Search results for: splitting methods.

Authors: Wen Po Cheng, Chia Yun Chung, Ruey Fang Yu, Chao Feng Chen

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The main objective of this research was to study the differences of aluminum hydrolytic products between two PACl preparation methods. These two methods were the acidification process of freshly formed amorphous Al(OH)₃ and the conventional alkalization process of aluminum chloride solution. According to Ferron test and ²⁷Al NMR analysis of those two PACl preparation procedures, the reaction rate constant (k) values and Al₁₃ percentage of acid addition process at high basicity value were both lower than those values of the alkaline addition process. The results showed that the molecular structure and size distribution of the aluminum species in both preparing methods were suspected to be significantly different at high basicity value.

Keywords: Polyaluminum chloride, Al13, amorphous aluminum hydroxide, Ferron test.

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Authors: P. Řehoř, D. Holátová, V. Doležalová

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Paper deals with analysis of strategic management methods in non-profit making organization in the Czech Republic. Strategic management represents an aggregate of methods and approaches that can be applied for managing organizations - in this article the organizations which associate owners and keepers of nonstate forest properties. Authors use these methods of strategic management: analysis of stakeholders, SWOT analysis and questionnaire inquiries. The questionnaire was distributed electronically via e-mail. In October 2013 we obtained data from a total of 84 questionnaires. Based on the results the authors recommend the using of confrontation strategy which improves the competitiveness of non-profit making organizations.

Keywords: Strategic management, non-profit making organization, strategy analysis, SWOT analysis, strategy, competitiveness.

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Authors: Belkacem Brahmi, Mohand Ouamer Bibi

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In this paper, we present a new method for solving quadratic programming problems, not strictly convex. Constraints of the problem are linear equalities and inequalities, with bounded variables. The suggested method combines the active-set strategies and support methods. The algorithm of the method and numerical experiments are presented, while comparing our approach with the active set method on randomly generated problems.

Keywords: Convex quadratic programming, dual support methods, active set methods.

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Authors: Ioannis N. Koukoulis, Clio G. Vossou, Christopher G. Provatidis

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The aim of the current work is to present a comparison among three popular optimization methods in the inverse elastostatics problem (IESP) of flaw detection within a solid. In more details, the performance of a simulated annealing, a Hooke & Jeeves and a sequential quadratic programming algorithm was studied in the test case of one circular flaw in a plate solved by both the boundary element (BEM) and the finite element method (FEM). The proposed optimization methods use a cost function that utilizes the displacements of the static response. The methods were ranked according to the required number of iterations to converge and to their ability to locate the global optimum. Hence, a clear impression regarding the performance of the aforementioned algorithms in flaw identification problems was obtained. Furthermore, the coupling of BEM or FEM with these optimization methods was investigated in order to track differences in their performance.

Keywords: Elastostatic, inverse problem, optimization.

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Authors: Taleb Hosni Abderrahmane, Berga Abdelmadjid

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The development of numerical analysis and its application to geomechanics problems have provided geotechnical engineers with extremely powerful tools. One of the most important problems in geotechnical engineering is the slope stability assessment. It is a very difficult task due to several aspects such the nature of the problem, experimental consideration, monitoring, controlling, and assessment. The main objective of this paper is to perform a comparative numerical study between the following methods: The Limit Equilibrium (LEM), Finite Element (FEM), Limit Analysis (LAM) and Distinct Element (DEM). The comparison is conducted in terms of the safety factors and the critical slip surfaces. Through the results, we see the feasibility to analyse slope stability by many methods.

Keywords: Comparison, factor of safety, geomechanics, numerical methods, slope analysis, slip surfaces.

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Authors: Jing Wu

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In this paper, we discuss semiconvergence of the alternating iterative methods for solving singular systems. The semiconvergence theories for the alternating methods are established when the coefficient matrix is a singular matrix. Furthermore, the corresponding comparison theorems are obtained.

Keywords: Alternating iterative method, Semiconvergence, Singular matrix.

