Search results for: Regularization Parameter Search.

Authors: M. Elsisi, M. Soliman, M. A. S. Aboelela, W. Mansour

Abstract:

This paper considers the design of Dual Proportional- Integral (DPI) Load Frequency Control (LFC), using gravitational search algorithm (GSA). The design is carried out for nonlinear hydrothermal power system where generation rate constraint (GRC) and governor dead band are considered. Furthermore, time delays imposed by governor-turbine, thermodynamic process, and communication channels are investigated. GSA is utilized to search for optimal controller parameters by minimizing a time-domain based objective function. GSA-based DPI has been compared to Ziegler- Nichols based PI, and Genetic Algorithm (GA) based PI controllers in order to demonstrate the superior efficiency of the proposed design. Simulation results are carried for a wide range of operating conditions and system parameters variations.

Keywords: Gravitational Search Algorithm (GSA), Load Frequency Control (LFC), Dual Proportional-Integral (DPI) controller.

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Authors: Phool Singh, Ashok Jangid, N. S. Tomer, Deepa Sinha

Abstract:

The aim of this paper is to investigate twodimensional unsteady flow of a viscous incompressible fluid about stagnation point on permeable stretching sheet in presence of time dependent free stream velocity. Fluid is considered in the influence of transverse magnetic field in the presence of radiation effect. Rosseland approximation is use to model the radiative heat transfer. Using time-dependent stream function, partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by using Runge-Kutta Fehlberg method with the help of Newton-Raphson shooting technique. In the present work the effect of unsteadiness parameter, magnetic field parameter, radiation parameter, stretching parameter and the Prandtl number on flow and heat transfer characteristics have been discussed. Skin-friction coefficient and Nusselt number at the sheet are computed and discussed. The results reported in the paper are in good agreement with published work in literature by other researchers.

Keywords: Magneto hydrodynamics, stretching sheet, thermal radiation, unsteady flow.

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Authors: Cha-Hwa Lin, Je-Wei Hu

Abstract:

The conventional GA combined with a local search algorithm, such as the 2-OPT, forms a hybrid genetic algorithm(HGA) for the traveling salesman problem (TSP). However, the geometric properties which are problem specific knowledge can be used to improve the search process of the HGA. Some tour segments (edges) of TSPs are fine while some maybe too long to appear in a short tour. This knowledge could constrain GAs to work out with fine tour segments without considering long tour segments as often. Consequently, a new algorithm is proposed, called intelligent-OPT hybrid genetic algorithm (IOHGA), to improve the GA and the 2-OPT algorithm in order to reduce the search time for the optimal solution. Based on the geometric properties, all the tour segments are assigned 2-level priorities to distinguish between good and bad genes. A simulation study was conducted to evaluate the performance of the IOHGA. The experimental results indicate that in general the IOHGA could obtain near-optimal solutions with less time and better accuracy than the hybrid genetic algorithm with simulated annealing algorithm (HGA(SA)).

Keywords: Traveling salesman problem, hybrid geneticalgorithm, priority selection, 2-OPT.

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Authors: Chakkrit Snae

Abstract:

Names are important in many societies, even in technologically oriented ones which use e.g. ID systems to identify individual people. Names such as surnames are the most important as they are used in many processes, such as identifying of people and genealogical research. On the other hand variation of names can be a major problem for the identification and search for people, e.g. web search or security reasons. Name matching presumes a-priori that the recorded name written in one alphabet reflects the phonetic identity of two samples or some transcription error in copying a previously recorded name. We add to this the lode that the two names imply the same person. This paper describes name variations and some basic description of various name matching algorithms developed to overcome name variation and to find reasonable variants of names which can be used to further increasing mismatches for record linkage and name search. The implementation contains algorithms for computing a range of fuzzy matching based on different types of algorithms, e.g. composite and hybrid methods and allowing us to test and measure algorithms for accuracy. NYSIIS, LIG2 and Phonex have been shown to perform well and provided sufficient flexibility to be included in the linkage/matching process for optimising name searching.

Keywords: Data mining, name matching algorithm, nominaldata, searching system.

