Search results for: class testing

Authors: Nouredine Bourahla, Farid Bouriche, Yacine Benghalia

Abstract:

Seismic qualification testing for equipments to be mounted on upper storeys of buildings is very demanding in terms of floor spectra. The latter is characterized by high accelerations amplitudes within a narrow frequency band. This article presents a method which permits to cover specified required response spectra beyond the shaking table capability by amplifying the acceleration amplitudes at an appropriate frequency range using a physical intermediate mounted on the platform of the shaker.

Keywords: floor spectra, response spectrum, seismicqualification testing, shaking table

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Authors: D. I. De Souza, D. R. Fonseca, R. Rocha

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In this paper we will develop further the sequential life test approach presented in a previous article by [1] using an underlying two parameter Weibull sampling distribution. The minimum life will be considered equal to zero. We will again provide rules for making one of the three possible decisions as each observation becomes available; that is: accept the null hypothesis H0; reject the null hypothesis H0; or obtain additional information by making another observation. The product being analyzed is a new type of a low alloy-high strength steel product. To estimate the shape and the scale parameters of the underlying Weibull model we will use a maximum likelihood approach for censored failure data. A new example will further develop the proposed sequential life testing approach.

Keywords: Sequential Life Testing, Underlying Weibull Model, Maximum Likelihood Approach, Hypothesis Testing.

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Authors: Areerut J.

Abstract:

Experimental Film Class Project is supported by the Institute for Research and Development at Suan Sunandha Rajabhat University. This project is purported to provide academic and professional services to improve the quality standards of the community and locals in accordance with the mission of the university, which is to improve and expand knowledge for the community and to develop and transfer such knowledge and professions to the next generation. Eventually, it leads to sustainable development because the development of human resources is deemed as the key for sustainable development. Moreover, the Experimental Film Class is an integral part of the teaching of film production at Suan Sunandha International School of Art (SISA). By means of giving opportunities to students for participation in projects by sharing experience, skill and knowledge and participation in field activities, it helps students in the film production major to enhance their abilities and potentials as preparation for their readiness in the marketplace. Additionally, in this class, we provide basic film knowledge, screenwriting techniques, editing and subtitles including uploading videos on social media such as YouTube and Facebook for the participant students.

Keywords: Experimental Film Class, Watbangkapom School, Participant students, Basic of film production, Film Workshop.

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Authors: František Mošna

Abstract:

E-learning has become an efficient and widespread means of education at all levels of human activities. Statistics is no exception. Unfortunately the main focus in statistics teaching is usually paid to the substitution in formulas. Suitable websites can simplify and automate calculations and provide more attention and time to the basic principles of statistics, mathematization of real-life situations and following interpretation of results. We now introduce our own web-site for hypothesis testing. Its didactic aspects, the technical possibilities of the individual tools, the experience of use and the advantages or disadvantages are discussed in this paper. This web-site is not a substitute for common statistical software but should significantly improve the teaching of statistics at universities.

Keywords: E-learning, hypothesis testing, PHP, websites.

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Authors: Arne Hitzmann, Philipp Wentscher, Alexander Gabel, Reinhard Gerndt

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Autonomous mobile robots can be found in a wide field of applications. Their types range from household robots over workshop robots to autonomous cars and many more. All of them undergo a number of testing steps during development, production and maintenance. This paper describes an approach to improve testing of robot behavior. It was inspired by the RoboCup @work competition that itself reflects a robotics benchmark for industrial robotics. There, scaled down versions of mobile industrial robots have to navigate through a workshop-like environment or operation area and have to perform tasks of manipulating and transporting work pieces. This paper will introduce an approach of automated vision-based testing of the behavior of the so called youBot robot, which is the most widely used robot platform in the RoboCup @work competition. The proposed system allows automated testing of multiple tries of the robot to perform a specific missions and it allows for the flexibility of the robot, e.g. selecting different paths between two tasks within a mission. The approach is based on a multi-camera setup using, off the shelf cameras and optical markers. It has been applied for test-driven development (TDD) and maintenance-like verification of the robot behavior and performance.

Keywords: Supervisory control, Testing, Markers, Mono Vision, Automation.

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Authors: Herminio Martínez-García, Juan Gámiz, Yolanda Bolea, Antoni Grau

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This article presents an interactive system for data acquisition in vehicle testing according to the test process defined in automotive directive 2004/104/EC. The project has been designed and developed by authors for the Spanish company Applus-LGAI. The developed project will result in a new process, which will involve the creation of braking cycle test defined in the aforementioned automotive directive. It will also allow the analysis of new vehicle features that was not feasible, allowing an increasing interaction with the vehicle. Potential users of this system in the short term will be vehicle manufacturers and in a medium term the system can be extended to testing other automotive components and EMC tests.

