Ju l 2 00 9 A generalization of Apostol ’ s Möbius functions of order k Antal

60 70 63 v 1 1 7 Ju l 2 00 6 The General Solution of Bianchi Type III Vacuum Cosmology

The second order Ordinary Differential Equation which describes the unknown part of the solution space of some vacuum Bianchi Cosmologies is completely integrated for Type III, thus obtaining the general solution to Einstein’s Field Equations for this case. Imposing the space-time generalization of a ”hidden” symmetry of the generic Type III spatial slice, enables us to retrieve a two-parameter...

ar X iv : a st ro - p h / 02 07 41 9 v 1 1 9 Ju l 2 00 2 Rarefaction Shocks , Shock Errors and Low Order of Accuracy in ZEUS

A generalization of Bertrand's test

One of the most practical routine tests for convergence of a positive series makes use of the ratio test. If this test fails, we can use Rabbe's test. When Rabbe's test fails the next sharper criteria which may sometimes be used is the Bertrand's test. If this test fails, we can use a generalization of Bertrand's test and such tests can be continued innitely. For simplicity, we call ratio test,...

1 1 Ju l 2 00 8 On quasiinvariants of S n of hook shape

Chalykh, Veselov and Feigin introduced the notions of quasiinvariants for Coxeter groups, which is a generalization of invariants. In [2], Bandlow and Musiker showed that for the symmetric group Sn of order n, the space of quasiinvariants has a decomposition indexed by standard tableaux. They gave a description of basis for the components indexed by standard tableaux of shape (n− 1, 1). In this...

Decomposition of H*-Algebra Valued Negative Definite Functions on Topological *-Semigroups

In the present paper, among other results, a decomposition formula is given for the w-bounded continuous negative definite functions of a topological *-semigroup S with a weight function w into a proper H*-algebra A in terms of w-bounded continuous positive definite A-valued functions on S. A generalization of a well-known result of K. Harzallah is obtained. An earlier conjecture of the author ...