Search results for: Software stability

Authors: Milan Paudel, Fook Fah Yap, Anil K. Bastola

Abstract:

The difficulties in riding small wheel bicycles and their lesser stability have been perceived for a long time. Although small wheel bicycles are designed using the similar approach and guidelines that have worked well for big wheel bicycles, the performance of the big wheelers and the smaller wheelers are markedly different. Since both the big wheelers and small wheelers have same fundamental geometry, most blame the small wheel for this discrepancy in the performance. This paper reviews existing guidelines for bicycle design, especially the front steering geometry for the bicycle, and provides a systematic and quantitative analysis of different wheel sized bicycles. A validated mathematical model has been used as a tool to assess the dynamic performance of the bicycles in term of their self-stability. The results obtained were found to corroborate the subjective perception of cyclists for small wheel bicycles. The current approach for small wheel bicycle design requires higher speed to be self-stable. However, it was found that increasing the headtube angle and selecting a proper trail could improve the dynamic performance of small wheel bicycles. A range of parameters for front steering geometry has been identified for small wheel bicycles that have comparable stability as big wheel bicycles. Interestingly, most of the identified geometries are found to be beyond the ISO recommended range and seem to counter the current approach of small wheel bicycle design. Therefore, it was successfully shown that the guidelines for big wheelers do not translate directly to small wheelers, but careful selection of the front geometry could make small wheel bicycles as stable as big wheel bicycles.

Keywords: Big wheel bicycle, design approach, ISO requirements, small wheel bicycle, stability and performance.

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Authors: Fathi Taibi

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The abnormal increase in the number of applications available for download in Android markets is a good indication that they are being reused. However, little is known about their real reusability potential. A considerable amount of these applications is reported as having a poor quality or being malicious. Hence, in this paper, an approach to measure the reusability potential of classes in Android applications is proposed. The approach is not meant specifically for this particular type of applications. Rather, it is intended for Object-Oriented (OO) software systems in general and aims also to provide means to discard the classes of low quality and defect prone applications from being reused directly through inheritance and instantiation. An empirical investigation is conducted to measure and rank the reusability potential of the classes of randomly selected Android applications. The results obtained are thoroughly analyzed in order to understand the extent of this potential and the factors influencing it.

Keywords: Reusability, Software Quality Factors, Software Metrics, Empirical Investigation, Object-Oriented Software, Android Applications.

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Authors: Long Jye Sheu

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This paper presents a linear stability analysis of natural convection in a horizontal layer of a viscoelastic nanofluid. The Oldroyd B model was utilized to describe the rheological behavior of a viscoelastic nanofluid. The model used for the nanofluid incorporated the effects of Brownian motion and thermophoresis. The onset criterion for stationary and oscillatory convection was derived analytically. The effects of the Deborah number, retardation parameters, concentration Rayleigh number, Prandtl number, and Lewis number on the stability of the system were investigated. Results indicated that there was competition among the processes of thermophoresis, Brownian diffusion, and viscoelasticity which caused oscillatory rather than stationary convection to occur. Oscillatory instability is possible with both bottom- and top-heavy nanoparticle distributions. Regimes of stationary and oscillatory convection for various parameters were derived and are discussed in detail.

Keywords: instability, viscoelastic, nanofluids, oscillatory, Brownian, thermophoresis

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Authors: Jun Liu, Feihang Zhou, Gungyi Wang

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This paper expounds on the direct-driven PMSG wind power system control strategy, and analyses the stability conditions of the system. The direct-driven PMSG wind power system may generate the intense mechanical vibration, when wind speed changes dramatically. This paper proposes a new type of torque control strategy, which increases the system damping effectively, mitigates mechanical vibration of the system, and enhances the stability conditions of the system. The simulation results verify the reliability of the new torque control strategy.

Keywords: Damping, direct-driven PMSG wind power system, mechanical vibration, torque control.

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Authors: Monica Hoedltke Pietruchinski, Andrey Ricardo Pimentel

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The teaching of computer programming for beginners has been generally considered as a difficult and challenging task. Several methodologies and research tools have been developed, however, the difficulty of teaching still remains. Our work integrates the state of the art in teaching programming with game software and further provides metrics for the evaluation of student performance in a collaborative activity of playing games. This paper aims to present a multi-agent system architecture to be incorporated to the educational collaborative game software for teaching programming that monitors, evaluates and encourages collaboration by the participants. A literature review has been made on the concepts of Collaborative Learning, Multi-agents systems, collaborative games and techniques to teach programming using these concepts simultaneously.