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Authors: N. B. Fedosenko, A.A Iatcenko, S.A. Levanov

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The paper shows some ability to manage two-phase flows arising from the use of unsteady effects. In one case, we consider the condition of fragmentation of the interface between the two components leads to the intensification of mixing. The problem is solved when the temporal and linear scale are small for the appearance of the developed mixing layer. Showing that exist such conditions for unsteady flow velocity at the surface of the channel, which will lead to the creation and fragmentation of vortices at Re numbers of order unity. Also showing that the Re is not a criterion of similarity for this type of flows, but we can introduce a criterion that depends on both the Re, and the frequency splitting of the vortices. It turned out that feature of this situation is that streamlines behave stable, and if we analyze the behavior of the interface between the components it satisfies all the properties of unstable flows. The other problem we consider the behavior of solid impurities in the extensive system of channels. Simulated unsteady periodic flow modeled breaths. Consider the behavior of the particles along the trajectories. It is shown that, depending on the mass and diameter of the particles, they can be collected in a caustic on the channel walls, stop in a certain place or fly back. Of interest is the distribution of particle velocity in frequency. It turned out that by choosing a behavior of the velocity field of the carrier gas can affect the trajectory of individual particles including force them to fly back.

Keywords: Two-phase, mixing, separating, flow control

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Authors: Emad Hazbkhah. Abdolreza Zahiri, Hossein Ghorbanizade Kharazi

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Reducing river sediments through path correction and preservation of river walls leads to considerable reduction of sedimentation at the pumping stations. Path correction and preservation of walls is not limited to one particular method but, depending on various conditions, a combination of several methods can be employed. In this article, we try to review and evaluate methods for preservation of river banks in order to reduce sediments.

Keywords: Erosion , River Banks , Sediments

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Authors: Jagabondhu Hazra, Avinash Sinha

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Economic dispatch problem is an optimization problem where objective function is highly non linear, non-convex, non-differentiable and may have multiple local minima. Therefore, classical optimization methods may not converge or get trapped to any local minima. This paper presents a comparative study of four different evolutionary algorithms i.e. genetic algorithm, bacteria foraging optimization, ant colony optimization and particle swarm optimization for solving the economic dispatch problem. All the methods are tested on IEEE 30 bus test system. Simulation results are presented to show the comparative performance of these methods.

Keywords: Ant colony optimization, bacteria foraging optimization, economic dispatch, evolutionary algorithm, genetic algorithm, particle swarm optimization.

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Authors: H. Higashiyama, M. Sappakittipakorn, M. Mizukoshi, O. Takahashi

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Ceramic Waste Aggregates (CWAs) were made from electric porcelain insulator wastes supplied from an electric power company, which were crushed and ground to fine aggregate sizes. In this study, to develop the CWA mortar as an eco–efficient, ground granulated blast–furnace slag (GGBS) as a Supplementary Cementitious Material (SCM) was incorporated. The water–to–binder ratio (W/B) of the CWA mortars was varied at 0.4, 0.5, and 0.6. The cement of the CWA mortar was replaced by GGBS at 20 and 40% by volume (at about 18 and 37% by weight). Mechanical properties of compressive and splitting tensile strengths, and elastic modulus were evaluated at the age of 7, 28, and 91 days. Moreover, the chloride ingress test was carried out on the CWA mortars in a 5.0% NaCl solution for 48 weeks. The chloride diffusion was assessed by using an electron probe microanalysis (EPMA). To consider the relation of the apparent chloride diffusion coefficient and the pore size, the pore size distribution test was also performed using a mercury intrusion porosimetry at the same time with the EPMA. The compressive strength of the CWA mortars with the GGBS was higher than that without the GGBS at the age of 28 and 91 days. The resistance to the chloride ingress of the CWA mortar was effective in proportion to the GGBS replacement level.

Keywords: Ceramic waste aggregate, Chloride diffusion, GGBS, Pore size distribution.

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Authors: Seo Young Kim, Toshimitsu Hamasaki

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Microarrays have become the effective, broadly used tools in biological and medical research to address a wide range of problems, including classification of disease subtypes and tumors. Many statistical methods are available for analyzing and systematizing these complex data into meaningful information, and one of the main goals in analyzing gene expression data is the detection of samples or genes with similar expression patterns. In this paper, we express and compare the performance of several clustering methods based on data preprocessing including strategies of normalization or noise clearness. We also evaluate each of these clustering methods with validation measures for both simulated data and real gene expression data. Consequently, clustering methods which are common used in microarray data analysis are affected by normalization and degree of noise and clearness for datasets.

