Search results for: multi-objective problems.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2451

Search results for: multi-objective problems.

1461 Adaptive Extended Kalman Filter for Ballistic Missile Tracking

Authors: Gaurav Kumar, Dharmbir Prasad, Rudra Pratap Singh

Abstract:

In the current work, adaptive extended Kalman filter (AEKF) is presented for solution of ground radar based ballistic missile (BM) tracking problem in re-entry phase with unknown ballistic coefficient. The estimation of trajectory of any BM in re-entry phase is extremely difficult, because of highly non-linear motion of BM. The estimation accuracy of AEKF has been tested for a typical test target tracking problem adopted from literature. Further, the approach of AEKF is compared with extended Kalman filter (EKF). The simulation result indicates the superiority of the AEKF in solving joint parameter and state estimation problems.

Keywords: Adaptive, AEKF, ballistic missile, EKF, re-entry phase, target tracking.

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1460 A Constructive Proof of the General Brouwer Fixed Point Theorem and Related Computational Results in General Non-Convex sets

Authors: Menglong Su, Shaoyun Shi, Qing Xu

Abstract:

In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.

Keywords: interior path following method, general Brouwer fixed point theorem, non-convex sets, globally convergent algorithm

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1459 The Harada Method – A Method for Employee Development during Production Ramp Up

Authors: M. Goerke, J. Gehrmann

Abstract:

Caused by shorter product life cycles and higher product variety the importance of production ramp ups is increasing. Even though companies are aware of that fact, up to 40% of the ramp up projects still miss technical and economical requirements. The success of a ramp up depends on the planning of human factors, organizational aspects and technological solutions. Since only partly considered in scientific literature, this paper lays its focus on the human factor during production ramp up. There are only incoherent methods which address the problems in this area. A systematic and holistic method to improve the capabilities of the employees during ramp up is missing. The Harada Method is a relatively young approach for developing highly-skilled workers. It consists of different worksheets which help employees to set guidelines and reach overall objectives. This approach is going to be transferred into a tool for ramp up management.

Keywords: Employee Development, Harada, Production Ramp Up.

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1458 A Parallel Algorithm for 2-D Cylindrical Geometry Transport Equation with Interface Corrections

Authors: Wei Jun-xia, Yuan Guang-wei, Yang Shu-lin, Shen Wei-dong

Abstract:

In order to make conventional implicit algorithm to be applicable in large scale parallel computers , an interface prediction and correction of discontinuous finite element method is presented to solve time-dependent neutron transport equations under 2-D cylindrical geometry. Domain decomposition is adopted in the computational domain.The numerical experiments show that our parallel algorithm with explicit prediction and implicit correction has good precision, parallelism and simplicity. Especially, it can reach perfect speedup even on hundreds of processors for large-scale problems.

Keywords: Transport Equation, Discontinuous Finite Element, Domain Decomposition, Interface Prediction And Correction

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1457 Changes in Vocational Teacher Training in Hungary: Challenges and Possibilities

Authors: A. Bacsa-Bán

Abstract:

The training of vocational education teachers in Hungary was a special training system before the Bologna system, but under the influence of the Bologna system, the structure and content of the training changed significantly. The training of vocational teachers, including engineering teacher and vocational trainers, is considerably different when compared to the training of public education teachers. This study aims to present these differences and peculiarities, problems, and issues of the training as well as to outline the possibilities of further development. During the study the following methods were implemented: empirical research among students and graduates of vocational teacher training, as well as analysis of the relevant literature. The study summarizes the research and theoretical results related to Vocational Education and Training (VET) teacher training over the past 15 years, with the aim of developing the training and mapping new directions in the field.

Keywords: Bologna system, vocational educators, vocational teachers, vocational teacher training.

