Search results for: generating function

Authors: H. Ozbasaran

Abstract:

Lateral torsional buckling is a global buckling mode which should be considered in design of slender structural members under flexure about their strong axis. It is possible to compute the load which causes lateral torsional buckling of a beam by finite element analysis, however, closed form equations are needed in engineering practice for calculation ease which can be obtained by using energy method. In lateral torsional buckling applications of energy method, a proper function for the critical lateral torsional buckling mode should be chosen which can be thought as the variation of twisting angle along the buckled beam. Accuracy of the results depends on how close is the chosen function to the exact mode. Since critical lateral torsional buckling mode of the cantilever I-beams varies due to material properties, section properties and loading case, the hardest step is to determine a proper mode function in application of energy method. This paper presents an approximate function for critical lateral torsional buckling mode of doubly symmetric cantilever I-beams. Coefficient matrices are calculated for concentrated load at free end, uniformly distributed load and constant moment along the beam cases. Critical lateral torsional buckling modes obtained by presented function and exact solutions are compared. It is found that the modes obtained by presented function coincide with differential equation solutions for considered loading cases.

Keywords: Buckling mode, cantilever, lateral-torsional buckling, I-beam.

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Authors: H. Bevrani, N. Najafi

Abstract:

This paper uses p-tolerance with the lowest posterior loss, quadratic loss function, average length criteria, average coverage criteria, and worst outcome criterion for computing of sample size to estimate proportion in Binomial probability function with Beta prior distribution. The proposed methodology is examined, and its effectiveness is shown.

Keywords: Bayesian inference, Beta-binomial Distribution, LPLcriteria, quadratic loss function.

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Authors: Hnin Hnin Kyi, Khaing Khaing Aye

Abstract:

Acoustic function plays an important role in aerodynamic mechanical engineering. It can classify the kind of air-vehicle such as subsonic or supersonic. Acoustic velocity relates with velocity and Mach number. Mach number relates again acoustic stability or instability condition. Mach number plays an important role in growth or decay in energy system. Acoustic is a function of temperature and temperature is directly proportional to pressure. If we control the pressure, we can control acoustic function. To get pressure stability condition, we apply Navier-Stokes equations.

Keywords: Acoustic velocity, Irrotational, Mach number, Rotational.

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Authors: Tsunwai Gary Yip

Abstract:

Phase locked loops for data links operating at 10 Gb/s or faster are low phase noise devices designed to operate with a low jitter reference clock. Characterization of their jitter transfer function is difficult because the intrinsic noise of the device is comparable to the random noise level in the reference clock signal. A linear model is proposed to account for the intrinsic noise of a PLL. The intrinsic noise data of a PLL for 10 Gb/s links is presented. The jitter transfer function of a PLL in a test chip for 12.8 Gb/s data links was determined in experiments using the 400 MHz reference clock as the source of simultaneous excitations over a wide range of frequency. The result shows that the PLL jitter transfer function can be approximated by a second order linear model.

Keywords: Intrinsic phase noise, jitter in data link, PLL jitter transfer function, high speed clocking in electronic circuit

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Authors: C. Pislaru, A. Shebani

Abstract:

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: Abdu Masanawa Sagir

Abstract:

In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations of the form y′′ = f(x,y), a < = x < = b with associated initial or boundary conditions. The continuaous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different three discrete schemes, each of order (4,4,4)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on linear and non-linear ordinary differential equations whose solutions are oscillatory or nearly periodic in nature, and the results obtained compared favourably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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Authors: Chetneti Srisa-an

Abstract:

In Knowledge and Data Engineering field, relational database is the best repository to store data in a real world. It has been using around the world more than eight decades. Normalization is the most important process for the analysis and design of relational databases. It aims at creating a set of relational tables with minimum data redundancy that preserve consistency and facilitate correct insertion, deletion, and modification. Normalization is a major task in the design of relational databases. Despite its importance, very few algorithms have been developed to be used in the design of commercial automatic normalization tools. It is also rare technique to do it automatically rather manually. Moreover, for a large and complex database as of now, it make even harder to do it manually. This paper presents a new complete automated relational database normalization method. It produces the directed graph and spanning tree, first. It then proceeds with generating the 2NF, 3NF and also BCNF normal forms. The benefit of this new algorithm is that it can cope with a large set of complex function dependencies.

