Mathematical Problems in Engineering The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Three-Phase Methodology Incorporating Scatter Search for Integrated Production, Inventory, and Distribution Routing Problem Mon, 06 Jul 2015 08:42:15 +0000 This paper proposes the use of scatter search metaheuristic to solve an integrated production, inventory, and distribution routing problem. The problem is based on a single production plant that produces a single product that is delivered to N geographically dispersed customers by a set of homogenous fleet of vehicles. The objective is to construct a production plan and delivery schedule to minimize the total costs and ensuring each customer’s demand is met over the planning horizon. We assumed that excess production can be stored at the plant or at customer’s sites within some limits, but stockouts due to backordering or backlogging are not allowed. Further testing on a set of benchmark problems to assess the effectiveness of our method is also carried out. We compare our results to the existing metaheuristic algorithms proposed in the literature. Noor Hasnah Moin and Titi Yuliana Copyright © 2015 Noor Hasnah Moin and Titi Yuliana. All rights reserved. Supervised Kernel Optimized Locality Preserving Projection with Its Application to Face Recognition and Palm Biometrics Mon, 06 Jul 2015 08:05:23 +0000 Kernel Locality Preserving Projection (KLPP) algorithm can effectively preserve the neighborhood structure of the database using the kernel trick. We have known that supervised KLPP (SKLPP) can preserve within-class geometric structures by using label information. However, the conventional SKLPP algorithm endures the kernel selection which has significant impact on the performances of SKLPP. In order to overcome this limitation, a method named supervised kernel optimized LPP (SKOLPP) is proposed in this paper, which can maximize the class separability in kernel learning. The proposed method maps the data from the original space to a higher dimensional kernel space using a data-dependent kernel. The adaptive parameters of the data-dependent kernel are automatically calculated through optimizing an objective function. Consequently, the nonlinear features extracted by SKOLPP have larger discriminative ability compared with SKLPP and are more adaptive to the input data. Experimental results on ORL, Yale, AR, and Palmprint databases showed the effectiveness of the proposed method. Chuang Lin, Jifeng Jiang, Xuefeng Zhao, Meng Pang, and Yanchun Ma Copyright © 2015 Chuang Lin et al. All rights reserved. Swarm Intelligence-Based Smart Energy Allocation Strategy for Charging Stations of Plug-In Hybrid Electric Vehicles Mon, 06 Jul 2015 07:09:38 +0000 Recent researches towards the use of green technologies to reduce pollution and higher penetration of renewable energy sources in the transportation sector have been gaining popularity. In this wake, extensive participation of plug-in hybrid electric vehicles (PHEVs) requires adequate charging allocation strategy using a combination of smart grid systems and smart charging infrastructures. Daytime charging stations will be needed for daily usage of PHEVs due to the limited all-electric range. Intelligent energy management is an important issue which has already drawn much attention of researchers. Most of these works require formulation of mathematical models with extensive use of computational intelligence-based optimization techniques to solve many technical problems. In this paper, gravitational search algorithm (GSA) has been applied and compared with another member of swarm family, particle swarm optimization (PSO), considering constraints such as energy price, remaining battery capacity, and remaining charging time. Simulation results obtained for maximizing the highly nonlinear objective function evaluate the performance of both techniques in terms of best fitness. Imran Rahman, Pandian M. Vasant, Balbir Singh Mahinder Singh, and M. Abdullah-Al-Wadud Copyright © 2015 Imran Rahman et al. All rights reserved. A Comprehensive Modeling of a Three-Phase Voltage Source PWM Converter Mon, 06 Jul 2015 06:51:24 +0000 This contribution reports the development of a time domain model of a three-phase voltage source converter (VSC) that can be used in the transient and steady state analysis of nonlinear power systems including their associated closed-loop control schemes. With this proposed model, the original discontinuous nonlinear power system can be transformed