Search results for: Saddle point problem

Authors: Nabil M. Hewahi, Motaz K. Saad

Abstract:

In large datasets, identifying exceptional or rare cases with respect to a group of similar cases is considered very significant problem. The traditional problem (Outlier Mining) is to find exception or rare cases in a dataset irrespective of the class label of these cases, they are considered rare events with respect to the whole dataset. In this research, we pose the problem that is Class Outliers Mining and a method to find out those outliers. The general definition of this problem is “given a set of observations with class labels, find those that arouse suspicions, taking into account the class labels". We introduce a novel definition of Outlier that is Class Outlier, and propose the Class Outlier Factor (COF) which measures the degree of being a Class Outlier for a data object. Our work includes a proposal of a new algorithm towards mining of the Class Outliers, presenting experimental results applied on various domains of real world datasets and finally a comparison study with other related methods is performed.

Keywords: Class Outliers, Distance-Based Approach, Outliers Mining.

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Authors: Xiaofei Hu, Zhiyu Cai, Weian Yao

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V-notch problem under dynamic loading condition is considered in this paper. In the time domain, the precise time domain expanding algorithm is employed, in which a self-adaptive technique is carried out to improve computing accuracy. By expanding variables in each time interval, the recursive finite element formulas are derived. In the space domain, a Symplectic Analytical Singular Element (SASE) for V-notch problem is constructed addressing the stress singularity of the notch tip. Combining with the conventional finite elements, the proposed SASE can be used to solve the dynamic stress intensity factors (DSIFs) in a simple way. Numerical results show that the proposed SASE for V-notch problem subjected to dynamic loading condition is effective and efficient.

Keywords: V-notch, dynamic stress intensity factor, finite element method, precise time domain expanding algorithm.

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

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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: Jianning Tang, Xiaofeng Wu

Abstract:

With the increasing demand for space use in multiple sectors (navigation, telecommunication, imagery, etc.), the deployment and maintenance demand of satellites are growing. Considering the high launching cost and the restrictions on weight and size of the payload when using launch vehicle, the technique of on-orbit manufacturing has obtained more attention because of its significant potential to support future space missions. 3D printing is the most promising manufacturing technology that could be applied in space. However, due to the lack of autonomous quality assessment, the operation of conventional 3D printers still relies on human presence to supervise the printing process. This paper is proposed to develop an automatic 3D reconstruction system aiming at detecting failures on the 3D printed objects through application of point cloud technology. Based on the data obtained from the point cloud, the 3D printer could locate the failure and repair the failure. The system will increase automation and provide 3D printing with more feasibilities for space use without human interference.

Keywords: 3D printing, quality assessment, point cloud, on-orbit manufacturing.

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Authors: S. Khanpour, A. Movaghar

Abstract:

The one of best robust search technique on large scale search area is heuristic and meta heuristic approaches. Especially in issue that the exploitation of combinatorial status in the large scale search area prevents the solution of the problem via classical calculating methods, so such problems is NP-complete. in this research, the problem of winner determination in combinatorial auctions have been formulated and by assessing older heuristic functions, we solve the problem by using of genetic algorithm and would show that this new method would result in better performance in comparison to other heuristic function such as simulated annealing greedy approach.

Keywords: Bids, genetic algorithm, heuristic, metaheuristic, simulated annealing greedy.

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Authors: Attapong T., Hong-Ming Ku, Nakarin M., Narin L., Alisa L, Jirut W.

