We extend the definition of Maslov index to a broad class non-Hamiltonian dynamical systems. To do this, we introduce family topological spaces--which call Maslov-Arnold spaces--that share key features with Lagrangian Grassmannian, and hence admit similar theory. This contains much more. construct examples, called hyperplane spaces, that are dense in larger than Grassmannian (which is submanifo...

We compute string field theory Hamiltonian matrix elements and compare them with matrix elements of the dilatation operator in gauge theory. We get precise agreement between the string field theory and gauge theory computations once the correct cubic Hamiltonian matrix elements in string field theory and a particular basis of states in gauge theory are used. We proceed to compute the matrix ele...

A Pariser-Parr-Pople (PPP) Hamiltonian of an 87~ electron system of the molecule octatetraene, represented in a configuration-interaction basis (CI basis), is analyzed with respect to the statistical properties of its matrix elements. Based on this analysis we develop an effective Hamiltonian, which represents virtual excitations by a Gaussian orthogonal ensemble (GOE). We also examine numerica...

Given a close 3-form H ∈ Ω 0 (M), we define a twisted bracket on the space Γ(TM) ⊕ Ω 0 (M). We define the group of H-twisted Hamiltonian symmetries Ham(M, J;H) as well as Hamiltonian action of Lie group and moment map in the category of (twisted) generalized complex manifold, which leads to generalized complex reduction much the same way as symplectic reduction is constructed. The definitions a...

for a fixed positive integer , we say a ring with identity is n-generalized right principally quasi-baer, if for any principal right ideal of , the right annihilator of is generated by an idempotent. this class of rings includes the right principally quasi-baer rings and hence all prime rings. a certain n-generalized principally quasi-baer subring of the matrix ring are studied, and connections...

‎The global generalized minimum residual (Gl-GMRES)‎ ‎method is examined for solving the generalized Sylvester matrix equation‎ ‎[sumlimits_{i = 1}^q {A_i } XB_i = C.]‎ ‎Some new theoretical results are elaborated for‎ ‎the proposed method by employing the Schur complement‎. ‎These results can be exploited to establish new convergence properties‎ ‎of the Gl-GMRES method for solving genera...

Structure-preserving numerical techniques for computation of eigenvalues and stable deflating subspaces of complex skew-Hamiltonian/Hamiltonian matrix pencils, with applications in control systems analysis and design, are presented. The techniques use specialized algorithms to exploit the structure of such matrix pencils: the skew-Hamiltonian/Hamiltonian Schur form decomposition and the periodi...

Skew-Hamiltonian and Hamiltonian eigenvalue problems arise from a number of applications, particularly in systems and control theory. The preservation of the underlying matrix structures often plays an important role in these applications and may lead to more accurate and more efficient computational methods. We will discuss the relation of structured and unstructured condition numbers for thes...