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1456 Analysis of DNA-Recognizing Enzyme Interaction using Deaminated Lesions

Authors: Seung Pil Pack

Abstract:

Deaminated lesions were produced via nitrosative oxidation of natural nucleobases; uracul (Ura, U) from cytosine (Cyt, C), hypoxanthine (Hyp, H) from adenine (Ade, A), and xanthine (Xan, X) and oxanine (Oxa, O) from guanine (Gua, G). Such damaged nucleobases may induce mutagenic problems, so that much attentions and efforts have been poured on the revealing of their mechanisms in vivo or in vitro. In this study, we employed these deaminated lesions as useful probes for analysis of DNA-binding/recognizing proteins or enzymes. Since the pyrimidine lesions such as Hyp, Oxa and Xan are employed as analogues of guanine, their comparative uses are informative for analyzing the role of Gua in DNA sequence in DNA-protein interaction. Several DNA oligomers containing such Hyp, Oxa or Xan substituted for Gua were designed to reveal the molecular interaction between DNA and protein. From this approach, we have got useful information to understand the molecular mechanisms of the DNA-recognizing enzymes, which have not ever been observed using conventional DNA oligomer composed of just natural nucleobases.

Keywords: Deaminated lesion, DNA-protein interaction, DNA-recognizing enzymes

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1455 Applications of High-Order Compact Finite Difference Scheme to Nonlinear Goursat Problems

Authors: Mohd Agos Salim Nasir, Ahmad Izani Md. Ismail

Abstract:

Several numerical schemes utilizing central difference approximations have been developed to solve the Goursat problem. However, in a recent years compact discretization methods which leads to high-order finite difference schemes have been used since it is capable of achieving better accuracy as well as preserving certain features of the equation e.g. linearity. The basic idea of the new scheme is to find the compact approximations to the derivative terms by differentiating centrally the governing equations. Our primary interest is to study the performance of the new scheme when applied to two Goursat partial differential equations against the traditional finite difference scheme.

Keywords: Goursat problem, partial differential equation, finite difference scheme, compact finite difference

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1454 A Second Law Assessment of Organic Rankine Cycle Depending on Source Temperature

Authors: Kyoung Hoon Kim

Abstract:

Organic Rankine Cycle (ORC) has potential in reducing fossil fuels and relaxing environmental problems. In this work performance analysis of ORC is conducted based on the second law of thermodynamics for recovery of low temperature heat source from 100oC to 140oC using R134a as the working fluid. Effects of system parameters such as turbine inlet pressure or source temperature are theoretically investigated on the exergy destructions (anergies) at various components of the system as well as net work production or exergy efficiency. Results show that the net work or exergy efficiency has a peak with respect to the turbine inlet pressure when the source temperature is low, however, increases monotonically with increasing turbine inlet pressure when the source temperature is high.

Keywords: Organic Rankine cycle (ORC), low temperature heat source, exergy, source temperature.

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1453 Comparative Study of Ant Colony and Genetic Algorithms for VLSI Circuit Partitioning

Authors: Sandeep Singh Gill, Rajeevan Chandel, Ashwani Chandel

Abstract:

This paper presents a comparative study of Ant Colony and Genetic Algorithms for VLSI circuit bi-partitioning. Ant colony optimization is an optimization method based on behaviour of social insects [27] whereas Genetic algorithm is an evolutionary optimization technique based on Darwinian Theory of natural evolution and its concept of survival of the fittest [19]. Both the methods are stochastic in nature and have been successfully applied to solve many Non Polynomial hard problems. Results obtained show that Genetic algorithms out perform Ant Colony optimization technique when tested on the VLSI circuit bi-partitioning problem.

Keywords: Partitioning, genetic algorithm, ant colony optimization, non-polynomial hard, netlist, mutation.

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1452 To Design Holistic Health Service Systems on the Internet

Authors: Åsa Smedberg

Abstract:

There are different kinds of online systems on the Internet for people who need support and develop new knowledge. Online communities and Ask the Expert systems are two such systems. In the health care area, the number of users of these systems has increased at a rapid pace. Interactions with medical trained experts take place online, and people with concerns about similar health problems come together to share experiences and advice. The systems are also used as storages and browsed for health information. Over the years, studies have been conducted of the usage of the different systems. However, in what ways the systems can be used together to enhance learning has not been explored. This paper presents results from a study of online health-communities and an Ask the Expert system for people who suffer from overweight. Differences and similarities in regards to posted issues and replies are discussed, and suggestions for a new holistic design of the two systems are presented.

Keywords: Learning, Ask the Expert, online community, healthcare, holistic, overweight.

