In this paper, we study limit cycle bifurcations for planar piecewise smooth near-Hamiltonian systems with nth-order polynomial perturbation. The linear differential two centers formed in ways, one is that a center-fold point at the origin, other origin and another unique center exists. We first explore expression of order Melnikov function. Then by using function method, give estimations numbe...

We say that a spanning eulerian subgraph F ⊂ G is a flower in a graph G if there is a vertex u ∈ V (G) (called the center of F ) such that all vertices of G except u are of the degree exactly 2 in F. A graph G has the flower property if every vertex of G is a center of a flower. Kaneko conjectured that G has the flower property if and only if G is hamiltonian. In the present paper we prove this...

We analyze standard theoretical models of solar energy conversion developed to study solar cells and photosynthetic systems. We show that assuming the energy transfer to the reaction center/electric circuit is through a decay rate or "sink", contradicts the second law of thermodynamics. We put forward a thermodynamically consistent alternative by explicitly considering parts of the reaction cen...

After a short review of the history and problems of relativistic Hamiltonian mechanics with action-at-a-distance inter-particle potentials, we study isolated two-body systems in the rest-frame instant form of dynamics. We give explicit expressions of the relevant relativistic notions of center of mass, we determine the generators of the Poincare’ group in presence of interactions and we show ho...

We analyze standard theoretical models of solar energy conversion developed to study solar cells and photosynthetic systems. We show that assuming the energy transfer to the reaction center/electric circuit is through a decay rate or “sink”, contradicts the second law of thermodynamics. We put forward a thermodynamically consistent alternative by explicitly considering parts of the reaction cen...

An investigation of the relativistic dynamics of N+1 spin-12 particles placed in an external, homogeneous magnetic field is carried out. The system can represent an atom with a fermion nucleus and N electrons. Quantum electrodynamical interactions, namely, projected Briet and magnetic interactions, are chosen to formulate the relativistic Hamiltonian. The quasi-free-particle picture is retained...

  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...