Search results for: Free- and open-source software

Authors: Andreas Litke, Kostas Zotos, Alexander Chatzigeorgiou, George Stephanides

Abstract:

The importance of low power consumption is widely acknowledged due to the increasing use of portable devices, which require minimizing the consumption of energy. Energy dissipation is heavily dependent on the software used in the system. Applying design patterns in object-oriented designs is a common practice nowadays. In this paper we analyze six design patterns and explore the effect of them on energy consumption and performance.

Keywords: Design Patterns, Embedded Systems, Energy Consumption, Performance Evaluation, Software Design and Development, Software Engineering.

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Authors: H. O. Barbosa, A. C. R. da Silva, C. M. de Almeida, E. M. dos Santos, F. O. de Sousa, F. B. da S. Souza, F. B. da S. Souza, F. de O. Lima, L. H. Albuquerque, R. F. do Valle Cunha

Abstract:

Software development is intrinsic human-based knowledge-intensive. Due to globalization, software development has become a complex challenge and we usually face barriers related to knowledge management, team building, costly testing processes, especially in distributed settings. In this paper, we present the use of experimental studies to improve our knowledge management process using the Wiki system. According to the results, it was possible to identify learning preferences from our software projects leader team, organize and improve the learning experience of our Wiki, and facilitate collaboration by newcomers to improve Wiki with new contents available in the Wiki.

Keywords: Mobile products, knowledge management process, Wiki system, Global Software Development.

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Authors: Xizhi Li

Abstract:

Both software applications and their development environment are becoming more and more distributed. This trend impacts not only the way software computes, but also how it looks. This article proposes a Human Computer Interface (HCI) template from three representative applications we have developed. These applications include a Multi-Agent System based software, a 3D Internet computer game with distributed game world logic, and a programming language environment used in constructing distributed neural network and its visualizations. HCI concepts that are common to these applications are described in abstract terms in the template. These include off-line presentation of global entities, entities inside a hierarchical namespace, communication and languages, reconfiguration of entity references in a graph, impersonation and access right, etc. We believe the metaphor that underlies an HCI concept as well as the relationships between a bunch of HCI concepts are crucial to the design of software systems and vice versa.

Keywords: HCI, MAS, computer game, programming language

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Authors: R. Alipour, F.Najarian

Abstract:

Because of high ductility, aluminum alloys, have been widely used as an important base of metal forming industries. But the main week point of these alloys is their low strength so in forming them with conventional methods like deep drawing, hydro forming, etc have been always faced with problems like fracture during of forming process. Because of this, recently using of explosive forming method for forming of these plates has been recommended. In this paper free explosive forming of A2024 aluminum alloy is numerically simulated and during it, explosion wave propagation process is studied. Consequences of this simulation can be effective in prediction of quality of production. These consequences are compared with an experimental test and show the superiority of this method to similar methods like hydro forming and deep drawing.

Keywords: Free explosive forming, CEL, Johnson cook.

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Authors: Layal Al Ait, Eduardo Corel, Kifah Tout, Burkhard Morgenstern

Abstract:

Background: Dialign is a DNA/Protein alignment tool for performing pairwise and multiple pairwise alignments through the comparison of gap-free segments (fragments) between sequence pairs. An alignment of two sequences is a chain of fragments, i.e local gap-free pairwise alignments, with the highest total score. METHOD: A new approach is defined in this article which relies on the concept of using three-dimensional fragments – i.e. local threeway alignments -- in the alignment process instead of twodimensional ones. These three-dimensional fragments are gap-free alignments constituting of equal-length segments belonging to three distinct sequences. RESULTS: The obtained results showed good improvments over the performance of DIALIGN.

Keywords: DIALIGN, Multiple sequence alignment, Threedimensional fragments.

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Authors: Pandiyarajan Thangaraj, Mangalaraja Ramalinga Viswanathan, Karthikeyan Balasubramanian, Héctor D. Mansilla, José Ruiz, David Contreras

Abstract:

In this work, we report, a systematic study on the structural and optical properties of Pr-doped ZnO nanostructures and PVA:Zn98Pr2O polymer matrix nanocomposites free standing films. These particles are synthesized through simple wet chemical route and solution casting technique at room temperature, respectively. Structural studies carried out by X-ray diffraction method confirm that the prepared pure ZnO and Pr doped ZnO nanostructures are in hexagonal wurtzite structure and the microstrain is increased upon doping. TEM analysis reveals that the prepared materials are in sheet like nature. Absorption spectra show free excitonic absorption band at 370 nm and red shift for the Pr doped ZnO nanostructures. The PVA:Zn98Pr2O composite film exhibits both free excitonic and PVA absorption bands at 282 nm. Fourier transform infrared spectral studies confirm the presence of A1 (TO) and E1 (TO) modes of Zn-O bond vibration and the formation of polymer composite materials.

