Journal of Applied Mathematics http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite Group Tue, 22 Jul 2014 10:09:31 +0000 http://www.hindawi.com/journals/jam/2014/921804/ Let be a maximal subgroup of finite group . For each chief factor of such that and , we called the order of the normal index of and a section of in . Using the concepts of normal index and c-section, we obtain some new characterizations of p-solvable, 2-supersolvable, and p-nilpotent. Na Tang and Xianhua Li Copyright © 2014 Na Tang and Xianhua Li. All rights reserved. Estimation of Unknown Functions of Iterative Difference Inequalities and Their Applications Tue, 22 Jul 2014 10:04:52 +0000 http://www.hindawi.com/journals/jam/2014/763761/ We establish some new nonlinear retarded finite difference inequalities. The results that we propose here can be used as tools in the theory of certain new classes of finite difference equations in various difference situations. We also give applications of the inequalities to show the usefulness of our results. Ricai Luo, Wu-Sheng Wang, and Honglei Xu Copyright © 2014 Ricai Luo et al. All rights reserved. Quad-Rotor Helicopter Autonomous Navigation Based on Vanishing Point Algorithm Tue, 22 Jul 2014 08:29:20 +0000 http://www.hindawi.com/journals/jam/2014/567057/ Quad-rotor helicopter is becoming popular increasingly as they can well implement many flight missions in more challenging environments, with lower risk of damaging itself and its surroundings. They are employed in many applications, from military operations to civilian tasks. Quad-rotor helicopter autonomous navigation based on the vanishing point fast estimation (VPFE) algorithm using clustering principle is implemented in this paper. For images collected by the camera of quad-rotor helicopter, the system executes the process of preprocessing of image, deleting noise interference, edge extracting using Canny operator, and extracting straight lines by randomized hough transformation (RHT) method. Then system obtains the position of vanishing point and regards it as destination point and finally controls the autonomous navigation of the quad-rotor helicopter by continuous modification according to the calculated navigation error. The experimental results show that the quad-rotor helicopter can implement the destination navigation well in the indoor environment. Jialiang Wang, Hai Zhao, Yuanguo Bi, Xingchi Chen, Ruofan Zeng, and Shiliang Shao Copyright © 2014 Jialiang Wang et al. All rights reserved. Comparison of a Fuzzy Genetic and Simulated Annealing Algorithm Approach for Project Time-Cost Tradeoff Tue, 22 Jul 2014 07:33:01 +0000 http://www.hindawi.com/journals/jam/2014/817921/ Project planning, defining the limitations and resources by leveling the resources available, have a great importance for the management projects. All these activities directly affect the duration and the cost of the project. To get a competitive value on the market, the project must be completed at the optimum time. In other to be competitive enough the optimum or near optimum solutions of time cost tradeoff and the resource leveling and resource constrained scheduling problems should be obtained in the planning phase of the project. One important aspect of the project management is activity crashing, that is, reducing activity time by adding more resources such as workers and overtime. It is important to decide the optimal crash plan to complete the project within the desired time period. The comparison of fuzzy simulated annealing and the genetic algorithm based on the crashing method is introduced in this paper to evaluate project networks and determine the optimum crashing configuration that minimizes the average project cost, caused by being late and crashing costs in the presence of vagueness and uncertainty. The evaluation results based on a real case study indicate that the method can be reliably applied to engineering projects. Nataša Glišović Copyright © 2014 Nataša Glišović. All rights reserved. Hopf Bifurcation Analysis in a New Chaotic System with Chaos Entanglement Function Tue, 22 Jul 2014 07:05:32 +0000 http://www.hindawi.com/journals/jam/2014/371509/ A new approach to generate chaotic phenomenon, called chaos entanglement, is introduced in this paper. The basic principle is to entangle two or multiple stable linear subsystems by entanglement functions to form an artificial chaotic system such that each of them evolves in a chaotic manner. The Hopf bifurcation of a