Table of contents

CONTENTS Introduction § 1. Normal forms of hyperbolic local families § 2. Deformations of germs of vector fields with a single zero eigenvalue § 3. Bifurcation of a separatrix loop of a saddle on the plane References

CONTENTS Introduction § 1. Measures, linear functional, and compactifications § 2. Category theoretical problems of measure theory § 3. Measures on metrizable compact spaces § 4. Measures on non-metrizable compact spaces § 5. The non-compact case § 6. Measures and mappings § 7. Barycentres of probability measures References

CONTENTS Introduction 1. Classes of CR-manifolds 1.1. The CR-structure 1.2. Examples 1.3. Embedded CR-manifolds 1.4. CR-manifolds in 1.5. Local defining functions 1.6. Remarks 2. CR-fields 2.1. CR-structure and complex fields 2.2. Basis CR-fields 2.3. Local CR-embeddings 2.4. CR-fields on an embedded manifold 2.5. Commuting bases 2.6. Operators adjoint to CR-fields 3. Annihilating forms. RC-manifolds 3.1. RC- and CR-manifolds 3.2. The real part of an RC-structure 3.3. Locally integrable RC-manifolds 3.4. Derived modules of 1-forms 3.5. CR-manifolds as flows 4. The Levi form 4.1. Definitions 4.2. Kernel of the Levi form 4.3. Zeros and the image 4.4. The Levi form of a bundle 4.5. Higher order forms 4.6. Geometric interpretation 5. CR-foliations 5.1. Complex foliations and the Levi form 5.2. CR-straightenings 5.3. A theorem on CR-foliations 5.4. Corollaries 5.5. Analytic sets on a CR-manifold 6. Defining functions 6.1. Local defining functions and the Levi form 6.2. A q-strictly pseudoconvex defining function 6.3. Critical points of Levi-rank q 6.4. q-pseudoconvex neighbourhoods of a CR-manifold 7. Totally real manifolds 7.1. Strictly pseudoconvex neighbourhoods 7.2. External tangency of pseudoconvex domains 7.3. Lagrangian manifolds in 7.4. Totally real embeddings 7.5. Symmetry principle References

CONTENTS Introduction 1. The factorization of polynomials 2. The construction of irreducible and primitive polynomials 3. The distribution of irreducible and primitive polynomials 4. Computation in finite fields 5. Coding theory and algebraic curves 6. Recurring sequences in finite fields 7. Some new applications of the theory of finite fields References