into a continuous system, while keeping the underlying harmonic nature of the VSC and avoiding typical and undesirable numerical problems associated with the large derivatives during the switching transitions. The development of this model was based on the dynamic Fourier series of the switching functions under a sinusoidal PWM modulation scheme, which require the calculation of the switching instants at each integration step; the switching instants and the dynamic Fourier series coefficients are calculated by explicit mathematical formulas. The proposed model of the VSC is suitable for the fast computation of the periodic steady state solution through the application of Newton method. Simulations were carried out in order to illustrate the benefits of the proposed VSC model. Juan Segundo-Ramírez, Rafael Peña-Gallardo, Aurelio Medina, Ciro Núñez-Gutiérrez, and Nancy Visairo-Cruz Copyright © 2015 Juan Segundo-Ramírez et al. All rights reserved. A Binary Cat Swarm Optimization Algorithm for the Non-Unicost Set Covering Problem Mon, 06 Jul 2015 06:39:43 +0000 The Set Covering Problem consists in finding a subset of columns in a zero-one matrix such that they cover all the rows of the matrix at a minimum cost. To solve the Set Covering Problem we use a metaheuristic called Binary Cat Swarm Optimization. This metaheuristic is a recent swarm metaheuristic technique based on the cat behavior. Domestic cats show the ability to hunt and are curious about moving objects. Based on this, the cats have two modes of behavior: seeking mode and tracing mode. We are the first ones to use this metaheuristic to solve this problem; our algorithm solves a set of 65 Set Covering Problem instances from OR-Library. Broderick Crawford, Ricardo Soto, Natalia Berríos, Franklin Johnson, Fernando Paredes, Carlos Castro, and Enrique Norero Copyright © 2015 Broderick Crawford et al. All rights reserved. Multipeak Mean Based Optimized Histogram Modification Framework Using Swarm Intelligence for Image Contrast Enhancement Mon, 06 Jul 2015 06:27:01 +0000 A novel approach, Multipeak mean based optimized histogram modification framework (MMOHM) is introduced for the purpose of enhancing the contrast as well as preserving essential details for any given gray scale and colour images. The basic idea of this technique is the calculation of multiple peaks (local maxima) from the original histogram. The mean value of multiple peaks is computed and the input image’s histogram is segmented into two subhistograms based on this multipeak mean () value. Then, a bicriteria optimization problem is formulated and the subhistograms are modified by selecting optimal contrast enhancement parameters. While formulating the enhancement parameters, particle swarm optimization is employed to find optimal values of them. Finally, the union of the modified subhistograms produces a contrast enhanced and details preserved output image. This mechanism enhances the contrast of the input image better than the existing contemporary HE methods. The performance of the proposed method is well supported by the contrast enhancement quantitative metrics such as discrete entropy, natural image quality evaluator, and absolute mean brightness error. P. Babu, V. Rajamani, and K. Balasubramanian Copyright © 2015 P. Babu et al. All rights reserved. Runge-Kutta Integration of the Equal Width Wave Equation Using the Method of Lines Sun, 05 Jul 2015 13:01:21 +0000 The equal width (EW) equation governs nonlinear wave phenomena like waves in shallow water. Numerical solution of the (EW) equation is obtained by using the method of lines (MOL) based on Runge-Kutta integration. Using von Neumann stability analysis, the scheme is found to be unconditionally stable. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Accuracy of the proposed method is discussed by computing the and error norms. The results are found in good agreement with exact solution. M. A. Banaja and H. O. Bakodah Copyright © 2015 M. A. Banaja and H. O. Bakodah. All rights reserved. A Thermal Infrared and Visible Images Fusion Based Approach for Multitarget Detection under Complex Environment Sun, 05 Jul 2015 09:22:08 +0000 Multitarget detection under complex environment is a challenging task, where the measured signal will be submerged by noise. D-S belief theory is an effective approach in dealing with Multitarget detection. However, there are some limitations of the general D-S belief theory under complex environment. For example, the basic