new chaotic system with chaos entanglement function is studied. More precisely, we study the stability and bifurcations of equilibrium in the new chaotic system. Besides, we controlled the system to any fixed point to eliminate the chaotic vibration by means of sliding mode method. And the numerical simulations were presented to confirm the effectiveness of the controller. Zhang Jiangang, Chu Yandong, Du Wenju, Chang Yingxiang, and An Xinlei Copyright © 2014 Zhang Jiangang et al. All rights reserved. The 2-Pebbling Property of the Middle Graph of Fan Graphs Tue, 22 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/jam/2014/304514/ A pebbling move on a graph consists of taking two pebbles off one vertex and placing one pebble on an adjacent vertex. The pebbling number of a connected graph , denoted by , is the least such that any distribution of pebbles on allows one pebble to be moved to any specified but arbitrary vertex by a sequence of pebbling moves. This paper determines the pebbling numbers and the 2-pebbling property of the middle graph of fan graphs. Yongsheng Ye, Fang Liu, and Caixia Shi Copyright © 2014 Yongsheng Ye et al. All rights reserved. Global Dynamics of a Host-Vector-Predator Mathematical Model Tue, 22 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/jam/2014/245650/ A mathematical model which links predator-vector(prey) and host-vector theory is proposed to examine the indirect effect of predators on vector-host dynamics. The equilibria and the basic reproduction number R0 are obtained. By constructing Lyapunov functional and using LaSalle’s invariance principle, global stability of both the disease-free and disease equilibria are obtained. Analytical results show that R0 provides threshold conditions on determining the uniform persistence and extinction of the disease, and predator density at any time should keep larger or equal to its equilibrium level for successful disease eradication. Finally, taking the predation rate as parameter, we provide numerical simulations for the impact of predators on vector-host disease control. It is illustrated that predators have a considerable influence on disease suppression by reducing the density of the vector population. Fengyan Zhou and Hongxing Yao Copyright © 2014 Fengyan Zhou and Hongxing Yao. All rights reserved. Stepped Fault Line Selection Method Based on Spectral Kurtosis and Relative Energy Entropy of Small Current to Ground System Tue, 22 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/jam/2014/726205/ This paper proposes a stepped selection method based on spectral kurtosis relative energy entropy. Firstly, the length and type of window function are set; then when fault occurs, enter step 1: the polarity of first half-wave extremes is analyzed; if the ratios of extremes between neighboring lines are positive, the bus bar is the fault line, else, the SK relative energy entropies are calculated, and then enter step 2: if the obtained entropy multiple is bigger than the threshold or equal to the threshold, the overhead line of max entropy corresponding is the fault line, if not, enter step 3: the line of max entropy corresponding is the fault line. At last, the applicability of the proposed algorithm is presented, and the comparison results are discussed. Xiaowei Wang, Xiangxiang Wei, Jie Gao, Yaxiao Hou, and Yanfang Wei Copyright © 2014 Xiaowei Wang et al. All rights reserved. Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces Mon, 21 Jul 2014 09:01:59 +0000 http://www.hindawi.com/journals/jam/2014/580686/ We study a strong convergence for a common fixed point of a finite family of quasi-Bregman nonexpansive mappings in the framework of real reflexive Banach spaces. As a consequence, convergence for a common fixed point of a finite family of Bergman relatively nonexpansive mappings is discussed. