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The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-20), Volume I, will be forthcoming.

Oscillations. --- Absolute value. --- Addition. --- Algebraic equation. --- Amplitude modulation. --- Angular frequency. --- Applied mathematics. --- Approximation. --- Boundary value problem. --- Coefficient. --- Complex analysis. --- Continuous function. --- Contradiction. --- Curve. --- Diagram (category theory). --- Differential equation. --- Dimensionless quantity. --- Discriminant. --- Eigenvalues and eigenvectors. --- Empty set. --- Equation. --- Experiment. --- Fourier. --- Frequency modulation. --- Homotopy. --- Implicit function theorem. --- Initial condition. --- Integer. --- Integral equation. --- Limit point. --- Linear map. --- Nonlinear system. --- Normal (geometry). --- Notation. --- Operator theory. --- Ordinary differential equation. --- Oscillation. --- Parameter. --- Periodic function. --- Phase space. --- Pure mathematics. --- Quantity. --- Rational function. --- Saddle point. --- Second derivative. --- Simply connected space. --- Singular perturbation. --- Solid torus. --- Special case. --- Suggestion. --- Summation. --- Tangent space. --- Theorem. --- Theory. --- Three-dimensional space (mathematics). --- Topology. --- Two-dimensional space. --- Uniqueness. --- Vacuum tube. --- Variable (mathematics). --- Vector field.

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The description for this book, K-Theory of Forms. (AM-98), Volume 98, will be forthcoming.

Category theory. Homological algebra --- 515.14 --- Algebraic topology --- 515.14 Algebraic topology --- Forms (Mathematics) --- K-theory --- Modules (Algebra) --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Rings (Algebra) --- Homology theory --- Quantics --- Mathematics --- K-theory. --- Abelian group. --- Addition. --- Algebraic K-theory. --- Algebraic topology. --- Approximation. --- Arithmetic. --- Canonical map. --- Coefficient. --- Cokernel. --- Computation. --- Coprime integers. --- Coset. --- Direct limit. --- Direct product. --- Division ring. --- Elementary matrix. --- Exact sequence. --- Finite group. --- Finite ring. --- Free module. --- Functor. --- General linear group. --- Global field. --- Group homomorphism. --- Group ring. --- Homology (mathematics). --- Integer. --- Invertible matrix. --- Isomorphism class. --- Linear map. --- Local field. --- Matrix group. --- Maxima and minima. --- Mayer–Vietoris sequence. --- Module (mathematics). --- Monoid. --- Morphism. --- Natural transformation. --- Normal subgroup. --- P-group. --- Parameter. --- Power of two. --- Product category. --- Projective module. --- Quadratic form. --- Requirement. --- Ring of integers. --- Semisimple algebra. --- Sesquilinear form. --- Special case. --- Steinberg group (K-theory). --- Steinberg group. --- Subcategory. --- Subgroup. --- Subspace topology. --- Surjective function. --- Theorem. --- Theory. --- Topological group. --- Topological ring. --- Topology. --- Torsion subgroup. --- Triviality (mathematics). --- Unification (computer science). --- Unitary group. --- Witt group. --- K-théorie

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The description for this book, Order-Preserving Maps and Integration Processes. (AM-31), Volume 31, will be forthcoming.

Group theory. --- Integrals. --- Abelian group. --- Addition. --- Axiom. --- Baire function. --- Banach space. --- Big O notation. --- Binary operation. --- Binary relation. --- Borel set. --- Bounded function. --- Cartesian product. --- Characteristic function (probability theory). --- Circumference. --- Closure (mathematics). --- Coefficient. --- Combination. --- Commutative algebra. --- Compact space. --- Complete lattice. --- Continuous function (set theory). --- Continuous function. --- Contradiction. --- Corollary. --- Coset. --- Countable set. --- Directed set. --- Domain of a function. --- Elementary function. --- Empty set. --- Equation. --- Equivalence class. --- Estimation. --- Existential quantification. --- Finite set. --- Fubini's theorem. --- Hilbert space. --- I0. --- Infimum and supremum. --- Integer. --- L-function. --- Lattice (order). --- Lebesgue integration. --- Limit (mathematics). --- Limit superior and limit inferior. --- Linear map. --- Measure (mathematics). --- Monotonic function. --- Natural number. --- Order of operations. --- Parity (mathematics). --- Partially ordered group. --- Partially ordered set. --- Pointwise convergence. --- Pointwise. --- Polynomial. --- Projection (linear algebra). --- Quadratic function. --- Real number. --- Requirement. --- Riemann integral. --- Riemann–Stieltjes integral. --- Scalar multiplication. --- Scientific notation. --- Self-adjoint operator. --- Set (mathematics). --- Set function. --- Sign (mathematics). --- Special case. --- Subset. --- Subtraction. --- Summation. --- Theorem. --- Unification (computer science). --- Upper and lower bounds.

