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Titlebook: Lie Groups, Differential Equations, and Geometry; Advances and Surveys Giovanni Falcone Book 2017 Springer International Publishing AG 2017

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Character, Multiplicity, and Decomposition Problems in the Representation Theory of Complex Lie Algg in algebraic Lie theory. For simplicity, the focus lies on the case of the category . of representations of a simple complex Lie algebra. We show how the approach yields a proof of the classical Kazhdan–Lusztig conjectures that avoids the theory of .-modules on flag varieties.
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Reduction of Some Semi-discrete Schemes for an Evolutionary Equation to Two-Layer Schemes and Estim are reduced to two-layer schemes. The solutions of these two-layer schemes are used to construct an approximate solution of the initial problem. By using the associated polynomials the estimates for the approximate solution error are proved.
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https://doi.org/10.1007/978-3-319-62181-4Geometry of Lie Algebras; Optimal COntrol; Homotopy Algebras; Loop Theory; Lie Theory; ordinary different
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Cohomology Operations Defining Cohomology Algebra of the Loop Space,..: ..(.). ⊗ ..(.). → ..(.), ., . = 0, 1, 2, 3, . which turn (..(.), {..}, {..}) into a ..-algebra. This structure defines on ..(.) a correct multiplication, thus determines a cohomology algebra ..(.).
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An Optimal Control Problem for a Nonlocal Problem on the Plane,Bitsadze–Samarski boundary value problem is proved for a linear differential equation of first order; the existence of a solution in the space . is proved and an a priori estimate is derived. A theorem on the necessary and sufficient condition of optimality is proved for a linear optimal control problem.
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