Formulas are obtained that express the Schur S-functions indexed by Young diagrams of rectangular shape as linear combinations of “mixed” products of Schur’s Sand Q-functions. The proof is achieved by using representations of the affine Lie algebra of type A (1) 1 . A realization of the basic representation that is of “D (2) 2 ”-type plays the central role.

Let M be a compact manifold. and D a Dirac type differential operator on M . Let A be a C ∗-algebra. Given a bundle W of A-modules over M (with connection), the operator D can be twisted with this bundle. One can then use a trace on A to define numerical indices of this twisted operator. We prove an explicit formula for this index. Our result does complement the Mishchenko-Fomenko index theorem...

Let E be a separable Banach space not containing a copy of l. The complexity of the l(n)’s inside E may be measured by Bourgain’s l-index [3] or by locating so called lα-spreading models [8]. It is easy to see that the existence of l 1 α-spreading models implies a large l-index. In general, the implication is not reversible [7, Remark 6.6(i)]. However, suppose that T is the standard Tsirelson s...

the topological indices, defined as the sum of contributions of all pairs of vertices (among which are the wiener, harary, hyper–wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.

introduction: among the environmental pollutions, noise is very important for its physiological  and psychological effects on human. traffic noise is one of the most important pollutants and the  hospitals  are  one  of  the  critical  places  regarding  this  type  of  noise.  for  these  reasons,  in  the  summer  of  1382,  the  traffic  noise  of  mashhad  main  streets  around  the  hospit...