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    On an efficient induction step with Nklt(X,D) -- notes to Todorov

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    Bianchi type I universes with dilaton and magnetic fields

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    We consider the dynamics of a Bianchi type I spacetime in the presence of dilaton and magnetic fields. The general solution of the Einstein-Maxwell dilaton field equations can be obtained in an exact parametric form. Depending on the numerical values of the parameters of the model there are three distinct classes of solutions. The time evolution of the mean anisotropy, shear and deceleration parameter is considered in detail and it is shown that a magnetic-dilaton anisotropic Bianchi type I geometry does not isotropize, the initial anisotropy being present in the universe for all times.Comment: 10 pages, 4 figure

    Characterization of the 4-canonical birationality of algebraic threefolds

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    In this article we present a 3-dimensional analogue of a well-known theorem of E. Bombieri (in 1973) which characterizes the bi-canonical birationality of surfaces of general type. Let XX be a projective minimal 3-fold of general type with Q\mathbb{Q}-factorial terminal singularities and the geometric genus pg(X)5p_g(X)\ge 5. We show that the 4-canonical map ϕ4\phi_4 is {\it not} birational onto its image if and only if XX is birationally fibred by a family C\mathscr{C} of irreducible curves of geometric genus 2 with KXC0=1K_X\cdot C_0=1 where C0C_0 is a general irreducible member in C\mathscr{C}.Comment: 25 pages, to appear in Mathematische Zeitschrif

    Space charge measurement in polymer insulated power cables using flat ground electrode PEA

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    Data processing methods used to accurately determine the space charge and electric stress distributions in DC power cables using the pulsed electroacoustic (PEA) system are described. Due to the coaxial geometry and the thick-walled insulation of highvoltage cables, factors such as divergence, attenuation and dispersion of the propagated acoustic pressure wave in the PEA can strongly influence the resultant measurements. These factors are taken into account ensuring accurate measurements to be made. Most importantly, a method is presented to determine the electric stress profile across the insulation due to both the divergent applied field and that as a consequence of trapped charge in the bulk of the insulating material. Results of spacecharge measurements and the corresponding derived electric stress distributions in XLPE DC cables are presented