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Membrane Technology
December 2013
Editorial Board
Publication date: December 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 11–12

December 2013
Valedictory Editorial
Publication date: December 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 11–12 Author(s): Philip Broadbridge
December 2013
A fuzzy logic based decision support system for evaluation of suppliers in supply chain management practices
Publication date: December 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 11–12 Author(s): Darshan Kumar, Jagdev Singh, Om Pal Singh, Seema Supply chain management is an increasingly important organizational concern, and proper evaluation of suppliers constitutes one essential element of supply chain success. Continuous evaluation of a particular supplier becomes more important considering the fact that in most industries the cost of raw materials and component parts constitutes the main cost of a product, such that in some cases it can account for up to 70%. However, there is little research that has helped the organizations in continuous evaluation of their suppliers. We propose a new model, based on fuzzy logic to handle the various attributes, associated with supplier evaluation problems. Four multi-input single output (MISO) mamdani fuzzy inference systems have been proposed for supplier evaluation. The proposed model has also been illustrated through a case study.
December 2013
Numerical solution of a nonlinear singular Volterra integral system by the Newton product integration method
Publication date: December 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 11–12 Author(s): B. Babayar-Razlighi, B. Soltanalizadeh In this paper, we consider a nonlinear system of Volterra integral equations, and apply Newton’s method to linearize it. We solve each step of Newton’s system by the product integration technique. Also, we provide the sufficient conditions for convergence of the numerical method. Finally, we give a test problem to illustrate the applicability and accuracy of the presented method.
December 2013
HAM and DQM solutions for slip flow over a flat plate in the presence of constant heat flux
Publication date: December 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 11–12 Author(s): M.A. Moghimi, H. Tabaei, A. Kimiaeifar In this paper, an analytical solution for boundary layer flow over a flat plate with slip flow and constant heat flux surface condition has been presented for the first time. The Navier–Stokes and energy equations are reduced by a similarity transform in order for a set of nonlinear ordinary differential equations to be formed. Then, governing equations will be solved analytically by using a kind of analytic technique for nonlinear problems which has been named the homotopy analysis method (HAM). The obtained results of this study have been compared with the results of differential quadrature method (DQM) as a promising numerical method. Very good agreement has been shown between analytical results and those obtained by DQ. Finally, effects of the Prandtl number and rarefaction parameter K on velocity and temperature profiles are investigated.
December 2013
Analytical mathematical feedback guidance scheme for low-thrust orbital plane change maneuvers
Publication date: December 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 11–12 Author(s): I. Shafieenejad, A.B. Novinzade, R. Shisheie This paper which is based on neighboring optimal control investigates the application of an analytical feedback guidance scheme for the problems of low-thrust orbital transfer. Neighboring optimal control is one of the methods that has been proposed for the closed-loop optimal guidance. This method focuses on expanding the cost function to second order and examining the robustness of the system by the feedback law gains. At first, the open-loop analytical guidance policy is considered as the optimal thrust steering program that will transfer the vehicle from the inclined low earth orbits to the high earth orbits. Secondly, proper feedback optimal guidance laws are analytically obtained to maintain the trajectories around their optimum with assessed disturbances. The proposed guidance scheme is distinguished for two desired performance indices as minimum-time and minimum-effort. Finally performance indices are compared and the best policy is obtained regarding the robustness of the two performance indices against disturbances.
December 2013
A multiresolution and smooth fictitious domain method for one-dimensional elliptical and Stefan problems
Publication date: December 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 11–12 Author(s): Ping Yin, Jacques Liandrat, Wanqiang Shen, Zhe Chen We present a wavelet based multiresolution method coupled with smooth fictitious domain and wavelet–vaguelette method to solve the one-dimensional elliptic problem equipped with Dirichlet boundary condition. Its advantages over the classical fictitious domain method are analyzed by interior error estimate and numerical examples. The efficiency of our method is pointed out by considering a Stefan problem with exact solution in one dimension.
