Monte Carlo simulations are performed to study the two-dimensional Potts models with q = 3 and 4 states on directed Small-World network. The disordered system is simulated applying the Heat bath Monte Carlo update algorithm. A first-order and second-order phase transition is found for q = 3 depending on the rewiring probability p, but for q = 4 the system presents only a first-order phase trans...

In this paper we present a new algorithm for solving the second order cone programming problems which we call the Q method. This algorithm is an extension of the Q method of Alizadeh Haeberly and Overton for the semidefinite programming problem.

In this paper we apply the Homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of Sturm-liouville type on $[0,pi]$ with Neumann conditions $(y'(0)=y'(pi)=0)$ where $q$ is a real-valued Sign-indefinite number of $C^{1}[0,pi]$ and $lambda$ is a real parameter.

In this paper, we combine the notions of completing and avoiding partial latin squares. Let P be a partial latin square of order n and let Q be the set of partial latin squares of order n that avoid P . We say that P is Q -completable if P can be completed to a latin square that avoids Q ∈ Q. We prove that if P has order 4t and contains at most t − 1 entries, then P is Q -completable for each Q...

This work examines the existence of (4q2,2q2 − q, q2 − q) difference sets, for q = p , where p is a prime and f is a positive integer. Suppose that G is a group of order 4q2 which has a normal subgroup K of order q such that G/K ∼= Cq × C2 × C2, where Cq,C2 are the cyclic groups of order q and 2 respectively. Under the assumption that p is greater than or equal to 5, this work shows that G does...