Abstract:

The quantum mechanics simulation was applied for calculating the interaction force between 2 molecules based on atomic level. For the simple extractive distillation system, it is ternary components consisting of 2 closed boiling point components (A,lower boiling point and B, higher boiling point) and solvent (S). The quantum mechanics simulation was used to calculate the intermolecular force (interaction force) between the closed boiling point components and solvents consisting of intermolecular between A-S and B-S. The requirement of the promising solvent for extractive distillation is that solvent (S) has to form stronger intermolecular force with only one component than the other component (A or B). In this study, the systems of aromatic-aromatic, aromatic-cycloparaffin, and paraffindiolefin systems were selected as the demonstration for solvent selection. This study defined new term using for screening the solvents called relative interaction force which is calculated from the quantum mechanics simulation. The results showed that relative interaction force gave the good agreement with the literature data (relative volatilities from the experiment). The reasons are discussed. Finally, this study suggests that quantum mechanics results can improve the relative volatility estimation for screening the solvents leading to reduce time and money consuming

Keywords: Extractive distillation, Interaction force, Quamtum mechanic, Relative volatility, Solvent extraction.

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Authors: Carol B. Collins, M. H. N Tabrizi

Abstract:

The purposes of this paper are to (1) promote excellence in computer science by suggesting a cohesive innovative approach to fill well documented deficiencies in current computer science education, (2) justify (using the authors' and others anecdotal evidence from both the classroom and the real world) why this approach holds great potential to successfully eliminate the deficiencies, (3) invite other professionals to join the authors in proof of concept research. The authors' experiences, though anecdotal, strongly suggest that a new approach involving visual modeling technologies should allow computer science programs to retain a greater percentage of prospective and declared majors as students become more engaged learners, more successful problem-solvers, and better prepared as programmers. In addition, the graduates of such computer science programs will make greater contributions to the profession as skilled problem-solvers. Instead of wearily rememorizing code as they move to the next course, students will have the problem-solving skills to think and work in more sophisticated and creative ways.

Keywords: Algorithms, CASE, UML, Problem-solving.

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Authors: S. Himran, B. Mire, N. Salam, L. Sule

Abstract:

This study was carried out experimentally and analytically about the performance of solar cell panel system for operating the pump coupled by dc-motor. The solar cell panel with total area 1.9848 m2 consists of three modules of 80 Wp each. The small centrifugal pump powered by dc-motor is operated to lift water from 1m to 7m heads in sequence and gives the amount of water pumped over the whole day from 08.00 to 16.00 h are 11988, 10851, 8874, 7695, 5760, 3600, 2340 L/d respectively. The hourly global solar radiation during the day is an average of 506 W/m2. This study also presents the I-V characteristics of the panel at global radiations 200, 400, 600, 800 and 1000 W/m2 matched with the operation of the pump at the above lifting heads. It proves that the only solar radiations 800 and 1000 W/m2 could provide lifting head from 1m to 7m. The analysis shows the best efficiency point of the performance of solar cell panel system occurs at the pumping head 2.89 m.

Keywords: Solar cell, dc- motor-pump, I-V characteristics, best efficiency point.

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Authors: M. Chen, S-Q. Zhang, X. Wang, D. Tate

Abstract:

This paper presents a numerical solution, namely limit and shakedown analysis, to predict the safety state of smart structures made of heterogeneous materials under unknown cyclic loadings, for instance, the flexure hinge in the micro-positioning stage driven by piezoelectric actuator. In combination of homogenization theory and finite-element method (FEM), the safety evaluation problem is converted to a large-scale nonlinear optimization programming for an acceptable bounded loading as the design reference. Furthermore, a general numerical scheme integrated with the FEM and interior-point-algorithm based optimization tool is developed, which makes the practical application possible.

Keywords: Limit state, shakedown analysis, homogenization, heterogeneous structure.

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Authors: Abida Harbi

Abstract:

We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic boundary value problem of the form -Δu = f(u), on two overlapping sub domains with non matching grids. We consider a domain which is the union of two overlapping sub domains where each sub domain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a Lipschitz assumption on the nonlinearity, we establish, on each sub domain, an optimal L∞ error estimate between the discrete Schwarz sequence and the exact solution of the boundary value problem.

Keywords: Error estimates, Finite elements, Nonlinear PDEs, Schwarz method.