December 2013
A finite iterative algorithm for the solution of Sylvester-conjugate matrix equations AV+BW=EV
December 2013
Multi-dimensional complex-valued Gabor wavelet networks
Publication date: December 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 11–12 Author(s): K.L. Mak, P. Peng, K.F.C. Yiu, L.K. Li This paper proposes a new complex-valued wavelet network based on Gabor transfer functions which have complex-valued weights, input/output variables and translation parameters. A learning algorithm is developed by using the technique of genetic algorithm to facilitate implementation of the network. The effectiveness of the proposed network is evaluated by applying the network to approximate several complicated nonlinear functions, and to tackle the 4-QAM (quadrature amplitude modulation) digital communications channel equalization and the image enhancement via feature extraction problems in signal processing. Indeed, the evaluation results obtained by testing the proposed wavelet network with real facial and textile fabric images clearly show that it is a very useful tool for solving problems in the field of complex-valued signal analysis.
December 2013
Solutions for a boundary value problem at resonance on [0,
December 2013
Applications of Opial inequalities on time scales on dynamic equations with damping terms
Publication date: December 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 11–12 Author(s): S.H. Saker In this paper, we will employ some dynamic inequalities of Opial’s type on time scales to prove several results related to the spacing between consecutive zeros of a solution of a second order dynamic equation with a damping term. We also obtain several results related to the spacing between a zero of the solution and/or a zero of its derivative. As a special case, we will establish some new results for differential and difference equations with damping terms. For illustration, we will derive some well-known results obtained for differential equations without damping terms. The results yield conditions for disfocality and disconjugacy for dynamic equations with damping terms on time scales.
December 2013
Airline network design and adjustment in response to fluctuation in jet fuel prices
Publication date: December 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 11–12 Author(s): Chaug-Ing Hsu, Wei-Yin Eie This study develops a series of models to determine aircraft types and flight frequencies on individual routes, and evaluate the reliability of proposed network planning during fluctuations in jet fuel prices. The reliability of individual routes is evaluated as to whether revenues from flights with initially proposed flight frequencies and aircraft types can accommodate variations in jet fuel expenditures. We define reliability as the probability that the proposed flight frequencies will operate in at least a break-even condition under future fuel price fluctuations. A case study is provided using an international airline in Taiwan to evaluate its network reliability in response to jet fuel price fluctuations in 2008. The results indicate that not only do routes with low load factors show low reliability, but long distance routes with high load factors also show low reliability during periods with high fuel prices. The results of the study provide effective ways to enhance commercial airline network designs in response to the uncertainty of jet fuel prices.
December 2013
A bi-objective stochastic optimization model for reliable warehouse network redesign
Publication date: December 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 11–12 Author(s): Jafar Razmi, AmirHossien Zahedi-Anaraki, MohammadSaleh Zakerinia This paper proposes a developed bi-objective two-stage stochastic mixed-integer linear programming model for redesigning a reliable warehouse network. In this model, the warehouses capacity which should be phased out, remained, or relocated to other warehouses, and the shipment quantity of the product between the network nodes with a consideration for two delivery lead times is to be determined. Unlike most previous works, considering two delivery lead times, the maximum capacity for each warehouse location, reliability and uncertainty are taken into account in this study. The proposed bi-objective model includes: (1) minimizing average costs including the sum of fixed, production, transportation, relocation and capacity extension costs; (2) maximizing the coverage percentage of customer demand delivered within the preferred delivery lead time. In order to obtain Pareto optimal solutions, a novel version of
December 2013
Viscosity approximation methods based on generalized contraction mappings for a countable family of strict pseudo-contractions, a general system of variational inequalities and a generalized mixed equilibrium problem in Banach spaces
Publication date: December 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 11–12 Author(s): Pongsakorn Sunthrayuth, Poom Kumam In this paper, we introduce viscosity approximation methods based on generalized contraction mappings for finding a set of common fixed points of a countable family of strict pseudo-contraction mappings, the common element of the set solutions of a general system of variational inequalities with Lipschitzian and relaxed cocoercive mappings and the set of solutions of a generalized mixed equilibrium problem. Furthermore, strong convergence theorems of the purposed iterative process are established in the framework of Banach spaces. The results presented in this paper improve and extend many recent important results.