belief assignment is difficult to establish, and the subjective factors will influence the update process of evidence. In this paper, a new Multitarget detection approach based on thermal infrared and visible images fusion is proposed. To easily characterize the defected heterogeneous image, a basic belief assignment based on the distance distribution function of heterogeneous characteristics is presented. Furthermore, to improve the discrimination and effectiveness of the Multitarget detection, a concept of comprehensive credibility is introduced into the proposed approach and a new update rule of evidence is designed. Finally, some experiments are carried out and the experimental results show the efficiency and effectiveness of the proposed approach in the Multitarget detection task. Xinnan Fan, Pengfei Shi, Jianjun Ni, and Min Li Copyright © 2015 Xinnan Fan et al. All rights reserved. An Effective Error Correction Scheme for Arithmetic Coding Sun, 05 Jul 2015 07:41:13 +0000 We propose an effective error correction technique for arithmetic coding with forbidden symbol. By predicting the occurrence of the subsequent forbidden symbols, the forbidden region is actually expanded and theoretically, a better error correction performance can be achieved. Moreover, a generalized stack algorithm is exploited to detect the forbidden symbol beforehand. The proposed approach is combined with the maximum a posteriori (MAP) metric to keep the highly probable decoding paths in the stack. Simulation results justify that our scheme performs better than the existing MAP methods on the error correction performance, especially at a low coding rate. Qiuzhen Lin, Kwok-Wo Wong, Ming Li, and Jianyong Chen Copyright © 2015 Qiuzhen Lin et al. All rights reserved. Topology Identification of Coupling Map Lattice under Sparsity Condition Sun, 05 Jul 2015 07:36:55 +0000 Coupling map lattice is an efficient mathematical model for studying complex systems. This paper studies the topology identification of coupled map lattice (CML) under the sparsity condition. We convert the identification problem into the problem of solving the underdetermined linear equations. The norm method is used to solve the underdetermined equations. The requirement of data characters and sampling times are discussed in detail. We find that the high entropy and small coupling coefficient data are suitable for the identification. When the measurement time is more than 2.86 times sparsity, the accuracy of identification can reach an acceptable level. And when the measurement time reaches 4 times sparsity, we can receive a fairly good accuracy. Jiangni Yu, Lixiang Li, and Yixian Yang Copyright © 2015 Jiangni Yu et al. All rights reserved. Automatic Freeway Incident Detection for Free Flow Conditions: A Vehicle Reidentification Based Approach Using Image Data from Sparsely Distributed Video Cameras Sun, 05 Jul 2015 06:56:56 +0000 This paper proposes a vehicle reidentification (VRI) based automatic incident algorithm (AID) for freeway system under free flow condition. An enhanced vehicle feature matching technique is adopted in the VRI component of the proposed system. In this study, arrival time interval, which is estimated based on the historical database, is introduced into the VRI component to improve the matching accuracy and reduce the incident detection time. Also, a screening method, which is based on the ratios of the matching probabilities, is introduced to the VRI component to further reduce false alarm rate. The proposed AID algorithm is tested on a 3.6 km segment of a closed freeway system in Bangkok, Thailand. The results show that in terms of incident detection time, the proposed AID algorithm outperforms the traditional vehicle count approach. Jiankai Wang and Agachai Sumalee Copyright © 2015 Jiankai Wang and Agachai Sumalee. All rights reserved. Effects of Temperature, Time, Magnesium, and Copper on the Wettability of Al/TiC System Sun, 05 Jul 2015 06:54:18 +0000 The effects of temperature, time, and the additions of magnesium and copper on the wetting behavior of Al/TiC are studied theoretically. Mathematical formula is presented in explicit form. The effect of each variable is investigated by using the obtained equation. It is observed that the time and temperature have a stronger effect on the wetting of TiC in comparison to other input parameters. The proposed model shows good agreement with test results and can be used to find the wetting behavior of Al/TiC. The findings