We consider an optimisation problem for the transient process in a quasi-linear dynamical system (contains small parameter at non-linearities) with performance index that is linear combination of energy costs and duration process. An algorithm constructing asymptotic approximations given order to solution this proposed. The based on decomposition by integer powers initial values adjoint variabl...

Let $$ {\overline{\mathrm{X}}}_{\uplambda} be the closure of I-orbit in affine Grassmanian Gr a simple algebraic group G adjoint type, where I is Iwahori subgroup and λ coweight G. We find algorithm which describes set Ψ(λ) all I-orbits terms coweights. introduce R-operators (associated to positive roots) on lattice G, exactly describe relation I-orbits. These operators satisfy Braid relations ...

One of the main applications free probability is to show that for appropriately chosen independent copies d random matrix models, any noncommutative polynomial in these variables has a spectral distribution converges asymptotically and can be described with help probability. This paper aims this extended rational functions, answering an open question by Roland Speicher. also provides approach a...

Let k be an algebraically closed field of characteristic p > 0 and let l be another prime number. O. Gabber and F. Loeser proved that for any algebraic torus T over k and any perverse l-adic sheaf F on T the Euler characteristic χ(F) is non-negative. We conjecture that the same result holds for any perverse sheaf F on a reductive group G over k which is equivariant with respect to the adjoint a...

Abstract The paper presents the results of optimization geometric parameters simplified wall jet cooling system using a modified Adjoint Shape method for algebraic systems equations (Discrete Optimization). modification consists in linearized discrete with replacement derivatives by their finite-volume approximations. flowed through duct and out from nozzle. was inclined at an angle 35 degrees ...

A normal complex algebraic variety X is called a symplectic variety (cf. [Be]) if its regular locus Xreg admits a holomorphic symplectic 2-form ω such that it extends to a holomorphic 2-form on a resolution f : X̃ → X. Affine symplectic varieties are constructed in various ways such as nilpotent orbit closures of a semisimple complex Lie algebra (cf. [CM]), Slodowy slices to nilpotent orbits (cf...