Keywords: Architecture of multi-agent systems, collaborative evaluation, collaboration assessment, gamifying educational software.

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Authors: J. Miao, C. W. Leung, C. S. Cheung, R. C. K. Leung

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The present project was conducted with the circumferential-fuel-jets inverse diffusion flame (CIDF) burner burning liquefied petroleum gas (LPG) enriched with 50% of hydrogen fuel (H2). The range of stable operation of the CIDF burner in terms of Reynolds number (from laminar to turbulent flow regions), equivalence ratio and fuel jet velocity of LPG of the 50% H2-LPG mixed fuel was identified. Experiments were also carried out to investigate the flame structures of the LPG flame and LPG enriched H2 flame. Experimental results obtained from these two flames were compared to fully explore the influence of hydrogen addition on flame stability. Flame heights obtained by burning these two kinds of fuels at various equivalence ratios were compared and correlated with the Global Momentum Ratio (GMR).

Keywords: Flame stability, hydrogen enriched LPG, inverse diffusion flame.

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Authors: Wenqin Wang, Shouming Zhong

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This paper presents the robust stability criteria for uncertain genetic regulatory networks with time-varying delays. One key point of the criterion is that the decomposition of the matrix ˜D into ˜D = ˜D1 + ˜D2. This decomposition corresponds to a decomposition of the delayed terms into two groups: the stabilizing ones and the destabilizing ones. This technique enables one to take the stabilizing effect of part of the delayed terms into account. Meanwhile, by choosing an appropriate new Lyapunov functional, a new delay-dependent stability criteria is obtained and formulated in terms of linear matrix inequalities (LMIs). Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results.

Keywords: Genetic regulatory network, Time-varying delay, Uncertain system, Lyapunov-Krasovskii functional

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Authors: Asfar Ali Khan

Abstract:

Analytical expression for maximum power transfer through a transmission line limited by voltage stability has been formulated using exact representation of transmission line with ABCD parameters. The expression has been used for plotting PV curve at different power factors of a radial transmission line. Limiting values of reactive power have been obtained.

Keywords: Power Transfer, PV Curve, Voltage Stability.

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Authors: T. H. Young, S. J. Huang, Y. S. Chiu

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This paper investigates the parametric stability of an axially moving web subjected to non-uniform in-plane edge excitations on two opposite, simply-supported edges. The web is modeled as a viscoelastic plate whose constitutive relation obeys the Kelvin-Voigt model, and the in-plane edge excitations are expressed as the sum of a static tension and a periodical perturbation. Due to the in-plane edge excitations, the moving plate may bring about parametric instability under certain situations. First, the in-plane stresses of the plate due to the non-uniform edge excitations are determined by solving the in-plane forced vibration problem. Then, the dependence on the spatial coordinates in the equation of transverse motion is eliminated by the generalized Galerkin method, which results in a set of discretized system equations in time. Finally, the method of multiple scales is utilized to solve the set of system equations analytically if the periodical perturbation of the in-plane edge excitations is much smaller as compared with the static tension of the plate, from which the stability boundaries of the moving plate are obtained. Numerical results reveal that only combination resonances of the summed-type appear under the in-plane edge excitations considered in this work.

Keywords: Axially moving viscoelastic plate, in-plane periodic excitation, non-uniformly distributed edge tension, dynamic stability.

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Authors: Fuyang Peng, Bo Deng, Chao Qi

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This paper presents the design and implementation of CASTE, a Cloud-based automatic software test environment. We first present the architecture of CASTE, then the main packages and classes of it are described in detail. CASTE is built upon a private Infrastructure as a Service platform. Through concentrated resource management of virtualized testing environment and automatic execution control of test scripts, we get a better solution to the testing resource utilization and test automation problem. Experiments on CASTE give very appealing results.

Keywords: Software testing, test environment, test script, cloud computing, IaaS, test automation.

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Authors: Changjin Xu

Abstract:

In this paper, a delayed prototype model is studied. Regarding the delay as a bifurcation parameter, we prove that a sequence of Hopf bifurcations will occur at the positive equilibrium when the delay increases. Using the normal form method and center manifold theory, some explicit formulae are worked out for determining the stability and the direction of the bifurcated periodic solutions. Finally, Computer simulations are carried out to explain some mathematical conclusions.