led to a new insight of the wetting process of TiC. Halil Ibrahim Kurt and Murat Oduncuoglu Copyright © 2015 Halil Ibrahim Kurt and Murat Oduncuoglu. All rights reserved. Adaptive Output Feedback Sliding Mode Control for Complex Interconnected Time-Delay Systems Sun, 05 Jul 2015 06:42:29 +0000 We extend the decentralized output feedback sliding mode control (SMC) scheme to stabilize a class of complex interconnected time-delay systems. First, sufficient conditions in terms of linear matrix inequalities are derived such that the equivalent reduced-order system in the sliding mode is asymptotically stable. Second, based on a new lemma, a decentralized adaptive sliding mode controller is designed to guarantee the finite time reachability of the system states by using output feedback only. The advantage of the proposed method is that two major assumptions, which are required in most existing SMC approaches, are both released. These assumptions are (1) disturbances are bounded by a known function of outputs and (2) the sliding matrix satisfies a matrix equation that guarantees the sliding mode. Finally, a numerical example is used to demonstrate the efficacy of the method. Van Van Huynh, Yao-Wen Tsai, and Phan Van Duc Copyright © 2015 Van Van Huynh et al. All rights reserved. An Analysis and Application of Fast Nonnegative Orthogonal Matching Pursuit for Image Categorization in Deep Networks Thu, 02 Jul 2015 12:20:08 +0000 Nonnegative orthogonal matching pursuit (NOMP) has been proven to be a more stable encoder for unsupervised sparse representation learning. However, previous research has shown that NOMP is suboptimal in terms of computational cost, as the coefficients selection and refinement using nonnegative least squares (NNLS) have been divided into two separate steps. It is found that this problem severely reduces the efficiency of encoding for large-scale image patches. In this work, we study fast nonnegative OMP (FNOMP) as an efficient encoder which can be accelerated by the implementation of factorization and iterations of coefficients in deep networks for full-size image categorization task. It is analyzed and demonstrated that using relatively simple gain-shape vector quantization for training dictionary, FNOMP not only performs more efficiently than NOMP for encoding but also significantly improves the classification accuracy compared to OMP based algorithm. In addition, FNOMP based algorithm is superior to other state-of-the-art methods on several publicly available benchmarks, that is, Oxford Flowers, UIUC-Sports, and Caltech101. Bo Wang, Jichang Guo, and Yan Zhang Copyright © 2015 Bo Wang et al. All rights reserved. Extreme Learning Machine on High Dimensional and Large Data Applications Thu, 02 Jul 2015 11:31:46 +0000 Zhiping Lin, Jiuwen Cao, Tao Chen, Yi Jin, Zhan-Li Sun, and Amaury Lendasse Copyright © 2015 Zhiping Lin et al. All rights reserved. Extreme Learning Machines on High Dimensional and Large Data Applications: A Survey Thu, 02 Jul 2015 11:31:01 +0000 Extreme learning machine (ELM) has been developed for single hidden layer feedforward neural networks (SLFNs). In ELM algorithm, the connections between the input layer and the hidden neurons are randomly assigned and remain unchanged during the learning process. The output connections are then tuned via minimizing the cost function through a linear system. The computational burden of ELM has been significantly reduced as the only cost is solving a linear system. The low computational complexity attracted a great deal of attention from the research community, especially for high dimensional and large data applications. This paper provides an up-to-date survey on the recent developments of ELM and its applications in high dimensional and large data. Comprehensive reviews on image processing, video processing, medical signal processing, and other popular large data applications with ELM are presented in the paper. Jiuwen Cao and Zhiping Lin Copyright © 2015 Jiuwen Cao and Zhiping Lin. All rights reserved. Clustering Ensemble for Identifying Defective Wafer Bin Map in Semiconductor Manufacturing Thu, 02 Jul 2015 11:09:50 +0000 Wafer bin map (WBM) represents specific defect pattern that provides information for diagnosing root causes of low yield in semiconductor manufacturing. In practice, most semiconductor engineers use subjective and time-consuming eyeball analysis to assess WBM patterns. Given shrinking feature sizes and increasing wafer sizes, various types of