December 2013
Study of Malus Asiatica Nakai’s firmness during different shelf lives based on visible/near-infrared spectroscopy
Publication date: December 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 11–12 Author(s): Jianxin Xue, Shujuan Zhang, Haixia Sun, Jingbo Zhou The feasibility of applying rapid and non-destructive analysis based on Visible/ Near-Infrared Spectroscopy (VIS/NIR spectrometer) in detecting Malus Asiatica Nakai’s firmness during different shelf lives was discussed in this manuscript. Based on the best preprocessing technique found for each method, calibration models established by Partial Least-Square (PLS), Principal Component Regression (PCR), and Least Squares-Support Vector Machine (LS-SVM) were compared. The optimal models for firmness of Malus Asiatica Nakai were obtained by PLS with SNV as the best pretreatment. On the 1st day of shelf life, the correlation coefficients of prediction (Rp) and the Root-Mean-Square Errors of Prediction (RMSEP) were 0.7999 and 0.7994, respectively. On the 4th day of shelf life, the indexes were 0.7494 and 0.5856. But with the extension of shelf life, weightlessness rate of Malus Asiatica Nakai was reduced, the mealiness phenomenon became serious, quality had dropped sharply, hence the research of Malus Asiatica Nakai became insignificant. Results showed that, the potential of non-destructive measure for predicting accepted fruit parameters enabled the determination of optimum harvest date and fruit quality in different shelf lives.
December 2013
Application of the optimal homotopy asymptotic method for solving a strongly nonlinear oscillatory system
Publication date: December 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 11–12 Author(s): A. Golbabai, M. Fardi, K. Sayevand In this paper, the optimal homotopy asymptotic method (OHAM) and the traditional homotopy analysis method (HAM) are used to obtain analytical solution for a strongly nonlinear oscillation. Moreover, the homotopy-pade technique is employed to accelerate the convergence of solution series of traditional HAM. Results show that the second-order approximation by the OHAM is quick convergence and more accurate than the high-order of approximation by the homotopy-pade technique.
December 2013
WITHDRAWN: A robust control strategy for a direct drive valve based on a voice coil motor
Publication date: December 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 11–12 Author(s): Baifen Liu, Ying Gao This article has been withdrawn at the request of the author(s) and/or editor. The Publisher apologizes for any inconvenience this may cause. The full Elsevier Policy on Article Withdrawal can be found at http://www.elsevier.com/locate/withdrawalpolicy.
December 2013
WITHDRAWN: Risk analysis and damage assessment of financial institutions in cyber attacks between nations
Publication date: December 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 11–12 Author(s): Won Hyung Park This article has been withdrawn at the request of the author(s) and/or editor. The Publisher apologizes for any inconvenience this may cause. The full Elsevier Policy on Article Withdrawal can be found at http://www.elsevier.com/locate/withdrawalpolicy.
November 2013
WITHDRAWN: A study on the influences of R&D investment on IT for the machine and material industry and the electronics industry
Publication date: December 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 11–12 Author(s): Seung-Ryung Oh, Kun Woo Kim This article has been withdrawn at the request of the author(s) and/or editor. The Publisher apologizes for any inconvenience this may cause. The full Elsevier Policy on Article Withdrawal can be found at http://www.elsevier.com/locate/withdrawalpolicy.
November 2013
Editorial Board
Publication date: November 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 9–10

November 2013
Computational simulation and risk analysis: An introduction of state of the art research
Publication date: November 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 9–10 Author(s): Desheng Dash Wu, David L. Olson In recent years, risk management and analysis has attracted a great deal of attention from both researchers and practitioners. Enterprise risk management has become an important topic in today’s more complex, interrelated global business environment, replete with threats from natural, political, economic, and technical sources. This survey and introductory article addresses computerized tools used for risk management and analysis. Risks are studied from perspectives of different disciplines, with a discussion of how various methods and tools are used to optimize risk management.