Keywords: Pr doped ZnO, polymer nanocomposites, optical properties.

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Authors: Giwrgos S. Gkarmpounis, Aikaterini G. Rokkou, Marios N. Moschakis

Abstract:

Increased energy consumption in the academic buildings, creates the need to implement energy saving measures and to take advantage of the renewable energy sources to cover the electrical needs of those buildings. An Academic Library will be used as a case study. With the aid of RETScreen software that takes into account the energy consumptions and characteristics of the Library Building, it is proved that measures such as the replacement of fluorescent lights with led lights, the installation of outdoor shading, the replacement of the openings and Building Management System installation, provide a high level of energy savings. Moreover, given the available space of the building and the climatic data, the installation of a photovoltaic system of 100 kW can also cover a serious amount of the building energy consumption, unlike a wind system that seems uncompromising. Lastly, HOMER software is used to compare the use of a photovoltaic system against a wind system in order to verify the results that came up from the RETScreen software concerning the renewable energy sources.

Keywords: Energy saving measures, homer software, renewable energy sources, RETScreen software, energy efficiency and quality.

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Authors: Ishak Hashim, Ammar Alsabery

Abstract:

The problem of conjugate free convection in a square cavity filled with nanofluid and heated from below by spatial wall temperature is studied numerically using the finite difference method. Water-based nanofluid with copper nanoparticles are chosen for the investigation. Governing equations are solved over a wide range of nanoparticle volume fraction (0 ≤ φ ≤ 0.2), wave number ((0 ≤ λ ≤ 4) and thermal conductivity ratio (0.44 ≤ Kr ≤ 6). The results presented for values of the governing parameters in terms of streamlines, isotherms and average Nusselt number. It is found that the flow behavior and the heat distribution are clearly enhanced with the increment of the non-uniform heating.

Keywords: Conjugate free convection, nanofluid, spatial temperature.

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Authors: A. Kerfah, K. Taïbi, S. Omeiri, M. Trari.

Abstract:

New lead-free ferroelectric relaxor ceramics were prepared by conventional solid-state synthesis in the BaTiO3-Bi2O3- Y2O3 systems. Some of these ceramics present a ferroelectric relaxor with transition temperature close to room temperature. These new materials are very interesting for applications and can replace leadbased ceramic to prevent the toxic pollutions during the preparation state. In the other hand, the energy band diagram shows the potentiality of these compounds for the solar energy conversion. Thus, some compositions have been tested successfully for H2 production upon visible light. The best activity occurs in alkaline media with a rate evolution of about 0.15 mL g-1 mn-1 and a quantum yield of 1% under polychromatic light.

Keywords: Ferroelectric, Hydrogen production, Lead-free, Photocatalysis.

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Authors: Leonardo A. Ambrosio, Carlos. H. Silva Santos, Ivan E. L. Rodrigues, Ayumi K. de Campos, Leandro A. Machado

Abstract:

In this work, we propose an algorithm developed under Python language for the modeling of ordinary scalar Bessel beams and their discrete superpositions and subsequent calculation of optical forces exerted over dielectric spherical particles. The mathematical formalism, based on the generalized Lorenz-Mie theory, is implemented in Python for its large number of free mathematical (as SciPy and NumPy), data visualization (Matplotlib and PyJamas) and multiprocessing libraries. We also propose an approach, provided by a synchronized Software as Service (SaaS) in cloud computing, to develop a user interface embedded on a mobile application, thus providing users with the necessary means to easily introduce desired unknowns and parameters and see the graphical outcomes of the simulations right at their mobile devices. Initially proposed as a free Android-based application, such an App enables data post-processing in cloud-based architectures and visualization of results, figures and numerical tables.

Keywords: Bessel Beams and Frozen Waves, Generalized Lorenz-Mie Theory, Numerical Methods, Optical Forces.