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Authors: Veronica Diaz Quezada

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In this article, the performance and errors are featured and analysed in the limit problems solving of a real-valued function, in correspondence to competency-based education in engineering careers, in the south of Chile. The methodological component is contextualised in a qualitative research, with a descriptive and explorative design, with elaboration, content validation and application of quantitative instruments, consisting of two parallel forms of open answer tests, based on limit application problems. The mathematical competences and errors made by students from five engineering careers from a public University are identified and characterized. Results show better performance only to solve routine-context problem-solving competence, thus they are oriented towards a rational solution or they use a suitable problem-solving method, achieving the correct solution. Regarding errors, most of them are related to techniques and the incorrect use of theorems and definitions of real-valued function limits of real variable.

Keywords: Engineering education, errors, limits, mathematics competences, problem solving.

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Authors: Zaheer Ahmad, Jehanzeb Khan Orakzai, Inam Shamsher, Awais Adnan

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This paper discusses the Urdu script characteristics, Urdu Nastaleeq and a simple but a novel and robust technique to recognize the printed Urdu script without a lexicon. Urdu being a family of Arabic script is cursive and complex script in its nature, the main complexity of Urdu compound/connected text is not its connections but the forms/shapes the characters change when it is placed at initial, middle or at the end of a word. The characters recognition technique presented here is using the inherited complexity of Urdu script to solve the problem. A word is scanned and analyzed for the level of its complexity, the point where the level of complexity changes is marked for a character, segmented and feeded to Neural Networks. A prototype of the system has been tested on Urdu text and currently achieves 93.4% accuracy on the average.

Keywords: Cursive Script, OCR, Urdu.

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Authors: Babak H. Tabrizi, Seyed Farid Ghaderi

Abstract:

Concurrent planning of project scheduling and material ordering has been increasingly addressed within last decades as an approach to improve the project execution costs. Therefore, we have taken the problem into consideration in this paper, aiming to maximize schedules quality robustness, in addition to minimize the relevant costs. In this regard, a bi-objective mathematical model is developed to formulate the problem. Moreover, it is possible to utilize the all-unit discount for materials purchasing. The problem is then solved by the E-constraint method, and the Pareto front is obtained for a variety of robustness values. The applicability and efficiency of the proposed model is tested by different numerical instances, finally.

Keywords: E-constraint method, material ordering, project management, project scheduling.

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Authors: M. S. Roslina, A. Noraziah

Abstract:

Malaysia government had been trying hard in order to find the most efficient methods in learning. However, it is hard to actually access and evaluate students whom will then be called an excellent student. It is because in our realties student who excellent is only excel in academic. This evaluation becomes a problem because it not balances in our real life interm of to get an excellent student in whole area in their involvement of curiculum and cocuriculum. To overcome this scenario, we designed a module for Student Idol to evaluate student through three categories which are academic, co-curiculum and leadership. All the categories have their own merit point. Using this method, student will be evaluated more accurate compared to the previously. So, teacher can easily evaluate their student without having any emotion factor, relation factor and others. As conclusion this system module will helps the development of student evaluation more accurate and valid in Student Idol.

Keywords: Evaluation, curiculum, co-curriculum, idol, systemmodule.

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Authors: Yerbol Sapargaliyev, Tatiana Kalganova

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Evolvable Hardware (EHW) has been regarded as adaptive system acquired by wide application market. Consumer market of any good requires diversity to satisfy consumers- preferences. Adaptation of EHW is a key technology that could provide individual approach to every particular user. This situation raises a question: how to set target for evolutionary algorithm? The existing techniques do not allow consumer to influence evolutionary process. Only designer at the moment is capable to influence the evolution. The proposed consumer-triggered evolution overcomes this problem by introducing new features to EHW that help adaptive system to obtain targets during consumer stage. Classification of EHW is given according to responsiveness, imitation of human behavior and target circuit response. Home intelligent water heating system is considered as an example.

Keywords: Actuators, consumer-triggered evolution, evolvable hardware, sensors.

