CONTENTS -- Preface -- Chapter I Integral and Pseudodifferential Operators -- 1. Pseudodifferential Operators of Second Order with Sign-Changed Characteristic Form Nguyen Minh Tri -- References -- 2. A Semilinear Nonclassical Pseudodifferential Boundary Value Problem in Sobolev Spaces 1 < p < 00 Nguyen Minh Chuong and Dang Anh Tuan -- 1. Introduction -- 2. Sobolev Spaces -- 3. Pseudodifferential Operators in R" -- 4. Pseudodifferential Operator in Ry -- 5. Pseudodifferential Operator on a Compact Domain C2 -- Ellipticity Condition -- 6. A Linear Non-classical Pseudodifferential Boundary Value Problem -- 7. A Semilinear Non Classical Pseudodifferential Boundary Value Problem -- References -- 3. Singular Integral Operators in Functional Spaces of Morrey Type Lubomira Softova -- 1. Definitions and Preliminary Results -- 2. Singular Integral Estimates -- References -- 4. Classification of Integral Transforms Vu Kim Tuan -- 1. Introduction -- 2. Convolution Transforms -- 2.1. Fourier convolution transforms -- 2.2. Laplace convolution transforms -- 2.3. Mellin convolution transforms -- 2.3.1. Mellin convolution transforms of Watson type -- 2.3.2. Mellin convolution transforms of Riemann-Liouville type -- 2.3.3. Mellin convolution transforms of Laplace type -- 2.4. Fourier cosine and sine convolution transforms -- 3. Nonconvolution Transforms -- 3.1. W i m p nonconvolution G-transform. -- 3.2. Transforms of Kontorovich-Lebedev type -- 3.3. The Buchholt nonconvolution G-transform -- 3.4. The cherry nonconvolution G-transform -- 3.5. Other nonconvolution G-transforms -- References -- Chapter II Partial Differential Equations -- 5. Unified Minimax Methods Martin Schechter -- 1. Introduction -- 2. Definitions and Theorems -- 3. Linking Subsets -- 4. A Method Using Homeomorphisms -- 5. A Method Using Metric Spaces.

6. A Method Using Homotopy Stable Families -- 7. Some Applications -- References -- 6. Some Remarks on Single Conservation Laws Mikio Tsuji and Peter Wagner -- 1. Introduction -- 2. Existence Domains of Solutions for Burgers Equation -- 3. A Single Conservation Law without Convexity Condition -- 4. Behavior of the Shock S1 -- 5 . Behavior of the Shock Sz -- References -- 7. Iterative Method for Solving a Mixed Boundary Value Problem for Biharmonic Type Equation Dung Quang A and Le Tung Son -- 1. Introduction -- 2. Reduction of the Problem to Boundary - Domain Operator Equation -- 3. Construction of Approximate Solution of the Original Problem Via a Perturbed Problem -- 4. Iterative Method for Solving the Perturbed Problem -- 5 . Numerical Experiments -- References -- 8. Numerical Solution to a Non-Linear Parabolic Boundary Control Problem Dinh Nho Hao, Nguyen Trung Thanh and H. Sahli -- 1. Introduction -- 2. The Control Problem and Its dc Representation -- 3. DCA and Continuation Techniques -- 3.1. DCA -- 3.1.1. -- 3.1.2. -- 3.1.3. -- 3.1.4. Let g be a conwex function. -- 3.1.5. Let g E I'o(X) and lower semi-continuous (lsc). -- 3.1.6. Consider the DC program -- 3.1.7. DC algorithm: -- 3.2. The Continuation Technique -- 4. Numerical Results -- 4.1. Numerical Examples -- References -- 9. A Class of Solutions to Maxwell's Equations in Matter and Associated Special Functions Peter Massopust -- 1. Introduction and Preliminaries -- 1.1. Basic Magnetostatics -- 1.2. Coordinate Systems -- 1.2.1. Cartesian Coordinates -- 1.2.2. Circular Cylindrical Coordinates -- 1.2.3. Spherical Coordinates -- 1.2.4. Parabolic Coordinates -- 1.2.5. Elliptic Cylindrical Coordinates -- 2. Cartesian V -- 3. Cylindrical V -- 4. Spherical V -- 4.1. Semi-spherical V -- 5. Parabolic V -- 5.1. Circular Parabolic V -- 5.2. Elliptic Parabolic V -- References.