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1451 Natural-Direction-Consistent 3D-Design and Printing Methods

Authors: Yasusi Kanada

Abstract:

Objects are usually horizontally sliced when printed by 3D printers. Therefore, if an object to be printed, such as a collection of fibers, originally has natural direction in shape, the printed direction contradicts with the natural direction. By using proper tools, such as field-oriented 3D paint software, field-oriented solid modelers, field-based tool-path generation software, and non-horizontal FDM 3D printers, the natural direction can be modeled and objects can be printed in a direction that is consistent with the natural direction. This consistence results in embodiment of momentum or force in expressions of the printed object. To achieve this goal, several design and manufacturing problems, but not all, have been solved. An application of this method is (Japanese) 3D calligraphy.

Keywords: 3D printing, Three-dimensional printing, Solid free-form fabrication, SFF, Fused deposition modeling, FDM, Additive manufacturing.

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1450 Why Developing Countries Are Lesser Innovators

Authors: Abdul Waheed

Abstract:

In this paper, we observe that developed countries are generally equipped with innovation capabilities and produce major chunk of the world-s knowledge and technology. The contribution of developing countries, on the other hand, is insignificant, and most of them far behind the global technological front. More specifically, we empirically observe that the developing world neither contributes substantially to the world-s scientific publications nor to the R&D activities. They also have lesser “absorptive capacity" and “technological capability", and their “innovation systems" are plagued with many problems. Finally, we argue that these countries can break the shackles and improve their innovation capabilities by pursuing genuine innovation policies on long-term basis with honesty and commitment.

Keywords: Absorptive capacity, Developing countries, Scientific publications, Technological capability

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1449 Some Characteristics of Systolic Arrays

Authors: Halil Snopce, Ilir Spahiu

Abstract:

In this paper is investigated a possible optimization of some linear algebra problems which can be solved by parallel processing using the special arrays called systolic arrays. In this paper are used some special types of transformations for the designing of these arrays. We show the characteristics of these arrays. The main focus is on discussing the advantages of these arrays in parallel computation of matrix product, with special approach to the designing of systolic array for matrix multiplication. Multiplication of large matrices requires a lot of computational time and its complexity is O(n3 ). There are developed many algorithms (both sequential and parallel) with the purpose of minimizing the time of calculations. Systolic arrays are good suited for this purpose. In this paper we show that using an appropriate transformation implicates in finding more optimal arrays for doing the calculations of this type.

Keywords: Data dependences, matrix multiplication, systolicarray, transformation matrix.

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1448 Comparison of Two Interval Models for Interval-Valued Differential Evolution

Authors: Hidehiko Okada

Abstract:

The author previously proposed an extension of differential evolution. The proposed method extends the processes of DE to handle interval numbers as genotype values so that DE can be applied to interval-valued optimization problems. The interval DE can employ either of two interval models, the lower and upper model or the center and width model, for specifying genotype values. Ability of the interval DE in searching for solutions may depend on the model. In this paper, the author compares the two models to investigate which model contributes better for the interval DE to find better solutions. Application of the interval DE is evolutionary training of interval-valued neural networks. A result of preliminary study indicates that the CW model is better than the LU model: the interval DE with the CW model could evolve better neural networks. 

Keywords: Evolutionary algorithms, differential evolution, neural network, neuroevolution, interval arithmetic.

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1447 Process of Revitalization of the City Centers in Poland: The Problem of Cooperation between Sectors

Authors: Ewa M. Boryczka

Abstract:

Contemporary city is a subject to rapid economic and social changes. Therefore, it requires an active policy designed to meet the diverse needs of their residents, build competitive position and capacity to compete with other cities. Competitiveness of cities depends largely on their resources but also to a large extent, on the policies and performance of local authorities. Cooperation with social sector also plays an important role, as it affects the use of resources and builds an advantage over other cities. The subject of this article is city's contemporary problems of development with particular emphasis on central areas. This issue is a starting point for reflection on the process of urban regeneration in medium size cities in Poland, as well as cooperation between various actors and their roles in the revitalization processes of Polish cities' centers.

Keywords: City, cooperation between sectors, crisis of city centers, revitalization.

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1446 Enhancing Privacy-Preserving Cloud Database Querying by Preventing Brute Force Attacks

Authors: Ambika Vishal Pawar, Ajay Dani

Abstract:

Considering the complexities involved in Cloud computing, there are still plenty of issues that affect the privacy of data in cloud environment. Unless these problems get solved, we think that the problem of preserving privacy in cloud databases is still open. In tokenization and homomorphic cryptography based solutions for privacy preserving cloud database querying, there is possibility that by colluding with service provider adversary may run brute force attacks that will reveal the attribute values.