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Authors: Vesna Kirandziska, Nevena Ackovska, Ana Madevska Bogdanova

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The problem of emotion recognition is a challenging problem. It is still an open problem from the aspect of both intelligent systems and psychology. In this paper, both voice features and facial features are used for building an emotion recognition system. A Support Vector Machine classifiers are built by using raw data from video recordings. In this paper, the results obtained for the emotion recognition are given, and a discussion about the validity and the expressiveness of different emotions is presented. A comparison between the classifiers build from facial data only, voice data only and from the combination of both data is made here. The need for a better combination of the information from facial expression and voice data is argued.

Keywords: Emotion recognition, facial recognition, signal processing, machine learning.

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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: Pankaj Chandna, Surinder Deswal, Arunesh Chandra, SK Sharma

Abstract:

Noise has adverse effect on human health and comfort. Noise not only cause hearing impairment, but it also acts as a causal factor for stress and raising systolic pressure. Additionally it can be a causal factor in work accidents, both by marking hazards and warning signals and by impeding concentration. Industry workers also suffer psychological and physical stress as well as hearing loss due to industrial noise. This paper proposes an approach to enable engineers to point out quantitatively the noisiest source for modification, while multiple machines are operating simultaneously. The model with the point source and spherical radiation in a free field was adopted to formulate the problem. The procedure works very well in ideal cases (point source and free field). However, most of the industrial noise problems are complicated by the fact that the noise is confined in a room. Reflections from the walls, floor, ceiling, and equipment in a room create a reverberant sound field that alters the sound wave characteristics from those for the free field. So the model was validated for relatively low absorption room at NIT Kurukshetra Central Workshop. The results of validation pointed out that the estimated sound power of noise sources under simultaneous conditions were on lower side, within the error limits 3.56 - 6.35 %. Thus suggesting the use of this methodology for practical implementation in industry. To demonstrate the application of the above analytical procedure for estimating the sound power of noise sources under simultaneous operating conditions, a manufacturing facility (Railway Workshop at Yamunanagar, India) having five sound sources (machines) on its workshop floor is considered in this study. The findings of the case study had identified the two most effective candidates (noise sources) for noise control in the Railway Workshop Yamunanagar, India. The study suggests that the modification in the design and/or replacement of these two identified noisiest sources (machine) would be necessary so as to achieve an effective reduction in noise levels. Further, the estimated data allows engineers to better understand the noise situations of the workplace and to revise the map when changes occur in noise level due to a workplace re-layout.

Keywords: Industrial noise, sound power level, multiple noise sources, sources contribution.

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Authors: Piyangkun Kukutapan, Siridech Boonsang

Abstract:

The article proposes maximum power point tracking without mechanical sensor using Multilayer Perceptron Neural Network (MLPNN). The aim of article is to reduce the cost and complexity but still retain efficiency. The experimental is that duty cycle is generated maximum power, if it has suitable qualification. The measured data from DC generator, voltage (V), current (I), power (P), turnover rate of power (dP), and turnover rate of voltage (dV) are used as input for MLPNN model. The output of this model is duty cycle for driving the converter. The experiment implemented using Arduino Uno board. This diagram is compared to MPPT using MLPNN and P&O control (Perturbation and Observation control). The experimental results show that the proposed MLPNN based approach is more efficiency than P&O algorithm for this application.

Keywords: Maximum power point tracking, multilayer perceptron neural network, optimal duty cycle.

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Authors: Jin Xu, Albert Y.S. Lam, Victor O.K. Li

Abstract:

Stock portfolio selection is a classic problem in finance, and it involves deciding how to allocate an institution-s or an individual-s wealth to a number of stocks, with certain investment objectives (return and risk). In this paper, we adopt the classical Markowitz mean-variance model and consider an additional common realistic constraint, namely, the cardinality constraint. Thus, stock portfolio optimization becomes a mixed-integer quadratic programming problem and it is difficult to be solved by exact optimization algorithms. Chemical Reaction Optimization (CRO), which mimics the molecular interactions in a chemical reaction process, is a population-based metaheuristic method. Two different types of CRO, named canonical CRO and Super Molecule-based CRO (S-CRO), are proposed to solve the stock portfolio selection problem. We test both canonical CRO and S-CRO on a benchmark and compare their performance under two criteria: Markowitz efficient frontier (Pareto frontier) and Sharpe ratio. Computational experiments suggest that S-CRO is promising in handling the stock portfolio optimization problem.

