Search results for: mixed integer linear programming.

Authors: Rukaiya Suleiman Umar, Annah Kwadu Medugu

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Moringa oleifera is mainly used as herbal medicine in most homes in Northern Nigeria. The plant is easy to grow and thrives very well regardless the type of soil. Use of moringa leaves in food production can yield attractive varieties on menu. This paper evaluates the acceptability of dishes produced with fresh moringa leaves with a view to promoting it in popular restaurants. A three course menu consisting of cream of moringa soup as the starter, mixed meat moringa sauce with semovita as the main dish and moringa roll as sweet was produced and served to a 60-member taste panel made of three groups of 20 each. Respondents were asked to rate the organoleptic qualities of the samples on a 10-point bipolar scale ranging from 1 (Dislike extremely) – 10 (Like extremely). Data collected were treated to one sample t-test and One Way ANOVA. Results show that the panelists extremely like the moringa products. It is recommended that Moringa oleifera should be incorporated into meals which is more readily acceptable than medicine.

Keywords: Moringa oleifera, food production, menu planning, healthy living.

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Authors: A.K.M. Khaled Ahsan Talukder, Taibun Nessa, Kaushik Roy

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The weight constrained shortest path problem (WCSPP) is one of most several known basic problems in combinatorial optimization. Because of its importance in many areas of applications such as computer science, engineering and operations research, many researchers have extensively studied the WCSPP. This paper mainly concentrates on the reduction of total search space for finding WCSP using some existing Genetic Algorithm (GA). For this purpose, some controlled schemes of genetic operators are adopted on list chromosome representation. This approach gives a near optimum solution with smaller elapsed generation than classical GA technique. From further analysis on the matter, a new generalized schema theorem is also developed from the philosophy of Holland-s theorem.

Keywords: Genetic Algorithm, Evolutionary Optimization, Multi Objective Optimization, Non-linear Schema Theorem, WCSPP.

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Authors: C. S. Sastry, Saurabh Jain, Ashish Mishra

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Image retrieval is a topic where scientific interest is currently high. The important steps associated with image retrieval system are the extraction of discriminative features and a feasible similarity metric for retrieving the database images that are similar in content with the search image. Gabor filtering is a widely adopted technique for feature extraction from the texture images. The recently proposed sparsity promoting l1-norm minimization technique finds the sparsest solution of an under-determined system of linear equations. In the present paper, the l1-norm minimization technique as a similarity metric is used in image retrieval. It is demonstrated through simulation results that the l1-norm minimization technique provides a promising alternative to existing similarity metrics. In particular, the cases where the l1-norm minimization technique works better than the Euclidean distance metric are singled out.

Keywords: l1-norm minimization, content based retrieval, modified Gabor function.

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Authors: Aichun Feng, Zhi-Min Chen, Jing Tang Xing

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A two-dimensional linear wave-body interaction problem can be solved using a desingularized integral method by placing free surface Rankine sources over calm water surface and satisfying boundary conditions at prescribed collocation points on the calm water surface. A new free-surface Rankine source distribution scheme, determined by the intersection points of free surface and body surface, is developed to reduce numerical computation cost. Associated with this, a new treatment is given to the intersection point. The present scheme results are in good agreement with traditional numerical results and measurements.

Keywords: Source point distribution, panel method, Rankine source, desingularized algorithm.

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Authors: Quy Dang Nguyen, Reza Nakhaie Jazar

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The paper investigates vibration dynamics of tire-road separation for a quarter-car model; this separation model is developed to be close to the real situation considering the tire is able to separate from the ground plane. A set of piecewise linear mathematical models is developed and matches the in-contact and no-contact states to be considered as mother models for further investigations. The bound dynamics are numerically simulated in the time response and phase portraits. The separation analysis may determine which values of suspension parameters can delay and avoid the no-contact phenomenon, which results in improving ride comfort and eliminating the potentially dangerous oscillation. Finally, model verification is carried out in the MSC-ADAMS environment.

Keywords: Quarter-car vibrations, tire-road separation, separation analysis, separation dynamics, ride comfort, ADAMS validation.