Keywords: Prototype model, Stability, Hopf bifurcation, Delay, Periodic solution.

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Authors: P. Naderi, S.M.T. Bathaee, R. Hoseinnezhad, R. Chini

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Using electrical machine in conventional vehicles, also called hybrid vehicles, has become a promising control scheme that enables some manners for fuel economy and driver assist for better stability. In this paper, vehicle stability control, fuel economy and Driving/Regeneration braking for a 4WD hybrid vehicle is investigated by using an electrical machine on each non-driven wheels. In front wheels driven vehicles, fuel economy and regenerative braking can be obtained by summing torques applied on rear wheels. On the other hand, unequal torques applied to rear wheels provides enhanced safety and path correction in steering. In this paper, a model with fourteen degrees of freedom is considered for vehicle body, tires and, suspension systems. Thereafter, powertrain subsystems are modeled. Considering an electrical machine on each rear wheel, a fuzzy controller is designed for each driving, braking, and stability conditions. Another fuzzy controller recognizes the vehicle requirements between the driving/regeneration and stability modes. Intelligent vehicle control to multi objective operation and forward simulation are the paper advantages. For reaching to these aims, power management control and yaw moment control will be done by three fuzzy controllers. Also, the above mentioned goals are weighted by another fuzzy sub-controller base on vehicle dynamic. Finally, Simulations performed in MATLAB/SIMULINK environment show that the proposed structure can enhance the vehicle performance in different modes effectively.

Keywords: Hybrid, pitch, roll, regeneration, yaw.

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Authors: Liping Zhang, Kelin Li

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In this paper, a class of impulsive BAM fuzzy cellular neural networks with time delays in the leakage terms is formulated and investigated. By establishing a delay differential inequality and M-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM fuzzy cellular neural networks with time delays in the leakage terms are obtained. In particular, a precise estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive perturbation intention. It is believed that these results are significant and useful for the design and applications of BAM fuzzy cellular neural networks. An example is given to show the effectiveness of the results obtained here.

Keywords: Global exponential stability, bidirectional associative memory, fuzzy cellular neural networks, leakage delays, impulses.

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Authors: Wei Hoo Chong

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System testing is actually done to the entire system against the Functional Requirement Specification and/or the System Requirement Specification. Moreover, it is an investigatory testing phase, where the focus is to have almost a destructive attitude and test not only the design, but also the behavior and even the believed expectations of the customer. It is also intended to test up to and beyond the bounds defined in the software/hardware requirements specifications. In Motorola®, Automated Testing is one of the testing methodologies uses by GSG-iSGT (Global Software Group - iDEN TM Subcriber Group-Test) to increase the testing volume, productivity and reduce test cycle-time in iDEN TM phones testing. Testing is able to produce more robust products before release to the market. In this paper, iHopper is proposed as a tool to perform stress test on iDEN TM phonse. We will discuss the value that automation has brought to iDEN TM Phone testing such as improving software quality in the iDEN TM phone together with some metrics. We will also look into the advantages of the proposed system and some discussion of the future work as well.

Keywords: Testing, automated testing, stress testing, software quality.

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Authors: Parvinder S. Sandhu, Porush Bassi, Amanpreet Singh Brar

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Various models have been derived by studying large number of completed software projects from various organizations and applications to explore how project sizes mapped into project effort. But, still there is a need to prediction accuracy of the models. As Neuro-fuzzy based system is able to approximate the non-linear function with more precision. So, Neuro-Fuzzy system is used as a soft computing approach to generate model by formulating the relationship based on its training. In this paper, Neuro-Fuzzy technique is used for software estimation modeling of on NASA software project data and performance of the developed models are compared with the Halstead, Walston-Felix, Bailey-Basili and Doty Models mentioned in the literature.

Keywords: Effort Estimation, Neural-Fuzzy Model, Halstead Model, Walston-Felix Model, Bailey-Basili Model, Doty Model.

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Authors: M. Baghdasaryan, A. Sukiasyan

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An algorithm for estimating the stable operation conditions of the synchronous motor of the ore mill electric drive is proposed. The stable operation conditions of the synchronous motor are revealed, taking into account the estimation of the q angle change and the technological factors. The stability condition obtained allows to ensure the stable operation of the motor in the synchronous mode, taking into account the nonlinear character of the mill loading. The developed algorithm gives an opportunity to present the undesirable phenomena, arising in the electric drive system. The obtained stability condition can be successfully applied for the optimal control of the electromechanical system of the mill.