November 2013
Simultaneous quantitative determination of Amlodipine and Atorvastatin in tablets using artificial neural networks
Publication date: November 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 9–10 Author(s): Mahmoud Reza Sohrabi, Parviz Abdolmaleki, Maryam Dehroudi Simultaneous spectrophotometric estimation of Atorvastatin Calcium and Amlodipine Besylate in Amostatine®  tablets were performed using UV–Vis spectroscopic and Artificial Neural Networks (ANN). Absorption spectra of two components were recorded in 200–350 (nm) wavelengths region with an interval of 4 nm. The calibration models were thoroughly evaluated at several concentration levels using the spectra of synthetic binary mixture (prepared using orthogonal design). Three layers feed-forward neural networks using the back-propagation algorithm (B.P) has been employed for building and testing models. Several parameters such as the number of neurons in the hidden layer, learning rate and the number of epochs were optimized. A general statistic function, Sum Square Error (SSE), was selected to evaluate the training process of ANN. The single Relative Standard Error (RSE) (%) of prediction for each component in real sample was calculated as 0.62 and 2.00 for Atorvastatin and Amlodipine, respectively. The results showed a very good agreement between true values and predicted concentration values. The proposed procedure is a simple, precise and convenient method for the determination of Atorvastatin and Amlodipine in commercial tablets.
November 2013
Optimal inventory policy with fixed and proportional transaction costs under a risk constraint
Publication date: November 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 9–10 Author(s): S.Y. Wang, K.F.C. Yiu, K.L. Mak The traditional inventory models focus on characterizing replenishment policies in order to maximize the total expected profit or to minimize the expected total cost over a planned horizon. However, for many companies, total inventory costs could be accounting for a fairly large amount of invested capital. In particular, raw material inventories should be viewed as a type of invested asset for a manufacturer with suitable risk control. This paper is intended to provide this perspective on inventory management that treats inventory problems within a wider context of financial risk management. In view of this, the optimal inventory problem under a VaR constraint is studied. The financial portfolio theory has been used to model the dynamics of inventories. A diverse portfolio consists of raw material inventories, which involve market risk because of price fluctuations as well as a risk-free bank account. The value-at-risk measure is applied thereto to control the inventory portfolio’s risk. The objective function is to maximize the utility of total portfolio value. In this model, the ordering cost is assumed to be fixed and the selling cost is proportional to the value. The inventory control problem is thus formulated as a continuous stochastic optimal control problem with fixed and proportional transaction costs under a continuous value-at-risk (VaR) constraint. The optimal inventory policies are derived by using stochastic optimal control theory and the optimal inventory level is reviewed and adjusted continuously. A numerical algorithm is proposed and the results illustrate how the raw material price, inventory level and VaR constraint are interrelated.
November 2013
Optimal investment with a corporate bond
Publication date: November 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 9–10 Author(s): Shibo Bian, Hailong Liu The present paper analyzes the optimal investment strategy in a corporate (defaultable) bond, a stock and a bank account in a continuous time model. We model the corporate bond price through a reduced-form approach and solve the dynamics of its price. The optimal investment process will be worked out first with a general risk-averse utility function, and then an optimal strategy with CARA utility will be presented using martingale methods. The optimal investment strategy is analyzed numerically for the CARA utility.
November 2013
Several consensus protocols with memory of multi-agent systems
Publication date: November 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 9–10 Author(s): Xin-Lei Feng, Ting-Zhu Huang, Jin-Liang Shao Financial risk management has focused on banking, accounting, and finance, and applied all kinds types of models to avoid those specific forms of risk. Risk management may be dealt with using the model of multi-agent systems. In this paper, we consider single-integrator kinematics and double-order-integrator dynamics consensus protocols. These consensus protocols with memory are presented by introducing the last state information (such as position, velocity) of the multi-agent. The numerical results show that these protocols have higher convergence speed.
November 2013
Measuring the capital charge for operational risk of a bank with the large deviation approach
Publication date: November 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 9–10 Author(s): Zhaoyang Lu In this paper, the large deviation approach for computing the capital charge for operational risk of a bank is explored. Firstly, the negatively-associated structure is utilized to measure the dependence between distinct operational loss cells. Secondly, the lower and upper bounds of the tail distribution function of total aggregated loss processes are determined. In addition, first order approximations using a value-at-risk measure are derived. Finally, an important example calculating the capital charge for operational risk under the class of a heavy-tailed distribution is provided.
