No abstract available

[en] In Minkowski-space the timelike relation incorporates the linear structure. General spacetime manifolds have to be causally restricted to achieve the result that the timelike relation incorporates the conformal structure. The author proposes to leave the spacetime unrestricted and to revise and review the definition of timelike relations. (Auth.)

[en] We show in this paper that the autonomous nonlinear dynamical system Σ(A,B,F): x' = Ax+Bu+F(x) is topologically equivalent to the linear dynamical system Σ(A,B,O): x' = Ax+Bu if the projection of A on the complement in Rⁿ of the controllable vectorial subspace is hyperbolic and if lipschitz constant of F is sufficiently small (^*) and F(x) = 0 when parallel x parallel is sufficiently large (^**). In particular, if Σ(A,B,O) is controllable, it is topologically equivalent to Σ(A,B,F) when it is only that F satisfy (^**). (author). 18 refs

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[en] The author describes briefly how quasi-catastrophe theory can explain the phenomena of the violation of certain conservation laws and other spontaneous changes in a given physical system like phase transitions etc. (Auth.)

[en] The Ahlfors-Bers-Teichmueller theory for arbitrary Riemann surfaces is outlined: Properties of conformal and quasi-conformal mappings are used to construct the Bers holomorphic model for Teichmueller space T; the holomorphic vector bundles of holomorphic q-differentials over T are also discussed. (author). 35 refs, 16 figs

[en] Given a super-Riemann surface defined by a Fuchsian group Γ, the global space of super-Beltrami differentials, parametrising deformations of the given superconformal structure, is defined and studied. The method (using vector fields satisfying an integrability condition) simplifies the definition considerably, and leads to natural analogues of the basic results in Beltrami theory. In particular we are able to state and solve the super-Beltrami equations, and to prove the global existence of the Bers embedding for super-Teichmueller space. These results provide a foundation for the study of the supermoduli space in genus > 1. (author)

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No abstract available

[en] A problem of gravitational singularities, which are considered as topological transitions (TT) is solved. A principle possibility of the evolution description through TTs in the theory of gravitation is shown. For this purpose the evolution is presented as some trajectory in the superspace of the Wiler-de Vittes 3-geometries. TTs are considered through one critical point of the Morse function