --- Quality of life. --- Rejuvenation (aging). --- Reproduction. --- Reproductive success. --- Rodent. --- Sampling error. --- Senescence. --- Sex differences in humans. --- Sex ratio. --- Sexual dimorphism. --- Sexual maturity. --- Sexual reproduction. --- Shoaling and schooling. --- Sociality. --- Species. --- Standard deviation. --- Survival rate. --- Trade-off. --- Vertebrate. --- Year.

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The ∂̄ Neumann problem is probably the most important and natural example of a non-elliptic boundary value problem, arising as it does from the Cauchy-Riemann equations. It has been known for some time how to prove solvability and regularity by the use of L2 methods. In this monograph the authors apply recent methods involving the Heisenberg group to obtain parametricies and to give sharp estimates in various function spaces, leading to a better understanding of the ∂̄ Neumann problem. The authors have added substantial background material to make the monograph more accessible to students.Originally published in 1977.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.

Partial differential equations --- Neumann problem. --- Neumann problem --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Boundary value problems --- Differential equations, Partial --- A priori estimate. --- Abuse of notation. --- Analytic continuation. --- Analytic function. --- Approximation. --- Asymptotic expansion. --- Asymptotic formula. --- Basis (linear algebra). --- Besov space. --- Boundary (topology). --- Boundary value problem. --- Boundedness. --- Calculation. --- Cauchy's integral formula. --- Cauchy–Riemann equations. --- Change of variables. --- Characterization (mathematics). --- Combination. --- Commutative property. --- Commutator. --- Complex analysis. --- Complex manifold. --- Complex number. --- Computation. --- Convolution. --- Coordinate system. --- Corollary. --- Counterexample. --- Derivative. --- Determinant. --- Differential equation. --- Dimension (vector space). --- Dimension. --- Dimensional analysis. --- Dirichlet boundary condition. --- Eigenvalues and eigenvectors. --- Elliptic boundary value problem. --- Equation. --- Error term. --- Estimation. --- Even and odd functions. --- Existential quantification. --- Function space. --- Fundamental solution. --- Green's theorem. --- Half-space (geometry). --- Hardy's inequality. --- Heisenberg group. --- Holomorphic function. --- Infimum and supremum. --- Integer. --- Integral curve. --- Integral expression. --- Inverse function. --- Invertible matrix. --- Iteration. --- Laplace's equation. --- Left inverse. --- Lie algebra. --- Lie group. --- Linear combination. --- Logarithm. --- Lp space. --- Mathematical induction. --- Neumann boundary condition. --- Notation. --- Open problem. --- Orthogonal complement. --- Orthogonality. --- Parametrix. --- Partial derivative. --- Pointwise. --- Polynomial. --- Principal branch. --- Principal part. --- Projection (linear algebra). --- Pseudo-differential operator. --- Quantity. --- Recursive definition. --- Schwartz space. --- Scientific notation. --- Second derivative. --- Self-adjoint. --- Singular value. --- Sobolev space. --- Special case. --- Standard basis. --- Stein manifold. --- Subgroup. --- Subset. --- Summation. --- Support (mathematics). --- Tangent bundle. --- Theorem. --- Theory. --- Upper half-plane. --- Variable (mathematics). --- Vector field. --- Volume element. --- Weak solution. --- Neumann, Problème de --- Equations aux derivees partielles --- Problemes aux limites

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Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place. For example, a closed p-adic analytic one-form defined on a simply-connected domain does not necessarily have a primitive in the class of analytic functions. In the early 1980s, Robert Coleman discovered a way to construct primitives of analytic one-forms on certain smooth p-adic analytic curves in a bigger class of functions. Since then, there have been several attempts to generalize his ideas to smooth p-adic analytic spaces of higher dimension, but the spaces considered were invariably associated with algebraic varieties. This book aims to show that every smooth p-adic analytic space is provided with a sheaf of functions that includes all analytic ones and satisfies a uniqueness property. It also contains local primitives of all closed one-forms with coefficients in the sheaf that, in the case considered by Coleman, coincide with those he constructed. In consequence, one constructs a parallel transport of local solutions of a unipotent differential equation and an integral of a closed one-form along a path so that both depend nontrivially on the homotopy class of the path. Both the author's previous results on geometric properties of smooth p-adic analytic spaces and the theory of isocrystals are further developed in this book, which is aimed at graduate students and mathematicians working in the areas of non-Archimedean analytic geometry, number theory, and algebraic geometry.

p-adic analysis. --- Analysis, p-adic --- Algebra --- Calculus --- Geometry, Algebraic --- Abelian category. --- Acting in. --- Addition. --- Aisle. --- Algebraic closure. --- Algebraic curve. --- Algebraic structure. --- Algebraic variety. --- Allegory (category theory). --- Analytic function. --- Analytic geometry. --- Analytic space. --- Archimedean property. --- Arithmetic. --- Banach algebra. --- Bertolt Brecht. --- Buttress. --- Centrality. --- Clerestory. --- Commutative diagram. --- Commutative property. --- Complex analysis. --- Contradiction. --- Corollary. --- Cosmetics. --- De Rham cohomology. --- Determinant. --- Diameter. --- Differential form. --- Dimension (vector space). --- Divisor. --- Elaboration. --- Embellishment. --- Equanimity. --- Equivalence class (music). --- Existential quantification. --- Facet (geometry). --- Femininity. --- Finite morphism. --- Formal scheme. --- Fred Astaire. --- Functor. --- Gavel. --- Generic point. --- Geometry. --- Gothic architecture. --- Homomorphism. --- Hypothesis. --- Imagery. --- Injective function. --- Irreducible component. --- Iterated integral. --- Linear combination. --- Logarithm. --- Marni Nixon. --- Masculinity. --- Mathematical induction. --- Mathematics. --- Mestizo. --- Metaphor. --- Morphism. --- Natural number. --- Neighbourhood (mathematics). --- Neuroticism. --- Noetherian. --- Notation. --- One-form. --- Open set. --- P-adic Hodge theory. --- P-adic number. --- Parallel transport. --- Patrick Swayze. --- Phrenology. --- Politics. --- Polynomial. --- Prediction. --- Proportion (architecture). --- Pullback. --- Purely inseparable extension. --- Reims. --- Requirement. --- Residue field. --- Rhomboid. --- Roland Barthes. --- Satire. --- Self-sufficiency. --- Separable extension. --- Sheaf (mathematics). --- Shuffle algebra. --- Subgroup. --- Suggestion. --- Technology. --- Tensor product. --- Theorem. --- Transept. --- Triforium. --- Tubular neighborhood. --- Underpinning. --- Writing. --- Zariski topology.