WBMs occur; thus, relying on human vision to judge defect patterns is complex, inconsistent, and unreliable. In this study, a clustering ensemble approach is proposed to bridge the gap, facilitating WBM pattern extraction and assisting engineer to recognize systematic defect patterns efficiently. The clustering ensemble approach not only generates diverse clusters in data space, but also integrates them in label space. First, the mountain function is used to transform data by using pattern density. Subsequently, k-means and particle swarm optimization (PSO) clustering algorithms are used to generate diversity partitions and various label results. Finally, the adaptive response theory (ART) neural network is used to attain consensus partitions and integration. An experiment was conducted to evaluate the effectiveness of proposed WBMs clustering ensemble approach. Several criterions in terms of sum of squared error, precision, recall, and F-measure were used for evaluating clustering results. The numerical results showed that the proposed approach outperforms the other individual clustering algorithm. Chia-Yu Hsu Copyright © 2015 Chia-Yu Hsu. All rights reserved. A Multicriteria Decision Model for Assessment of Failure Consequences in the RCM Approach Thu, 02 Jul 2015 10:49:40 +0000 This paper proposes a multicriteria decision model based on MAUT (Multiattribute Utility Theory) incorporated into an RCM (Reliability Centered Maintenance) approach in order to provide a better assessment of the consequences of failure, allowing a more effective maintenance planning. MAUT provides an evaluation of probability distributions on each attribute as well as trade-offs involving lotteries. The model proposed takes advantage of such evaluations and it also restructures consequence groups established in an RCM approach into new five dimensions. As a result, overall indices of utility are computed for each failure mode analyzed. With these values, the ranking of the alternatives is established. The decision-maker’s preferences are taken into account so that the final result for each failure mode incorporates subjective aspects based on the decision-maker’s perceptions and behavior. Marcelo H. Alencar and Adiel T. de Almeida Copyright © 2015 Marcelo H. Alencar and Adiel T. de Almeida. All rights reserved. Phase Error Caused by Speed Mismatch Analysis in the Line-Scan Defect Detection by Using Fourier Transform Technique Thu, 02 Jul 2015 09:53:48 +0000 The phase error caused by the speed mismatch issue is researched in the line-scan images capturing 3D profile measurement. The experimental system is constructed by a line-scan CCD camera, an object moving device, a digital fringe pattern projector, and a personal computer. In the experiment procedure, the detected object is moving relative to the image capturing system by using a motorized translation stage in a stable velocity. The digital fringe pattern is projected onto the detected object, and then the deformed patterns are captured and recorded in the computer. The object surface profile can be calculated by the Fourier transform profilometry. However, the moving speed mismatch error will still exist in most of the engineering application occasion even after an image system calibration. When the moving speed of the detected object is faster than the expected value, the captured image will be compressed in the moving direction of the detected object. In order to overcome this kind of measurement error, an image recovering algorithm is proposed to reconstruct the original compressed image. Thus, the phase values can be extracted much more accurately by the reconstructed images. And then, the phase error distribution caused by the speed mismatch is analyzed by the simulation and experimental methods. Eryi Hu and Yuan Hu Copyright © 2015 Eryi Hu and Yuan Hu. All rights reserved. Conditional Optimization and One Inverse Boundary Value Problem Thu, 02 Jul 2015 08:38:54 +0000 Here we construct different approximate solutions of the plane inverse boundary value problem of aerohydrodynamics. In order to do this we solve some conditional optimization problems in the norms , , and  and some of their generalizations. We present the example clarifying the mathematical constructions and show that the supremum norm generalization seems to be the optimal one of all the functionals considered in the paper. Pyotr N. Ivanshin Copyright © 2015 Pyotr N. Ivanshin. All rights reserved. Symmetry Analysis and Conservation