29 research outputs found

    Homology class of a Lagrangian Klein bottle

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    It is shown that an embedded Lagrangian Klein bottle represents a non-trivial mod 2 homology class in a compact symplectic four-manifold (X,ω)(X,\omega) with c1(X)⋅[ω]>0c_1(X)\cdot[\omega]>0. (In versions 1 and 2, the last assumption was missing. A counterexample to this general claim and the first proof of the corrected result have been found by Vsevolod Shevchishin.) As a corollary one obtains that the Klein bottle does not admit a Lagrangian embedding into the standard symplectic four-space.Comment: Version 3 - completely rewritten to correct a mistake; Version 4 - minor edits, added references; AMSLaTeX, 6 page

    Nuclear reactions in hot stellar matter and nuclear surface deformation

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    Cross-sections for capture reactions of charged particles in hot stellar matter turn out be increased by the quadrupole surface oscillations, if the corresponding phonon energies are of the order of the star temperature. The increase is studied in a model that combines barrier distribution induced by surface oscillations and tunneling. The capture of charged particles by nuclei with well-deformed ground-state is enhanced in stellar matter. It is found that the influence of quadrupole surface deformation on the nuclear reactions in stars grows, when mass and proton numbers in colliding nuclei increase.Comment: 12 pages, 10 figure

    Large-scale unit commitment under uncertainty: an updated literature survey

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    The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject
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