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Authors: Chien-Hua Lee, Cheng-Yi Chen

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The stability test problem for homogeneous large-scale perturbed bilinear time-delay systems subjected to constrained inputs is considered in this paper. Both nonlinear uncertainties and interval systems are discussed. By utilizing the Lyapunove equation approach associated with linear algebraic techniques, several delay-independent criteria are presented to guarantee the robust stability of the overall systems. The main feature of the presented results is that although the Lyapunov stability theorem is used, they do not involve any Lyapunov equation which may be unsolvable. Furthermore, it is seen the proposed schemes can be applied to solve the stability analysis problem of large-scale time-delay systems.

Keywords: homogeneous bilinear system, constrained input, time-delay, uncertainty, transient response, decay rate.

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Authors: G. Çelik Gül, F. Kurtuluş

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Colemanite is the most common borate mineral, and the main source of the boron required by plants, human, and earth. Transition metals exhibit optical and physical properties such as; non-linear optical character, structural diversity, thermal stability, long cycle life and luminescent radiation. The doping of colemanite with a transition metal, bring it very interesting and attractive properties which make them applicable in industry. Iron doped calcium borate was synthesized by conventional solid state method at 1200 °C for 12 h with a systematic pathway. X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, scanning electron microscopy/energy dispersive analyze (SEM/EDS) were used to characterize structural and morphological properties. Also, thermal properties were recorded by thermogravimetric-differential thermal analysis (TG/DTA). 

Keywords: Colemanite, conventional synthesis, powder x-ray diffraction, borates.

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Authors: P. Suryakumari, P. Kantarao

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Optimal Power Flow (OPF) problem in electrical power system is considered as a static, non-linear, multi-objective or a single objective optimization problem. This paper presents an algorithm for solving the voltage stability objective reactive power dispatch problem in a power system .The proposed approach employs cat swarm optimization algorithm for optimal settings of RPD control variables. Generator terminal voltages, reactive power generation of the capacitor banks and tap changing transformer setting are taken as the optimization variables. CSO algorithm is tested on standard IEEE 30 bus system and the results are compared with other methods to prove the effectiveness of the new algorithm. As a result, the proposed method is the best for solving optimal reactive power dispatch problem.

Keywords: RPD problem, voltage stability enhancement, CSO algorithm.

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Authors: Sidshchadhaa Aumted, Shuhei Shiina, Hiroshi Takami

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In this paper, we propose an advanced ILQ control for the buck-converter via two-degrees of freedom servo-system. Our presented strategy is based on Inverse Linear Quadratic (ILQ) servo-system controller without solving Riccati-s equation directly. The optimal controller of the current and voltage control system is designed. The stability and robust control are analyzed. A conscious and persistent effort has been made to improve ILQ control via two-degrees of freedom guarantees the optimal gains on the basis of polynomial pole assignment, which our results of the proposed strategy shows that the advanced ILQ control can be controlled independently the step response and the disturbance response by appending a feed-forward compensator.

Keywords: Optimal voltage control, inverse LQ design method, second order polynomial, two-degrees of freedom.

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Authors: Marzuki Khalid, RubiyahYusof, AnisSalwaMohdKhairuddin

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An automated wood recognition system is designed to classify tropical wood species.The wood features are extracted based on two feature extractors: Basic Grey Level Aura Matrix (BGLAM) technique and statistical properties of pores distribution (SPPD) technique. Due to the nonlinearity of the tropical wood species separation boundaries, a pre classification stage is proposed which consists ofKmeans clusteringand kernel discriminant analysis (KDA). Finally, Linear Discriminant Analysis (LDA) classifier and KNearest Neighbour (KNN) are implemented for comparison purposes. The study involves comparison of the system with and without pre classification using KNN classifier and LDA classifier.The results show that the inclusion of the pre classification stage has improved the accuracy of both the LDA and KNN classifiers by more than 12%.