Keywords: Relational Database, Functional Dependency, Automatic Normalization, Primary Key, Spanning tree.

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Authors: Panpan Xu, Shulin Sui

Abstract:

The crossover probability and mutation probability are the two important factors in genetic algorithm. The adaptive genetic algorithm can improve the convergence performance of genetic algorithm, in which the crossover probability and mutation probability are adaptively designed with the changes of fitness value. We apply adaptive genetic algorithm into a function optimization problem. The numerical experiment represents that adaptive genetic algorithm improves the convergence speed and avoids local convergence.

Keywords: Genetic algorithm, Adaptive genetic algorithm, Function optimization.

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Authors: Tsunwai Gary Yip

Abstract:

Phase locked loops in 10 Gb/s and faster data links are low phase noise devices. Characterization of their phase jitter transfer functions is difficult because the intrinsic noise of the PLLs is comparable to the phase noise of the reference clock signal. The problem is solved by using a linear model to account for the intrinsic noise. This study also introduces a novel technique for measuring the transfer function. It involves the use of the reference clock as a source of wideband excitation, in contrast to the commonly used sinusoidal excitations at discrete frequencies. The data reported here include the intrinsic noise of a PLL for 10 Gb/s links and the jitter transfer function of a PLL for 12.8 Gb/s links. The measured transfer function suggests that the PLL responded like a second order linear system to a low noise reference clock.

Keywords: Intrinsic phase noise, jitter in data link, PLL jitter transfer function, high speed clocking in electronic circuit

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Authors: Bing Yu , Xingshi He

Abstract:

In this paper, Differential Evolution (DE) algorithm, a new promising evolutionary algorithm, is proposed to train Radial Basis Function (RBF) network related to automatic configuration of network architecture. Classification tasks on data sets: Iris, Wine, New-thyroid, and Glass are conducted to measure the performance of neural networks. Compared with a standard RBF training algorithm in Matlab neural network toolbox, DE achieves more rational architecture for RBF networks. The resulting networks hence obtain strong generalization abilities.

Keywords: differential evolution, neural network, Rbf function

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Authors: Yoichi Hikino, Mutsuto Kawahara

Abstract:

The purpose of this study is to derive optimal shapes of a body located in viscous flows by the finite element method using the acoustic velocity and the four-step explicit scheme. The formulation is based on an optimal control theory in which a performance function of the fluid force is introduced. The performance function should be minimized satisfying the state equation. This problem can be transformed into the minimization problem without constraint conditions by using the adjoint equation with adjoint variables corresponding to the state equation. The performance function is defined by the drag and lift forces acting on the body. The weighted gradient method is applied as a minimization technique, the Galerkin finite element method is used as a spatial discretization and the four-step explicit scheme is used as a temporal discretization to solve the state equation and the adjoint equation. As the interpolation, the orthogonal basis bubble function for velocity and the linear function for pressure are employed. In case that the orthogonal basis bubble function is used, the mass matrix can be diagonalized without any artificial centralization. The shape optimization is performed by the presented method.

Keywords: Shape Optimization, Optimal Control Theory, Finite Element Method, Weighted Gradient Method, Fluid Force, Orthogonal Basis Bubble Function, Four-step Explicit Scheme, Acoustic Velocity.

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Authors: Lars Laußat, Manfred Helmus, Kamil Szczesny, Markus König

Abstract:

As one result of the project “Reactive Construction Project Scheduling using Real Time Construction Logistic Data and Simulation”, a procedure for using data about uncertain resource availability assumptions in reactive scheduling processes has been developed. Prediction data about resource availability is generated in a formalized way using real-time monitoring data e.g. from auto-ID systems on the construction site and in the supply chains. The paper focusses on the formalization of the procedure for monitoring construction logistic processes, for the detection of disturbance and for generating of new and uncertain scheduling assumptions for the reactive resource constrained simulation procedure that is and will be further described in other papers.