November 2013
Parametric VaR with goodness-of-fit tests based on EDF statistics for extreme returns
Publication date: November 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 9–10 Author(s): Herick Fernando Moralles, Daisy Aparecida do Nascimento Rebelatto, Alexandre Sartoris Parametric VaR (Value-at-Risk) is widely used due to its simplicity and easy calculation. However, the normality assumption, often used in the estimation of the parametric VaR, does not provide satisfactory estimates for risk exposure. Therefore, this study suggests a method for computing the parametric VaR based on goodness-of-fit tests using the empirical distribution function (EDF) for extreme returns, and compares the feasibility of this method for the banking sector in an emerging market and in a developed one. The paper also discusses possible theoretical contributions in related fields like enterprise risk management (ERM).
November 2013
Bargaining in supply chain with price and promotional effort dependent demand
Publication date: November 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 9–10 Author(s): Desheng Dash Wu This paper investigates the bargaining equilibrium behavior of an industry with two competing supply chains. The demand in each supply chain is modeled using the downward-sloping linear function with respect to both price and promotional effort. The optimality is established through Nash bargaining when the two competing manufacturers distribute through two independent competing retailers. We show, when both price and promotional effort dependent demand is present, that both the traditional Manufacturer Stackelberg (MS) and the Vertical Integration (VI) are special cases of our Nash bargaining game. We conclude that both sales promotional service and price dominates bargaining on only one factor. We yield several conclusions about the provision of promotional service level by each supply chain to coordinate the channel.
October 2013
The impact of distribution on value-at-risk measures
Publication date: November 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 9–10 Author(s): David L. Olson, Desheng Wu Value at risk is a popular approach to aid financial risk management. Questions about the appropriateness of the measure have arisen since the related 2008 bubble collapses in some US housing markets and the global financial market. These questions include the presence of fat tails and their impact. This paper compares results based upon assumptions of normality and logistic distributions, comparing portfolios generated with various probabilistic models. Computations are applied to real stock data. Optimization models are described, with simulation models evaluating comparative model performance. Chi-square tests indicated that logistic distribution better fit the data than the normal distribution. The error implied by value-at-risk assumptions is demonstrated through Monte Carlo simulation.
October 2013
Editorial Board
Publication date: October 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 7–8

October 2013
A new multi-symplectic Euler box scheme for the BBM equation
Publication date: October 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 7–8 Author(s): Haochen Li, Jianqiang Sun A new scheme for the BBM equation with the accuracy order of O (
October 2013
Approximate solution of linear differential equations
Publication date: October 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 7–8 Author(s): Nadhem ECHI This paper presents an efficient approach for determining the solution of linear differential equations. The linear ordinary differential equation is first converted to a Volterra integral equation. By solving the resulting Volterra equation by means of Taylor’s expansion, different approaches based on differentiation and integration methods are employed to reduce the resulting integral equation to a system of linear equations for the unknown and its derivatives. The approximate solution of the linear differential equation is thereby obtained. A test example demonstrates the effectiveness of the method and gives the efficiency and high accuracy of the proposed method.
October 2013
Spreading speeds and travelling waves for non-monotone time-delayed 2D lattice systems
Publication date: October 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 7–8 Author(s): Zhi-Xian Yu, Weiguo Zhang, Xiaoming Wang In this paper, a non-monotone time delayed 2D lattice system with global interaction is studied. The important feature of the model is the reflection of the joint effect of the diffusion dynamics, the nonlocal delayed effect and the direction of propagation. The existence of travelling waves for the wave speed c
October 2013
Solution of system of the mixed Volterra–Fredholm integral equations by an analytical method
Publication date: October 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 7–8 Author(s): M. Ghasemi, M. Fardi, R. Khoshsiar Ghaziani In this paper, we present an analytical method to solve systems of the mixed Volterra–Fredholm integral equations (VFIEs) of the second kind. By using the so called
October 2013
A novel identification method for Wiener systems with the limited information
Publication date: October 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 7–8 Author(s): Qibing Jin, Jun Dou, Feng Ding, Liting Cao To solve the problem caused by the lack of the structure of the nonlinearity in Wiener systems identification, we propose a new approach to identify the linear part and the nonlinear part of a Wiener system in sequence by using the limited information on the nonlinearity. The linear part of the system is identified firstly based on the limited information of the nonlinearity, such as sign information, monotonic information and then, we construct the internal signals to identify the structure and the parameters of the Wiener systems. A novel Particle Swarm Optimization–Rosenbrock (PSO–Rosenbrock) algorithm is developed and the numerical simulation shows that the identification procedure proposed in this paper is effective.