Keywords: Tropical wood species, nonlinear data, featureextractors, classification

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Authors: A. R. Rashid, A. S. Siti, F. R. Siti, A. R. Reena, H. S. S. Sharifah, F. Z. Nurul, W. A. Nazni

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This study was conducted to examine the effects of ketum extract on development of Chrysomya rufifacies and to analyze the presence of mitragynine in the larvae samples. 110 newly emerged first instar larvae of C. rufifacies were introduced on ketum extract-mixed cow liver at doses of 0, 20, 40 and 60g. Blowfly development rate was determined with 12 hour intervals and mitragynine in larvae was extracted and quantitated. C. rufifacies in control group took about 192 hours to complete their development from first instar larvae to adult blowfly; meanwhile blowfly form from the highest dose of ketum was 264 hours. Mitragynine was detected in all groups of treatment, except for control. In conclusion, the presence of mitragynine in C. rufifacies is affected in delaying development rates of the blowfly for up to 62 hours or 3 days. Chemical analysis of mitragynine from larvae samples showed that this alkaloid present in all specimens analyzed. 

Keywords: Chrysomya rufifacies, Ketum, Mitragynine, Postmortem Interval (PMI).

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Authors: Nadaniela Egidi, Pierluigi Maponi

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The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts and its two-dimensional formulation is a Fredholm integral equation of second kind. This integral equation provides a formulation for the direct scattering problem but has to be solved several times in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. To improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning and propose an algorithm to evaluate the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e. Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem.

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Authors: Kesari Verma, Aniruddha S. Thoke, Pritam Singh

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Automatic face detection is a complex problem in image processing. Many methods exist to solve this problem such as template matching, Fisher Linear Discriminate, Neural Networks, SVM, and MRC. Success has been achieved with each method to varying degrees and complexities. In proposed algorithm we used upright, frontal faces for single gray scale images with decent resolution and under good lighting condition. In the field of face recognition technique the single face is matched with single face from the training dataset. The author proposed a neural network based face detection algorithm from the photographs as well as if any test data appears it check from the online scanned training dataset. Experimental result shows that the algorithm detected up to 95% accuracy for any image.

Keywords: Face Detection, Face Recognition, NN Approach, PCA Algorithm.

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Authors: Ihor Trots, Yuriy Tasinkevych, Andrzej Nowicki, Marcin Lewandowski

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The paper presents the multi-element synthetic transmit aperture (MSTA) method with a small number of elements transmitting and all elements apertures in medical ultrasound imaging. As compared to the other methods MSTA allows to increase the system frame rate and provides the best compromise between penetration depth and lateral resolution. In the experiments a 128-element linear transducer array with 0.3 mm pitch excited by a burst pulse of 125 ns duration were used. The comparison of 2D ultrasound images of tissue mimicking phantom obtained using the STA and the MSTA methods is presented to demonstrate the benefits of the second approach. The results were obtained using SA algorithm with transmit and receive signals correction based on a single element directivity function.

Keywords: Beamforming, frame rate, synthetic aperture, ultrasound imaging

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Authors: Liudmyla Koliechkina, Olena Dvirna

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The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: Discrete set, linear combinatorial optimization, multi-objective optimization, multipermutation, Pareto solutions, partial permutation set, permutation, structural graph.

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Authors: C. Pislaru, A. Shebani

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This paper uses the radial basis function neural network (RBFNN) for system identification of nonlinear systems. Five nonlinear systems are used to examine the activity of RBFNN in system modeling of nonlinear systems; the five nonlinear systems are dual tank system, single tank system, DC motor system, and two academic models. The feed forward method is considered in this work for modelling the non-linear dynamic models, where the KMeans clustering algorithm used in this paper to select the centers of radial basis function network, because it is reliable, offers fast convergence and can handle large data sets. The least mean square method is used to adjust the weights to the output layer, and Euclidean distance method used to measure the width of the Gaussian function.

Keywords: System identification, Nonlinear system, Neural networks, RBF neural network.

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Authors: Mohd Noah A. Rahman, Afzaal H. Seyal, Sharul T. Tajuddin, Hartiny Md Azmi

Abstract:

Taking into consideration the real time situation specifically the higher academic institutions, small, medium to large companies, public to private sectors and the remaining sectors, do experience the inventory or asset shrinkages due to theft, loss or even inventory tracking errors. This happening is due to a zero or poor security systems and measures being taken and implemented in their organizations. Henceforth, implementing the Radio Frequency Identification (RFID) technology into any manual or existing web-based system or web application can simply deter and will eventually solve certain major issues to serve better data retrieval and data access. Having said, this manual or existing system can be enhanced into a mobile-based system or application. In addition to that, the availability of internet connections can aid better services of the system. Such involvement of various technologies resulting various privileges to individuals or organizations in terms of accessibility, availability, mobility, efficiency, effectiveness, real-time information and also security. This paper will look deeper into the integration of mobile devices with RFID technologies with the purpose of asset tracking and control. Next, it is to be followed by the development and utilization of MongoDB as the main database to store data and its association with RFID technology. Finally, the development of a web based system which can be viewed in a mobile based formation with the aid of Hypertext Preprocessor (PHP), MongoDB, Hyper-Text Markup Language 5 (HTML5), Android, JavaScript and AJAX programming language.

Keywords: RFID, asset tracking system, MongoDB, NoSQL.

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Authors: Rafat Alshorman, Walter Hussak

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Existing work in temporal logic on representing the execution of infinitely many transactions, uses linear-time temporal logic (LTL) and only models two-step transactions. In this paper, we use the comparatively efficient branching-time computational tree logic CTL and extend the transaction model to a class of multistep transactions, by introducing distinguished propositional variables to represent the read and write steps of n multi-step transactions accessing m data items infinitely many times. We prove that the well known correspondence between acyclicity of conflict graphs and serializability for finite schedules, extends to infinite schedules. Furthermore, in the case of transactions accessing the same set of data items in (possibly) different orders, serializability corresponds to the absence of cycles of length two. This result is used to give an efficient encoding of the serializability condition into CTL.

Keywords: computational tree logic, serializability, multi-step transactions.

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Authors: Yasar Bicer, Serif Yilmaz

Abstract:

In present study, two kinds of thermal power plant ashes; one the fly ash and the other waste ash are mixed with adhesive tragacanth and cement to produce new composite materials. 48 new samples are produced by varying the percentages of the fly ash, waste ash, cement and tragacanth. The new samples are subjected to some tests to find out their properties such as thermal conductivity, compressive strength, tensile strength and sucking capability of water. It is found that; the thermal conductivity decreases with increasing amount of tragacanth in the mixture. The compressive, tensile strength increases when the rate of tragacanth is up to 1%, whilst as the amount of tragacanth increases up to 1.5%, the compressive, tensile strength decreases slightly. The rate of water absorption of samples was more than 30%. From this result, it is concluded that these materials can not be used as external plaster or internal plaster material that faces to water. They can be used in internal plaster unless touching water and they can be used as cover plaster under roof and riprap material in sandwich panels. It is also found that, these materials can be cut with saw, drilled with screw and painted with any kind of paint.

Keywords: Fly ash, tragacanth, cement, composite material.

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Authors: Jiming Yang

Abstract:

A kind of singularly perturbed boundary value problems is under consideration. In order to obtain its approximation, simple upwind difference discretization is applied. We use a moving mesh iterative algorithm based on equi-distributing of the arc-length function of the current computed piecewise linear solution. First, a maximum norm a posteriori error estimate on an arbitrary mesh is derived using a different method from the one carried out by Chen [Advances in Computational Mathematics, 24(1-4) (2006), 197-212.]. Then, basing on the properties of discrete Green-s function and the presented posteriori error estimate, we theoretically prove that the discrete solutions computed by the algorithm are first-order uniformly convergent with respect to the perturbation parameter ε.

Keywords: Convergence analysis, green's function, singularly perturbed, equi-distribution, moving mesh.

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Authors: Seong-wan Baik, Soo-young Ye, Byeong-cheol Choi, Gye-rok Jeon

Abstract:

The measurement of anesthetic depth is necessary in anesthesiology. NN10 is very simple method among the RR intervals analysis methods. NN10 parameter means the numbers of above the 10 ms intervals of the normal to normal RR intervals. Bispectrum analysis is defined as 2D FFT. EEG signal reflected the non-linear peristalsis phenomena according to the change brain function. After analyzing the bispectrum of the 2 dimension, the most significant power spectrum density peaks appeared abundantly at the specific area in awakening and anesthesia state. These points are utilized to create the new index since many peaks appeared at the specific area in the frequency coordinate. The measured range of an index was 0-100. An index is 20-50 at an anesthesia, while the index is 90-60 at the awake. In this paper, the relation between NN10 parameter using ECG and bisepctrum index using EEG is observed to estimate the depth of anesthesia during anesthesia and then we estimated the utility of the anesthetic.