Keywords: Auto-ID, Construction Logistic, Fuzzy, Monitoring, RFID, Scheduling.

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Authors: K. C. Meher, R. K. Swain, C. K. Chanda

Abstract:

This paper gives an intuition regarding glowworm swarm optimization (GSO) technique to solve dynamic economic dispatch (DED) problems of thermal generating units. The objective of the problem is to schedule optimal power generation of dedicated thermal units over a specific time band. In this study, Glowworm swarm optimization technique enables a swarm of agents to split into subgroup, exhibit simultaneous taxis towards each other and rendezvous at multiple optima (not necessarily equal) of a given multimodal function. The feasibility of the GSO method has been tested on ten-unit-test systems where the power balance constraints, operating limits, valve point effects, and ramp rate limits are taken into account. The results obtained by the proposed technique are compared with other heuristic techniques. The results show that GSO technique is capable of producing better results.

Keywords: Dynamic economic dispatch, Glowworm swarm optimization, Luciferin, Valve–point loading effect, Ramp rate limits.

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Authors: U.K. Saha, L.K. Arora

Abstract:

The multiindex Mittag-Leffler (M-L) function and the multiindex Dzrbashjan-Gelfond-Leontiev (D-G-L) differentiation and integration play a very pivotal role in the theory and applications of generalized fractional calculus. The object of this paper is to investigate the relations that exist between the Riemann-Liouville fractional calculus and multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration with multiindex Mittag-Leffler function.

Keywords: Multiindex Mittag-Leffler function, Multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration, Riemann-Liouville fractional integrals and derivatives.

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Authors: Byung-Joo Oh

Abstract:

This paper describes a method to improve the robustness of a face recognition system based on the combination of two compensating classifiers. The face images are preprocessed by the appearance-based statistical approaches such as Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA). LDA features of the face image are taken as the input of the Radial Basis Function Network (RBFN). The proposed approach has been tested on the ORL database. The experimental results show that the LDA+RBFN algorithm has achieved a recognition rate of 93.5%

Keywords: Face recognition, linear discriminant analysis, radial basis function network.

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Authors: M. Beisenbi, A. Sagymbay, S. Beisembina, A. Satpayeva

Abstract:

In this paper, the problem of unstable and deterministic chaotic processes in control systems is considered. The synthesis of a control system in the class of two-parameter structurally stable mappings is demonstrated. This is realized via the gradient-velocity method of Lyapunov vector functions. It is shown that the gradient-velocity method of Lyapunov vector functions allows generating an aperiodic robust stable system with the desired characteristics. A simple solution to the problem of synthesis of control systems for unstable and deterministic chaotic processes is obtained. Moreover, it is applicable for complex systems.

Keywords: Control system synthesis, deterministic chaotic processes, Lyapunov vector function, robust stability, structurally stable mappings.

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Authors: M. Govindarajan, R. M.Chandrasekaran

Abstract:

Text data mining is a process of exploratory data analysis. Classification maps data into predefined groups or classes. It is often referred to as supervised learning because the classes are determined before examining the data. This paper describes proposed radial basis function Classifier that performs comparative crossvalidation for existing radial basis function Classifier. The feasibility and the benefits of the proposed approach are demonstrated by means of data mining problem: direct Marketing. Direct marketing has become an important application field of data mining. Comparative Cross-validation involves estimation of accuracy by either stratified k-fold cross-validation or equivalent repeated random subsampling. While the proposed method may have high bias; its performance (accuracy estimation in our case) may be poor due to high variance. Thus the accuracy with proposed radial basis function Classifier was less than with the existing radial basis function Classifier. However there is smaller the improvement in runtime and larger improvement in precision and recall. In the proposed method Classification accuracy and prediction accuracy are determined where the prediction accuracy is comparatively high.

Keywords: Text Data Mining, Comparative Cross-validation, Radial Basis Function, runtime, accuracy.