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Authors: Young-Seok Choi

Abstract:

This work presents a new type of the affine projection (AP) algorithms which incorporate the sparsity condition of a system. To exploit the sparsity of the system, a weighted l1-norm regularization is imposed on the cost function of the AP algorithm. Minimizing the cost function with a subgradient calculus and choosing two distinct weighting for l1-norm, two stochastic gradient based sparsity regularized AP (SR-AP) algorithms are developed. Experimental results exhibit that the SR-AP algorithms outperform the typical AP counterparts for identifying sparse systems.

Keywords: System identification, adaptive filter, affine projection, sparsity, sparse system.

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Authors: Halil Ibrahim Demir, Abdullah Hulusi Kokcam, Fuat Simsir, Özer Uygun

Abstract:

Traditionally, three important manufacturing functions which are process planning, scheduling and due-date assignment are performed sequentially and separately. Although there are numerous works on the integration of process planning and scheduling and plenty of works focusing on scheduling with due date assignment, there are only a few works on integrated process planning, scheduling and due-date assignment. Although due-dates are determined without taking into account of weights of the customers in the literature, here weighted due-date assignment is employed to get better performance. Jobs are scheduled according to weighted earliest due date dispatching rule and due dates are determined according to some popular due date assignment methods by taking into account of the weights of each job. Simulated Annealing, Evolutionary Strategies, Random Search, hybrid of Random Search and Simulated Annealing, and hybrid of Random Search and Evolutionary Strategies, are applied as solution techniques. Three important manufacturing functions are integrated step-by-step and higher integration levels are found better. Search meta-heuristics are found to be very useful while improving performance measure.

Keywords: Evolutionary strategies, hybrid searches, process planning, simulated annealing, weighted due-date assignment, weighted scheduling.

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Authors: Mohammad Zavid Parvez, Manoranjan Paul

Abstract:

A seizure prediction method is proposed by extracting global features using phase correlation between adjacent epochs for detecting relative changes and local features using fluctuation/ deviation within an epoch for determining fine changes of different EEG signals. A classifier and a regularization technique are applied for the reduction of false alarms and improvement of the overall prediction accuracy. The experiments show that the proposed method outperforms the state-of-the-art methods and provides high prediction accuracy (i.e., 97.70%) with low false alarm using EEG signals in different brain locations from a benchmark data set.

Keywords: Epilepsy, Seizure, Phase Correlation, Fluctuation, Deviation.

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Authors: Grigorios N. Beligiannis, Georgios A. Tsirogiannis, Panayotis E. Pintelas

Abstract:

In this contribution, a way to enhance the performance of the classic Genetic Algorithm is proposed. The idea of restarting a Genetic Algorithm is applied in order to obtain better knowledge of the solution space of the problem. A new operator of 'insertion' is introduced so as to exploit (utilize) the information that has already been collected before the restarting procedure. Finally, numerical experiments comparing the performance of the classic Genetic Algorithm and the Genetic Algorithm with restartings, for some well known test functions, are given.

Keywords: Genetic Algorithms, Restartings, Search space exploration, Search space exploitation.

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Authors: Chatchai Pesee

Abstract:

This paper examines long-range dependence or longmemory of financial time series on the exchange rate data by the fractional Brownian motion (fBm). The principle of spectral density function in Section 2 is used to find the range of Hurst parameter (H) of the fBm. If 0< H <1/2, then it has a short-range dependence (SRD). It simulates long-memory or long-range dependence (LRD) if 1/2< H <1. The curve of exchange rate data is fBm because of the specific appearance of the Hurst parameter (H). Furthermore, some of the definitions of the fBm, long-range dependence and selfsimilarity are reviewed in Section II as well. Our results indicate that there exists a long-memory or a long-range dependence (LRD) for the exchange rate data in section III. Long-range dependence of the exchange rate data and estimation of the Hurst parameter (H) are discussed in Section IV, while a conclusion is discussed in Section V.

Keywords: Fractional Brownian motion, long-rangedependence, memory, short-range dependence.