Keywords: Anesthesia, Bispectrum index, ECG, EEG

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Authors: Fernando Pérez, Humberto Sossa, Rigoberto Martínez, Daniel Lorias, Arturo Minor

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This paper presents a system for tracking the movement of laparoscopic instruments which is based on an orthogonal system of webcams and video image processing. The movements are captured with two webcams placed orthogonally inside of the physical trainer. On the image, the instruments were detected by using color markers placed on the distal tip of each instrument. The 3D position of the tip of the instrument within the work space was obtained by linear triangulation method. Preliminary results showed linearity and repeatability in the motion tracking with a resolution of 0.616 mm in each axis; the accuracy of the system showed a 3D instrument positioning error of 1.009 ± 0.101 mm. This tool is a portable and low-cost alternative to traditional tracking devices and a trustable method for the objective evaluation of the surgeon’s surgical skills.

Keywords: Laparoscopic Surgery, Orthogonal Vision, Tracking Instruments, Triangulation.

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Authors: Rashid S. S., Alam M. Z.

Abstract:

A statistical optimization of the saccharification process of EFB was studied. The statistical analysis was done by applying faced centered central composite design (FCCCD) under response surface methodology (RSM). In this investigation, EFB dose, enzyme dose and saccharification period was examined, and the maximum 53.45% (w/w) yield of reducing sugar was found with 4% (w/v) of EFB, 10% (v/v) of enzyme after 120 hours of incubation. It can be calculated that the conversion rate of cellulose content of the substrate is more than 75% (w/w) which can be considered as a remarkable achievement. All the variables, linear, quadratic and interaction coefficient, were found to be highly significant, other than two coefficients, one quadratic and another interaction coefficient. The coefficient of determination (R2) is 0.9898 that confirms a satisfactory data and indicated that approximately 98.98% of the variability in the dependent variable, saccharification of EFB, could be explained by this model.

Keywords: Face centered central composite design (FCCCD), Liquid state bioconversion (LSB), Palm oil mill effluent, Trichoderma reesei RUT C-30.

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Authors: Ramirez D. Edgar I., Angeles H. José J., Ruiz C. Osvaldo, Jacobo A. Victor H., Ortiz P. Armando

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Knowledge of bone mechanical properties is important for bone substitutes design and fabrication, and more efficient prostheses development. The aim of this study is to characterize the viscoelastic behavior of bone specimens, through stress relaxation and fatigue tests performed to trabecular bone samples from bovine femoral heads. Relaxation tests consisted on preloading the samples at five different magnitudes and evaluate them for 1020 seconds, adjusting the results to a KWW mathematical model. Fatigue tests consisted of 700 load cycles and analyze their status at the end of the tests. As a conclusion we have that between relaxation stress and each preload there is linear relation and for samples with initial Young´s modulus greater than 1.5 GPa showed no effects due fatigue test loading cycles.

Keywords: Bone viscoelasticity, fatigue test, stress relaxation test, trabecular bone properties.

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Authors: K. Govender, M. Sinclair

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This paper demonstrates a proof of concept whereby shorter trips and land use densification can be promoted through an alternative approach to planning and implementation of road infrastructure in the South African context. It briefly discusses how the development of the Compact City concept relies on a combination of promoting shorter trips and densification through a change in focus in road infrastructure provision. The methodology developed in this paper uses a traffic model to test the impact of synthesized deterrence functions on congestion locations in the road network through the assignment of traffic on the study network. The results from this study demonstrate that intelligent planning of road infrastructure can indeed promote reduced urban sprawl, increased residential density and mixed-use areas which are supported by an efficient public transport system; and reduced dependence on the freeway network with a fixed road infrastructure budget. The study has resonance for all cities where urban sprawl is seemingly unstoppable.

Keywords: Compact cities, densification, road infrastructure planning, transportation modeling.