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common solution of a finite family equilibrium problem and a common zero of a finite family of maximal monotone mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings. Mohammed Ali Alghamdi, Naseer Shahzad, and Habtu Zegeye Copyright © 2014 Mohammed Ali Alghamdi et al. All rights reserved. Zeros of Analytic Continued -Euler Polynomials and -Euler Zeta Function Mon, 21 Jul 2014 07:57:37 +0000 http://www.hindawi.com/journals/jam/2014/806239/ We study that the -Euler numbers and -Euler polynomials are analytic continued to and . We investigate the new concept of dynamics of the zeros of analytic continued polynomials. Finally, we observe an interesting phenomenon of ‘‘scattering’’ of the zeros of . C. S. Ryoo Copyright © 2014 C. S. Ryoo. All rights reserved. A Comparative Study: Globality versus Locality for Graph Construction in Discriminant Analysis Mon, 21 Jul 2014 07:52:41 +0000 http://www.hindawi.com/journals/jam/2014/965602/ Local graph based discriminant analysis (DA) algorithms recently have attracted increasing attention to mitigate the limitations of global (graph) DA algorithms. However, there are few particular concerns on the following important issues: whether the local construction is better than the global one for intraclass and interclass graphs, which (intraclass or interclass) graph should locally or globally be constructed? and, further how they should be effectively jointed for good discriminant performances. In this paper, pursuing our previous studies on the graph construction and DA, we firstly address the issues involved above, and then by jointly utilizing both the globality and the locality, we develop, respectively, a Globally marginal and Locally compact Discriminant Analysis (GmLcDA) algorithm based on so-introduced global interclass and local intraclass graphs and a Locally marginal and Globally compact Discriminant Analysis (LmGcDA) based on so-introduced local interclass and global intraclass graphs, the purpose of which is not to show how novel the algorithms are but to illustrate the analyses in theory. Further, by comprehensively comparing the Locally marginal and Locally compact DA (LmLcDA) based on locality alone, the Globally marginal and Globally compact Discriminant Analysis (GmGcDA) just based on globality alone, GmLcDA, and LmGcDA, we suggest that the joint of locally constructed intraclass and globally constructed interclass graphs is more discriminant. Bo Yang and Songcan Chen Copyright © 2014 Bo Yang and Songcan Chen. All rights reserved. Adaptive Combination Forecasting Model Based on Area Correlation Degree with Application to China’s Energy Consumption Mon, 21 Jul 2014 06:50:22 +0000 http://www.hindawi.com/journals/jam/2014/845807/ To accurately forecast energy consumption plays a vital part in rational energy planning formulation for a country. This study applies individual models (BP, GM (1, 1), triple exponential smoothing model, and polynomial trend extrapolation model) and combination forecasting models to predict China’s energy consumption. Since area correlation degree (ACD) can comprehensively evaluate both the correlation and fitting error of forecasting model, it is more effective to evaluate the performance of forecasting model. Firstly, the forecasting model’s performances rank in line with ACD. Then ACD is firstly proposed to choose individual models for combination and determine combination weight in this paper. Forecast results show that combination models usually have more accurate forecasting performance than individual models. The new method based on ACD shows its superiority in determining combination weights, compared with some other combination weight assignment methods such as: entropy weight method, reciprocal of mean absolute percentage error weight method, and optimal method of absolute percentage error minimization. By using combination forecasting model based on ACD, China’s energy consumption will be up to 5.7988 billion tons of standard coal in 2018. Zhou Cheng and Chen XiYang Copyright © 2014 Zhou Cheng and Chen XiYang. All rights reserved. Video Object Tracking in Neural Axons with Fluorescence Microscopy Images Mon, 21 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/jam/2014/423876/ Neurofilament is an important type of intercellular cargos transmitted in neural axons. Given fluorescence microscopy images, existing methods extract neurofilament movement patterns by manual tracking. In this paper, we describe two automated tracking methods for analyzing neurofilament movement based on two different techniques: constrained particle filtering and tracking-by-detection. First, we introduce the constrained particle filtering approach. In this approach, the orientation and position of a particle are constrained by the axon’s shape such that fewer particles are necessary for tracking neurofilament movement than object tracking techniques based on generic particle filtering. Secondly, a tracking-by-detection approach to neurofilament tracking is presented. For this approach, the axon is decomposed into blocks, and the blocks encompassing the