Keywords: Electric drive, synchronous motor, ore mill, stability, technological factors.

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Authors: Lili Wang

Abstract:

By using the estimation of the Cauchy matrix of linear impulsive differential equations and Banach fixed point theorem as well as Gronwall-Bellman’s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for an impulsive neural networks with distributed delays. An example is presented to illustrate the feasibility and  effectiveness of the results.

Keywords: Almost periodic solution, Exponential stability, Neural networks, Impulses.

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Authors: E. Ansari-Piri, N. Eghbali

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Let A and B be two linear algebras. A linear map ϕ : A → B is called an n-homomorphism if ϕ(a1...an) = ϕ(a1)...ϕ(an) for all a1, ..., an ∈ A. In this note we have a verification on the behavior of almost n-multiplicative linear maps with n > 2 in the fuzzy normed spaces

Keywords: Almost multiplicative maps, n-homomorphism maps, almost n-multiplicative maps, fuzzy normed space, stability.

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Authors: Dae-Hee Son, Soon-Ryul Nam

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The power system frequency falls when disturbance such as rapid increase of system load or loss of a generating unit occurs in power systems. Especially, increase in the number of renewable generating units has a bad influence on the power system because of loss of generating unit depending on the circumstance. Conventional technologies use frequency droop control battery output for the frequency regulation and balance between supply and demand. If power is supplied using the fast output characteristic of the battery, power system stability can be further more improved. To improve the power system stability, we propose battery output control using ROCOF (Rate of Change of Frequency) in this paper. The bigger the power difference between the supply and the demand, the bigger the ROCOF drops. Battery output is controlled proportionally to the magnitude of the ROCOF, allowing for faster response to power imbalances. To simulate the control method of battery output system, we develop the user defined model using PSS/E and confirm that power system stability is improved by comparing with frequency droop control.

Keywords: PSS/E user defined model, power deviation, frequency droop control, ROCOF, rate of change of frequency.

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Authors: Mahmoud A. Mahmoud, Ashraf Osman

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In this study, the different approaches currently followed by design codes to assess the stability of buildings utilizing concrete moment resisting frames structural system are evaluated. For such purpose, a parametric study was performed. It involved analyzing group of concrete moment resisting frames having different slenderness ratios (height/width ratios), designed for different lateral loads to vertical loads ratios and constructed using ordinary reinforced concrete and high strength concrete for stability check and overall buckling using code approaches and computer buckling analysis. The objectives were to examine the influence of such parameters that directly linked to frames’ lateral stiffness on the buildings’ stability and evaluates the code approach in view of buckling analysis results. Based on this study, it was concluded that, the most susceptible buildings to instability and magnification of second order effects are buildings having high aspect ratios (height/width ratio), having low lateral to vertical loads ratio and utilizing construction materials of high strength. In addition, the study showed that the instability limits imposed by codes are mainly mathematical to ensure reliable analysis not a physical ones and that they are in general conservative. Also, it has been shown that the upper limit set by one of the codes that second order moment for structural elements should be limited to 1.4 the first order moment is not justified, instead, the overall story check is more reliable.

Keywords: Buckling, lateral stability, p-delta, second order.

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Authors: Parvinder S. Sandhu, Manisha Prashar, Pourush Bassi, Atul Bisht

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Software effort estimation is the process of predicting the most realistic use of effort required to develop or maintain software based on incomplete, uncertain and/or noisy input. Effort estimates may be used as input to project plans, iteration plans, budgets. There are various models like Halstead, Walston-Felix, Bailey-Basili, Doty and GA Based models which have already used to estimate the software effort for projects. In this study Statistical Models, Fuzzy-GA and Neuro-Fuzzy (NF) Inference Systems are experimented to estimate the software effort for projects. The performances of the developed models were tested on NASA software project datasets and results are compared with the Halstead, Walston-Felix, Bailey-Basili, Doty and Genetic Algorithm Based models mentioned in the literature. The result shows that the NF Model has the lowest MMRE and RMSE values. The NF Model shows the best results as compared with the Fuzzy-GA based hybrid Inference System and other existing Models that are being used for the Effort Prediction with lowest MMRE and RMSE values.

