A graph that contains a Hamiltonian cycle is called a Hamiltonian graph. In this paper we compute the first and the second geometric – arithmetic indices of Hamiltonian graphs. Then we apply our results to obtain some bounds for fullerene.

This research, works with the effective Hamiltonian and the quark model. Using, the decay rates of matter-antimatter of b quark was investigated. We described the effective Hamiltonian theory which was applied to the calculation of current-current (Q1,2), QCD penguin (Q3,…,6), magnetic dipole (Q8) and electroweak penguin (Q7,…,10) decay rates. The gluonic penguin structure of hadronic decays ...

In this research we work with the effective Hamiltonian and the quark model. We investigate the decay rates of matter-antimatter of quark. We describe the effective Hamiltonian theory and apply this theory to the calculation of current-current ( ), QCD penguin ( ), magnetic dipole ( ) and electroweak penguin ( ) decay rates. The gluonic penguin structure of hadronic decays is studied thro...

We study a new non-local hierarchy of equations of the isentropic gas dynamics type where the pressure is a non-local function of the density. We show that the hierarchy of equations is integrable. We construct the two compatible Hamiltonian structures and show that the first structure has three distinct Casimirs while the second has one. The existence of Casimirs allows us to extend the flows ...

We follow Dirac and write the Schrödinger equation in an algebraic form which is representation-free. The imaginary and real parts of this equation are respectively the Liouville equation, which involves the commutator of the Hamiltonian with the density operator and an equation for the time development of the phase operator that involves the anti-commutator of the Hamiltonian with the density ...

Abstract. We study an algorithm for the numerical solution of algebraic matrix Riccati equations that arise in linear optimal control problems. The algorithm can be considered to be a multishift technique, which uses only orthogonal symplectic similarity transformations to compute a Lagrangian invariant subspace of the associated Hamiltonian matrix. We describe the details of this method and co...

An algebraic realization of the quantum rotor for non-zero spin values (integer as well as half-integer) is established by constructing a model Hamiltonian out of rotationally invariant functions of the generators of SU(3). The eigenvalues of this Hamiltonian in the leading normal-SU(3) symmetry for 25Mg and the so-called leading pseudo-SU(3) symmetries for 159Dy and 165Er are compared with the...

The Lieb-Robinson theorem states that locality is approximately preserved in the dynamics of quantum lattice systems. Whenever one has finite-dimensional constituents, observables evolving in time under a local Hamiltonian will essentially grow linearly in their support, up to exponentially suppressed corrections. In this work, we formulate Lieb-Robinson bounds for general harmonic systems on g...