There are also four appendices. Let K be a field of characteristic 0, and let C be a commutative K-algebra. which makes C into a Lie algebra, and is a biderivation (i.e. a derivation in each argument). The pair C, {−, −} is called a Poisson algebra. Poisson brackets arise in several ways. Example 1.1. Classical Hamiltonian mechanics. Here K = R, X is an even dimensional differentiable manifold ...

In this paper we study a queueing system with state-dependent services and state-dependent vacations, or simply G/M(n)/1/K. Since the service rate is state-dependent, this system includes G/M/c and G/M/c/K queues with various types of station vacations as special cases. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length...

Let G be a finite group and k a field of characteristic p dividing |G|. Then Greenlees has developed a spectral sequence whose E2 term is the local cohomology of H∗(G, k) with respect to the maximal ideal, and which converges to H∗(G, k). Greenlees and Lyubeznik have used Grothendieck’s dual localization to provide a localized form of this spectral sequence with respect to a homogeneous prime i...

In this paper, we introduce the fusion product of a generic pair of co-adjoint orbits. This construction provides the geometric dual object to the product in Verlinde fusion algebra. The latter is a quantum deformation of the standard tensor product, the fusion product constructed here is the corresponding deformation of the Cartesian product. Let G be a connected and simply-connected compact s...

12 Figure 8: Blending using two diierent magnitudes of T 2 i (t) = dC(t) dt n(u(t); v(t)). (a) (b) (c) Figure 9: Spout connection to the Utah teapot rounding using T 2 i (t) = dC(t) dt n(u(t); v(t)). 5 i (t) = (S u (u(t); v(t))r(t) + S v (u(t); v(t))s(t)). method, which is guaranteed to be perpendicular to the rail curves in Euclidean space. Figure 9 shows the original teapot (a), the lleted te...

in this paper we introduce and study besselian $g$-frames. we show that the kernel of associated synthesis operator for a besselian $g$-frame is finite dimensional. we also introduce $alpha$-dual of a $g$-frame and we get some results when we use the hilbert-schmidt norm for the members of a $g$-frame in a finite dimensional hilbert space.