In this paper we propose a solution by defining the variant of K –means clustering algorithm that effectively detects such brute force attacks and enhances privacy of cloud database querying by preventing this attacks.

Keywords: Privacy, Database, Cloud Computing, Clustering, K-means, Cryptography.

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1445 2D and 3D Finite Element Method Packages of CEMTool for Engineering PDE Problems

Authors: Choon Ki Ahn, Jung Hun Park, Wook Hyun Kwon

Abstract:

CEMTool is a command style design and analyzing package for scientific and technological algorithm and a matrix based computation language. In this paper, we present new 2D & 3D finite element method (FEM) packages for CEMTool. We discuss the detailed structures and the important features of pre-processor, solver, and post-processor of CEMTool 2D & 3D FEM packages. In contrast to the existing MATLAB PDE Toolbox, our proposed FEM packages can deal with the combination of the reserved words. Also, we can control the mesh in a very effective way. With the introduction of new mesh generation algorithm and fast solving technique, our FEM packages can guarantee the shorter computational time than MATLAB PDE Toolbox. Consequently, with our new FEM packages, we can overcome some disadvantages or limitations of the existing MATLAB PDE Toolbox.

Keywords: CEMTool, Finite element method (FEM), Numericalanalysis, Partial differential equation (PDE)

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1444 Influence of Intermediate Principal Stress on Solution of Planar Stability Problems

Authors: M. Jahanandish, M. B. Zeydabadinejad

Abstract:

In this paper, von Mises and Drucker-Prager yield criteria, as typical ones that consider the effect of intermediate principal stress σ2, have been selected and employed for investigating the influence of σ2 on the solution of a typical stability problem. The bearing capacity factors have been calculated under plane strain condition (strip footing) and axisymmetric condition (circular footing) using the method of stress characteristics together with the criteria mentioned. Different levels of σ2 relative to the other two principal stresses have been considered. While a higher σ2 entry in yield criterion gives a higher bearing capacity; its entry in equilibrium equations (axisymmetric) causes substantial reduction.

Keywords: Intermediate principal stress, plane strain, axisymmetric, yield criteria.

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1443 Analyzing Convergence of IT and Energy Industry Based on Social System Framework

Authors: Giseob Byun, Ji Yeon Cho, Bong Gyou Lee

Abstract:

The purpose of this study is to analyze Green IT industry in major developed countries and to suggest overall directions for IT-Energy convergence industry. Recently, IT industry is pointed out as a problem such as environmental pollution, energy exhaustion, and high energy consumption. Therefore, Green IT gets focused which concerns as solution of these problems. However, since it is a beginning stage of this convergence area, there are only a few studies of IT-Energy convergence industry. According to this, this study examined the major developed countries in terms of institution arrangements, resources, markets and companies based on Van de Ven(1999)'s social system framework that shows relationship among key components of industrial infrastructure. Subsequently, the direction of the future study of convergence on IT and Energy industry is proposed.

Keywords: Green IT, Energy industry, Convergence, Social System Framework.

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1442 Teaching Students the Black Magic of Electromagnetic Compatibility

Authors: Dag A.H. Samuelsen, Olaf H. Graven

Abstract:

Introducing Electromagnetic Interference and Electromagnetic Compatibility, or “The Art of Black Magic", for engineering students might be a terrifying experience both for students and tutors. Removing the obstacle of large, expensive facilities like a fully fitted EMC laboratory and hours of complex theory, this paper demonstrates a design of a laboratory setup for student exercises, giving students experience in the basics of EMC/EMI problems that may challenge the functionality and stability of embedded system designs. This is done using a simple laboratory installation and basic measurement equipment such as a medium cost digital storage oscilloscope, at the cost of not knowing the exact magnitude of the noise components, but rather if the noise is significant or not, as well as the source of the noise. A group of students have performed a trial exercise with good results and feedback.

Keywords: EMC, EMI, engineering project, student laboratory.