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Authors: Katsunori Miura, Kiyoshi Akama, Hiroshi Mabuchi

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In the Equivalent Transformation (ET) computation model, a program is constructed by the successive accumulation of ET rules. A method by meta-computation by which a correct ET rule is generated has been proposed. Although the method covers a broad range in the generation of ET rules, all important ET rules are not necessarily generated. Generation of more ET rules can be achieved by supplementing generation methods which are specialized for important ET rules. A Specialization-by-Equation (Speq) rule is one of those important rules. A Speq rule describes a procedure in which two variables included in an atom conjunction are equalized due to predicate constraints. In this paper, we propose an algorithm that systematically and recursively generate Speq rules and discuss its effectiveness in the synthesis of ET programs. A Speq rule is generated based on proof of a logical formula consisting of given atom set and dis-equality. The proof is carried out by utilizing some ET rules and the ultimately obtained rules in generating Speq rules.

Keywords: Equivalent transformation, ET rule, Equation of two variables, Rule generation, Specialization-by-Equation rule

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Authors: Satyendra Nath Mandal, J. Pal Choudhury, Dilip De, S. R. Bhadra Chaudhuri

Abstract:

The selection for plantation of a particular type of mustard plant depending on its productivity (pod yield) at the stage of maturity. The growth of mustard plant dependent on some parameters of that plant, these are shoot length, number of leaves, number of roots and roots length etc. As the plant is growing, some leaves may be fall down and some new leaves may come, so it can not gives the idea to develop the relationship with the seeds weight at mature stage of that plant. It is not possible to find the number of roots and root length of mustard plant at growing stage that will be harmful of this plant as roots goes deeper to deeper inside the land. Only the value of shoot length which increases in course of time can be measured at different time instances. Weather parameters are maximum and minimum humidity, rain fall, maximum and minimum temperature may effect the growth of the plant. The parameters of pollution, water, soil, distance and crop management may be dominant factors of growth of plant and its productivity. Considering all parameters, the growth of the plant is very uncertain, fuzzy environment can be considered for the prediction of shoot length at maturity of the plant. Fuzzification plays a greater role for fuzzification of data, which is based on certain membership functions. Here an effort has been made to fuzzify the original data based on gaussian function, triangular function, s-function, Trapezoidal and L –function. After that all fuzzified data are defuzzified to get normal form. Finally the error analysis (calculation of forecasting error and average error) indicates the membership function appropriate for fuzzification of data and use to predict the shoot length at maturity. The result is also verified using residual (Absolute Residual, Maximum of Absolute Residual, Mean Absolute Residual, Mean of Mean Absolute Residual, Median of Absolute Residual and Standard Deviation) analysis.

Keywords: Fuzzification, defuzzification, gaussian function, triangular function, trapezoidal function, s-function, , membership function, residual analysis.

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Authors: S. Choodoung, U. Smutkupt

Abstract:

This study systemizes processes and methods in wooden furniture design that contains uniqueness in function and aesthetics. The study was done by research and analysis for designer-s consideration factors that affect function and production. Therefore, the study result indicates that such factors are design process (planning for design, product specifications, concept design, product architecture, industrial design, production), design evaluation as well as wooden furniture design dependent factors i.e. art (art style; furniture history, form), functionality (the strength and durability, area place, using), material (appropriate to function, wood mechanical properties), joints, cost, safety, and social responsibility. Specifically, all aforementioned factors affect good design. Resulting from direct experience gained through user-s usage, the designer must design the wooden furniture systemically and effectively. As a result, this study selected dinning armchair as a case study with all involving factors and all design process stated in this study.

Keywords: Furniture Design, Function Design, Aesthetic, Wooden Furniture.

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Authors: Tao Peng, Jing Zhao, Yanqing Xu, Jing Cai

Abstract:

Due to missing/ambiguous boundaries between the prostate and neighboring structures, the presence of shadow artifacts, as well as the large variability in prostate shapes, ultrasound prostate segmentation is challenging. To handle these issues, this paper develops a hybrid method for ultrasound prostate segmentation by combining an optimized closed principal curve-based method and the evolutionary neural network; the former can fit curves with great curvature and generate a contour composed of line segments connected by sorted vertices, and the latter is used to express an appropriate map function (represented by parameters of evolutionary neural network) for generating the smooth prostate contour to match the ground truth contour. Both qualitative and quantitative experimental results showed that our proposed method obtains accurate and robust performances.