moving neurofilaments are detected by graph labeling using Markov random field. Finally, we compare two tracking methods by performing tracking experiments on real time-lapse image sequences of neurofilament movement, and the experimental results show that both methods demonstrate good performance in comparison with the existing approaches, and the tracking accuracy of the tracing-by-detection approach is slightly better between the two. Liang Yuan and Junda Zhu Copyright © 2014 Liang Yuan and Junda Zhu. All rights reserved. Novel Global Harmony Search Algorithm for Least Absolute Deviation Mon, 21 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/jam/2014/632975/ The method of least absolute deviation (LAD) finds applications in many areas, due to its robustness compared to the least squares regression (LSR) method. LAD is robust in that it is resistant to outliers in the data. This may be helpful in studies where outliers may be ignored. Since LAD is nonsmooth optimization problem, this paper proposed a metaheuristics algorithm named novel global harmony search (NGHS) for solving. Numerical results show that the NGHS method has good convergence property and effective in solving LAD. Longquan Yong Copyright © 2014 Longquan Yong. All rights reserved. Blind Channel Estimation Based on Multilevel Lloyd-Max Iteration for Nonconstant Modulus Constellations Sun, 20 Jul 2014 12:10:03 +0000 http://www.hindawi.com/journals/jam/2014/146207/ In wireless communications, knowledge of channel coefficients is required for coherent demodulation. Lloyd-Max iteration is an innovative blind channel estimation method for narrowband fading channels. In this paper, it is proved that blind channel estimation based on single-level Lloyd-Max (SL-LM) iteration is not reliable for nonconstant modulus constellations (NMC). Then, we introduce multilevel Lloyd-Max (ML-LM) iteration to solve this problem. Firstly, by dividing NMC into subsets, Lloyd-Max iteration is used in multilevel. Then, the estimation information is transmitted from one level to another. By doing this, accurate blind channel estimation for NMC is achieved. Moreover, when the number of received symbols is small, we propose the lacking constellations equalization algorithm to reduce the influence of lacking constellations. Finally, phase ambiguity of ML-LM iteration is also investigated in the paper. ML-LM iteration can be more robust to the phase of fading coefficient by dividing NMC into subsets properly. As the signal-to-noise ratio (SNR) increases, numerical results show that the proposed method’s mean-square error curve converges remarkably to the least squares (LS) bound with a small number of iterations. Xiaotian Li, Jing Lei, Wei Liu, Erbao Li, and Yanbin Li Copyright © 2014 Xiaotian Li et al. All rights reserved. A Concentration Phenomenon for p-Laplacian Equation Sun, 20 Jul 2014 11:25:28 +0000 http://www.hindawi.com/journals/jam/2014/148902/ It is proved that if the bounded function of coefficient in the following equation   is positive in a region contained in Ω and negative outside the region, the sets shrink to a point as , and then the sequence generated by the nontrivial solution of the same equation, corresponding to , will concentrate at with respect to and certain -norms. In addition, if the sets shrink to finite points, the corresponding ground states only concentrate at one of these points. These conclusions extend the results proved in the work of Ackermann and Szulkin (2013) for case . Yansheng Zhong Copyright © 2014 Yansheng Zhong. All rights reserved. Visual Tracking Using Max-Average Pooling and Weight-Selection Strategy Sun, 20 Jul 2014 07:18:30 +0000 http://www.hindawi.com/journals/jam/2014/828907/ Many modern visual tracking algorithms incorporate spatial pooling, max pooling, or average pooling, which is to achieve invariance to feature transformations and better robustness to occlusion, illumination change, and position variation. In this paper, max-average pooling method and Weight-selection strategy are proposed with a hybrid framework, which is combined with sparse representation and particle filter, to exploit the spatial information of an object and make good compromises to ensure the correctness of the results in this framework. Challenges can be well considered by the proposed algorithm. Experimental results demonstrate the effectiveness and robustness of the proposed algorithm compared with the state-of-the-art methods on challenging sequences. Suguo