Gas diffusion in a cylindrical coal sample – A general solution,approximation and error analyses

The analytical mathematical solutions of gas concentration and fractional gas loss for the diffusion of gas in a cylindrical coal sample were given with detailed mathematical derivations by assuming that the diffusion of gas through the coal matrix is concentration gradient-driven and obeys the Fick’s Second Law of Diffusion.The analytical solutions were approximated in case of small values of time and the error analyses associated with the approximation were also undertaken.The results indicate that the square root relationship of gas release in the early stage of desorption,which is widely used to provide a simple and fast estimation of the lost gas,is the first term of the approximation,and care must be taken in using the square root relationship as a significant error might be introduced with increase in the lost time and decrease in effective diameter of a cylindrical coal sample.

APPROXIMATE SAMPLING THEOREM FOR BIVARIATE CONTINUOUS FUNCTION

An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution . The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation , a piece-wise linear function , and posseses an explicit computation formula . Therefore the mask of the refinement equation is selected according to one' s requirement, so that one may controll the decay speed of the approximate sampling function .

Flight Schedule Recovery under Uncertain Airport Capacity

Airlines adjust their flight schedules to satisfy more stringent airport capacity constraints caused by inclement weather or other unexpected disruptions.The problem will be more important and complicated if uncertain disruptions occur in hub airports.A two-stage stochastic programming model was established to deal with the realtime flight schedule recovery and passenger re-accommodation problem.The first-stage model represents the flight re-timing and re-fleeting decision in current time period when capacity information is deterministic,while the second-stage recourse model evaluates the passenger delay given the first-stage solutions when one future scenario is realized.Aiming at the large size of the problem and requirement for quick response,an algorithmic framework combining the sample average approximation and heuristic method was proposed.The computational results indicated of that the proposed method could obtain solutions with around 5% optimal gaps,and the computing time was linearly positive to the sample size.

Nonuniform sampling and approximation in Sobolev space from perturbation of the framelet system

The Sobolev space H^(■)(R^(d)),where■>d/2,is an important function space that has many applications in various areas of research.Attributed to the inertia of a measurement instrument,it is desirable in sampling theory to recover a function by its nonuniform sampling.In the present paper,based on dual framelet systems for the Sobolev space pair(H^(s)(R^(d)),H^(-s)(R^(d))),where d/2<s<■,we investigate the problem of constructing the approximations to all the functions in H^(■)(R^(d))by nonuniform sampling.We first establish the convergence rate of the framelet series in(H^(s)(R^(d)),H^(-s)(R^(d))),and then construct the framelet approximation operator that acts on the entire space H^(■)(R^(d)).We examine the stability property for the framelet approximation operator with respect to the perturbations of shift parameters,and obtain an estimate bound for the perturbation error.Our result shows that under the condition d/2<s<■,the approximation operator is robust to shift perturbations.Motivated by Hamm(2015)’s work on nonuniform sampling and approximation in the Sobolev space,we do not require the perturbation sequence to be in■^(α)(Z^(d)).Our results allow us to establish the approximation for every function in H^(■)(R^(d))by nonuniform sampling.In particular,the approximation error is robust to the jittering of the samples.

A Projection and Contraction Method for P-Order Cone Constraint Stochastic Variational Inequality Problem

In this paper, we study the p-order cone constraint stochastic variational inequality problem. We first take the sample average approximation method to deal with the expectation and gain an approximation problem, further the rationality is given. When the underlying function is Lipschitz continuous, we acquire a projection and contraction algorithm to solve the approximation problem. In the end, the method is applied to some numerical experiments and the effectiveness of the algorithm is verified.

SAMPLE AVERAGE APPROXIMATION METHOD FOR A CLASS OF STOCHASTIC VARIATIONAL INEQUALITY PROBLEMS

This paper considers a class of stochastic variational inequality problems. As proposed by Jiang and Xu （2008）, by using the so-called regularized gap function, the authors formulate the problems as constrained optimization problems and then propose a sample average approximation method for solving the problems. Under some moderate conditions, the authors investigate the limiting behavior of the optimal values and the optimal solutions of the approximation problems. Finally, some numerical results are reported to show efficiency of the proposed method.

A case study on sample average approximation method for stochastic supply chain network design problem

This study aims to solve a typical long-term strategic decision problem on supply chain network design with consideration to uncertain demands. Existing methods for these problems are either deterministic or limited in scale. We analyze the impact of uncertainty on demand based on actual large data from industrial companies.Deterministic equivalent model with nonanticipativity constraints, branch-and-fix coordination, sample average approximation(SAA) with Bayesian bootstrap, and Latin hypercube sampling were adopted to analyze stochastic demands. A computational study of supply chain network with front-ends in Europe and back-ends in Asia is presented to highlight the importance of stochastic factors in these problems and the efficiency of our proposed solution approach.

A novel cooperative mid-course guidance scheme for multiple intercepting missiles

In the interception engagement,if the target movement information is not accurate enough for the mid-course guidance of intercepting missiles,the interception mission may fail as a result of large handover errors.This paper proposes a novel cooperative mid-course guidance scheme for multiple missiles to intercept a target under the condition of large detection errors.Under this scheme,the launch and interception moments are staggered for different missiles.The earlier launched missiles can obtain a relatively accurate detection to the target during their terminal guidance,based on which the latter missiles are permitted to eliminate the handover error in the mid-course guidance.A significant merit of this scheme is that the available resources are fully exploited and less missiles are needed to achieve the interception mission.To this end,first,the design of cooperative handover parameters is formulated as an optimization problem.Then,an algorithm based on Monte Carlo sampling and stochastic approximation is proposed to solve this optimization problem,and the convergence of the algorithm is proved as well.Finally,simulation experiments are carried out to validate the effectiveness of the proposed cooperative scheme and algorithm.

A two-stage skilled manpower planning model with demand uncertainty

Purpose-Human resources are one of the most important and effective elements for companies.In other words,employees are a competitive advantage.This issue is more vital in the supply chains and production systems,because of high need for manpower in the different specification.Therefore,manpower planning is an important,essential and complex task.The purpose of this paper is to present a manpower planning model for production departments.The authors consider workforce with individual and hierarchical skills with skill substitution in the planning.Assuming workforce demand as a factor of uncertainty,a two-stage stochastic model is proposed.Design/methodology/approach–To solve the proposed mixed-integer model in the real-world cases and large-scale problems,a Benders’decomposition algorithm is introduced.Some test instances are solved,with scenarios generated by Monte Carlo method.For some test instances,to find the number of suitable scenarios,the authors use the sample average approximation method and to generate scenarios,the authors use Latin hypercube sampling method.Findings–The results show a reasonable performance in terms of both quality and solution time.Finally,the paper concludes with some analysis of the results and suggestions for further research.Originality/value–Researchers have attracted to other uncertainty factors such as costs and products demand in the literature,and have little attention to workforce demand as an uncertainty factor.Furthermore,most of the time,researchers assume that there is no difference between the education level and skill,while they are not necessarily equivalent.Hence,this paper enters these elements into decision making.