Keywords: Neuro-Fuzzy Model, Halstead Model, Walston-Felix Model, Bailey-Basili Model, Doty Model, GA Based Model, Genetic Algorithm.

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Authors: M. Battira, R. Bessaih

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We numerically study the three-dimensional magnetohydrodynamics (MHD) stability of oscillatory natural convection flow in a rectangular cavity, with free top surface, filled with a liquid metal, having an aspect ratio equal to A=L/H=5, and subjected to a transversal temperature gradient and a uniform magnetic field oriented in x and z directions. The finite volume method was used in order to solve the equations of continuity, momentum, energy, and potential. The stability diagram obtained in this study highlights the dependence of the critical value of the Grashof number Grcrit , with the increase of the Hartmann number Ha for two orientations of the magnetic field. This study confirms the possibility of stabilization of a liquid metal flow in natural convection by application of a magnetic field and shows that the flow stability is more important when the direction of magnetic field is longitudinal than when the direction is transversal.

Keywords: Natural convection, Magnetic field, Oscillatory, Cavity, Liquid metal.

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Authors: Raluca Iulia Iulian

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The question of interethnic and interreligious conflicts in ex-Yugoslavia receives much attention within the framework of the international context created after 1991 because of the impact of these conflicts on the security and the stability of the region of Balkans and of Europe. This paper focuses on the rationales leading to the declaration of independence by Kosovo according to ethnic and religious criteria and analyzes why these same rationales were not applied in Bosnia and Herzegovina. The approach undertaken aims at comparatively examining the cases of Kosovo, and Bosnia and Herzegovina. At the same time, it aims at understanding the political decision making of the international community in the case of Kosovo. Specifically, was this a good political decision for the security and the stability of the region of Balkans, of Europe, or even for global security and stability? This research starts with an overview on the European security framework post 1991, paying particular attention to Kosovo and Bosnia and Herzegovina. It then presents the theoretical and methodological framework and compares the representative cases. Using the constructivism issue and the comparative methodology, it arrives at the results of the study. An important issue of the paper is the thesis that this event modifies the principles of international law and creates dangerous precedents for regional stability in the Balkans.

Keywords: Interethnic and interreligious conflict, security andstability, superpower.

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Authors: Anne Sørebø

Abstract:

The present study was designed to test how fulfillment of three basic psychological needs influence students development of perceived usefulness (PU) and ease of use (EOU) in connection with use of a spreadsheet. Both PU and EOU are assumed to be critical for development of students' willingness to utilize spreadsheet in future work within business administration. A questionnaire was completed by 196 business students in Norway. We found that satisfying the need for competence and autonomy is most critical for willingness to utilize the software package. The results also indicate that satisfying the need for relatedness, surprisingly, has no influence on students’ willingness to utilize the software package. A key implication of the present research is that teachers mainly should focus on fulfilling students need for competence and self-determination when the purpose is to motivate them to utilize new software. That students’ should develop their own competence when using a new technology is somewhat obvious, but that the feeling of being self-determined needs to be a complementary element in this connection is not necessary seen as obvious.

Keywords: Spreadsheet, business students, technology acceptance, basic psychological needs.

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Authors: Ali Taee Zade, Siamak Rasulzadeh, Reza Torkashvan

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Although Model Driven Architecture has taken successful steps toward model-based software development, this approach still faces complex situations and ambiguous questions while applying to real world software systems. One of these questions - which has taken the most interest and focus - is how model transforms between different abstraction levels, MDA proposes. In this paper, we propose an approach based on Story Driven Modeling and Aspect Oriented Programming to ease these transformations. Service Oriented Architecture is taken as the target model to test the proposed mechanism in a functional system. Service Oriented Architecture and Model Driven Architecture [1] are both considered as the frontiers of their own domain in the software world. Following components - which was the greatest step after object oriented - SOA is introduced, focusing on more integrated and automated software solutions. On the other hand - and from the designers' point of view - MDA is just initiating another evolution. MDA is considered as the next big step after UML in designing domain.

Keywords: SOA, MDA, SDM, Model Transformation, Middleware Transparency, Aspects and Jini.