Keywords: Ultrasound prostate segmentation, optimized closed polygonal segment method, evolutionary neural network, smooth mathematical model.

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Authors: Hazem J. Smadi

Abstract:

FMEA has been used for several years and proved its efficiency for system’s risk analysis due to failures. Risk priority number found in FMEA is used to rank failure modes that may occur in a system. There are some guidelines in the literature to assign the values of FMEA components known as Severity, Occurrence and Detection. This paper propose a method to assign the value for occurrence in more realistic manner representing the state of the system under study rather than depending totally on the experience of the analyst. This method uses the hazard function of a system to determine the value of occurrence depending on the behavior of the hazard being constant, increasing or decreasing.

Keywords: FMEA, Hazard Function, Risk Priority Number.

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Authors: S. H. Yahaya, J. M. Ali, T.A. Abdullah

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The exploration of this paper will focus on the Cshaped transition curve. This curve is designed by using the concept of circle to circle where one circle lies inside other. The degree of smoothness employed is curvature continuity. The function used in designing the C-curve is Bézier-like cubic function. This function has a low degree, flexible for the interactive design of curves and surfaces and has a shape parameter. The shape parameter is used to control the C-shape curve. Once the C-shaped curve design is completed, this curve will be applied to design spur gear tooth. After the tooth design procedure is finished, the design will be analyzed by using Finite Element Analysis (FEA). This analysis is used to find out the applicability of the tooth design and the gear material that chosen. In this research, Cast Iron 4.5 % Carbon, ASTM A-48 is selected as a gear material.

Keywords: Bézier-like cubic function, Curvature continuity, Cshapedtransition curve, Spur gear tooth.

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Authors: A. Vani, M. N. Mamatha

Abstract:

Visual signal processing in human beings occurs in the occipital lobe of the brain. The signals that are generated in the brain are universal for all the human beings and they are called Visual Evoked Potential (VEP). Generally, the visually impaired people lose sight because of severe damage to only the eyes natural photo sensors, but the occipital lobe will still be functioning. In this paper, a technique of artificially generating VEP is proposed to enhance the visual ability of the subject. The system uses the electrical photoreceptors to capture image, process the image, to detect and recognize the subject or object. This voltage is further processed and can transmit wirelessly to a BIOMEMS implanted into occipital lobe of the patient’s brain. The proposed BIOMEMS consists of array of electrodes that generate the neuron potential which is similar to VEP of normal people. Thus, the neurons get the visual data from the BioMEMS which helps in generating partial vision or sight for the visually challenged patient. 

Keywords: Visual evoked potential, OpenViBe, BioMEMS, Neuro prosthesis.

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Authors: Zeitoun D. G., Thierry Dana-Picard

Abstract:

The study of a real function of two real variables can be supported by visualization using a Computer Algebra System (CAS). One type of constraints of the system is due to the algorithms implemented, yielding continuous approximations of the given function by interpolation. This often masks discontinuities of the function and can provide strange plots, not compatible with the mathematics. In recent years, point based geometry has gained increasing attention as an alternative surface representation, both for efficient rendering and for flexible geometry processing of complex surfaces. In this paper we present different artifacts created by mesh surfaces near discontinuities and propose a point based method that controls and reduces these artifacts. A least squares penalty method for an automatic generation of the mesh that controls the behavior of the chosen function is presented. The special feature of this method is the ability to improve the accuracy of the surface visualization near a set of interior points where the function may be discontinuous. The present method is formulated as a minimax problem and the non uniform mesh is generated using an iterative algorithm. Results show that for large poorly conditioned matrices, the new algorithm gives more accurate results than the classical preconditioned conjugate algorithm.