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Authors: M. Senthil Arumugam, M.V.C. Rao

Abstract:

This paper presents a novel two-phase hybrid optimization algorithm with hybrid genetic operators to solve the optimal control problem of a single stage hybrid manufacturing system. The proposed hybrid real coded genetic algorithm (HRCGA) is developed in such a way that a simple real coded GA acts as a base level search, which makes a quick decision to direct the search towards the optimal region, and a local search method is next employed to do fine tuning. The hybrid genetic operators involved in the proposed algorithm improve both the quality of the solution and convergence speed. The phase–1 uses conventional real coded genetic algorithm (RCGA), while optimisation by direct search and systematic reduction of the size of search region is employed in the phase – 2. A typical numerical example of an optimal control problem with the number of jobs varying from 10 to 50 is included to illustrate the efficacy of the proposed algorithm. Several statistical analyses are done to compare the validity of the proposed algorithm with the conventional RCGA and PSO techniques. Hypothesis t – test and analysis of variance (ANOVA) test are also carried out to validate the effectiveness of the proposed algorithm. The results clearly demonstrate that the proposed algorithm not only improves the quality but also is more efficient in converging to the optimal value faster. They can outperform the conventional real coded GA (RCGA) and the efficient particle swarm optimisation (PSO) algorithm in quality of the optimal solution and also in terms of convergence to the actual optimum value.

Keywords: Hybrid systems, optimal control, real coded genetic algorithm (RCGA), Particle swarm optimization (PSO), Hybrid real coded GA (HRCGA), and Hybrid genetic operators.

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Authors: H. Panahi, S. Asadi

Abstract:

In this paper, the estimation of the stress-strength parameter R = P(Y < X), when X and Y are independent and both are Lomax distributions with the common scale parameters but different shape parameters is studied. The maximum likelihood estimator of R is derived. Assuming that the common scale parameter is known, the bayes estimator and exact confidence interval of R are discussed. Simulation study to investigate performance of the different proposed methods has been carried out.

Keywords: Stress-Strength model; maximum likelihoodestimator; Bayes estimator; Lomax distribution

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Authors: T. N. Sindhu, M. Aslam

Abstract:

A comprehensive Bayesian analysis has been carried out in the context of informative and non-informative priors for the shape parameter of the Burr type X distribution under different symmetric and asymmetric loss functions. Elicitation of hyperparameter through prior predictive approach is also discussed. Also we derive the expression for posterior predictive distributions, predictive intervals and the credible Intervals. As an illustration, comparisons of these estimators are made through simulation study.

Keywords: Credible Intervals, Loss Functions, Posterior Predictive Distributions, Predictive Intervals.

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Authors: Hei-Chia Wang, Che-Tsung Yang

Abstract:

While the explosive increase in information published on the Web, researchers have to filter information when searching for conference related information. To make it easier for users to search related information, this paper uses Topic Maps and social information to implement ontology since ontology can provide the formalisms and knowledge structuring for comprehensive and transportable machine understanding that digital information requires. Besides enhancing information in Topic Maps, this paper proposes a method of constructing research Topic Maps considering social information. First, extract conference data from the web. Then extract conference topics and the relationships between them through the proposed method. Finally visualize it for users to search and browse. This paper uses ontology, containing abundant of knowledge hierarchy structure, to facilitate researchers getting useful search results. However, most previous ontology construction methods didn-t take “people" into account. So this paper also analyzes the social information which helps researchers find the possibilities of cooperation/combination as well as associations between research topics, and tries to offer better results.

Keywords: Ontology, topic maps, social information, co-authorship.

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Authors: Guowei Hou, Lixin Yu, Wei Zhuang, Hui Qin, Xue Yang

Abstract:

Formal verification is proposed to ensure the correctness of the design and make functional verification more efficient. As cache plays a vital role in the design of System on Chip (SoC), and cache with Memory Management Unit (MMU) and cache memory unit makes the state space too large for simulation to verify, then a formal verification is presented for such system design. In the paper, a formal model checking verification flow is suggested and a new cache memory model which is called “exhaustive search model” is proposed. Instead of using large size ram to denote the whole cache memory, exhaustive search model employs just two cache blocks. For cache system contains data cache (Dcache) and instruction cache (Icache), Dcache memory model and Icache memory model are established separately using the same mechanism. At last, the novel model is employed to the verification of a cache which is module of a custom-built SoC system that has been applied in practical, and the result shows that the cache system is verified correctly using the exhaustive search model, and it makes the verification much more manageable and flexible.

Keywords: Cache system, formal verification, novel model, System on Chip (SoC).