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Authors: M. Bouhadef, K. Bouzelha-Hammoum, T. Guendouzen-Dabouz, A. Younsi, T. Zitoun

Abstract:

The aim of this paper is to report the different experimental studies, conducted in the laboratory, dealing with the flow in the presence of an obstacle lying in a rectangular hydraulic channel. Both subcritical and supercritical regimes are considered. Generally, when considering the theoretical problem of the free-surface flow, in a fluid domain of finite depth, due to the presence of an obstacle, we suppose that the water is an inviscid fluid, which means that there is no sheared velocity profile, but constant upstream. In a hydraulic channel, it is impossible to satisfy this condition. Indeed, water is a viscous fluid and its velocity is null at the bottom. The two configurations are presented, i.e. a flow over an obstacle and a towed obstacle in a resting fluid.

Keywords: Experiments, free-surface flow, hydraulic channel, subcritical regime, supercritical flow.

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Authors: S.H. Mirtalaie, M. Mohammadi, M.A. Hajabasi, F.Hejripour

Abstract:

In this paper the Differential Quadrature Method (DQM) is employed to study the coupled lateral-torsional free vibration behavior of the laminated composite beams. In such structures due to the fiber orientations in various layers, the lateral displacement leads to a twisting moment. The coupling of lateral and torsional vibrations is modeled by the bending-twisting material coupling rigidity. In the present study, in addition to the material coupling, the effects of shear deformation and rotary inertia are taken into account in the definition of the potential and kinetic energies of the beam. The governing differential equations of motion which form a system of three coupled PDEs are solved numerically using DQ procedure under different boundary conditions consist of the combinations of simply, clamped, free and other end conditions. The resulting natural frequencies and mode shapes for cantilever beam are compared with similar results in the literature and good agreement is achieved.

Keywords: Differential Quadrature Method, Free vibration, Laminated composite beam, Material coupling.

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Authors: G. Sevilla, S. Zapata, F. Giraldo, E. Torres, C. Collazos

Abstract:

This work describes a framework for teaching of global software engineering (GSE) in university undergraduate programs. This framework proposes a method of teaching that incorporates adequate techniques of software requirements elicitation and validated tools of communication, critical aspects to global software development scenarios. The use of proposed framework allows teachers to simulate small software development companies formed by Latin American students, which build information systems. Students from three Latin American universities played the roles of engineers by applying an iterative development of a requirements specification in a global software project. The proposed framework involves the use of a specific purpose Wiki for asynchronous communication between the participants of the process. It is also a practice to improve the quality of software requirements that are formulated by the students. The additional motivation of students to participate in these practices, in conjunction with peers from other countries, is a significant additional factor that positively contributes to the learning process. The framework promotes skills for communication, negotiation, and other complementary competencies that are useful for working on GSE scenarios.

Keywords: Requirements analysis, distributed requirements engineering, practical experiences, collaborative support.

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Authors: Beata Czarnacka-Chrobot

Abstract:

Execution of Business Software Systems (BSS) Development and Enhancement Projects (D&EP) is characterized by the exceptionally low effectiveness, leading to considerable financial losses. The general reason for low effectiveness of such projects is that they are inappropriately managed. One of the factors of proper BSS D&EP management is suitable (reliable and objective) method of project work effort estimation since this is what determines correct estimation of its major attributes: project cost and duration. BSS D&EP is usually considered to be accomplished effectively if product of a planned functionality is delivered without cost and time overrun. The goal of this paper is to prove that choosing approach to the BSS D&EP work effort estimation has a considerable influence on the effectiveness of such projects execution.

Keywords: Business software systems, development and enhancement projects, effectiveness, work effort estimation methods, software product size, software product functionality, project duration, project cost.

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Authors: K. Indra Gandhi

Abstract:

Wireless Sensor Networks (WSNs) have always been characterized for application-specific sensing, relaying and collection of information for further analysis. However, software development was not considered as a separate entity in this process of data collection which has posed severe limitations on the software development for WSN. Software development for WSN is a complex process since the components involved are data-driven, network-driven and application-driven in nature. This implies that there is a tremendous need for the separation of concern from the software development perspective. A layered approach for developing data acquisition design based on Model Driven Development (MDD) has been proposed as the sensed data collection process itself varies depending upon the application taken into consideration. This work focuses on the layered view of the data acquisition process so as to ease the software point of development. A metamodel has been proposed that enables reusability and realization of the software development as an adaptable component for WSN systems. Further, observing users perception indicates that proposed model helps in improving the programmer's productivity by realizing the collaborative system involved.

Keywords: Model-driven development, wireless sensor networks, data acquisition, separation of concern, layered design.