Keywords: Stock portfolio selection, Markowitz model, Chemical Reaction Optimization, Sharpe ratio

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Authors: Wajdi Bellil, Chokri Ben Amar, Adel M. Alimi

Abstract:

An application of Beta wavelet networks to synthesize pass-high and pass-low wavelet filters is investigated in this work. A Beta wavelet network is constructed using a parametric function called Beta function in order to resolve some nonlinear approximation problem. We combine the filter design theory with wavelet network approximation to synthesize perfect filter reconstruction. The order filter is given by the number of neurons in the hidden layer of the neural network. In this paper we use only the first derivative of Beta function to illustrate the proposed design procedures and exhibit its performance.

Keywords: Beta wavelets, Wavenet, multiresolution analysis, perfect filter reconstruction, salient point detect, repeatability.

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Authors: Anastasiia Yu. Timofeeva

Abstract:

Two new algorithms for nonparametric estimation of errors-in-variables models are proposed. The first algorithm is based on penalized regression spline. The spline is represented as a piecewise-linear function and for each linear portion orthogonal regression is estimated. This algorithm is iterative. The second algorithm involves locally weighted regression estimation. When the independent variable is measured with error such estimation is a complex nonlinear optimization problem. The simulation results have shown the advantage of the second algorithm under the assumption that true smoothing parameters values are known. Nevertheless the use of some indexes of fit to smoothing parameters selection gives the similar results and has an oversmoothing effect.

Keywords: Grade point average, orthogonal regression, penalized regression spline, locally weighted regression.

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Authors: Siti Nor Hafizah binti Mohd Zaid, Mohamed Abdel-Maguid, Abdel-Hamid Soliman

Abstract:

An Advance Driver Assistance System (ADAS) is a computer system on board a vehicle which is used to reduce the risk of vehicular accidents by monitoring factors relating to the driver, vehicle and environment and taking some action when a risk is identified. Much work has been done on assessing vehicle and environmental state but there is still comparatively little published work that tackles the problem of driver state. Visual attention is one such driver state. In fact, some researchers claim that lack of attention is the main cause of accidents as factors such as fatigue, alcohol or drug use, distraction and speeding all impair the driver-s capacity to pay attention to the vehicle and road conditions [1]. This seems to imply that the main cause of accidents is inappropriate driver behaviour in cases where the driver is not giving full attention while driving. The work presented in this paper proposes an ADAS system which uses an image based template matching algorithm to detect if a driver is failing to observe particular windscreen cells. This is achieved by dividing the windscreen into 24 uniform cells (4 rows of 6 columns) and matching video images of the driver-s left eye with eye-gesture templates drawn from images of the driver looking at the centre of each windscreen cell. The main contribution of this paper is to assess the accuracy of this approach using Receiver Operating Characteristic analysis. The results of our evaluation give a sensitivity value of 84.3% and a specificity value of 85.0% for the eye-gesture template approach indicating that it may be useful for driver point of regard determinations.

Keywords: Advanced Driver Assistance Systems, Eye-Tracking, Hazard Detection.

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Authors: Dominik Krimpmann

Abstract:

Information technology and information systems are currently at a tipping point. The digital age fundamentally transforms a large number of industries in the ways they work. Lines between business and technology blur. Researchers have acknowledged that this is the time in which the IT/IS organisation needs to re-strategize itself. In this paper, the author provides a structured review of the IS and organisation design literature addressing the question of how the digital age changes the design categories of an IT/IS organisation design. The findings show that most papers just analyse single aspects of either IT/IS relevant information or generic organisation design elements but miss a holistic ‘big-picture’ onto an IT/IS organisation design. This paper creates a holistic IT/IS organisation design framework bringing together the IS research strand, the digital strand and the generic organisation design strand. The research identified four IT/IS organisation design categories (strategy, structure, processes and people) and discusses the importance of two additional categories (sourcing and governance). The authors findings point to a first anchor point from which further research needs to be conducted to develop a holistic IT/IS organisation design framework.