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Authors: Songtao Chang, Yongji Wang, Lei Liu, Dangjun Zhao

Abstract:

Reentry trajectory optimization is a multi-constraints optimal control problem which is hard to solve. To tackle it, we proposed a new algorithm named CDEN(Constrained Differential Evolution Newton-Raphson Algorithm) based on Differential Evolution( DE) and Newton-Raphson.We transform the infinite dimensional optimal control problem to parameter optimization which is finite dimensional by discretize control parameter. In order to simplify the problem, we figure out the control parameter-s scope by process constraints. To handle constraints, we proposed a parameterless constraints handle process. Through comprehensive analyze the problem, we use a new algorithm integrated by DE and Newton-Raphson to solve it. It is validated by a reentry vehicle X-33, simulation results indicated that the algorithm is effective and robust.

Keywords: reentry vehicle, trajectory optimization, constraint optimal, differential evolution.

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Authors: Eleni Aggelogiannaki, Haralambos Sarimveis

Abstract:

In this work, a radial basis function (RBF) neural network is developed for the identification of hyperbolic distributed parameter systems (DPSs). This empirical model is based only on process input-output data and used for the estimation of the controlled variables at specific locations, without the need of online solution of partial differential equations (PDEs). The nonlinear model that is obtained is suitably transformed to a nonlinear state space formulation that also takes into account the model mismatch. A stable robust control law is implemented for the attenuation of external disturbances. The proposed identification and control methodology is applied on a long duct, a common component of thermal systems, for a flow based control of temperature distribution. The closed loop performance is significantly improved in comparison to existing control methodologies.

Keywords: Hyperbolic Distributed Parameter Systems, Radial Basis Function Neural Networks, H∞ control, Thermal systems.

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Authors: Suguru Ochiai, Toru Yabuki, Yoshiki Yamaguchi, Yuetsu Kodama

Abstract:

In this paper, we propose a Connect6 solver which adopts a hybrid approach based on a tree-search algorithm and image processing techniques. The solver must deal with the complicated computation and provide high performance in order to make real-time decisions. The proposed approach enables the solver to be implemented on a single Spartan-6 XC6SLX45 FPGA produced by XILINX without using any external devices. The compact implementation is achieved through image processing techniques to optimize a tree-search algorithm of the Connect6 game. The tree search is widely used in computer games and the optimal search brings the best move in every turn of a computer game. Thus, many tree-search algorithms such as Minimax algorithm and artificial intelligence approaches have been widely proposed in this field. However, there is one fundamental problem in this area; the computation time increases rapidly in response to the growth of the game tree. It means the larger the game tree is, the bigger the circuit size is because of their highly parallel computation characteristics. Here, this paper aims to reduce the size of a Connect6 game tree using image processing techniques and its position symmetric property. The proposed solver is composed of four computational modules: a two-dimensional checkmate strategy checker, a template matching module, a skilful-line predictor, and a next-move selector. These modules work well together in selecting next moves from some candidates and the total amount of their circuits is small. The details of the hardware design for an FPGA implementation are described and the performance of this design is also shown in this paper.

Keywords: Connect6, pattern matching, game-tree reduction, hardware direct computation

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Authors: M. Moosavi, H. Khatibzadeh

Abstract:

In this article, we study demiclosed and strongly quasi-nonexpansive of a sequence generated by the proximal point algorithm for a finite family of quasi-nonexpansive mappings in Hadamard spaces. Δ-convergence of iterations for the sequence of strongly quasi-nonexpansive mappings as well as the strong convergence of the Halpern type regularization of them to a common fixed point of sequence are also established. Our results generalize and improve several previously known results of the existing literature.

Keywords: Fixed point, Hadamard space, proximal point algorithm, quasi-nonexpansive sequence of mappings, resolvent.

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Authors: Martin Dostal, Dalibor Fiala, Karel Ježek

Abstract:

In this paper we would like to introduce some of the best practices of using semantic markup and its significance in the success of web applications. Search engines are one of the best ways to reach potential customers and are some of the main indicators of web sites' fruitfulness. We will introduce the most important semantic vocabularies which are used by Google and Yahoo. Afterwards, we will explain the process of semantic markup implementation and its significance for search engines and other semantic markup consumers. We will describe techniques for slow conceiving RDFa markup to our web application for collecting Call for papers (CFP) announcements.

Keywords: Call for papers, Google, RDFa, semantic markup, semantic web, Yahoo.