Keywords: Function singularities, mesh generation, point allocation, visualization, collocation least squares method, Augmented Lagrangian method, Uzawa's Algorithm, Preconditioned Conjugate Gradien

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Authors: Ahmed S. Al-Abdulwahab

Abstract:

Generation system reliability assessment is an important task which can be performed using deterministic or probabilistic techniques. The probabilistic approaches have significant advantages over the deterministic methods. However, more complicated modeling is required by the probabilistic approaches. Power generation model is a basic requirement for this assessment. One form of the generation models is the well known capacity outage probability table (COPT). Different analytical techniques have been used to construct the COPT. These approaches require considerable mathematical modeling of the generating units. The unit-s models are combined to build the COPT which will add more burdens on the process of creating the COPT. Decimal to Binary Conversion (DBC) technique is widely and commonly applied in electronic systems and computing This paper proposes a novel utilization of the DBC to create the COPT without engaging in analytical modeling or time consuming simulations. The simple binary representation , “0 " and “1 " is used to model the states o f generating units. The proposed technique is proven to be an effective approach to build the generation model.

Keywords: Decimal to Binary, generation, reliability.

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Authors: Myung-Gon Yoon, Jung-Ho Moon, Tae Kwon Ha

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This paper studies a robust stabilization problem of a single agent in a multi-agent consensus system composed of identical agents, when the network topology of the system is completely unknown. It is shown that the transfer function of an agent in a consensus system can be described as a multiplicative perturbation of the isolated agent transfer function in frequency domain. From an existing robust stabilization result, we present sufficient conditions for a robust stabilization of an agent against unknown network topology.

Keywords: Multi-agent System, Robust Stabilization, Transfer Function.

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Authors: M. R. Aghaebrahimi, S. H. Zahiri, M. Amiri

Abstract:

The necessity of solving multi dimensional complicated scientific problems beside the necessity of several objective functions optimization are the most motive reason of born of artificial intelligence and heuristic methods. In this paper, we introduce a new method for multiobjective optimization based on learning automata. In the proposed method, search space divides into separate hyper-cubes and each cube is considered as an action. After gathering of all objective functions with separate weights, the cumulative function is considered as the fitness function. By the application of all the cubes to the cumulative function, we calculate the amount of amplification of each action and the algorithm continues its way to find the best solutions. In this Method, a lateral memory is used to gather the significant points of each iteration of the algorithm. Finally, by considering the domination factor, pareto front is estimated. Results of several experiments show the effectiveness of this method in comparison with genetic algorithm based method.

Keywords: Function optimization, Multiobjective optimization, Learning automata.

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Authors: S. R. Nikhashemi, L. Haj Paim, Ali Khatibi

Abstract:

Structural Equation Modeling (SEM) was used to test a hypothesized model explaining Malaysian hypermarket customers’ perceptions of brand trust (BT), customer perceived value (CPV) and perceived service quality (PSQ) on building their brand loyalty (CBL) and generating positive word-of-mouth communication (WOM). Self-administered questionnaires were used to collect data from 374 Malaysian hypermarket customers from Mydin, Tesco, Aeon Big and Giant in Kuala Lumpur, a metropolitan city of Malaysia. The data strongly supported the model exhibiting that BT, CPV and PSQ are prerequisite factors in building customer brand loyalty, while PSQ has the strongest effect on prediction of customer brand loyalty compared to other factors. Besides, the present study suggests the effect of the aforementioned factors via customer brand loyalty strongly contributes to generate positive word of mouth communication.

Keywords: Brand trust, perceived value, perceived service quality, brand loyalty, positive word of mouth communication.

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Authors: Mohammad Reza Ghasemi, Amin Ghorbani

Abstract:

The main goal of the present work is to decrease the computational burden for optimum design of steel frames with frequency constraints using a new type of neural networks called Wavelet Neural Network. It is contested to train a suitable neural network for frequency approximation work as the analysis program. The combination of wavelet theory and Neural Networks (NN) has lead to the development of wavelet neural networks. Wavelet neural networks are feed-forward networks using wavelet as activation function. Wavelets are mathematical functions within suitable inner parameters, which help them to approximate arbitrary functions. WNN was used to predict the frequency of the structures. In WNN a RAtional function with Second order Poles (RASP) wavelet was used as a transfer function. It is shown that the convergence speed was faster than other neural networks. Also comparisons of WNN with the embedded Artificial Neural Network (ANN) and with approximate techniques and also with analytical solutions are available in the literature.

Keywords: Weight Minimization, Frequency Constraints, Steel Frames, ANN, WNN, RASP Function.

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