Zhu and Junping Du Copyright © 2014 Suguo Zhu and Junping Du. All rights reserved. An Improved Extended Information Filter SLAM Algorithm Based on Omnidirectional Vision Sun, 20 Jul 2014 06:28:30 +0000 http://www.hindawi.com/journals/jam/2014/948505/ In the SLAM application, omnidirectional vision extracts wide scale information and more features from environments. Traditional algorithms bring enormous computational complexity to omnidirectional vision SLAM. An improved extended information filter SLAM algorithm based on omnidirectional vision is presented in this paper. Based on the analysis of structure a characteristics of the information matrix, this algorithm improves computational efficiency. Considering the characteristics of omnidirectional images, an improved sparsification rule is also proposed. The sparse observation information has been utilized and the strongest global correlation has been maintained. So the accuracy of the estimated result is ensured by using proper sparsification of the information matrix. Then, through the error analysis, the error caused by sparsification can be eliminated by a relocation method. The results of experiments show that this method makes full use of the characteristic of repeated observations for landmarks in omnidirectional vision and maintains great efficiency and high reliability in mapping and localization. Jingchuan Wang and Weidong Chen Copyright © 2014 Jingchuan Wang and Weidong Chen. All rights reserved. An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions Thu, 17 Jul 2014 11:57:00 +0000 http://www.hindawi.com/journals/jam/2014/893765/ We present an approximate nonsmooth algorithm to solve a minimization problem, in which the objective function is the sum of a maximum eigenvalue function of matrices and a convex function. The essential idea to solve the optimization problem in this paper is similar to the thought of proximal bundle method, but the difference is that we choose approximate subgradient and function value to construct approximate cutting-plane model to solve the above mentioned problem. An important advantage of the approximate cutting-plane model for objective function is that it is more stable than cutting-plane model. In addition, the approximate proximal bundle method algorithm can be given. Furthermore, the sequences generated by the algorithm converge to the optimal solution of the original problem. Wei Wang, Lingling Zhang, Miao Chen, and Sida Lin Copyright © 2014 Wei Wang et al. All rights reserved. Weaker Regularity Conditions and Sparse Recovery in High-Dimensional Regression Thu, 17 Jul 2014 11:44:29 +0000 http://www.hindawi.com/journals/jam/2014/946241/ Regularity conditions play a pivotal role for sparse recovery in high-dimensional regression. In this paper, we present a weaker regularity condition and further discuss the relationships with other regularity conditions, such as restricted eigenvalue condition. We study the behavior of our new condition for design matrices with independent random columns uniformly drawn on the unit sphere. Moreover, the present paper shows that, under a sparsity scenario, the Lasso estimator and Dantzig selector exhibit similar behavior. Based on both methods, we derive, in parallel, more precise bounds for the estimation loss and the prediction risk in the linear regression model when the number of variables can be much larger than the sample size. Shiqing Wang, Yan Shi, and Limin Su Copyright © 2014 Shiqing Wang et al. All rights reserved. A Spline Smoothing Newton Method for Semi-Infinite Minimax Problems Thu, 17 Jul 2014 11:42:52 +0000 http://www.hindawi.com/journals/jam/2014/852074/ Based on discretization methods for solving semi-infinite programming problems, this paper presents a spline smoothing Newton method for semi-infinite minimax problems. The spline smoothing technique uses a smooth cubic spline instead of max function and only few components in the max function are computed; that is, it introduces an active set technique, so it is more efficient for solving large-scale minimax problems arising from the discretization of semi-infinite minimax problems. Numerical tests show that the new method is very efficient. Li Dong, Bo Yu, and Yu Xiao Copyright © 2014 Li Dong et al. All rights reserved. Link Prediction via Convex Nonnegative Matrix Factorization on Multiscale Blocks Thu, 17 Jul 2014 11:27:58 +0000 http://www.hindawi.com/journals/jam/2014/786156/ Low rank matrices approximations have been