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Authors: I. Turk Cakir, B. Hacisahinoglu, S. Kartal, A. Yilmaz, A. Yilmaz, Z. Uysal, O. Cakir

Abstract:

In the search for new physics beyond the Standard Model, Flavour Changing Neutral Current (FCNC) is a good research field in terms of the observability at future colliders. Increased Higgs production with higher energy and luminosity in colliders is essential for verification or falsification of our knowledge of physics and predictions, and the search for new physics. Prospective electron-proton collider constituent of the Future Circular Collider project is FCC-eh. It offers great sensitivity due to its high luminosity and low interference. In this work, thq FCNC interaction vertex with off-shell top quark decay at electron-proton colliders is studied. By using MadGraph5_aMC@NLO multi-purpose event generator, observability of tuh and tch couplings are obtained with equal coupling scenario. Upper limit on branching ratio of tree level top quark FCNC decay is determined as 0.012% at FCC-eh with 1 ab ^−1 luminosity.

Keywords: FCC, FCNC, Higgs Boson, Top Quark.

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Authors: Young-Seok Choi

Abstract:

This paper presents a normalized subband adaptive filtering (NSAF) algorithm to cope with the sparsity condition of an underlying system in the context of compressive sensing. By regularizing a weighted l1-norm of the filter taps estimate onto the cost function of the NSAF and utilizing a subgradient analysis, the update recursion of the l1-norm constraint NSAF is derived. Considering two distinct weighted l1-norm regularization cases, two versions of the l1-norm constraint NSAF are presented. Simulation results clearly indicate the superior performance of the proposed l1-norm constraint NSAFs comparing with the classical NSAF.

Keywords: Subband adaptive filtering, sparsity constraint, weighted l1-norm.

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Authors: Sanaa Chafik, ImaneDaoudi, Mounim A. El Yacoubi, Hamid El Ouardi

Abstract:

Locality Sensitive Hashing (LSH) is one of the most promising techniques for solving nearest neighbour search problem in high dimensional space. Euclidean LSH is the most popular variation of LSH that has been successfully applied in many multimedia applications. However, the Euclidean LSH presents limitations that affect structure and query performances. The main limitation of the Euclidean LSH is the large memory consumption. In order to achieve a good accuracy, a large number of hash tables is required. In this paper, we propose a new hashing algorithm to overcome the storage space problem and improve query time, while keeping a good accuracy as similar to that achieved by the original Euclidean LSH. The Experimental results on a real large-scale dataset show that the proposed approach achieves good performances and consumes less memory than the Euclidean LSH.

Keywords: Approximate Nearest Neighbor Search, Content based image retrieval (CBIR), Curse of dimensionality, Locality sensitive hashing, Multidimensional indexing, Scalability.

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Authors: David Lindström

Abstract:

We evaluate the performance of a numerical method for global optimization of expensive functions. The method is using a response surface to guide the search for the global optimum. This metamodel could be based on radial basis functions, kriging, or a combination of different models. We discuss how to set the cyclic parameters of the optimization method to get a balance between local and global search. We also discuss the eventual problem with Runge oscillations in the response surface.

Keywords: Expensive function, infill sampling criterion, kriging, global optimization, response surface, Runge phenomenon.

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Authors: H.Panahi, S.Asadi

Abstract:

In this article, we consider the estimation of P[Y < X], when strength, X and stress, Y are two independent variables of Burr Type XII distribution. The MLE of the R based on one simple iterative procedure is obtained. Assuming that the common parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator of P[Y < X] are discussed. The exact confidence interval of the R is also obtained. Monte Carlo simulations are performed to compare the different proposed methods.

Keywords: Stress-Strength model, Maximum likelihood estimator, Bayes estimator, Burr type XII distribution.

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Authors: Wullapa Wongsinlatam

Abstract:

Back propagation algorithm (BP) is a widely used technique in artificial neural network and has been used as a tool for solving the time series problems, such as decreasing training time, maximizing the ability to fall into local minima, and optimizing sensitivity of the initial weights and bias. This paper proposes an improvement of a BP technique which is called IM-COH algorithm (IM-COH). By combining IM-COH algorithm with cuckoo search algorithm (CS), the result is cuckoo search improved control output hidden layer algorithm (CS-IM-COH). This new algorithm has a better ability in optimizing sensitivity of the initial weights and bias than the original BP algorithm. In this research, the algorithm of CS-IM-COH is compared with the original BP, the IM-COH, and the original BP with CS (CS-BP). Furthermore, the selected benchmarks, four time series samples, are shown in this research for illustration. The research shows that the CS-IM-COH algorithm give the best forecasting results compared with the selected samples.