Keywords: IT/IS strategy, IT/IS organisation design, digital age, organisational effectiveness, literature review.

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Authors: Tun Myat Aung, Ni Ni Hla

Abstract:

This paper begins by describing basic properties of finite field and elliptic curve cryptography over prime field and binary field. Then we discuss the discrete logarithm problem for elliptic curves and its properties. We study the general common attacks on elliptic curve discrete logarithm problem such as the Baby Step, Giant Step method, Pollard’s rho method and Pohlig-Hellman method, and describe in detail experiments of these attacks over prime field and binary field. The paper finishes by describing expected running time of the attacks and suggesting strong elliptic curves that are not susceptible to these attacks.c

Keywords: Discrete logarithm problem, general attacks, elliptic curves, strong curves, prime field, binary field, attack experiments.

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Authors: S. Balaji

Abstract:

An edge based local search algorithm, called ELS, is proposed for the maximum clique problem (MCP), a well-known combinatorial optimization problem. ELS is a two phased local search method effectively £nds the near optimal solutions for the MCP. A parameter ’support’ of vertices de£ned in the ELS greatly reduces the more number of random selections among vertices and also the number of iterations and running times. Computational results on BHOSLIB and DIMACS benchmark graphs indicate that ELS is capable of achieving state-of-the-art-performance for the maximum clique with reasonable average running times.

Keywords: Maximum clique, local search, heuristic, NP-complete.

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Authors: S. Pathomsiri, P. Sukaboon

Abstract:

The National Blood Center, Thai Red Cross Society is responsible for providing blood to hospitals all over the country. When any hospital needs blood, it will have to send the vehicle to pick up at the NBC. There are a lot of vehicles to pick up blood at the NBC every day. Each vehicle is usually empty for inbound trip and a little loaded for outbound. The NBC realized such waste or loss and there have been the third party offered to distribute blood and charge for fee. This paper proposes to apply the vehicle routing problem (VRP) for estimating the fair price. The idea is tested with the real data during seven-day period of 6 – 12 July 2010 to estimate the fair price for transporting blood in Bangkok Metropolitan Region.

Keywords: Blood Supply Chain, Vehicle Routing Problem, Heuristic, Saving Algorithm, Fair Price.

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Authors: A. Seidl, Th. Schmidt

Abstract:

Meshless Finite Element Methods, namely element-free Galerkin and point-interpolation method were implemented and tested concerning their applicability to typical engineering problems like electrical fields and structural mechanics. A class-structure was developed which allows a consistent implementation of these methods together with classical FEM in a common framework. Strengths and weaknesses of the methods under investigation are discussed. As a result of this work joint usage of meshless methods together with classical Finite Elements are recommended.

Keywords: Finite Elements, meshless, element-free Galerkin, point-interpolation.

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Authors: Alemayehu Geremew Negash

Abstract:

We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E.  

Keywords: Common fixed point, Mann iteration, Multivalued mapping, weak convergence.

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Authors: M. Bouinoun, M. Bouhadef

Abstract:

The present study is concerned with the problem of determining the shape of the free surface flow in a hydraulic channel which has an uneven bottom. For the mathematical formulation of the problem, the fluid of the two-dimensional irrotational steady flow in water is assumed inviscid and incompressible. The solutions of the nonlinear problem are obtained by using the usual conformal mapping theory and Hilbert’s technique. An experimental study, for comparing the obtained results, has been conducted in a hydraulic channel (subcritical regime and supercritical regime). 

Keywords: Free-surface flow, experiments, numerical method, uneven bottom, supercritical regime, subcritical regime.

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