The renormalization of the effective QCD-Hamiltonian theory for the quarkantiquark channel is performed in terms of a renormalized or fixed-point Hamiltonian that leads to subtracted dynamical equations. The fixed pointHamiltonian brings the renormalization conditions as well as the counterterms that render the theory finite. The approach is renormalization group invariant. The parameters of th...

In this paper, non-Hamiltonian systems with holonomic constraints are treated by a generalization of Dirac's formalism. Non-Hamiltonian phase space flows can be described by generalized antisymmetric brackets or by general Liouville operators which cannot be derived from brackets. Both situations are treated. In the first case, a Nosé-Dirac bracket is introduced as an example. In the second one...

In the 70’s, Nekhorochev proved that for an analytic nearly integrable Hamiltonian system, the action variables of the unperturbed Hamiltonian remain nearly constant over an exponentially long time with respect to the size of the perturbation, provided that the unperturbed Hamiltonian satisfies some generic transversality condition known as steepness. Using theorems of real subanalytic geometry...

Irreversible port Hamiltonian systems are a class of pseudo Hamiltonian systems that expresses both the conservation of energy and the irreversible entropy production as a structural property. These systems encompass a large class of irreversible themordynamic systems, such as heat exchangers and chemical reactors, and also multi-energy systems such as coupled mechanicthermodynamic systems. In ...

We consider 2×2–Hamiltonian systems of the form y′(t) = zJH(t)y(t), t ∈ [s−, s+). If a system of this form is in the limit point case, an analytic function is associated with it, namely its Titchmarsh–Weyl coefficient qH . The (global) uniqueness theorem due to L. de Branges says that the Hamiltonian H is (up to reparameterization) uniquely determined by the function qH . In the present paper w...

Control contact systems represent controlled (or open) irreversible processes which allow to represent simultaneously the energy conservation and the irreversible creation of entropy. Such systems systematically arise in models established in Chemical Engineering. The differential-geometric of these systems is a contact form in the same manner as the symplectic 2-form is associated to Hamiltoni...

Control contact systems represent controlled (or open) irreversible processes which allow to represent simultaneously the energy conservation and the irreversible creation of entropy. Such systems systematically arise in models established in Chemical Engineering. The differential-geometric of these systems is a contact form in the same manner as the symplectic 2-form is associated to Hamiltoni...

  The traveling salesman problem is a well-known and important combinatorial optimization problem. The goal of this problem is to find the shortest Hamiltonian path that visits each city in a given list exactly once and then returns to the starting city. In this paper, for the first time, the shortest Hamiltonian path is achieved for 1071 Iranian cities. For solving this large-scale problem, tw...

In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...

Many papers on the fully connected cubic networks have been published for the past several years due to its favorite properties. In this paper, we consider the fault-tolerant hamiltonian connectivity and fault-tolerant hamiltonicity of the fully connected cubic network. We use FCCNn to denote the fully connected cubic network of level n. Let G = (V, E) be a graph. The fault-tolerant hamiltonian...