We introduce the notion of Hamiltonian spaces for Manin pairs over manifolds, using the so-called generalized Dirac structures. As an example, we describe Hamiltonian spaces of a quasi-Lie bialgebroid using this general framework. We also discuss reduction of Hamiltonian spaces of this general type.

In this work, the issue of computing a real logarithm of a real matrix is addressed. After a brief review of some known methods, more attention is paid to three methods: (i) Padé approximation techniques, (ii) Newton’s method, and (iii) a series expansion method. Newton’s method has not been previously treated in the literature; we address commutativity issues, and simplify the algorithmic form...

ityl or positive realness in a VLSI model is an important property Passivity in a VLSI model is an important property to guarantee stato guarantee stable global simulation [3,7]. Existing DS passivity ble global simulation. Most VLSI models are naturally described tests are restrnctive in different aspects. For example, the extended as descriptor systems (DSs) or singular state spaces. Passivit...

in this paper, we consider an arbitrary binary polynomial sequence {a_n} and then give a lower triangular matrix representation of this sequence. as main result, we obtain a factorization of the innite generalized pascal matrix in terms of this new matrix, using a riordan group approach. further some interesting results and applications are derived.

A hamiltonian graph G of order n is k-ordered, 2 ≤ k ≤ n, if for every sequence v1, v2, . . . , vk of k distinct vertices of G, there exists a hamiltonian cycle that encounters v1, v2, . . . , vk in this order. Theorems by Dirac and Ore, presenting sufficient conditions for a graph to be hamiltonian, are generalized to k-ordered hamiltonian graphs. The existence of k-ordered graphs with small m...

For a given real invertible skew-symmetric matrix H, we characterize the real 2n×2n matrices X that allow an H-Hamiltonian polar decomposition of the type X = UA, where U is a real H-symplectic matrix (UTHU = H) and A is a real H-Hamiltonian matrix (HA = −ATH).