Selected works of Wen-tsun Wu / Wen-tsun Wu.

Format:

Book

Author/Creator:

Wu, Wen-tsün.

Standardized Title:

Selections. 2008

Language:

English

Subjects (All):

Algebraic topology.

Computer science--Mathematics.

Computer science.

Physical Description:

1 online resource (477 p.)

Place of Publication:

Hackensack, N.J. : World Scientific, c2008.

Language Note:

English

Summary:

This important book presents all the major works of Professor Wen-Tsun Wu, a widely respected Chinese mathematician who has made great contributions in the fields of topology and computer mathematics throughout his research career.The book covers Wu's papers from 1948 to 2005 and provides a comprehensive overview of his major achievements in algebraic topology, computer mathematics, and history of ancient Chinese mathematics. In algebraic topology, he discovered Wu classes and Wu formulas for Stiefel-Whitney classes of sphere bundles or differential manifolds, established an imbedding theory w

Contents:

Contents; Foreword; 1. On the product of sphere bundles and the duality theorem modulo two; 2. Classes caracteristiques et i-carrks d'une variBtk; 3. Les i-carrhs dans une vari6tk grassmannihne; 4. On the realization of complexes in Euclidean spaces I; 1. LINEAR REALIZATION OF COMPLEXES IN EUCLIDEAN SPACES; 2. THE IMBEDDING COCHAIN OF AN ALMOST SEMI-LINEAR REALIZATION; 3. DEFINITION OF IMBEDDING CLASS&; 4 . THE REALIZABILITY OF ANY COCYCLE IN THE IMBEDDING CLASSES; 5. RELATIONS BETWEEN Ym-' AND ern - 1 ' 2 = ern; 6. EXPLICIT EXPRESSIONS OF CERTAIN REPRESENTATIVE &CYCLES IN

7. EXPLICIT EXPRESSIONS FOR CERTAIN REPRESENTATIVE COCYCLES IN em8. RELATIONS BETWEEN @ AND THEIR TOPOLOGICAL INVARIANCE; 9, COMPLEXES REALIZABLE IN R""'"" BUT NOT IN R""; 10. ANOTHER EXAMPLE OF Van Kam~en[~l AND ITS GENERALIZATION; REFERENCES; 5. On the realization of complexes in Euclidean spaces I11; 1. Several constructions; 2. Main theorem-the n e c e s s a r y and sufficient condition for K"" c R2"" when n > 2; 3. Some sufficient conditions for K"" C R2""; BIBLIOGRAPHY; 6. On universal invariant forms; 1. Introduction; 2. Infinite Group of Volume-preserving Transformations

3. Regular Transformation Infinite Group- H.C. Lee's Theorem; 4. Tangential Transformation Infinite group; 5. Regular Transformation Infinite Group Possessing Definite Symmetry; References; 7. Theory of I*-functor in algebraic topology - Effective calculation and axiomatization of I*-functor on complexes; 1. I*-FUNCTOR 0F K/L AND K U K; II. J-CONSTRUCTION OF DCA-MORPHISM g: M

+ N in CASE N =I*(S""); III. PRIVILEGED MORPHISMS OF MINIMAL MODELS; Iv. J-CONSTRUCTION DETERMINED BY COhtBINATORIAL SPHERES I N K; v. EFFECTIVE CALCULATIONS AND Axrouanc SYSTEM OP I-FUNCTOR ON Xo; REFERENCES

8. On the decision problem and the mechanization of theorem-proving in elementary geometry; Abstract; I. Formulation of the problem; 11. Examples; Ill. Some lemmas; IV. Proofs of the theorems; Bibliography; 9. Toward mechanization of geometry - Some comments on Hilbert's "Grundlagen der Geometrie''; 10. The out-in complementary principle; Simple Applications and the Theory of Proportion; Gnomon, Shadow and Double Differences; The Gbugu Theorem; Gou, Gu, Xuan, Their Sums and Differences and Methods of Finding One from the Others; Qin Jiushao's Formula 1; Extracting the Square or Cubic Root

Quadratic Equations; Theory of Volumes and Liu Hui's Principle; The Xianchu Theorem; Volume of the Sphere and the Principle of Zu Geng; Other Applications; Conclusion; 11. A constructive theory of differential algebraic geometry based on works of J. F. Ritt with particular applications to mechanical theorem-proving in differential geometries; REFERENCES; 12. Basic principles of mechanical theorem-proving in elementary geometries; 1. INTRODUCTION; 2. WELL-ORDERING OF A POLYNOMIAL SET.; 3. A CONSTRUCTIVE THEORY OF ALGEBRAIC VARIETIES; 4. PROOF OF THE ALGEBRAIC MECHANIZATION THEOREM

5. PROGRAMMING AND EXAMPLES.

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9786611933678

9781281933676

1281933678

9789812791085

9812791086