Laws of a Generalized Two-Dimensional Nonlinear KP-MEW Equation Thu, 02 Jul 2015 08:11:20 +0000 Lie symmetry analysis is performed on a generalized two-dimensional nonlinear Kadomtsev-Petviashvili-modified equal width equation. The symmetries and adjoint representations for this equation are given and an optimal system of one-dimensional subalgebras is derived. The similarity reductions and exact solutions with the aid of -expansion method are obtained based on the optimal systems of one-dimensional subalgebras. Finally conservation laws are constructed by using the multiplier method. Khadijo Rashid Adem and Chaudry Masood Khalique Copyright © 2015 Khadijo Rashid Adem and Chaudry Masood Khalique. All rights reserved. A New Approach and Solution Technique to Solve Time Fractional Nonlinear Reaction-Diffusion Equations Thu, 02 Jul 2015 08:08:32 +0000 A new application of the hybrid generalized differential transform and finite difference method is proposed by solving time fractional nonlinear reaction-diffusion equations. This method is a combination of the multi-time-stepping temporal generalized differential transform and the spatial finite difference methods. The procedure first converts the time-evolutionary equations into Poisson equations which are then solved using the central difference method. The temporal differential transform method as used in the paper takes care of stability and the finite difference method on the resulting equation results in a system of diagonally dominant linear algebraic equations. The Gauss-Seidel iterative procedure then used to solve the linear system thus has assured convergence. To have optimized convergence rate, numerical experiments were done by using a combination of factors involving multi-time-stepping, spatial step size, and degree of the polynomial fit in time. It is shown that the hybrid technique is reliable, accurate, and easy to apply. Inci Cilingir Sungu and Huseyin Demir Copyright © 2015 Inci Cilingir Sungu and Huseyin Demir. All rights reserved. Reducing the Size of Combinatorial Optimization Problems Using the Operator Vaccine by Fuzzy Selector with Adaptive Heuristics Thu, 02 Jul 2015 06:27:41 +0000 Nowadays, solving optimally combinatorial problems is an open problem. Determining the best arrangement of elements proves being a very complex task that becomes critical when the problem size increases. Researchers have proposed various algorithms for solving Combinatorial Optimization Problems (COPs) that take into account the scalability; however, issues are still presented with larger COPs concerning hardware limitations such as memory and CPU speed. It has been shown that the Reduce-Optimize-Expand (ROE) method can solve COPs faster with the same resources; in this methodology, the reduction step is the most important procedure since inappropriate reductions, applied to the problem, will produce suboptimal results on the subsequent stages. In this work, an algorithm to improve the reduction step is proposed. It is based on a fuzzy inference system to classify portions of the problem and remove them, allowing COPs solving algorithms to utilize better the hardware resources by dealing with smaller problem sizes, and the use of metadata and adaptive heuristics. The Travelling Salesman Problem has been used as a case of study; instances that range from 343 to 3056 cities were used to prove that the fuzzy logic approach produces a higher percentage of successful reductions. Oscar Montiel and Francisco Javier Díaz Delgadillo Copyright © 2015 Oscar Montiel and Francisco Javier Díaz Delgadillo. All rights reserved. A Class of Parameter Estimation Methods for Nonlinear Muskingum Model Using Hybrid Invasive Weed Optimization Algorithm Thu, 02 Jul 2015 06:18:14 +0000 Nonlinear Muskingum models are important tools in hydrological forecasting. In this paper, we have come up with a class of new discretization schemes including a parameter to approximate the nonlinear Muskingum model based on general trapezoid formulas. The accuracy of these schemes is second order, if , but interestingly when , the accuracy of the presented scheme gets improved to third order. Then, the present schemes are transformed into an unconstrained optimization problem which can be solved by a hybrid invasive weed optimization (HIWO) algorithm. Finally, a numerical example is provided to illustrate the effectiveness of the present methods. The numerical results substantiate the fact that the presented methods have