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Authors: Aomar Anane, Omar Chakrone, Loubna Moutaouekkil

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As p-Laplacian equations have been widely applied in field of the fluid mechanics and nonlinear elastic mechanics, it is necessary to investigate the periodic solutions of functional differential equations involving the scalar p-Laplacian. By using Mawhin’s continuation theorem, we study the existence of periodic solutions for p-Laplacian neutral Rayleigh equation (ϕp(x(t)−c(t)x(t − r))) + f(x(t)) + g1(x(t − τ1(t, |x|∞))) + β(t)g2(x(t − τ2(t, |x|∞))) = e(t), It is meaningful that the functions c(t) and β(t) are allowed to change signs in this paper, which are different from the corresponding ones of known literature.

Keywords: periodic solution, neutral Rayleigh equation, variable sign, Deviating argument, p-Laplacian, Mawhin’s continuation.

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Authors: Suppara Charoenpoom

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The objectives of this research was to design and develop a quality management of the school buildings and environment. A quantitative and qualitative mixed research methodology was used. The population sample included 14 directors of primary schools. Two research tools were used. The first research tool included an in-depth interview and questionnaire. The second research tool included the Quality Business Process and Quality Work Procedure, and a Key Performance Indicator of each activity. The statistics included mean and standard deviation. The findings for the development of a quality management process of buildings and environment administration of the basic schools consisted of one quality business process (QBP) and seven quality work processes (QWP). The result from the experts’ evaluation revealed that the process and implementation of quality management of the school buildings and environment has passed the inspection process with consensus. This implies that the process of quality management of the school buildings and environment is suitable for implementation. Moreover, the level of agreement in the feasibility of the implementation of this plan had the mean in the range of 0.64-1.00 which suggests the design of the new plan is acceptable.

Keywords: Process, Building, Environment.

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Authors: Jin Zhang, Wing Lon Ng

Abstract:

In recent years, copulas have become very popular in financial research and actuarial science as they are more flexible in modelling the co-movements and relationships of risk factors as compared to the conventional linear correlation coefficient by Pearson. However, a precise estimation of the copula parameters is vital in order to correctly capture the (possibly nonlinear) dependence structure and joint tail events. In this study, we employ two optimization heuristics, namely Differential Evolution and Threshold Accepting to tackle the parameter estimation of multivariate t distribution models in the EML approach. Since the evolutionary optimizer does not rely on gradient search, the EML approach can be applied to estimation of more complicated copula models such as high-dimensional copulas. Our experimental study shows that the proposed method provides more robust and more accurate estimates as compared to the IFM approach.

Keywords: Copula Models, Student t Copula, Parameter Inference, Differential Evolution, Threshold Accepting.

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Authors: John Kabuba, Antoine Mulaba-Bafubiandi, Kim Battle

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In this study a neural network (NN) was proposed to predict the sorption of binary mixture of copper-cobalt ions into clinoptilolite as ion-exchanger. The configuration of the backpropagation neural network giving the smallest mean square error was three-layer NN with tangent sigmoid transfer function at hidden layer with 10 neurons, linear transfer function at output layer and Levenberg-Marquardt backpropagation training algorithm. Experiments have been carried out in the batch reactor to obtain equilibrium data of the individual sorption and the mixture of coppercobalt ions. The obtained modeling results have shown that the used of neural network has better adjusted the equilibrium data of the binary system when compared with the conventional sorption isotherm models.

Keywords: Adsorption isotherm, binary system, neural network; sorption

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Authors: Xuran Zhang, Huiru Chen

Abstract:

In recent years, China has made great efforts to cultivate and develop the housing rental market, especially the rental-type public housing, which has been paid attention to by all sectors of the society. This paper takes Hangzhou rental-type public housing as the research object, and divides it into three development stages according to the different supply modes of rental-type public housing. Through data collection and field research, the paper summarizes the spatial characteristics of rental-type public housing from the five perspectives of spatial planning, spatial layout, spatial integration, spatial organization and spatial configuration. On this basis, the paper proposes the optimization of the spatial layout. The study concludes that the spatial layout of rental-type public housing should be coordinated with the development of urban planning. When planning and constructing, it is necessary to select more mixed construction modes, to be properly centralized, and to improve the surrounding transportation service facilities.  It is hoped that the recommendations in this paper will provide a reference for the further development of rental-type public housing in Hangzhou.

Keywords: Hangzhou, rental-type public housing, spatial distribution, spatial optimization.

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