Keywords: Automotive process, data acquisition system, electromagnetic compatibility (EMC) testing, European Directive 2004/104/EC.

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Authors: Hassan Ezzaidi, Jean Rouat

Abstract:

Recently many research has been conducted to retrieve pertinent parameters and adequate models for automatic music genre classification. In this paper, two measures based upon information theory concepts are investigated for mapping the features space to decision space. A Gaussian Mixture Model (GMM) is used as a baseline and reference system. Various strategies are proposed for training and testing sessions with matched or mismatched conditions, long training and long testing, long training and short testing. For all experiments, the file sections used for testing are never been used during training. With matched conditions all examined measures yield the best and similar scores (almost 100%). With mismatched conditions, the proposed measures yield better scores than the GMM baseline system, especially for the short testing case. It is also observed that the average discrimination information measure is most appropriate for music category classifications and on the other hand the divergence measure is more suitable for music subcategory classifications.

Keywords: Audio feature, information measures, music genre.

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Authors: M. Rominu, C. Sinescu, A.G. Podoleanu

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The purpose of this study is to present a non invasive method for the marginal adaptation evaluation in class V composite restorations. Standardized class V cavities, prepared in human extracted teeth, were filled with Premise (Kerr) composite. The specimens were thermo cycled. The interfaces were examined by Optical Coherence Tomography method (OCT) combined with the confocal microscopy and fluorescence. The optical configuration uses two single mode directional couplers with a superluminiscent diode as the source at 1300 nm. The scanning procedure is similar to that used in any confocal microscope, where the fast scanning is enface (line rate) and the depth scanning is much slower (at the frame rate). Gaps at the interfaces as well as inside the composite resin materials were identified. OCT has numerous advantages which justify its use in vivo as well as in vitro in comparison with conventional techniques.

Keywords: Class V Cavities, Marginal Adaptation, Optical Coherence Tomography Fluorescence, Confocal Microscopy

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Authors: Md. Shafiqul Islam, Abdullah Khan, Sharon Kao-Walter, Li Jian

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Shear testing is one of the most complex testing areas where available methods and specimen geometries are different from each other. Therefore, a modified shear test specimen (MSTS) combining the simple uniaxial test with a zone of interest (ZOI) is tested which gives almost the pure shear. In this study, material parameters of polypropylene (PP) and high density polyethylene (HDPE) are first measured by tensile tests with a dogbone shaped specimen. These parameters are then used as an input for the finite element analysis. Secondly, a specially designed specimen (MSTS) is used to perform the shear stress tests in a tensile testing machine to get the results in terms of forces and extension, crack initiation etc. Scanning Electron Microscopy (SEM) is also performed on the shear fracture surface to find material behavior. These experiments are then simulated by finite element method and compared with the experimental results in order to confirm the simulation model. Shear stress state is inspected to find the usability of the proposed shear specimen. Finally, a geometry correction factor can be established for these two materials in this specific loading and geometry with notch using Linear Elastic Fracture Mechanics (LEFM). By these results, strain energy of shear failure and stress intensity factor (SIF) of shear of these two polymers are discussed in the special application of the screw cap opening of the medical or food packages with a temper evidence safety solution.

Keywords: Shear test specimen, Stress intensity factor, Finite Element simulation, Scanning electron microscopy, Screw cap opening.

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Authors: Robertoes K. K. Wibowo, Siswoyo Soekarno, Irma Puspitasari

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Indonesian people use trains for their transportation, especially they use economy class train transportation because it is cheaper and has a more precise schedule than any other ground transportation. Nevertheless, the economy class passenger seat raises some inconvenience issues for passengers. This is due to the design of the chair on the economic class of trains that did not adjusted to the shape of anthropometry of Indonesian people. Thus, research needs to be conducted on the design of the seats in the economic class of trains. The purpose of this research is to make the design of economy class passenger seats ergonomic. This research method uses questionnaires and anthropometry measurements. The data obtained is processed using House of Quality of Ergonomic Function Development. From the results of analysis and data processing were obtained important changes from the original design. Ergonomic chair design according to the analysis is a stainless steel frame, seat height 390 mm, with a seat width for each passenger of 400 mm and a depth of 400 mm. Design of the backrest has a height of 840 mm, width of 430 mm and length of 300 mm that can move at the angle of 105-115 degrees. The width of the footrest is 42 mm and 400 mm length. The thickness of the seat cushion is 100 mm.

Keywords: Chair, ergonomics, function development, train passenger.

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Authors: Yang Jiang, Zhuchao Yu, Zhu Wang, Xueying Hong

Abstract:

Reference point effects of top managers exerts an influence on managerial decision-making behaviors. We introduces the main idea of developing the decision behavior testing system designed for top manager in team task circumstance. According to the theory of the reference point effect, study of testing experiments in the reference point effect is carried out. Under managerial decision-making simulation environment, a platform is designed for testing reference point effect. The system uses the outcome of the value of the reference point to report the characteristics of the decision behavior of top managers.