used in link prediction for networks, which are usually global optimal methods and lack of using the local information. The block structure is a significant local feature of matrices: entities in the same block have similar values, which implies that links are more likely to be found within dense blocks. We use this insight to give a probabilistic latent variable model for finding missing links by convex nonnegative matrix factorization with block detection. The experiments show that this method gives better prediction accuracy than original method alone. Different from the original low rank matrices approximations methods for link prediction, the sparseness of solutions is in accord with the sparse property for most real complex networks. Scaling to massive size network, we use the block information mapping matrices onto distributed architectures and give a divide-and-conquer prediction method. The experiments show that it gives better results than common neighbors method when the networks have a large number of missing links. Enming Dong, Jianping Li, and Zheng Xie Copyright © 2014 Enming Dong et al. All rights reserved. Retracted: Iterative Schemes by a New Generalized Resolvent for a Monotone Mapping and a Relatively Weak Nonexpansive Mapping Thu, 17 Jul 2014 08:07:58 +0000 http://www.hindawi.com/journals/jam/2014/279526/ Journal of Applied Mathematics Copyright © 2014 Journal of Applied Mathematics. All rights reserved. Convergence of Relaxed Matrix Parallel Multisplitting Chaotic Methods for -Matrices Thu, 17 Jul 2014 08:01:26 +0000 http://www.hindawi.com/journals/jam/2014/594185/ Based on the methods presented by Song and Yuan (1994), we construct relaxed matrix parallel multisplitting chaotic generalized USAOR-style methods by introducing more relaxed parameters and analyze the convergence of our methods when coefficient matrices are H-matrices or irreducible diagonally dominant matrices. The parameters can be adjusted suitably so that the convergence property of methods can be substantially improved. Furthermore, we further study some applied convergence results of methods to be convenient for carrying out numerical experiments. Finally, we give some numerical examples, which show that our convergence results are applied and easily carried out. Li-Tao Zhang, Jian-Lei Li, Tong-Xiang Gu, and Xing-Ping Liu Copyright © 2014 Li-Tao Zhang et al. All rights reserved. A Fairness Relation Based on the Asymmetric Choquet Integral and Its Application in Network Resource Allocation Problems Thu, 17 Jul 2014 07:53:39 +0000 http://www.hindawi.com/journals/jam/2014/725974/ The recent problem of network resource allocation is studied where pairs of users could be in a favourable situation, given that the allocation scheme is refined by some add-on technology. The general question here is whether the additional effort can be effective with regard to the user’s experience of fairness. The computational approach proposed in this paper to handle this question is based on the framework of relational optimization. For representing different weightings for different pairs of users, the use of a fuzzy measure appears to be reasonable. The generalized Choquet integrals are discussed from the viewpoint of representing fairness and it is concluded that the asymmetric Choquet integral is the most suitable approach. A binary relation using the asymmetric Choquet integral is proposed. In case of a supermodular fuzzy measure, this is a transitive and cycle-free relation. The price of fairness with regard to a wireless channel allocation problem taking channel interference into account is experimentally studied and it can be seen that the asymmetric on relation actually selects allocations that perform on average between maxmin fairness and proportional fairness, and being more close to maxmin fairness as long as channel interference is not high. Aoi Honda and Mario Köppen Copyright © 2014 Aoi Honda and Mario Köppen. All rights reserved. Development of the Korean Spine Database and Automatic Surface Mesh Intersection Algorithm for Constructing e-Spine Simulator Thu, 17 Jul 2014 06:39:14 +0000 http://www.hindawi.com/journals/jam/2014/471756/ By 2026, Korea is expected to surpass the UN’s definition of an aged society and reach the level of a superaged society. With an aging population come increased disorders involving the spine. To prevent unnecessary spinal surgery and support scientific diagnosis of spinal disease and systematic prediction of