‎The global FOM and GMRES algorithms are among the effective‎ ‎methods to solve Sylvester matrix equations‎. ‎In this paper‎, ‎we‎ ‎study these algorithms in the case that the coefficient matrices‎ ‎are real symmetric (real symmetric positive definite) and extract‎ ‎two CG-type algorithms for solving generalized Sylvester matrix‎ ‎equations‎. ‎The proposed methods are iterative projection metho...

We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.

We realize the current algebra of a Kac-Moody algebra as a quotient of a semi-direct product of the Kac-Moody Lie algebra and the free Lie algebra of the Kac-Moody algebra. We use this realization to study the representations of the current algebra. In particular we see that every ad-invariant ideal in the symmetric algebra of the Kac-Moody algebra gives rise in a canonical way to a representat...

The form π is unique up to a character twist, while ν is simply the central character of Π. The central character ω of π may be chosen to be of finite order. Moreover, we may choose π such that, for any finite place v, πv is unramified, resp. Steinberg, when Πv ⊗ νv is unramified, resp. Steinberg. Here Ad(π) denotes the Adjoint of π, a selfdual automorphic form on GL(3)/F , defined to be sym2(π...

The Boolean lattice 2[n] is the power set of [n] ordered by inclusion. A chain c0 ⊂ · · · ⊂ ck in 2[n] is rank-symmetric, if |ci|+ |ck−i| = n for i = 0, . . . , k; and it is symmetric, if |ci| = (n− k)/2 + i. We prove that there exist a bijection p : [n] → [n] and a partial ordering < on [n](>n/2) satisfying the following properties: • ⊂ is an extension of < on [n](>n/2); • if C ⊂ [n](>n/2) is ...

A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, a complete classification of connected pentavalent symmetric graphs of order 12p is given for each prime p. As a result, a connected pentavalent symmetric graph of order 12p exists if and only if p = 2, 3, 5 or 11, and up to isomorphism, there are only nine such graphs: one for each p = 2, 3 ...

For many L-functions of arithmetic interest, the values on or close to the edge of the region of absolute convergence are of great importance, as shown for instance by the proof of the Prime Number Theorem (equivalent to non-vanishing of ζ(s) for Re(s) = 1). Other examples are the Dirichlet L-functions (e.g., because of the Dirichlet class-number formula) and the symmetric square L-functions of...