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Authors: Abdul Halim Bhuiyan, M. A. Alim, Md. Nasir Uddin

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This paper is concerned with the effect of Hartmann number on the free convective flow in a square cavity with different positions of heated square block. The two-dimensional Physical and mathematical model have been developed, and mathematical model includes the system of governing mass, momentum and energy equations are solved by the finite element method. The calculations have been computed for Prandtl number Pr = 0.71, the Rayleigh number Ra = 1000 and the different values of Hartmann number. The results are illustrated with the streamlines, isotherms, velocity and temperature fields as well as local Nusselt number.

Keywords: Finite element method, free convection, Hartmann number, square cavity.

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Authors: A. Goel, S.C. Gupta, S.K.Wasan

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Testable software has two inherent properties – observability and controllability. Observability facilitates observation of internal behavior of software to required degree of detail. Controllability allows creation of difficult-to-achieve states prior to execution of various tests. In this paper, we describe COTT, a Controllability and Observability Testing Tool, to create testable object-oriented software. COTT provides a framework that helps the user to instrument object-oriented software to build the required controllability and observability. During testing, the tool facilitates creation of difficult-to-achieve states required for testing of difficultto- test conditions and observation of internal details of execution at unit, integration and system levels. The execution observations are logged in a test log file, which are used for post analysis and to generate test coverage reports.

Keywords: Controllability, Observability, Test Coverage and Testing Tool.

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Authors: Parvinder S. Sandhu, Sandeep Khimta, Kiranpreet Kaur

Abstract:

The prediction of Software quality during development life cycle of software project helps the development organization to make efficient use of available resource to produce the product of highest quality. “Whether a module is faulty or not" approach can be used to predict quality of a software module. There are numbers of software quality prediction models described in the literature based upon genetic algorithms, artificial neural network and other data mining algorithms. One of the promising aspects for quality prediction is based on clustering techniques. Most quality prediction models that are based on clustering techniques make use of K-means, Mixture-of-Guassians, Self-Organizing Map, Neural Gas and fuzzy K-means algorithm for prediction. In all these techniques a predefined structure is required that is number of neurons or clusters should be known before we start clustering process. But in case of Growing Neural Gas there is no need of predetermining the quantity of neurons and the topology of the structure to be used and it starts with a minimal neurons structure that is incremented during training until it reaches a maximum number user defined limits for clusters. Hence, in this work we have used Growing Neural Gas as underlying cluster algorithm that produces the initial set of labeled cluster from training data set and thereafter this set of clusters is used to predict the quality of test data set of software modules. The best testing results shows 80% accuracy in evaluating the quality of software modules. Hence, the proposed technique can be used by programmers in evaluating the quality of modules during software development.

Keywords: Growing Neural Gas, data clustering, fault prediction.

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Authors: Arsalan Ali Shah, Zafar I. Malik, Shaukat Ali

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Peer-to-Peer (P2P) is a self-organizing resource sharing network with no centralized authority or infrastructure, which makes it unpredictable and vulnerable. In this paper, we propose architecture to make the peer-to-peer network more centralized, predictable, and safer to use by implementing trust and stopping free riding.

Keywords: File Share, Free Riding, Peer-to-Peer, Trust.

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Authors: M. R.Isvandzibaei, A.Jahani

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In the present work, study of the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of boundary conditions on the natural frequencies of the FG cylindrical shell. The study is carried out using third order shear deformation shell theory. The analysis is carried out using Hamilton's principle. The governing equations of motion of FG cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of constituent volume fractions and the effects of free-free and clamped-clamped boundary conditions.

Keywords: Vibration, FGM, cylindrical shell, Hamilton's principle.

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Authors: Zhizhong Jiang, Peter Naudé, Craig Comstock

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Software development has experienced remarkable progress in the past decade. However, due to the rising complexity and magnitude of the project the development productivity has not been consistently improved. By analyzing the latest ISBSG data repository with 4106 projects, we discovered that software development productivity has actually undergone irregular variations between the years 1995 and 2005. Considering the factors significant to the productivity, we found its variations are primarily caused by the variations of average team size and the unbalanced uses of the less productive language 3GL.

Keywords: Productivity, Programming Languages, SoftwareEngineering, Team Size.