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1441 Neutrosophic Multiple Criteria Decision Making Analysis Method for Selecting Stealth Fighter Aircraft

Authors: C. Ardil

Abstract:

In this paper, a neutrosophic multiple criteria decision analysis method is proposed to select stealth fighter aircraft. Neutrosophic multiple criteria decision analysis methods are used to analyze the neutrosophic environment and give results under uncertainty and incompleteness. Neutrosophic numbers are used to evaluate alternatives over a set of evaluation criteria in decision making problems. Finally, the proposed model is applied to a practical decision problem for selecting stealth fighter aircraft.

Keywords: neutrosophic sets, multiple criteria decision making analysis, stealth fighter aircraft, aircraft selection, MCDMA, SVNNs

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1440 The Effects of Roots Action of Tropical Green Roofs–Replication of German FLL in Singapore

Authors: Kian. Kai. Tan, Michael. Yit. Lin. Chew, Nyuk. Hien. Wong

Abstract:

Green Roofs offers numerous advantages, including lowering ambient temperature, which is of increasing interest due to global warming concerns. However, there are technical problems pertaining to waterproofing to be resolved. Currently, the only recognized green roof waterproofing test is the German standard FLL. This paper examines the potential of replicating the test in tropical climate and reducing the test duration by using pre-grown plants. A three year old sample and a new setup were used for this experimental study. The new setup was prepared with close reference to the FLL standards and was compared against the three year old sample. Results showed that the waterproofing membrane was damaged by plant roots in both setups. Joints integrity was also challenged.

Keywords: Building plants, green roof, sustainability, waterproofing membrane

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1439 Spatial thinking Issues: Towards Rural Sociological Research Agenda in the Third Millennium

Authors: Abdel-Samad M. Ali

Abstract:

Does the spatial perspective provide a common thread for rural sociology? Have rural sociologists succeeded in bringing order to their data using spatial analysis models and techniques? A trial answer to such questions, as touchstones of theoretical and applied sociological studies in rural areas, is the point at issue in the present paper. Spatial analyses have changed the way rural sociologists approach scientific problems. Rural sociology is spatial by nature because much, if not most, of its research topics has a spatial “awareness." However, such spatial awareness is not quite the same as spatial analysis because it is not typically associated with underlying theories and hypotheses about spatial patterns that are designed to be tested for their specific spatial content. This paper presents pressing issues for future research to reintroduce mainstream rural sociology to the concept of space.

Keywords: Maps, Rural Sociology, Space, Spatial variations

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1438 Natural Gas Sweetening by Wetted-Wire Column

Authors: Sarah Taheri, Shahram Ghanbari Pakdehi, Arash Rezaei

Abstract:

Natural gas usually includes H2S component which is very toxic, hazardous and corrosive to environment, human being and process equipments, respectively. Therefore, sweetening of the gas (separation of H2S) is inevitable. To achieve this purpose, using packed-bed columns with liquid absorbents such as MEA or DEA is very common. Due to some problems of usual packed columns especially high pressure drop of gas phase, a novel kind of them called wetted-wire column (WWC) has been invented. The column decreases the pressure drop significantly and improves the absorption efficiency. The packings are very thin rods (like wire) and as long as column. The column has 100 wires with a triangular arrangement and counter current flows of gas and liquid phases. The observation showed that at the same conditions, the absorption performance was quite comparable to conventional packed-bed towers and a very low pressure drop.

Keywords: H2S, Natural gas, separation, wetted-wire column (WWC).

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1437 The Roles of Natural and Anthropogenic Factors of Ecological State in the Lake Peipsi

Authors: Galya Kapanen, Jaan–Mati Punning, Irina Blinova, Külli Kangur

Abstract:

In this paper we discuss the problems of the long-term management policy of Lake Peipsi and the roles of natural and anthropogenic factors in the ecological state of the lake. The reduction of the pollution during the last 15 years could not give significant changes of the chemical composition of the water, what implicates the essential role that natural factors have on the ecological state of lake. One of the most important factors having impact on the hydrochemical cycles and ecological state is the hydrological regime which is clearly expressed in L. Peipsi. The absence on clear interrelations of climate cycles and nutrients suggest that complex abiotic and biotic interactions, which take place in the lake ecosystem, plays a significant role in the matter circulation mechanism within lake.

Keywords: Lake Peipsi, ecosystem, eutrophication, waterfluctuation, NAO.