Keywords: Gene expression, clustering, data preprocessing.

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Authors: A. Galashev

Abstract:

Absorption spectra of infra-red (IR) radiation of the disperse water medium absorbing the most important greenhouse gases: CO2 , N2O , CH4 , C2H2 , C2H6 have been calculated by the molecular dynamics method. Loss of the absorbing ability at the formation of clusters due to a reduction of the number of centers interacting with IR radiation, results in an anti-greenhouse effect. Absorption of O3 molecules by the (H2O)50 cluster is investigated at its interaction with Cl- ions. The splitting of ozone molecule on atoms near to cluster surface was observed. Interaction of water cluster with Cl- ions causes the increase of integrated intensity of emission spectra of IR radiation, and also essential reduction of the similar characteristic of Raman spectrum. Relative integrated intensity of absorption of IR radiation for small water clusters was designed. Dependences of the quantity of weight on altitude for vapor of monomers, clusters, droplets, crystals and mass of all moisture were determined. The anti-greenhouse effect of clusters was defined as the difference of increases of average global temperature of the Earth, caused by absorption of IR radiation by free water molecules forming clusters, and absorption of clusters themselves. The greenhouse effect caused by clusters makes 0.53 K, and the antigreenhouse one is equal to 1.14 K. The increase of concentration of CO2 in the atmosphere does not always correlate with the amplification of greenhouse effect.

Keywords: Greenhouse gases, infrared absorption and Raman spectra, molecular dynamics method, water clusters.

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Authors: Manpreet Singh, Parvinder Singh Sandhu, Reet Kamal Kaur

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Protein structure determination and prediction has been a focal research subject in the field of bioinformatics due to the importance of protein structure in understanding the biological and chemical activities of organisms. The experimental methods used by biotechnologists to determine the structures of proteins demand sophisticated equipment and time. A host of computational methods are developed to predict the location of secondary structure elements in proteins for complementing or creating insights into experimental results. However, prediction accuracies of these methods rarely exceed 70%.

Keywords: Protein, Secondary Structure, Prediction, DNA, RNA.

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Authors: M.Imanova, G.Mehdiyeva, V.Ibrahimov

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Solution of some practical problems is reduced to the solution of the integro-differential equations. But for the numerical solution of such equations basically quadrature methods or its combination with multistep or one-step methods are used. The quadrature methods basically is applied to calculation of the integral participating in right hand side of integro-differential equations. As this integral is of Volterra type, it is obvious that at replacement with its integrated sum the upper limit of the sum depends on a current point in which values of the integral are defined. Thus we receive the integrated sum with variable boundary, to work with is hardly. Therefore multistep method with the constant coefficients, which is free from noted lack and gives the way for finding it-s coefficients is present.

Keywords: Volterra integro-differential equations, multistepmethods, finite-difference methods, initial value problem

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Authors: Min Sang Lee, Hee Jae Shin, In Pyo Cha, Sun Ho Ko, Hyun Kyung Yoon, Hong Gun Kim, Lee Ku Kwac

Abstract:

The prepreg process among the CFRP (Carbon Fiber Reinforced Plastic) forming methods is the short term of ‘Pre-impregnation’, which is widely used for aerospace composites that require a high quality property such as a fiber-reinforced woven fabric, in which an epoxy hardening resin is impregnated the reality. However, that this process requires continuous researches and developments for its commercialization because the delamination characteristically develops between the layers when a great weight is loaded from outside to supplement such demerit, three lamination methods among the prepreg lamination methods of CFRP were designed to minimize the delamination between the layers due to external impacts. Further, the newly designed methods and the existing lamination methods were analyzed through a mechanical characteristic test, Interlaminar Shear Strength test. The Interlaminar Shear Strength test result confirmed that the newly proposed three lamination methods, i.e. the Roll, Half and Zigzag laminations, presented more excellent strengths compared to the conventional Ply lamination. The interlaminar shear strength in the roll method with relatively dense fiber distribution was approximately 1.75% higher than that in the existing ply lamination method, and in the half method, it was approximately 0.78% higher.

Keywords: Carbon Fiber Reinforced Plastic (CFRP), Pre-Impregnation, Laminating Method, Interlaminar Shear Strength (ILSS).