better precision in estimating the parameters of nonlinear Muskingum models. Aijia Ouyang, Li-Bin Liu, Zhou Sheng, and Fan Wu Copyright © 2015 Aijia Ouyang et al. All rights reserved. Numerical Reconstruction of Spring-Mass System from Two Nondisjoint Spectra Wed, 01 Jul 2015 12:35:46 +0000 A new numerical procedure is presented to reconstruct a fixed-free spring-mass system from two auxiliary spectra, which are nondisjoint. The method is a modification of the fast orthogonal reduction algorithm, which is less computationally expensive than others in the literature. Numerical results are obtained, showing the accuracy of the algorithm. Hubert Pickmann, Juan C. Egaña, and Ricardo L. Soto Copyright © 2015 Hubert Pickmann et al. All rights reserved. Structural Properties of the Unobservable Subspace Wed, 01 Jul 2015 11:26:49 +0000 The structural properties of the unobservable subspace are explored. In particular the canonical decomposition of the unobservable subspace as a direct sum of cyclic subspaces as well as the conditions for this subspace to be spectral for the system matrix is studied. These properties are applied to simple input-simple output (SISO) feedback systems by connecting the spectral decomposition of the unobservable subspace to the total cancellation of unobservable modes in the compensator with multiple transmission zeros in the plant. Juan Ignacio Mulero Martínez and Alfonso Baños Copyright © 2015 Juan Ignacio Mulero Martínez and Alfonso Baños. All rights reserved. On Analysis of Fractional Navier-Stokes Equations via Nonsingular Solutions and Approximation Wed, 01 Jul 2015 09:40:30 +0000 Until now, all the investigations on fractional or generalized Navier-Stokes equations have been done under some restrictions on the different values that can take the fractional order derivative parameter . In this paper, we analyze the existence and stability of nonsingular solutions to fractional Navier-Stokes equations of type () defined below. In the case where , we show that the stability of the (quadratic) convergence, when exploiting Newton’s method, can only be ensured when the first guess is sufficiently near the solution . We provide interesting well-posedness and existence results for the fractional model in two other cases, namely, when and Emile Franc Doungmo Goufo and Stella Mugisha Copyright © 2015 Emile Franc Doungmo Goufo and Stella Mugisha. All rights reserved. Inverse Problems via the “Generalized Collage Theorem” for Vector-Valued Lax-Milgram-Based Variational Problems Wed, 01 Jul 2015 09:34:51 +0000 We present an extended version of the Generalized Collage Theorem to deal with inverse problems for vector-valued Lax-Milgram systems. Numerical examples show how the method works in practical cases. H. Kunze, D. La Torre, K. Levere, and M. Ruiz Galán Copyright © 2015 H. Kunze et al. All rights reserved. The Optimization of Chiller Loading by Adaptive Neuro-Fuzzy Inference System and Genetic Algorithms Wed, 01 Jul 2015 08:49:48 +0000 A central air-conditioning (AC) system includes the chiller, chiller water pump, cooling water pump, cooling tower, and chilled water secondary pumps. Among these devices, the chiller consumes most power of the central AC system. In this paper, the adaptive neuro-fuzzy inference system (ANFIS) and genetic algorithm (GA) were utilized for optimizing the chiller loading. The ANFIS could construct a power consumption model of the chiller, reduce modeling period, and maintain the accuracy. GA could optimize the chiller loading for better energy efficiency. The simulating results indicated that ANFIS combined with GA could optimize the chiller loading. The power consumption was reduced by 6.32–18.96% when partial load ratio was located at the range of 0.6~0.95. The chiller power consumption model established by ANFIS could also increase the convergence speed. Therefore, the ANFIS with GA could optimize the chiller loading for reducing power consumption. Jyun-Ting Lu, Yung-Chung Chang, and Cheng-Yi Ho Copyright © 2015 Jyun-Ting Lu et al. All rights reserved. Some Identities Involving the Derivative of the First Kind Chebyshev Polynomials Wed, 01 Jul 2015 08:23:25 +0000 We use the combinatorial method and algebraic manipulations to obtain several interesting identities involving the power sums of the derivative of the first kind Chebyshev polynomials. This solved an open problem proposed by Li (2015). Tingting Wang and Han Zhang Copyright © 2015 Tingting Wang and Han Zhang. All rights reserved.