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Authors: Praveen Saraswat, Vipin Kumar Verma, Rudraman Singh

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The unsteady transient free convection flow of an incompressible dissipative viscous fluid between parallel plates at different distances have been investigated under porous medium. Due to presence of heat flux under the influence of uniform transverse magnetic field the velocity distribution and the temperature distribution, is shown graphically. Since exact solution is not possible so we find parametrical solution by perturbation technique. The result is shown in graph for different parameters. We notice that heat generation effects fluid velocity keeping in which of free convection which cools.

Keywords: Transient, Convection, MHD, Viscous, Porous.

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Authors: Wenqing Fan, Yixuan Cheng, Wei Huang

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The diversity and complexity of modern IT systems make it almost impossible for internal teams to find vulnerabilities in all software before the software is officially released. The emergence of threat intelligence and vulnerability reporting policy has greatly reduced the burden on software vendors and organizations to find vulnerabilities. However, to prove the existence of the reported vulnerability, it is necessary but difficult for security incident response team to build a deliberated vulnerable environment from the vulnerability report with limited and incomplete information. This paper presents a structured, standardized, machine-oriented vulnerability intelligence format, that can be used to automate the orchestration of Deliberated Vulnerable Environment (DVE). This paper highlights the important role of software configuration and proof of vulnerable specifications in vulnerability intelligence, and proposes a triad model, which is called DIR (Dependency Configuration, Installation Configuration, Runtime Configuration), to define software configuration. Finally, this paper has also implemented a prototype system to demonstrate that the orchestration of DVE can be automated with the intelligence.

Keywords: DIR Triad Model, DVE, vulnerability intelligence, vulnerability recurrence.

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Authors: Amal S. Al-Badi, Ali H. Al-Badi

Abstract:

Many organizations are opting to adopt Open Source Software (OSS) as it is the current trend to rely on each other rather than on companies (Software vendors). It is a clear shift from organizations to individuals, the concept being to rely on collective participation rather than companies/vendors.

The main objectives of this research are 1) to identify the current level of OSS usage in Sultan Qaboos University; 2) to identify the potential benefits of using OSS in educational institutes; 3) to identify the OSS applications that are most likely to be used within an educational institute; 4) to identify the existing and potential barriers to the successful adoption of OSS in education.

To achieve these objectives a two-stage research method was conducted. First a rigorous literature review of previously published material was performed (interpretive/descriptive approach), and then a set of interviews were conducted with the IT professionals at Sultan Qaboos University in Oman in order to explore the extent and nature of their usage of OSS.

Keywords: Open source software; social software, e-learning 2.0, Web 2.0, connectivism, personal learning environment (PLE), OpenID, OpenSocial and OpenCourseWare.

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Authors: Izzati K. Khalid, Nor Fadzillah M. Mokhtar, Norihan Md. Arifin

Abstract:

The effect of internal heat generation is applied to the Rayleigh-Benard convection in a horizontal micropolar fluid layer. The bounding surfaces of the liquids are considered to be rigid-free, rigid-rigid and free-free with the combination of isothermal on the spin-vanishing boundaries. A linear stability analysis is used and the Galerkin method is employed to find the critical stability parameters numerically. It is shown that the critical Rayleigh number decreases as the value of internal heat generation increase and hence destabilize the system.

Keywords: Internal heat generation, micropolar fluid, rayleighbenard convection.

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Authors: Sunitha Ramanujam, Hany El Yamany, Miriam A. M. Capretz

Abstract:

Software reliability, defined as the probability of a software system or application functioning without failure or errors over a defined period of time, has been an important area of research for over three decades. Several research efforts aimed at developing models to improve reliability are currently underway. One of the most popular approaches to software reliability adopted by some of these research efforts involves the use of operational profiles to predict how software applications will be used. Operational profiles are a quantification of usage patterns for a software application. The research presented in this paper investigates an innovative multiagent framework for automatic creation and management of operational profiles for generic distributed systems after their release into the market. The architecture of the proposed Operational Profile MAS (Multi-Agent System) is presented along with detailed descriptions of the various models arrived at following the analysis and design phases of the proposed system. The operational profile in this paper is extended to comprise seven different profiles. Further, the criticality of operations is defined using a new composed metrics in order to organize the testing process as well as to decrease the time and cost involved in this process. A prototype implementation of the proposed MAS is included as proof-of-concept and the framework is considered as a step towards making distributed systems intelligent and self-managing.