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Authors: Kei Kawamorita, Ryouta Kasahara, Yuuki Mochizuki, Kenichiro Noguchi

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A separation-kernel-based operating system (OS) has been designed for use in secure embedded systems by applying formal methods to the design of the separation-kernel part. The separation kernel is a small OS kernel that provides an abstract distributed environment on a single CPU. The design of the separation kernel was verified using two formal methods, the B method and the Spin model checker. A newly designed semi-formal method, the extended state transition method, was also applied. An OS comprising the separation-kernel part and additional OS services on top of the separation kernel was prototyped on the Intel IA-32 architecture. Developing and testing of a prototype embedded application, a point-of-sale application, on the prototype OS demonstrated that the proposed architecture and the use of formal methods to design its kernel part are effective for achieving a secure embedded system having a high-assurance separation kernel.

Keywords: B method, embedded systems, extended state transition, formal methods, separation kernel, Spin.

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Authors: Pelin Yildiz

Abstract:

The term interactive education indicates the meaning related with multidisciplinary aspects of distance education following contemporary means around a common basis with different functional requirements. The aim of this paper is to reflect the new techniques in education with the new methods and inventions. These methods are better supplied by interactivity. The integration of interactive facilities in the discipline of education with distance learning is not a new concept but in addition the usage of these methods on design issue is newly being adapted to design education. In this paper the general approach of this method and after the analysis of different samples, the advantages and disadvantages of these approaches are being identified. The method of this paper is to evaluate the related samples and then analyzing the main hypothesis. The main focus is to mention the formation processes of this education. Technological developments in education should be filtered around the necessities of the design education and the structure of the system could then be formed or renewed. The conclusion indicates that interactive methods of education in design issue is a meaning capturing not only technical and computational intelligence aspects but also aesthetical and artistic approaches coming together around the same purpose.

Keywords: Interactive education, distance learning, designeducation, computational intelligence.

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Authors: L. Melecký

Abstract:

Measurement of competitiveness between countries or regions is an important topic of many economic analysis and scientific papers. In European Union (EU), there is no mainstream approach of competitiveness evaluation and measuring. There are many opinions and methods of measurement and evaluation of competitiveness between states or regions at national and European level. The methods differ in structure of using the indicators of competitiveness and ways of their processing. The aim of the paper is to analyze main sources of competitive potential of the EU Member States with the help of Factor analysis (FA) and to classify the EU Member States to homogeneous units (clusters) according to the similarity of selected indicators of competitiveness factors by Cluster analysis (CA) in reference years 2000 and 2011. The theoretical part of the paper is devoted to the fundamental bases of competitiveness and the methodology of FA and CA methods. The empirical part of the paper deals with the evaluation of competitiveness factors in the EU Member States and cluster comparison of evaluated countries by cluster analysis. 

Keywords: Competitiveness, cluster analysis, EU, factor analysis, multivariate methods.

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Authors: Guy Rosman, Alexander M. Bronstein, Michael M. Bronstein, Ron Kimmel

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We present a new algorithm for nonlinear dimensionality reduction that consistently uses global information, and that enables understanding the intrinsic geometry of non-convex manifolds. Compared to methods that consider only local information, our method appears to be more robust to noise. Unlike most methods that incorporate global information, the proposed approach automatically handles non-convexity of the data manifold. We demonstrate the performance of our algorithm and compare it to state-of-the-art methods on synthetic as well as real data.

Keywords: Dimensionality reduction, manifold learning, multidimensional scaling, geodesic distance, boundary detection.

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Authors: Ramandeep Behl, S. S. Motsa

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The main focus of this manuscript is to provide a highly efficient two-point sixth-order family of super-Halley type methods that do not require any second-order derivative evaluation for obtaining simple roots of nonlinear equations, numerically. Each member of the proposed family requires two evaluations of the given function and two evaluations of the first-order derivative per iteration. By using Mathematica-9 with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm t he t heoretical d evelopment. From their basins of attraction, it has been observed that the proposed methods have better stability and robustness as compared to the other sixth-order methods available in the literature.

Keywords: Basins of attraction, nonlinear equations, simple roots, Super-Halley.

