A heuristic procedure for the Capacitated m-Ring-Star problem

In this paper we propose a heuristic method to solve the Capacitated m-Ring-Star Problem which has many practical applications in communication networks. The problem consists of finding m rings (simple cycles) visiting a central depot, a subset of customers and a subset of potential (Steiner) nodes, while customers not belonging to any ring must be “allocated” to a visited (customer or Steiner) node. Moreover, the rings must be node-disjoint and the number of customers allocated or visited in a ring cannot be greater than the capacity Q given as an input parameter. The objective is to minimize the total visiting and allocation costs. The problem is a generalization of the Traveling Salesman Problem, hence it is NP-hard. In the proposed heuristic, after the construction phase, a series of different local search procedures are applied iteratively. This method incorporates some random aspects by perturbing the current solution through a “shaking” procedure which is applied whenever the algorithm remains in a local optimum for a given number of iterations. Computational experiments on the benchmark instances of the literature show that the proposed heuristic is able to obtain, within a short computing time, most of the optimal solutions and can improve some of the best known results.     

Effect of partial immunity on transmission dynamics of dengue disease with optimal control

Dengue fever is one of the most dangerous vector‐borne diseases in the world in terms of death and economic cost. Hence, the modeling of dengue fever is of great significance to understand the dynamics of dengue. In this paper, we extend dengue disease transmission models by including transmit vaccinated class, in which a portion of recovered individual loses immunity and moves to the susceptibles with limited immunity and hence a less transmission probability. We obtain the threshold dynamics governed by the basic reproduction number R₀; it is shown that the disease‐free equilibrium is locally asymptotically stable if R₀ ≤ 1, and the system is uniformly persistence if R₀ > 1. We do sensitivity analysis in order to identify the key factors that greatly affect the dengue infection, and the partial rank correlation coefficient (PRCC) values for R₀ shows that the bitting rate is the most effective in lowering dengue new infections, and moreover, control of mosquito size plays an essential role in reducing equilibrium level of dengue infection. Hence, the public are highly suggested to control population size of mosquitoes and to use mosquito nets. By formulating the control objective, associated with the low infection and costs, we propose an optimal control question. By the application of optimal control theory, we analyze the existence of optimal control and obtain necessary conditions for optimal controls. Numerical simulations are carried out to show the effectiveness of control strategies; these simulations recommended that control measures such as protection from mosquito bites and mosquito eradication strategies effectively control and eradicate the dengue infections during the whole epidemic.     

Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces

Let (X,?) be a partially ordered set and d be a complete metric on X. Let F,G be two set-valued mappings on X. We obtained sufficient conditions for the existence of common fixed point of F and G satisfying an implicit relation in partially ordered set X.     

Cyclicity of the adjoint of weighted composition operators on the hilbert space of analytic functions

In this paper, we discuss the hypercyclicity, supercyclicity and cyclicity of the adjoint of a weighted composition operator on a Hilbert space of analytic functions.     

Metrically Regular Mapping and Its Utilization to Convergence Analysis of a Restricted Inexact Newton-Type Method

In the present paper,we study the restricted inexact Newton-type method for solving the generalized equation 0∈f(x)+F(x),where X and Y are Banach spaces,f:X→Y is a Frechet differentiable function and F:X■Y is a set-valued mapping with closed graph.We establish the convergence criteria of the restricted inexact Newton-type method,which guarantees the existence of any sequence generated by this method and show this generated sequence is convergent linearly and quadratically according to the particular assumptions on the Frechet derivative of f.Indeed,we obtain semilocal and local convergence results of restricted inexact Newton-type method for solving the above generalized equation when the Frechet derivative of f is continuous and Lipschitz continuous as well as f+F is metrically regular.An application of this method to variational inequality is given.In addition,a numerical experiment is given which illustrates the theoretical result.     

On the index of powers of edge ideals

The index of a graded ideal measures the number of linear steps in the graded minimal free resolution of the ideal. In this paper, we study the index of powers and squarefree powers of edge ideals. Our results indicate that the index as a function of the power of an edge ideal I is strictly increasing if I is linearly presented. Examples show that this needs not to be the case for monomial ideals generated in degree greater than two.     

A modified pseudospectral method for solving trajectory optimization problems with singular arc

This paper presents a direct method based on Legendre–Radau pseudospectral method for efficient and accurate solution of a class of singular optimal control problems. In this scheme, based on a priori knowledge of control, the problem is transformed to a multidomain formulation, in which the switching points appear as unknown parameters. Then, by utilizing Legendre‐Radau pseudospectral method, a nonlinear programming problem is derived which can be solved by the well‐developed parameter optimization algorithms. The main advantages of the present method are its superior accuracy and ability to capture the switching times. Accuracy and performance of the proposed method are examined by means of some numerical experiments. Copyright © 2016 John Wiley & Sons, Ltd.     

Improved equation of state for ionic liquids using surface tension

The major objective of this work was the development of a reliable model to describe volumetric properties of ionic liquids (ILs). In this regard, we have applied the Ihm–Song–Mason equation of state (EOS) to some phosphonium- and imidazolium-based ILs. Three temperature-dependent parameters in the equation of state have been scaled based on the surface tension and the liquid density at room temperature. In order to improve the predictive power of the mentioned EOS for ILs, we have proposed using a simple modification. We have taken 1,228 experimental points to show the reliability of the improved EOS. The comparison of predicted densities with literature data over a broad range of temperature, 293–472 K, and pressures up to 200 MPa led to encouraging results. The average absolute deviation of calculated densities from literature values was found to be 0.75%.