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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.

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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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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.

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The description for this book, Linear Inequalities and Related Systems. (AM-38), Volume 38, will be forthcoming.

Operational research. Game theory --- Linear programming. --- Matrices. --- Game theory. --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Production scheduling --- Programming (Mathematics) --- Banach space. --- Basic solution (linear programming). --- Big O notation. --- Bilinear form. --- Boundary (topology). --- Brouwer fixed-point theorem. --- Characterization (mathematics). --- Coefficient. --- Combination. --- Computation. --- Computational problem. --- Convex combination. --- Convex cone. --- Convex hull. --- Convex set. --- Corollary. --- Correlation and dependence. --- Cramer's rule. --- Cyclic permutation. --- Dedekind cut. --- Degeneracy (mathematics). --- Determinant. --- Diagram (category theory). --- Dilworth's theorem. --- Dimension (vector space). --- Directional derivative. --- Disjoint sets. --- Doubly stochastic matrix. --- Dual space. --- Duality (mathematics). --- Duality (optimization). --- Eigenvalues and eigenvectors. --- Elementary proof. --- Equation solving. --- Equation. --- Equivalence class. --- Euclidean space. --- Existence theorem. --- Existential quantification. --- Extreme point. --- Fixed-point theorem. --- Functional analysis. --- Fundamental theorem. --- General equilibrium theory. --- Hall's theorem. --- Hilbert space. --- Incidence matrix. --- Inequality (mathematics). --- Infimum and supremum. --- Invertible matrix. --- Kakutani fixed-point theorem. --- Lagrange multiplier. --- Linear equation. --- Linear inequality. --- Linear map. --- Linear space (geometry). --- Linear subspace. --- Loss function. --- Main diagonal. --- Mathematical induction. --- Mathematical optimization. --- Mathematical problem. --- Max-flow min-cut theorem. --- Maxima and minima. --- Maximal set. --- Maximum flow problem. --- Menger's theorem. --- Minor (linear algebra). --- Monotonic function. --- N-vector. --- Nonlinear programming. --- Nonnegative matrix. --- Parity (mathematics). --- Partially ordered set. --- Permutation matrix. --- Permutation. --- Polyhedron. --- Quantity. --- Representation theorem. --- Row and column vectors. --- Scientific notation. --- Sensitivity analysis. --- Set notation. --- Sign (mathematics). --- Simplex algorithm. --- Simultaneous equations. --- Solution set. --- Special case. --- Subset. --- Summation. --- System of linear equations. --- Theorem. --- Transpose. --- Unit sphere. --- Unit vector. --- Upper and lower bounds. --- Variable (mathematics). --- Vector space. --- Von Neumann's theorem.

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The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-36), Volume III, will be forthcoming.

Oscillations. --- Addition. --- Almost periodic function. --- Analytic function. --- Analytic manifold. --- Asymptote. --- Asymptotic analysis. --- Banach space. --- Basis (linear algebra). --- Betti number. --- Big O notation. --- Boundary (topology). --- Boundary value problem. --- Boundedness. --- Calculation. --- Cartesian coordinate system. --- Characteristic equation. --- Characteristic exponent. --- Coefficient matrix. --- Coefficient. --- Combination. --- Complex number. --- Complex space. --- Connected space. --- Continuous function. --- Counterexample. --- Curve. --- Degeneracy (mathematics). --- Degrees of freedom (statistics). --- Derivative. --- Determinant. --- Differentiable function. --- Differential equation. --- Dissipative system. --- Eigenvalues and eigenvectors. --- Equation. --- Existence theorem. --- Existential quantification. --- Exterior (topology). --- First variation. --- Fixed-point theorem. --- Fundamental theorem. --- Geometry. --- Half-space (geometry). --- Homeomorphism. --- Homotopy. --- Hyperbolic sector. --- Identity matrix. --- Imaginary number. --- Implicit function. --- Infimum and supremum. --- Integral curve. --- Interior (topology). --- Intersection (set theory). --- Interval (mathematics). --- Invertible matrix. --- Jacobian matrix and determinant. --- Jordan curve theorem. --- Limit cycle. --- Limit point. --- Limit set. --- Line at infinity. --- Linear approximation. --- Linear differential equation. --- Linear equation. --- Linear map. --- Lipschitz continuity. --- Matrix (mathematics). --- Monotonic function. --- N-vector. --- Nonlinear system. --- Ordinary differential equation. --- Parameter. --- Parametric equation. --- Parametrization. --- Partial derivative. --- Periodic function. --- Phase plane. --- Phase space. --- Point at infinity. --- Polynomial. --- Projective plane. --- Quantity. --- Saddle point. --- Scientific notation. --- Second derivative. --- Separatrix (mathematics). --- Sign (mathematics). --- Simultaneous equations. --- Singular perturbation. --- Special case. --- Submanifold. --- Summation. --- Tangent. --- Taylor series. --- Theorem. --- Theory. --- Topology. --- Vector field. --- Velocity. --- Zero of a function.