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Authors: Renáta Iváncsy, Sándor Juhász

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Web usage mining has become a popular research area, as a huge amount of data is available online. These data can be used for several purposes, such as web personalization, web structure enhancement, web navigation prediction etc. However, the raw log files are not directly usable; they have to be preprocessed in order to transform them into a suitable format for different data mining tasks. One of the key issues in the preprocessing phase is to identify web users. Identifying users based on web log files is not a straightforward problem, thus various methods have been developed. There are several difficulties that have to be overcome, such as client side caching, changing and shared IP addresses and so on. This paper presents three different methods for identifying web users. Two of them are the most commonly used methods in web log mining systems, whereas the third on is our novel approach that uses a complex cookie-based method to identify web users. Furthermore we also take steps towards identifying the individuals behind the impersonal web users. To demonstrate the efficiency of the new method we developed an implementation called Web Activity Tracking (WAT) system that aims at a more precise distinction of web users based on log data. We present some statistical analysis created by the WAT on real data about the behavior of the Hungarian web users and a comprehensive analysis and comparison of the three methods

Keywords: Data preparation, Tracking individuals, Web useridentification, Web usage mining

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Authors: Parvaneh Shabanzadeh, Malik Hj Abu Hassan, Leong Wah June, Maryam Mohagheghtabar

Abstract:

Clustering is one of an interesting data mining topics that can be applied in many fields. Recently, the problem of cluster analysis is formulated as a problem of nonsmooth, nonconvex optimization, and an algorithm for solving the cluster analysis problem based on nonsmooth optimization techniques is developed. This optimization problem has a number of characteristics that make it challenging: it has many local minimum, the optimization variables can be either continuous or categorical, and there are no exact analytical derivatives. In this study we show how to apply a particular class of optimization methods known as pattern search methods to address these challenges. These methods do not explicitly use derivatives, an important feature that has not been addressed in previous studies. Results of numerical experiments are presented which demonstrate the effectiveness of the proposed method.

Keywords: Clustering functions, Non-smooth Optimization, Nonconvex Optimization, Pattern Search Method.

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Authors: R. Manaffar, R. Maleki, S. Zare, N. Agh, S. Soltanian, B. Sehatnia, P. Sorgeloos, P. Bossier, G. Van Stappen

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Artemia is one of the most conspicuous invertebrates associated with aquaculture. It can be considered as a model organism, offering numerous advantages for comprehensive and multidisciplinary studies using morphologic or molecular methods. Since DNA extraction is an important step of any molecular experiment, a new and a rapid method of DNA extraction from adult Artemia was described in this study. Besides, the efficiency of this technique was compared with two widely used alternative techniques, namely Chelex® 100 resin and SDS-chloroform methods. Data analysis revealed that the new method is the easiest and the most cost effective method among the other methods which allows a quick and efficient extraction of DNA from the adult animal.

Keywords: APD, Artemia, DNA extraction, Molecularexperiments

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Authors: Jörg Lassig, Stefanie Thiem

Abstract:

The objective of this paper is the introduction to a unified optimization framework for research and education. The OPTILIB framework implements different general purpose algorithms for combinatorial optimization and minimum search on standard continuous test functions. The preferences of this library are the straightforward integration of new optimization algorithms and problems as well as the visualization of the optimization process of different methods exploring the search space exclusively or for the real time visualization of different methods in parallel. Further the usage of several implemented methods is presented on the basis of two use cases, where the focus is especially on the algorithm visualization. First it is demonstrated how different methods can be compared conveniently using OPTILIB on the example of different iterative improvement schemes for the TRAVELING SALESMAN PROBLEM. A second study emphasizes how the framework can be used to find global minima in the continuous domain.

Keywords: Global Optimization Heuristics, Particle Swarm Optimization, Ensemble Based Threshold Accepting, Ruin and Recreate

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Authors: Bayar Shahab

Abstract:

The fast development of technology that has advanced neuroscience and human interaction with computers has enabled solutions to various problems and issues of this new era. The Brain-Computer Interface (BCI) has opened the door to several new research areas and have been able to provide solutions to critical and vital issues such as supporting a paralyzed patient to interact with the outside world, controlling a robot arm, playing games in VR with the brain, driving a wheelchair. This review presents the state-of-the-art methods and improvements of canonical correlation analyses (CCA), an SSVEP-based BCI method. These are the methods used to extract EEG signal features or, to be said differently, the features of interest that we are looking for in the EEG analyses. Each of the methods from oldest to newest has been discussed while comparing their advantages and disadvantages. This would create a great context and help researchers understand the most state-of-the-art methods available in this field, their pros and cons, and their mathematical representations and usage. This work makes a vital contribution to the existing field of study. It differs from other similar recently published works by providing the following: (1) stating most of the main methods used in this field in a hierarchical way, (2) explaining the pros and cons of each method and their performance, (3) presenting the gaps that exist at the end of each method that can improve the understanding and open doors to new researches or improvements. 