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The description for this book, An Introduction to Linear Transformations in Hilbert Space. (AM-4), Volume 4, will be forthcoming.

Transformations (Mathematics) --- Hyperspace. --- Additive function. --- Adjoint. --- Affine space. --- Axiom. --- Banach space. --- Boundary value problem. --- Cartesian coordinate system. --- Characteristic function (probability theory). --- Combination. --- Commutative property. --- Compact space. --- Contradiction. --- Coordinate system. --- Corollary. --- Countable set. --- Differential operator. --- Dimension (vector space). --- Effective method. --- Equation. --- Existential quantification. --- Fourier transform. --- Function (mathematics). --- Group algebra. --- Hamiltonian mechanics. --- Hamiltonian system. --- Hilbert space. --- Integral transform. --- Jacobi matrix. --- Lebesgue integration. --- Limit point. --- Linear combination. --- Linear map. --- Linear space (geometry). --- Mathematics. --- Measure (mathematics). --- Metric space. --- Moment problem. --- Mutual exclusivity. --- Necessity and sufficiency. --- Normal operator. --- Operational calculus. --- Orthonormality. --- Rational number. --- Self-adjoint operator. --- Self-adjoint. --- Statistic. --- Step function. --- Subset. --- Summation. --- System of linear equations. --- Theorem. --- Topological group. --- Topology. --- Unit sphere. --- Unitary transformation. --- Vector space. --- Weak convergence (Hilbert space). --- Weak convergence.

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This book discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory. It is intended not only for specialists in partial differential equations or probability theory but also for specialists in asymptotic methods and in functional analysis. It is also of interest to physicists who use functional integrals in their research. The work contains results that have not previously appeared in book form, including research contributions of the author.

Partial differential equations --- Differential equations, Partial. --- Probabilities. --- Integration, Functional. --- Functional integration --- Functional analysis --- Integrals, Generalized --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- A priori estimate. --- Absolute continuity. --- Almost surely. --- Analytic continuation. --- Axiom. --- Big O notation. --- Boundary (topology). --- Boundary value problem. --- Bounded function. --- Calculation. --- Cauchy problem. --- Central limit theorem. --- Characteristic function (probability theory). --- Chebyshev's inequality. --- Coefficient. --- Comparison theorem. --- Continuous function (set theory). --- Continuous function. --- Convergence of random variables. --- Cylinder set. --- Degeneracy (mathematics). --- Derivative. --- Differential equation. --- Differential operator. --- Diffusion equation. --- Diffusion process. --- Dimension (vector space). --- Direct method in the calculus of variations. --- Dirichlet boundary condition. --- Dirichlet problem. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Elliptic operator. --- Elliptic partial differential equation. --- Equation. --- Existence theorem. --- Exponential function. --- Feynman–Kac formula. --- Fokker–Planck equation. --- Function space. --- Functional analysis. --- Fundamental solution. --- Gaussian measure. --- Girsanov theorem. --- Hessian matrix. --- Hölder condition. --- Independence (probability theory). --- Integral curve. --- Integral equation. --- Invariant measure. --- Iterated logarithm. --- Itô's lemma. --- Joint probability distribution. --- Laplace operator. --- Laplace's equation. --- Lebesgue measure. --- Limit (mathematics). --- Limit cycle. --- Limit point. --- Linear differential equation. --- Linear map. --- Lipschitz continuity. --- Markov chain. --- Markov process. --- Markov property. --- Maximum principle. --- Mean value theorem. --- Measure (mathematics). --- Modulus of continuity. --- Moment (mathematics). --- Monotonic function. --- Navier–Stokes equations. --- Nonlinear system. --- Ordinary differential equation. --- Parameter. --- Partial differential equation. --- Periodic function. --- Poisson kernel. --- Probabilistic method. --- Probability space. --- Probability theory. --- Probability. --- Random function. --- Regularization (mathematics). --- Schrödinger equation. --- Self-adjoint operator. --- Sign (mathematics). --- Simultaneous equations. --- Smoothness. --- State-space representation. --- Stochastic calculus. --- Stochastic differential equation. --- Stochastic. --- Support (mathematics). --- Theorem. --- Theory. --- Uniqueness theorem. --- Variable (mathematics). --- Weak convergence (Hilbert space). --- Wiener process.