Keywords: Software reliability, Software testing, Metrics, Distributed systems, Multi-agent systems

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Authors: Radomir Perzina, Jaroslav Ramik

Abstract:

The Analytic Hierarchy Process is frequently used approach for solving decision making problems. There exists wide range of software programs utilizing that approach. Their main disadvantage is that they are relatively expensive and missing intermediate calculations. This work introduces a Microsoft Excel add-in called DAME – Decision Analysis Module for Excel. Comparing to other computer programs DAME is free, can work with scenarios or multiple decision makers and displays intermediate calculations. Users can structure their decision models into three levels – scenarios/users, criteria and variants. Items on all levels can be evaluated either by weights or pair-wise comparisons. There are provided three different methods for the evaluation of the weights of criteria, the variants as well as the scenarios – Saaty’s Method, Geometric Mean Method and Fuller’s Triangle Method. Multiplicative and additive syntheses are supported. The proposed software package is demonstrated on couple of illustrating examples of real life decision problems.

Keywords: Analytic hierarchy process, multi-criteria decision making, pair-wise comparisons, Microsoft Excel, Scenarios.

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Authors: N. Phattanakulkaewmorie, T. Paseephol, A.Moongngarm

Abstract:

This study investigated the effect of germination on chemical compositions, physio-chemical properties of malted (germinated) red sorghum flours and evaluated characteristics of gluten free breads from sorghum flour. Results showed that germinated sorghum flour had higher amylase activity, swelling power and solubility at 95°C, but lower in the peak, break down, final and set back viscosities than ungerminated sample (p≤0.05). Five gluten free breads made from sorghum flour blends, with different ratios of ungerminated and germinated sorghum flour, were compared for the physical properties with those made from wheat flour. Crumb hardness, cohesiveness, gumminess and chewiness of sorghum breads were found significantly higher than those of wheat bread. With increasing of ungerminated flour proportion, the bread hardness increased while the cohesiveness declined. Sorghum breads appeared red to human eyes with a*values of 10.41-15.77.Their crust and crumb colors differed significantly from those of wheat bread.

Keywords: Flour, germination, gluten free bread, sorghum.

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Authors: Javad Khazaei, Rick S. Blum

Abstract:

Distributed control is an efficient and flexible approach for coordination of multi-agent systems. One of the main challenges in designing a distributed controller is identifying the governing dynamics of the dynamical systems. Data-driven system identification is currently undergoing a revolution. With the availability of high-fidelity measurements and historical data, model-free identification of dynamical systems can facilitate the control design without tedious modeling of high-dimensional and/or nonlinear systems. This paper develops a distributed control design using consensus theory for linear and nonlinear dynamical systems using sparse identification of system dynamics. Compared with existing consensus designs that heavily rely on knowing the detailed system dynamics, the proposed model-free design can accurately capture the dynamics of the system with available measurements and input data and provide guaranteed performance in consensus and tracking problems. Heterogeneous damped oscillators are chosen as examples of dynamical system for validation purposes.

Keywords: Consensus tracking, distributed control, model-free control, sparse identification of dynamical systems.

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Authors: R .Lassoued, M. Guenfoud

Abstract:

An accurate procedure to determine free vibrations of beams and plates is presented. The natural frequencies are exact solutions of governing vibration equations witch load to a nonlinear homogeny system. The bilinear and linear structures considered simulate a bridge. The dynamic behavior of this one is analyzed by using the theory of the orthotropic plate simply supported on two sides and free on the two others. The plate can be excited by a convoy of constant or harmonic loads. The determination of the dynamic response of the structures considered requires knowledge of the free frequencies and the shape modes of vibrations. Our work is in this context. Indeed, we are interested to develop a self-consistent calculation of the Eigen frequencies. The formulation is based on the determination of the solution of the differential equations of vibrations. The boundary conditions corresponding to the shape modes permit to lead to a homogeneous system. Determination of the noncommonplace solutions of this system led to a nonlinear problem in Eigen frequencies. We thus, develop a computer code for the determination of the eigenvalues. It is based on a method of bisection with interpolation whose precision reaches 10 -12. Moreover, to determine the corresponding modes, the calculation algorithm that we develop uses the method of Gauss with a partial optimization of the "pivots" combined with an inverse power procedure. The Eigen frequencies of a plate simply supported along two opposite sides while considering the two other free sides are thus analyzed. The results could be generalized with the case of a beam by regarding it as a plate with low width. We give, in this paper, some examples of treated cases. The comparison with results presented in the literature is completely satisfactory.

Keywords: Free frequencies, beams, rectangular plates.

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