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Authors: George Eleftherakis, Petros Kefalas, Anna Sotiriadou, Evangelos Kehris

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Recent advances in both the testing and verification of software based on formal specifications of the system to be built have reached a point where the ideas can be applied in a powerful way in the design of agent-based systems. The software engineering research has highlighted a number of important issues: the importance of the type of modeling technique used; the careful design of the model to enable powerful testing techniques to be used; the automated verification of the behavioural properties of the system; the need to provide a mechanism for translating the formal models into executable software in a simple and transparent way. This paper introduces the use of the X-machine formalism as a tool for modeling biology inspired agents proposing the use of the techniques built around X-machine models for the construction of effective, and reliable agent-based software systems.

Keywords: Biology inspired agent, formal methods, x-machines.

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Authors: Zhou Xiong, Kang Shao Bo, Yang Bo

Abstract:

To date, high-performance structural steel has been widely used for columns in construction practices due to its significant advantages over conventional steel. However, the same design approach with conventional steel columns is still adopted in the design of high-performance steel columns. As a result, its superior properties cannot be fully considered in design. This paper conducts a test and finite element analysis on the overall stability behaviour of welded Q460GJ steel box columns. In the test, four steel columns with different slenderness and width-to-thickness ratio were compressed under an axial compression testing machine. And finite element models were established in which material nonlinearity and residual stress distributions of test columns were included. Then, comparisons were made between test results and finite element result, it showed that finite element analysis results are agree well with the test result. It means that the test and finite element model are reliable. Then, we compared the test result with the design value calculated by current code, the result showed that Q460GJ steel box columns have the higher overall buckling capacity than the design value. It is necessary to update the design curves for Q460GJ steel columns so that the overall stability capacity of Q460GJ box columns can be designed appropriately.

Keywords: Axial compression, Finite element analysis, Overall stability, Q460GJ steel, Welded box columns.

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Authors: Atakan Kurt, Arzu Naiboğlu

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We present an implementation of an Online Exhibition System (OES) web service(s) that reflects our experiences with using web service development packages and software process models. The system provides major functionality that exists in similar packages. While developing such a complex web service, we gained insightful experience (i) in the traditional software development processes: waterfall model and evolutionary development and their fitness to web services development, (ii) in the fitness and effectiveness of a major web services development kit.

Keywords: Web Services, Online Exhibition System, Software Engineering, Waterfall Model, e-business.

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Authors: Meng Fanchao, Zhan Dechen, Xu Xiaofei

Abstract:

Software reuse can be considered as the most realistic and promising way to improve software engineering productivity and quality. Automated assistance for software reuse involves the representation, classification, retrieval and adaptation of components. The representation and retrieval of components are important to software reuse in Component-Based on Software Development (CBSD). However, current industrial component models mainly focus on the implement techniques and ignore the semantic information about component, so it is difficult to retrieve the components that satisfy user-s requirements. This paper presents a method of business component retrieval based on specification matching to solve the software reuse of enterprise information system. First, a business component model oriented reuse is proposed. In our model, the business data type is represented as sign data type based on XML, which can express the variable business data type that can describe the variety of business operations. Based on this model, we propose specification match relationships in two levels: business operation level and business component level. In business operation level, we use input business data types, output business data types and the taxonomy of business operations evaluate the similarity between business operations. In the business component level, we propose five specification matches between business components. To retrieval reusable business components, we propose the measure of similarity degrees to calculate the similarities between business components. Finally, a business component retrieval command like SQL is proposed to help user to retrieve approximate business components from component repository.

Keywords: Business component, business operation, business data type, specification matching.

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Authors: M. Najafi, F. Rahimi Dehgolan

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In this paper, the dynamic modeling of a single-link flexible beam with a tip mass is given by using Hamilton's principle. The link has been rotational and translational motion and it was assumed that the beam is moving with a harmonic velocity about a constant mean velocity. Non-linearity has been introduced by including the non-linear strain to the analysis. Dynamic model is obtained by Euler-Bernoulli beam assumption and modal expansion method. Also, the effects of rotary inertia, axial force, and associated boundary conditions of the dynamic model were analyzed. Since the complex boundary value problem cannot be solved analytically, the multiple scale method is utilized to obtain an approximate solution. Finally, the effects of several conditions on the differences among the behavior of the non-linear term, mean velocity on natural frequencies and the system stability are discussed.

Keywords: Non-linear vibration, stability, axially moving beam, bifurcation, multiple scales method.

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