Contents -- Preface -- The Mobius equivalent isothermic surfaces in S3(1) and Backlund transformations -- S0 Introduction -- S2 The isothermic surfaces in S3(1) -- S3 The Backlund transformations of (2.17) and (2.18) -- Acknowledgments -- References -- Asymptotic behavior of Yang-Mills flow in higher dimensions -- S1. INTRODUCTION -- S2. ENERGY INEQUALITY BOCHNER TYPE INEQUALITY MONOTONICITY FORMULA AND PARTIAL REGULARITY THEOREM FOR YANG-MLLLS FLOW -- S3. THE ESTIMATES OF HIGHER DERIVATIVES OF CURVATURES OF YANG-MILLS FLOW -- S4. PROOF OF MAIN THEOREM -- S5. APPENDIX -- REFERENCES -- The essential spectrum on complete noncompact Riemannian manifolds with asymptotically nonnegative radial Ricci curvature -- 1.INTRODUCTION -- 2. SYMBOLS AND SOME LEMMAS -- 3.THE PROOF OF THEOREM 1 -- REFERENCES -- Complete submanifolds in Euclidean spaces with constant scalar curvature -- 1. INTRODUCTION -- 2. PRELIMINARIES -- 3. COMPLETE HYPERSURFACES -- 4. COMPLETE SUBMANIFOLDS -- REFERENCES -- On mathematical ship lofting -- References -- Some developments in spectral methods for nonlinear partial differential equations in unbounded domains -- 1. Introduction -- 2. Hermite Spectral Method and Lagaerre spectral method -- 3. Jacobi Spectral Method -- 4. Rational Spectral Method -- Acknowledgments -- References -- The Darboux transformation and local isometric immersions of space forms -- 1 Introduction -- 2 Preliminaries -- 3 Non-umbilically isometric immersions of space forms -- 4 Darboux transformation -- 5 The construction of local isometric immersions derived from a trivial solution -- Acknowledgments -- References -- On the Nirenberg problem -- S1. Introduction -- S2. Kazdan-Warner condition -- S3. Existence of solutions -- S4. Preliminaries -- S5. Main steps of proofs -- References.

Periodic mean curvature and Bezier curves -- 1. Introduction -- 2. Periodic surfaces of revolution -- 3. Closed curves -- 4. Bezier curves -- References -- Almost complex manifolds and a differential geometric criterion for hyperbolicity -- 0. Introduction -- 1. Almost complex manifolds -- 2. Canonical connections for almost Hermitian manifolds -- 3. Almost complex submanifolds -- 4. Conformal changes -- 5. Differential geometric criterion for hyperbolicity -- References -- Thom isomorphism of equivariant cohomology -- 1. Introduction -- 2. Equivariant Cohomology -- 3. Kobayashi Lemma -- 4. The Thorn Isommorphism of the Normal Bundle -- References -- Horizontally conformal F-harmonic maps -- 1 Introduction -- 2 The Fundamental Equation for a Horizontally Conformal Map -- 3 An Extension of Baird and Eells' Result -- 4 F-harmonicity of Horizontally Conformal Maps -- References -- Harmonic maps between Carnot spaces -- 1. Introduction -- 2. Carnot Spaces -- 3. Asymptotic Behavior of Proper Harmonic Maps -- Acknowledgments -- References -- Harmonic cohomology groups on compact symplectic nilmanifolds -- 1. Introduction -- 2. Operators on O*(M) and harmonic cohomology group -- 3. Harmonic cohomology group of nilmanifolds -- 4. Examples -- References -- A survey of complete manifolds with bounded radial curvature function -- 1. Introduction -- 2. Model surfaces -- 3. Generalized Alexandrov Toponogov Comparison Theorems -- 4. Maximal diameter theorem -- References -- Yang-Mills connections over compact symplectic manifolds -- S0. Introduction -- S1. Preliminary -- S2. Yang-Mills connections over Kahler manifolds -- S3. Yang-Mills connections over strongly pseudoconvex CR manifolds -- S4. Symplectic manifolds -- S5. Yang-Mills connections over symplectic manifolds -- REFERENCES.

Nonlinear Schrodinger systems associated with Hermitian symmetric Lie algebras -- 1. Three classical integrable systems -- 2. Schrodinger-like systems associated with Hermitian symmetric Lie algebras -- 3. Gauge equivalence -- 4. The correspondence between Heisenberg model and nonlinear Schrodinger equation with (quasi)-periodic boundary condition -- 5. Concluding remarks -- Acknowledgments -- References -- On the Hensel lift of a polynomial -- 1. Introduction -- 2. Existence and Uniqueness -- 3. An Algorithm to Compute the Hensel Lift -- References -- Some advances related particle systems - Estimation for eigenvalue and new w24 field -- I Application of coupling method to estimate the first eigenvalue -- II w24 quantum fields and polymer measures -- III Sketch of the Main Proof of I -- REFERENCES -- A note on locally real hyperbolic space with finite volume -- 1. Introduction -- 2. The construction of harmonic maps of finite energy -- 3. Some properties of the harmonic maps -- 4. The proof of the theorem -- References -- Interesting properties of the sets: N2{12 22 32 ...] N3[13 23 33...] and N4[14 24 34...] -- Acknowledgments -- References -- List of participants.