treatment outcomes, we have been developing e-Spine, which is a computer simulation model of the human spine. In this paper, we present the Korean spine database and automatic surface mesh intersection algorithm to construct e-Spine. To date, the Korean spine database has collected spine data from 77 cadavers and 298 patients. The spine data consists of 2D images from CT, MRI, or X-ray, 3D shapes, geometry data, and property data. The volume and quality of the Korean spine database are now the world’s highest ones. In addition, our triangular surface mesh intersection algorithm automatically remeshes the spine-implant intersection model to make it valid for finite element analysis (FEA). This makes it possible to run the FEA using the spine-implant mesh model without any manual effort. Our database and surface mesh intersection algorithm will offer great value and utility in the diagnosis, treatment, and rehabilitation of patients suffering from spinal diseases. Dongmin Seo, Hanmin Jung, Won-Kyung Sung, and Dukyun Nam Copyright © 2014 Dongmin Seo et al. All rights reserved. Fuzzy Optimization of Option Pricing Model and Its Application in Land Expropriation Thu, 17 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/jam/2014/635898/ Option pricing is irreversible, fuzzy, and flexible. The fuzzy measure which is used for real option pricing is a useful supplement to the traditional real option pricing method. Based on the review of the concepts of the mean and variance of trapezoidal fuzzy number and the combination with the Carlsson-Fuller model, the trapezoidal fuzzy variable can be used to represent the current price of land expropriation and the sale price of land on the option day. Fuzzy Black-Scholes option pricing model can be constructed under fuzzy environment and problems also can be solved and discussed through numerical examples. Aimin Heng, Qian Chen, and Yingshuang Tan Copyright © 2014 Aimin Heng et al. All rights reserved. Price of Fairness on Networked Auctions Thu, 17 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/jam/2014/860747/ We consider an auction design problem under network flow constraints. We focus on pricing mechanisms that provide fair solutions, where fairness is defined in absolute and relative terms. The absolute fairness is equivalent to “no individual losses” assumption. The relative fairness can be verbalized as follows: no agent can be treated worse than any other in similar circumstances. Ensuring the fairness conditions makes only part of the social welfare available in the auction to be distributed on pure market rules. The rest of welfare must be distributed without market rules and constitutes the so-called price of fairness. We prove that there exists the minimum of price of fairness and that it is achieved when uniform unconstrained market price is used as the base price. The price of fairness takes into account costs of forced offers and compensations for lost profits. The final payments can be different than locational marginal pricing. That means that the widely applied locational marginal pricing mechanism does not in general minimize the price of fairness. Mariusz Kaleta Copyright © 2014 Mariusz Kaleta. All rights reserved. Weighted Dual Covariance Moore-Penrose Inverses with respect to an Invertible Element in -Algebras Wed, 16 Jul 2014 11:02:31 +0000 http://www.hindawi.com/journals/jam/2014/918107/ We study several algebraic properties of dual covariance and weighted dual covariance sets in rings with involution and -algebras. Moreover, we show that the weighted dual covariance set, seen as a multivalued map, has some kind of continuity. Also, we prove weighed dual covariance set invariant under the bijection multiplicative -functions. Hesam Mahzoon Copyright © 2014 Hesam Mahzoon. All rights reserved. Asymptotic Modeling of the Thin Film Flow with a Pressure-Dependent Viscosity Wed, 16 Jul 2014 09:16:17 +0000 http://www.hindawi.com/journals/jam/2014/217174/ We study the lubrication process with incompressible fluid taking into account the dependence of the viscosity on the pressure. Assuming that the viscosity-pressure relation is given by the well-known Barus law, we derive an effective model using asymptotic analysis with respect to the film thickness. The key idea is to conveniently transform the governing system and then apply two-scale expansion technique. Eduard Marušić-Paloka and Igor Pažanin Copyright © 2014 Eduard Marušić-Paloka and Igor Pažanin. All rights reserved.