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    On nilpotent evolution algebras

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    The type and several invariant subspaces related to the upper annihilating series of finite-dimensional nilpotent evolution algebras are introduced. These invariants can be easily computed from any natural basis. Some families of nilpotent evolution algebras, defined in terms of a nondegenerate symmetric bilinear form and some commuting symmetric diagonalizable endomorphisms relative to the form, are explicitly constructed. Both the invariants and these families are used to review and complete the classification of nilpotent evolution algebras up to dimension five over algebraically closed fields.Comment: 19 page

    Evolution

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    Black Hole Evolution

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    Black hole formation and evaporation is studied in the semiclassical approximation in simple 1+1-dimensional models, with emphasis on issues related to Hawking's information paradox. Exact semiclassical solutions are described and questions of boundary conditions and vacuum stability are discussed. The validity of the semiclassical approximation has been called into question in the context of the information puzzle. A different approach, where black hole evolution is assumed to be unitary, is described. It requires unusual causal properties and kinematic behavior of matter that may be realized in string theory. Based on lectures given at the 1994 Trieste Spring SchoolComment: 30 pages, 8 figures, late

    Evolution is Viral: The Theory of Collective Discontinuous Evolution

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    Herein will be discussed the problems associated with the origin of species according to Darwinist processes of individual mutations. We will argue that individual mutations cannot be the driving force of species origination. A far more probable explanation is a process of collective mutation that affects numerous individuals near simultaneously akin to an infectious disease. These types of mutations might be precipitated by viruses which would create a discontinuous leap into another species. Such a mechanism also sheds light on the increased rate of evolution observed currently
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