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1436 Causes of Rotor Distortions and Applicable Common Straightening Methods for Turbine Rotors and Shafts

Authors: Esmaeil Poursaeidi, Mostafa Kamalzadeh Yazdi

Abstract:

Different problems may causes distortion of the rotor, and hence vibration, which is the most severe damage of the turbine rotors. In many years different techniques have been developed for the straightening of bent rotors. The method for straightening can be selected according to initial information from preliminary inspections and tests such as nondestructive tests, chemical analysis, run out tests and also a knowledge of the shaft material. This article covers the various causes of excessive bends and then some applicable common straightening methods are reviewed. Finally, hot spotting is opted for a particular bent rotor. A 325 MW steam turbine rotor is modeled and finite element analyses are arranged to investigate this straightening process. Results of experimental data show that performing the exact hot spot straightening process reduced the bending of the rotor significantly.

Keywords: Distortion, FEM, Hot Spot Area, Rotor Straightening

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1435 Controller Synthesis of Switched Positive Systems with Bounded Time-Varying Delays

Authors: Xinhui Wang, Xiuyong Ding

Abstract:

This paper addresses the controller synthesis problem of discrete-time switched positive systems with bounded time-varying delays. Based on the switched copositive Lyapunov function approach, some necessary and sufficient conditions for the existence of state-feedback controller are presented as a set of linear programming and linear matrix inequality problems, hence easy to be verified. Another advantage is that the state-feedback law is independent on time-varying delays and initial conditions. A numerical example is provided to illustrate the effectiveness and feasibility of the developed controller.

Keywords: Switched copositive Lyapunov functions, positive linear systems, switched systems, time-varying delays, stabilization.

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1434 Web Log Mining by an Improved AprioriAll Algorithm

Authors: Wang Tong, He Pi-lian

Abstract:

This paper sets forth the possibility and importance about applying Data Mining in Web logs mining and shows some problems in the conventional searching engines. Then it offers an improved algorithm based on the original AprioriAll algorithm which has been used in Web logs mining widely. The new algorithm adds the property of the User ID during the every step of producing the candidate set and every step of scanning the database by which to decide whether an item in the candidate set should be put into the large set which will be used to produce next candidate set. At the meantime, in order to reduce the number of the database scanning, the new algorithm, by using the property of the Apriori algorithm, limits the size of the candidate set in time whenever it is produced. Test results show the improved algorithm has a more lower complexity of time and space, better restrain noise and fit the capacity of memory.

Keywords: Candidate Sets Pruning, Data Mining, ImprovedAlgorithm, Noise Restrain, Web Log

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1433 Laser Welded Ni-Cr Dental Alloys Inspection

Authors: Porojan S., Sandu L., Topală F.

Abstract:

Minor problems arising from optimizations by welding of fixed prostheses frameworks can be identified by macroscopic and microscopic visual inspection. The purpose of this study was to highlight the visible discontinuities present in the laser welds of dental Ni-Cr alloys. Ni-Cr base metal alloys designated for fixed prostheses manufacture were selected for the experiments. Using cast plates, preliminary tests were conducted by laser welding. Macroscopic visual inspection was done carefully to assess the defects of the welding rib. Electron microscopy images allowed visualization of small discontinuities, which escapes visual inspection. Making comparison to Ni-Cr alloys taken in the experiment and laser welded, after visual analysis, the best welds appear for Heraenium NA alloy.

Keywords: macroscopic visual inspection, electron microscopyimages, Ni-Cr dental alloys, laser welding.

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1432 Stochastic Scheduling to Minimize Expected Lateness in Multiple Identical Machines

Authors: Ghulam Zakria, Zailin Guan , Yasser Riaz Awan, Wan Lizhi

Abstract:

There are many real world problems in which parameters like the arrival time of new jobs, failure of resources, and completion time of jobs change continuously. This paper tackles the problem of scheduling jobs with random due dates on multiple identical machines in a stochastic environment. First to assign jobs to different machine centers LPT scheduling methods have been used, after that the particular sequence of jobs to be processed on the machine have been found using simple stochastic techniques. The performance parameter under consideration has been the maximum lateness concerning the stochastic due dates which are independent and exponentially distributed. At the end a relevant problem has been solved using the techniques in the paper..

Keywords: Quantity Production Flow Shop, LPT Scheduling, Stochastic Scheduling, Maximum Lateness, Random Due Dates

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