October 2013
The parameter sensibility analysis for fishing box tap based on the overall process of elastoplasticity in oil and gas wells
Publication date: October 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 7–8 Author(s): Xiao-Hua Zhu, Yu Wang, Hua Tong In view that the selections of box tap and thread making parameters are still groundless and lack scientific evidence, which has caused many practical engineering problems, such as long fishing cycle and low success rate, this study establishes a mathematical model such that fish is fished by the box tap based on the theory of large deformation and principle of virtual work. The analysis and evaluation methods of the whole elastoplasticity process for tapping and fishing are proposed as well in accordance with Johnson and Cook’s experimental model and separation criterion in our study. In addition, the effects of such factors (drilling pressure, rotation speed, box tap strength, taper and pitch) on the thread making capacity of the box tap and the new thread strength of fish have been systemically analyzed. In the case study, the paper derives the safety rotation speed range of tapping, the optimal box tap tape and parameter combination of fishing, and the maximum allowable lifting power. The results obtained in our study show that the analyzing model and evaluation methods are quite reasonable and can be generally applied, which will be of great significance for the enhancement of fishing efficiency in future industry.
October 2013
Upgraded Petri net model and analysis of adaptive and static arithmetic coding
Publication date: October 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 7–8 Author(s): Perica
October 2013
Stability analysis of switched systems with general nonlinear disturbances
Publication date: October 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 7–8 Author(s): Jiu-Gang Dong This paper studies the stability of switched systems with general nonlinear disturbances. By using generalized Gronwall–Bellman inequalities, we obtain stability results for the systems with arbitrary switching laws. Finally, an example is given to illustrate the effectiveness of the results obtained.
September 2013
Comparative study of different B-spline approaches for functional data
Publication date: October 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 7–8 Author(s): A.M. Aguilera, M.C. Aguilera-Morillo The sample observations of a functional variable are functions that come from the observation of a statistical variable in a continuous argument that in most cases is the time. But in practice, the sample functions are observed in a finite set of points. Then, the first step in functional data analysis is to reconstruct the functional form of sample curves from discrete observations. The sample curves are usually represented in terms of basis functions and the basis coefficients are fitted by interpolation, when data are observed without error, or by least squares approximation, in the other case. The main purpose of this paper is to compare three different approaches for estimating smooth sample curves observed with error in terms of B -spline basis: regression splines (non-penalized least squares approximation), smoothing splines (continuous roughness penalty) and P -splines (discrete roughness penalty). The performance of these spline smoothing approaches is studied via a simulation study and several applications with real data. Cross-validation and generalized cross-validation are adapted to select a common smoothing parameter for all sample curves with the roughness penalty approaches. From the results, it is concluded that both penalized approaches drastically reduced the mean squared errors with respect to the original smooth sample curves with P -splines giving the best approximations with less computational cost.