Keywords: Artificial neural networks, back propagation algorithm, time series, local minima problem, metaheuristic optimization.

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Authors: St. Karagiannis, A. I. Dounis, T. Chalastras, P. Tiropanis, D. Papachristos

Abstract:

This work presents the design of an expert system that aims in the procurement of patient medial background and in the search for suitable skin test selections. Skin testing is the tool used most widely to diagnose allergies. The language of expert systems CLIPS is used as a tool of designing. Finally, we present the evaluation of the proposed expert system which was achieved with the import of certain medical cases and the system produced with suitable successful skin tests.

Keywords: Artificial intelligence, expert system - CLIPS, allergy and skin test.

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Authors: Jaibir S. Yadav, Dimple, Vinod K. Sharma

Abstract:

Molar excess Volumes, VE ijk and speeds of sound , uijk of 2-pyrrolidinone (i) + benzene or toluene (j) + ethanol (k) ternary mixture have been measured as a function of composition at 308.15 K. The observed speeds of sound data have been utilized to determine excess isentropic compressiblities, ( E S κ )ijk of ternary (i + j + k) mixtures. Molar excess volumes, VE ijk and excess isentropic compressibilities, ( E S κ )ijk data have fitted to the Redlich-Kister equation to calculate ternary adjustable parameters and standard deviations. The Moelywn-Huggins concept (Huggins in Polymer 12: 389-399, 1971) of connectivity between the surfaces of the constituents of binary mixtures has been extended to ternary mixtures (using the concept of a connectivity parameter of third degree of molecules, 3ξ , which inturn depends on its topology) to obtain an expression that describes well the measured VE ijk and ( E S κ )ijk data.

Keywords: Connectivity parameter of third degree, 3ξ, Excess isentropic compressibilities, ( ES κ )ijk, Interaction energy parameter, χ, Molar excess volumes, VEijk, Speeds of sound, uijk.

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Authors: Hongyan Dai

Abstract:

This work presents a matched field processing (MFP) algorithm based on Dopplerlet transform for estimating the motion parameters of a sound source moving along a straight line and with a constant speed by using a piecewise strategy, which can significantly reduce the computational burden. Monte Carlo simulation results and an experimental result are presented to verify the effectiveness of the algorithm advocated.

Keywords: matched field processing; Dopplerlet transform; motion parameter estimation; piecewise strategy

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Authors: Ezad Hafidz Hafidzuddin, Roslinda Nazar, Norihan M. Arifin, Ioan Pop

Abstract:

In this paper, the problem of steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is considered. The similarity transformations are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual solutions are found for a certain range of the suction and stretching/shrinking parameters. The effects of the suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed.

Keywords: Boundary Layer, Exponentially Stretching/Shrinking Sheet, Generalized Slip, Heat Transfer, Numerical Solutions.

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Authors: J. Tospornsampan, I. Kita, M. Ishii, Y. Kitamura

Abstract:

In this paper a combination approach of two heuristic-based algorithms: genetic algorithm and tabu search is proposed. It has been developed to obtain the least cost based on the split-pipe design of looped water distribution network. The proposed combination algorithm has been applied to solve the three well-known water distribution networks taken from the literature. The development of the combination of these two heuristic-based algorithms for optimization is aimed at enhancing their strengths and compensating their weaknesses. Tabu search is rather systematic and deterministic that uses adaptive memory in search process, while genetic algorithm is probabilistic and stochastic optimization technique in which the solution space is explored by generating candidate solutions. Split-pipe design may not be realistic in practice but in optimization purpose, optimal solutions are always achieved with split-pipe design. The solutions obtained in this study have proved that the least cost solutions obtained from the split-pipe design are always better than those obtained from the single pipe design. The results obtained from the combination approach show its ability and effectiveness to solve combinatorial optimization problems. The solutions obtained are very satisfactory and high quality in which the solutions of two networks are found to be the lowest-cost solutions yet presented in the literature. The concept of combination approach proposed in this study is expected to contribute some useful benefits in diverse problems.

Keywords: GAs, Heuristics, Looped network, Least-cost design, Pipe network, Optimization, TS

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