Keywords: reference point effect, decision-making behavior, top manager, managerial decision-making simulation environment.

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Authors: E. K. A. Ogunshile

Abstract:

This paper is aimed at creating an Automatic Java X-Machine testing tool for software development. The nature of software development is changing; thus, the type of software testing tools required is also changing. Software is growing increasingly complex and, in part due to commercial impetus for faster software releases with new features and value, increasingly in danger of containing faults. These faults can incur huge cost for software development organisations and users; Cambridge Judge Business School’s research estimated the cost of software bugs to the global economy is $312 billion. Beyond the cost, faster software development methodologies and increasing expectations on developers to become testers is driving demand for faster, automated, and effective tools to prevent potential faults as early as possible in the software development lifecycle. Using X-Machine theory, this paper will explore a new tool to address software complexity, changing expectations on developers, faster development pressures and methodologies, with a view to reducing the huge cost of fixing software bugs.

Keywords: Conformance testing, finite state machine, software testing, X-Machine.

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Authors: Miklos Taliga

Abstract:

In the present case study we examined the development and testing methods of systems that contain safety-critical elements in different industrial fields. Consequentially, we observed the classical object-oriented development and testing environment, as both medical technology and automobile industry approaches the development of safety critical elements that way. Subsequently, we examined model-based development. We introduce the quality parameters that define development and testing. While taking modern agile methodology (scrum) into consideration, we examined whether and to what extent the methodologies we found fit into this environment.

Keywords: Safety-critical elements, quality management, unit verification, model base testing, agile methods, scrum, metamodel, object-oriented programming, field specific modelling, sprint, user story, UML Standard.

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Authors: Keshav Pujeri, Pranesh Jain, Krutibas Panda

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Significant changes in oil and gas drilling have emphasized the need to verify the integrity and reliability of drill stem components. Defects are inevitable in cast components, regardless of application; but if these defects go undetected, any severe defect could cause down-hole failure. One such defect is shrinkage porosity. Castings with lower level shrinkage porosity (CB levels 1 and 2) have scattered pores and do not occupy large volumes; so pressure testing and helium leak testing (HLT) are sufficient for qualifying the castings. However, castings with shrinkage porosity of CB level 3 and higher, behave erratically under pressure testing and HLT making these techniques insufficient for evaluating the castings- integrity. This paper presents a case study to highlight how the radiography technique is much more effective than pressure testing and HLT.

Keywords: Casting Defects, Interconnects, Leak Check, Pressure Test, Radiography.

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Authors: Melis Inalpulat, Levent Genc

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In the present study, an attempt was made to state the Land Use Land Cover (LULC) transformation over three decades around the urban regions of Balıkesir, Bursa, and Çanakkale provincial centers (PCs) in Turkey. Landsat imageries acquired in 1984, 1999 and 2014 were used to determine the LULC change. Images were classified using the supervised classification technique and five main LULC classes were considered including forest (F), agricultural land (A), residential area (urban) - bare soil (R-B), water surface (W), and other (O). Change detection analyses were conducted for 1984-1999 and 1999-2014, and the results were evaluated. Conversions of LULC types to R-B class were investigated. In addition, population changes (1985-2014) were assessed depending on census data, the relations between population and the urban areas were stated, and future populations and urban area needs were forecasted for 2030. The results of LULC analysis indicated that urban areas, which are covered under R-B class, were expanded in all PCs. During 1984-1999 R-B class within Balıkesir, Bursa and Çanakkale PCs were found to have increased by 7.1%, 8.4%, and 2.9%, respectively. The trend continued in the 1999-2014 term and the increment percentages reached to 15.7%, 15.5%, and 10.2% at the end of 30-year period (1984-2014). Furthermore, since A class in all provinces was found to be the principal contributor for the R-B class, urban sprawl lead to the loss of agricultural lands. Moreover, the areas of R-B classes were highly correlated with population within all PCs (R²>0.992). Depending on this situation, both future populations and R-B class areas were forecasted. The estimated values of increase in the R-B class areas for Balıkesir, Bursa, and Çanakkale PCs were 1,586 ha, 7,999 ha and 854 ha, respectively. Due to this fact, the forecasted values for 2,030 are 7,838 ha, 27,866, and 2,486 ha for Balıkesir, Bursa, and Çanakkale, and thus, 7.7%, 8.2%, and 9.7% more R-B class areas are expected to locate in PCs in respect to the same order.

Keywords: Landsat, LULC change, population, urban sprawl.