10. On the Cauchy Problem for a Quasilinear Weakly Hyperbolic System in Two Variables and Applications to that for Weakly Hyperbolic Classical Monge- Ampkre Equations Ha Tien Ngoan and Nguyen Thi Nga -- 1. Introduction -- 2. Hyperbolicity -- 3. Reduced System -- 4. Diagonalization -- 5. Application to the Classical Weakly Hyperbolic Monge- AmpGre Equation -- 6. Examples -- References -- 11. Some Singular Perturbation Problems Related to the Navier- Stokes Equations Makram Hamouda and Roger Temam -- 1. Introduction -- 2. Correctors of Order 0 and 1 -- 3. The Corrector of Order N ( N 2 2) -- 3.1. Preliminary results -- 4. Convergence Result -- 5. The Nonlinear Case -- 5.1. Corrector of order zero -- 5.2. Corrector of order one -- 5.2.1. Construction of the corrector 8'9' -- 5.2.2. Convergeme result: th,e main theorem -- Appendix -- Acknowledgements -- References -- Chapter III Geometric Analysis -- 12. Monotone Invariants and Embeddings of Statistical Manifolds Le Hong Van -- 1. Introduction -- 2. Statistical Models and Statistical Manifolds -- 2.1. Example of a Weak Fisher Metric -- 2.2. The Fisher Metric on the Space (CapN)+ of all positive probability distributions on ilN (see also Refs. 1,496) -- 2.3. Divergence Potential (see 1 , l d ) -- 2.4. Chentsov-Amari connections -- 2.5. Statistical Submanif olds -- 2.6. Statistical Models and Statistical Manifolds -- 3. Embeddings of Linear Statistical Spaces -- 3.1. Race Type of a Symmetric 3-tensor -- 3.2. Commasses as Monotone Invariants -- 4. Monotone Invariants and Obstructions to Embeddings of Statistical Manifolds -- 4.1. Examples -- 4.2. Diameters of Statistical Manifolds -- 5. Existence of Isostatistical Embeddings into CupN -- Acknowledgement -- References -- 13. Graded Cech Cohomology in Noncommutative Geometry Do Ngoc Diep -- 1. Introduction.

2. Preparation: Differential Systems and the Cyclic Theory -- 2.1. Differential Systems, Following Kashiwara -- 2.2. Fields of C*-algebras and Sheafification -- 3. Z2-graded c e c h Cohomology -- 3.1. Grothendieclc Topos -- 3.2. The Standard Cosimplicial Complex of a Continuous Functor -- 3.3. The Periodic Cyclic Bicomplex -- 4. Homotopy Invariance and Morita Invariance -- 5. Comparison with the Classical Cech Cohomology Theory -- Acknowledgments -- References -- 14. Sobolev Spaces with Weight on Riemannian Manifolds Nguyen Manh Chuong and Le DUC Thinh -- 1. Introduction -- 2. Sobolev Spaces with Weighted Norm on Riemannian Manifold -- References -- Chapter IV Stochastic and Infinite-Dimentional Analysis -- 15. Stochastic Population Control and RSDE with Jumps Situ Rong -- 1. A Deterministic Population Dynamical System -- 2. RSDE for Stochastic Population Dynamical System -- 3. Existence of Solutions to RSDE with Jumps -- 4. Stochastic Population Solutions and Their Properties -- 5. The Optimal Stochastic Population Control -- References -- 16. Noncausal Stochastic Calculus Revisited - Around the So-called Ogawa Integral Shigeyoshi Ogawa -- 1. Introduction -- 2. Noncausal Problems in Stochastic Analysis -- 3. Review of the Noncausal Stochastic Calculus -- 3.1. Causal functions and the B-diflerentiability -- 3.2. Noncausal stochastic integral -- 3.3. Equivalent expressions and variants -- 3.4. Condition for the integrability - in the framework of the Homogeneous Chaos theory -- 3.5. Relation between symmetric and noncausal integrals -- 4. Applications to the Noncausal SDEs -- 4.1. Noncausal Cauchy problem -- 4.2. Discussions for the more general cases -- 5. Question of Uniqueness - Noncausal It8 Formula -- References -- 17. Infinite-Dimensional Stochastic Analysis and Foundations of Quantum Mechanics Andrei Khrennikov -- 1. Introduction.

2. Infinite-dimensional analysis -- 3 . Dequantization -- 3.1. Classical and quantum statistical models -- 3.2. Asymptotic Gaussian analysis -- 4. Gaussian underground for pure states -- 5. Pure states as one-dimensional projections of spatial white-noise -- 5.1. The finite-dimensional case -- 5.2. Prequantum white noise field -- 6. Unbounded operators -- References -- 18. Noncommutative Trigonometry and Quantum Mechanics Karl Gustafson -- 1. Introduction, Background, and Summary -- 2. Essentials of the Noncommutative Trigonometry -- 3. Quick Summary of Applications to Date -- 4. The Bell Inequalities of Quantum Theory -- 5. The Zeno Problem of Quantum Theory -- Acknowledgements -- References.