September 2013
Editorial Board
Publication date: September 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 5–6

September 2013
The measurement of undesirable output based-on DEA in E&E: Models development and empirical analysis
Publication date: September 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 5–6 Author(s): Wendong Lv, Zhixiang Zhou, Hong Huang
September 2013
Resource allocation models’ construction for the reduction of undesirable outputs based on DEA methods
Publication date: September 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 5–6 Author(s): Hong Li, Wei Yang, Zhixiang Zhou, Chengming Huang During the fast developing process of the Chinese economy, China consumes lots of energy and environmental pollution caused by energy consumption currently urgently needs solving. So, paying more attention to energy saving and emission reduction is very important. Therefore, to reasonably allocate resources and reduce emissions in China’s different regions has practical significance. So this paper firstly considers the model construction method for resource allocation considering undesirable outputs between different decision making units based on the DEA framework under the CRS and VRS assumption. We have proposed some resource allocation models as a multiple objective linear problem which considers the input reduction, desirable output reduction and undesirable output reduction. Then, to demonstrate the practical application of the resource allocation model, numerical examples are used to illustrate the approach. In addition, we explore the resource allocation problem of China’s regions in 2006–2010. The empirical results show that the resource allocation models dealing with undesirable outputs have effective configuration results, that is, the reduction proportion for desirable output is smaller than the reduction proportion for undesirable output. From the resource allocation results in China’s regions, we find that the eastern area has more emission reduction than the central and western areas corresponding to the same energy consumption reduction, and the energy and environmental policy should focus more on the central and western areas. All of these conclusions will give some policy recommendations on saving energy and reducing pollution emissions.
September 2013
Environmental efficiency of electric power industry in the Yangtze River Delta
Publication date: September 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 5–6 Author(s): Ye Tao, Shilong Zhang There are 16 cities in the Yangtze River Delta and this region plays a leading role in Chinese economic growth. A great deal of power is needed for the economic growth and social development in the Yangtze River Delta, but the local firms’ production and people’s living are often disturbed by shortages of power. From 2000 to 2010, the power output of the regional electric power industry was accompanied by a large amount of undesirable outputs. Environmental Data Envelopment Analysis (DEA) technology is applied. Two DEA models incorporating undesirable outputs are constructed and used to measure the environmental efficiency of the electric power industry in the Yangtze River Delta from 2000 to 2010. Both constant return of scale and variable return of scale are considered. Some meaningful findings are obtained from the measurement results of the 16 cities and of the whole region.
September 2013
Measuring the environmental efficiency of the Chinese industrial sector: A directional distance function approach
Publication date: September 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 5–6 Author(s): Peng Yuan, Shi Cheng, Jia Sun, Wenbo Liang This paper presents a directional distance function approach to measure two technical efficiencies with respect to the two technologies characterized by strong and weak disposability of pollutants. The environmental efficiency index, defined as the ratio of the two technical efficiencies, reflects the opportunity cost to transform the strong disposability of pollutants into a weak one. The proposed approach is applied to measure the environmental efficiency index of the Chinese industrial sector, with the input and output data of the sector in 284 cities at the prefecture level and above in China from 2003 to 2009, including the emissions of wastewater, sulfur dioxide, and soot. Several factors of environmental efficiency are also investigated by using a panel Tobit model.
September 2013
The convergence test of transformation performance of resource cities in China considering undesirable output
Publication date: September 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 5–6 Author(s): Feng Dong, Ruyin Long, Hong Chen, Xiaohui Li, Xiaoyan Liu The main challenge for sustainable development of resource cities is to work out a feasible strategy for transformation processes. This paper introduces a new approach for analysis of transformation performance. Using the environmental production technology and a Malmquist resource performance index (MRPI), we conduct
September 2013
Analysis of Beijing’s environmental efficiency and related factors using a DEA model that considers undesirable outputs
Publication date: September 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 5–6 Author(s): Xian-Guo Li, Jing Yang, Xue-Jing Liu In this study, the environmental efficiency of Beijing in the past five years is evaluated using a data envelopment analysis (DEA) model that considers undesirable outputs. We analyze the factors that influence the environmental efficiency of Beijing using a two-step method. In the first step, a DEA model is used to assess the environmental efficiency of Beijing. In the second step, the efficiency from the first step is used as a dependent variable and factors that impact the environmental efficiency are used as independent variables. The regression model and the coefficients of the independent variables determine which factors influence the environmental efficiency and the strength of the influence. Finally, we interpret the enlightenment to the reality and the future development based on its results. The conclusion shows that the environmental efficiency of Beijing over 2005–2009 has been rising. From 2005 to 2007, the environmental efficiency of Beijing continued to increase. In 2008, the environmental efficiency reached a maximum. In 2009, Beijing maintained a high environmental efficiency. The proportion of the tertiary industry to the whole industries is the most important factor that impacts Beijing’s environmental efficiency, that is, Beijing’s industrial structure has the most influence on the city’s environmental efficiency.