Keywords: BCI, CCA, SSVEP, EEG

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Authors: S. Sarumathi, N. Shanthi, M. Sharmila

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Over the past epoch a rampant amount of work has been done in the data clustering research under the unsupervised learning technique in Data mining. Furthermore several algorithms and methods have been proposed focusing on clustering different data types, representation of cluster models, and accuracy rates of the clusters. However no single clustering algorithm proves to be the most efficient in providing best results. Accordingly in order to find the solution to this issue a new technique, called Cluster ensemble method was bloomed. This cluster ensemble is a good alternative approach for facing the cluster analysis problem. The main hope of the cluster ensemble is to merge different clustering solutions in such a way to achieve accuracy and to improve the quality of individual data clustering. Due to the substantial and unremitting development of new methods in the sphere of data mining and also the incessant interest in inventing new algorithms, makes obligatory to scrutinize a critical analysis of the existing techniques and the future novelty. This paper exposes the comparative study of different cluster ensemble methods along with their features, systematic working process and the average accuracy and error rates of each ensemble methods. Consequently this speculative and comprehensive analysis will be very useful for the community of clustering practitioners and also helps in deciding the most suitable one to rectify the problem in hand.

Keywords: Clustering, Cluster Ensemble methods, Co-association matrix, Consensus function, Median partition.

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Authors: Dylan M. Copeland

Abstract:

We present new finite element methods for Helmholtz and Maxwell equations on general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coefficients are admissible. The resulting approximation on the element surfaces can be extended throughout the domain via representation formulas. Numerical experiments confirm that the convergence behavior on tetrahedral meshes is comparable to that of standard finite element methods, and equally good performance is attained on more general meshes.

Keywords: Boundary elements, finite elements, Helmholtz equation, Maxwell equations.

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Authors: Yuri B. Cesarino, Vinícius R. Domingues, Darym J. F. Campos

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Developing countries have some restrains towards the adoption of new technologies and construction methods. Some nations, such as Brazil, still use conventional construction methodologies, knowing its lesser cost-effectiveness. This research has been conducted to demonstrate how industrialized construction methods should be implemented in Brazil, especially in times of need. Using the common sense among different authors with different perspectives, it is clear that the second method is more suitable for construction development because of its great advantages. However, it is unlikely for this process to be adopted in the country as a result of several social-economic restraints. Nonetheless, Brazilian engineers have a major challenge ahead of them, and it will take more than creativity to solve such an issue.

Keywords: Brazilian engineers, construction methods, industrialized construction, infrastructure.

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Authors: Ahmed H. Abdel-Kareem, Hala. Abousafa, Omia S. El-Hadidi

Abstract:

The results of an experimental program conducted on seventeen simply supported concrete beams to study the effect of transverse reinforcement on the behavior of lap splice of steel reinforcement in tension zones in high strength concrete beams, are presented. The parameters included in the experimental program were the concrete compressive strength, the lap splice length, the amount of transverse reinforcement provided within the splice region, and the shape of transverse reinforcement around spliced bars. The experimental results showed that the displacement ductility increased and the mode of failure changed from splitting bond failure to flexural failure when the amount of transverse reinforcement in splice region increased, and the compressive strength increased up to 100 MPa. The presence of transverse reinforcement around spliced bars had pronounced effect on increasing the ultimate load, the ultimate deflection, and the displacement ductility. The prediction of maximum steel stresses for spliced bars using ACI 318-05 building code was compared with the experimental results. The comparison showed that the effect of transverse reinforcement around spliced bars has to be considered into the design equations for lap splice length in high strength concrete beams.

Keywords: Ductility, high strength concrete, tension lap splice, transverse reinforcement, steel stresses.

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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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