Cluster Synchronization in a Complex Dynamical Network with Two Nonidentical Clusters

This paper further investigates cluster synchronization in a complex dynamical network with two-cluster. Each cluster contains a number of identical dynamical systems, however, the subsystems composing the two clusters can be different, i.e., the individual dynamical system in one cluster can differ from that in the other cluster. Complete synchronization within each cluster is possible only if each node from one cluster receives the same input from nodes in other cluster. In this case, the stability condition of one-cluster synchronization is known to contain two terms： the first accounts for the contribution of the inner-cluster coupling structure while the second is simply an extra linear term, which can be deduced by the ＂same-input＂ condition. Applying the connection graph stability method, the authors obtain an upper bound of input strength for one cluster if the first account is known, by which the synchronizability of cluster can be scaled. For different clusters, there are different upper bound of input strength by virtue of different dynamics and the corresponding cluster structure. Moreover, two illustrative examples are presented and the numerical simulations coincide with the theoretical analysis.     

Coordinating production and recycling decisions with stochastic demand and return

In this paper, the joint production and recycling problem is investigated for a hybrid manufacturing and remanufacturing system where brand-new products are produced in the manufacturing plant and recycled products are remanufactured into as-new products in the remanufacturing facility. Both the brand-new products and remanufactured products are used to satisfy customer demands. Returns of used products that are recycled from customers are assumed to be stochastic and nonlinearly price-dependent. A mathematical model is proposed to maximize the overall profit of the system through simultaneously optimizing the production and recycling decisions, subject to two capacity constraints — the manufacturing capacity and the remanufacturing capacity. Based on Lagrangian relaxation method, subgradient algorithm and heuristic algorithm, a solution approach is developed to solve the problem. A representative example is presented to illustrate the system, and managerial analysis indicates that the uncertainties in demand and return have much influence on the production and recycling policy. In addition, twenty randomly produced examples are solved, and computational results show that the solution approach can obtain very good solutions for all examples in reasonable time.     

Coordinating pricing and inventory decisions in a bounded production system with uncertain yield

Most inventory researches assume that production level can fluctuate arbitrarily. However, large fluctuation of the production level in many firms may be much costly. This paper addresses the coordinating pricing and inventory control problem in a bounded production system with uncertain yield, in which the production level is constrained between a maximum and minimum level in each period and the price can be adjusted dynamically. We show that the optimal policy is the interval base-stock-list-price policy. Also, we study the impact of the production bounds and uncertainty of the yield on the production system. Numerical experiments are also performed to study the impact of parameters on the system.     

The M/PH/1 queue with working vacations and vacation interruption

We study an M/PH/1 queue with phase type working vacation and vacation interruption where the vacation time follows a phase type distribution. The server serves the customers at a lower rate in a vacation period. The server comes back to the regular busy period at a service completion without completing the vacation. Such policy is called vacation interruption. In terms of quasi birth and death process and matrix-geometric solution method, we obtain the stationary queue length distribution. Moreover we obtain the conditional stochastic decomposition structures of queue length and waiting time when the service time distribution in the regular busy period is exponential.     

Two-scale finite element Green’s function approximations with applications to electrostatic potential computation

<正> In this paper,a two-scale finite element approach is proposed and analyzed for approximationsof Green's function in three-dimensions.This approach is based on a two-scale finite elementspace defined,respectively,on the whole domain with size H and on some subdomain containing singularpoints with size h (h H).It is shown that this two-scale discretization approach is very efficient.In particular,the two-scale discretization approach is applied to solve Poisson-Boltzmann equationssuccessfully.     

Removable ears of 1-extendable graphs

<正> Carvalho,Lucchesi and Murty proved that any 1-extendable graph G different from K_2and C_(2n)has at least Δ(G)edge-disjoint removable ears,and any brick G distinct from K_4 and■hasat least Δ(G)-2 removable edges,where Δ(G)denotes the maximum degree of G.In this paper,weimprove the lower bounds for numbers of removable ears and removable edges of 1-extendable graphs.It is proved that any 1-extendable graph G different from K_2 and C_(2n)has at least χ′(G)edge-disjointremovable ears,and any brick G distinct from K_4 and■has at least χ′(G)-2 removable edges,whereχ′(G)denotes the edge-chromatic number of G.     

Multilevel Innovation in Remote Networked Schools

Small remote rural schools in Quebec face an ongoing challenge to provide similar quality educational services than bigger schools. Since 2002, the Remote Network Schools (RNS) initiative afforded schools the opportunity to reinvent their practice by using online tools to experience collaborative learning activities with other remote schools. Teachers and students experienced quality learning and demonstrated agency by implementing the RNS in their context. Measures include: diversity of learning activities, quality of online classroom interactions, changes in teacher beliefs, and shifts in teacher and student roles. Our results show that it is a viable operating method for such schools and that other schools could contemplate implementing such innovative practices.     

Nonlinear Langevin model with product stochasticity for biological networks: The case of the Schnakenberg model

Langevin equation is widely used to study the stochastic effects in molecular networks, as it often approximates well the underlying chemical master equation. However, frequently it is not clear when such an approximation is applicable and when it breaks down. This paper studies the simple Schnakenberg model consisting of three reversible reactions and two molecular species whose concentrations vary. To reduce the residual errors from the conventional formulation of the Langevin equation, the authors propose to explicitly model the effective coupling between macroscopic concentrations of different molecular species. The results show that this formulation is effective in correcting residual errors from the original uncoupled Langevin equation and can approximate the underlying chemical master equation very accurately.     

Optimal control of multisolution ordinary differential equations in the absence of convexity

<正> In this paper,the authors study an optimal control problem governed by a class of multistateordinary differential equations in the absence of convexity.To overcome the difficulty that thecorresponding approximate optimal control problem may have no solution,relaxed controls are introduced.With the help of relaxation theory,Pontryagin's maximum principle for the optimal pairs ofthe original control problem is obtained.In the end of this paper,the authors discuss the applicationof the maximum principle by an example.     

Interior penalty bilinear IFE discontinuous Galerkin methods for elliptic equations with discontinuous coefficient

<正> This paper applies bilinear immersed finite elements (IFEs) in the interior penalty discontinuousGalerkin (DG) methods for solving a second order elliptic equation with discontinuous coefficient.A discontinuous bilinear IFE space is constructed and applied to both the symmetric and nonsymmetricinterior penalty DG formulations.The new methods can solve an interface problem on a Cartesianmesh independent of the interface with local refinement at any locations needed even if the interfacehas a nontrivial geometry.Numerical examples are provided to show features of these methods.