Table of contents

CONTENTS § 1. Introduction § 2. Relations in an Engel Lie algebra and its associative enveloping algebra § 3. Nilpotency of homogeneous Engel Lie algebras with a chain of ideals of special type § 4. Quasi-identities in Engel Lie algebras § 5. Nilpotency of an Engel Lie algebra generated by finitely many elements of nil-index 2 § 6. Nilpotency of an Engel Lie algebra in general References

CONTENTS Introduction Terminology and notation § 1. Some concepts and estimates from the theory of cardinal invariants § 2. Topological homogeneity and the exponent of a space in the Vietoris topology § 3. Homogeneity, products and retracts of homogeneous spaces § 4. Pracharacter, predensity, integrability by character, and the existence of G_δ-points in compact spaces § 5. Continuous images of topological groups § 6. Some additional results on homogeneity and topological groups References

CONTENTS Introduction § 1. Torus orbits and strata on the Grassmannian § 2. Matroids and strata on the Grassmannian § 3. The moment mapping and toric varieties § 4. The geometry of compact homogeneous spaces § 5. Definition of a stratum via the moment mapping § 6. Strata and Schubert cells § 7. Polytopes corresponding to strata § 8. The general (W,Q)-matroid § 9. Examples of strata References

CONTENTS Introduction Chapter I. Existence and uniqueness of generalized solutions of the Cauchy problem and of initial boundary-value problems § 1.1. Theorems of existence and non-existence § 1.2. Uniqueness theorems Chapter II. Estimates and differential properties of generalized solutions § 2.1. The character of the dependence on the data § 2.2. Regularity and non-regularity Chapter III. Behaviour of generalized solutions for small values of time § 3.1. Finite rate of propagation of perturbations § 3.2. Inertia § 3.3. Shrinking of the size of the support Chapter IV. Behaviour of generalized solutions for large values of time § 4.1. Stabilization in finite time § 4.2. Localization of perturbations § 4.3. Asymptotic formulae References