September 2013
Transverse and longitudinal analysis of the environmental efficiency of Chinese industries
Publication date: September 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 5–6 Author(s): Hongqi Wang, Xueyuan Wang, Yuqi Wang In this paper, the environmental efficiencies of 39 industrial sectors are measured using a non-radical, non-oriented slacks-based measure (SBM) model that considers the environmental impact of each industry. The economic efficiency of each industrial sector is measured using traditional data envelope analysis (DEA) methods and the differences between environmental efficiency and economic efficiency are analyzed using the transverse analysis method. A total of 39 industrial sectors are examined within three main industrial sectors (mining, manufacturing, and supply). Using the longitudinal analysis method, the environmental efficiencies of the three main industrial sectors from 2002 to 2009 are analyzed using the average value of their sub-industries’ environmental efficiencies. The time regression equation of the three industrial fields’ environmental efficiencies is examined using a regression analysis method. Based on these results, tactics for enhancing the environmental efficiency of Chinese industries are suggested in accordance with the characteristics of each industrial sector’s environmental efficiency.
September 2013
Undesirable input–output two-phase DEA model in an environmental performance audit
Publication date: September 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 5–6 Author(s): Rongbing Huang, Yuhui Li Widespread environmental concern provides an opportunity for the development of environmental auditing. This study aims to analyze ideas that address evaluation difficulties in an environmental performance audit and to promote the application of environmental performance audit in energy saving and emission reduction toward a high-end direction. An improved data envelopment analysis (DEA) model is applied in the environmental performance audit by data translation and the transformation method. With benchmark management considered, a two-phase DEA model algorithm is proposed to solve restricted inputs and outputs for pollutants or wastes as well as to overcome the relative efficiency of defects in traditional DEA evaluation. In the case study of a domestic sewage treatment plant, the model is found to improve the flexibility and effectiveness of the application.
September 2013
A stochastic DEA model considering undesirable outputs with weak disposability
Publication date: September 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 5–6 Author(s): Chong Wu, Yongli Li, Qian Liu, Kunsheng Wang This paper proposes a stochastic DEA model considering undesirable outputs with weak disposability which not only can deal with the existence of random errors in the collected data, but also depicts the production rules uncovered by weak disposability of the undesirable outputs. This model introduces the concept of risk to define the efficiency of decision making units (DMUs), and utilizes the correlationship matrix of all the variables to portray the weak disposability. On the basis of probability distribution properties, the probabilistic form of the model is transformed to the equivalent deterministic one which is able to be solved. In the application of the model, the environment efficiency evaluation problem is chosen to validate the model by designing different levels of random errors and comparing the new model with the old one. In conclusion, the model, with broad applicability has a more superior analysis capacity than the existing model.

Environmental efficiency of industrial sectors in China: An improved weighted SBM model
Publication date: September 2013
Source:Mathematical and Computer Modelling, Volume 58, Issues 5–6 Author(s): Yan Zhou, Dapeng Liang, Xinpeng Xing Utilizing undesirable outputs, a weighted SBM model was proposed in our study. Weights of undesirable outputs and weights of fossil energy were established, based on energy scarcity and the effect on the environment caused by undesirable outputs respectively. Then the environmental efficiency of industrial sectors in China are assessed with the improved weighted SMB. To eliminate the difference in energy structure and undesirable outputs structure, energy inputs and undesirable outputs were employed as classification indicators. Industrial sectors were classified into four groups. Results of the environmental efficiency assessed by three methods showed that the improved SBM model has stronger discrimination power than the previous SBM. The efficiency score measured by the improved SBM is close to the score measured by the SBM model. However, there is an obvious gap between the CCR and the improved SBM. Finally, it is easy to find key indices that have a great impact on the environmental efficiency with the improved SBM.
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