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Authors: Walid S. Abd El-hamid, Sherif S. El-Etriby, Mohiy M. Hadhoud

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Regression testing is a maintenance activity applied to modified software to provide confidence that the changed parts are correct and that the unchanged parts have not been adversely affected by the modifications. Regression test selection techniques reduce the cost of regression testing, by selecting a subset of an existing test suite to use in retesting modified programs. This paper presents the first general regression-test-selection technique, which based on code and allows selecting test cases for any programs written in any programming language. Then it handles incomplete program. We also describe RTSDiff, a regression-test-selection system that implements the proposed technique. The results of the empirical studied that performed in four programming languages java, C#, Cµ and Visual basic show that the efficiency and effective in reducing the size of test suit.

Keywords: Regression testing, testing, test selection, softwareevolution, software maintenance.

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

Abstract:

Cast metal inlays can be used on molars requiring a class II restoration instead amalgam and offer a durable alternative. Because it is known that class II inlays may increase the susceptibility to fracture, it is important to ensure optimal performance in selection of the adequate preparation design to reduce stresses in teeth structures and also in the restorations. The aim of the study was to investigate the influence of preparation design on stress distribution in molars with different class II preparations and in cast metal inlays. The first step of the study was to achieve 3D models in order to analyze teeth and cast metal class II inlays. The geometry of the intact tooth was obtained by 3D scanning using a manufactured device. With a NURBS modeling program the preparations and the appropriately inlays were designed. 3D models of first upper molars of the same shape and size were created. Inlay cavities designs were created using literature data. The geometrical model was exported and the mesh structure of the solid 3D model was created for structural simulations. Stresses were located around the occlusal contact areas. For the studied cases, the stress values were not significant influenced by the taper of the preparation. it was demonstrated stresses are higher in the cast metal restorations and therefore the strength of the teeth is not affected.

Keywords: cast metal inlays, class II restoration, molars, 3D models, structural simulations.

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Authors: Mehran Garmehi, Yasser Mansouri

Abstract:

There are two paradigms proposed to provide QoS for Internet applications: Integrated service (IntServ) and Differentiated service (DiffServ).Intserv is not appropriate for large network like Internet. Because is very complex. Therefore, to reduce the complexity of QoS management, DiffServ was introduced to provide QoS within a domain using aggregation of flow and per- class service. In theses networks QoS between classes is constant and it allows low priority traffic to be effected from high priority traffic, which is not suitable. In this paper, we proposed a fuzzy controller, which reduced the effect of low priority class on higher priority ones. Our simulations shows that, our approach reduces the latency dependency of low priority class on higher priority ones, in an effective manner.

Keywords: QoS, Differentiated Service (DiffServ), FuzzyController, Delay.

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Authors: S. Bennoud, S. Hocine, H. Slme

Abstract:

Developments in turbine cooling technology play an important role in increasing the thermal efficiency and the power output of recent gas turbines, in particular the turbojets.

Advanced turbojets operate at high temperatures to improve thermal efficiency and power output. These temperatures are far above the permissible metal temperatures. Therefore, there is a critical need to cool the blades in order to give theirs a maximum life period for safe operation.

The focused objective of this work is to calculate the turbojet performances, as well as the calculation of turbine blades cooling.

The developed application able the calculation of turbojet performances to different altitudes in order to find a point of optimal use making possible to maintain the turbine blades at an acceptable maximum temperature and to limit the local variations in temperatures in order to guarantee their integrity during all the lifespan of the engine.

Keywords: Brayton cycle, Turbine Blades Cooling, Turbojet Cycle, turbojet performances.

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Authors: Nidhi Gadura

Abstract:

To ensure student success in a non-majors biology course, a flipped classroom pedagogical approach was developed and implemented. All students were assigned online lectures to listen to before they come to class. A three hour lecture was split into one hour of online component, one hour of in class lecture and one hour of worksheets done by students in the classroom. This deviation from a traditional 3 hour in class lecture has resulted in increased student interest in science as well as better understanding of difficult scientific concepts. A pre and post survey was given to measure the interest in the subject and grades were used to measure the success rates. While the overall grade average did not change dramatically, students reported a much better appreciation of biology. Also, students overwhelmingly like the use of worksheets in class to help them understand the concepts. They liked the fact that they could listen to lectures at their own pace on line and even repeat if needed. The flipped classroom approach turned out to work really well our non-science majors and the author is ready to implement this in other classrooms.

Keywords: Flipped classroom, non-science majors, pedagogy, technological pedagogical model.

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Authors: Ghada S. Moussa

Abstract:

With the increase in population along with economic prosperity, an enormous increase in the number and types of vehicles on the roads occurred. This fact brings a growing need for efficiently yet effectively classifying vehicles into their corresponding categories, which play a crucial role in many areas of infrastructure planning and traffic management.

This paper presents two vehicle-type classification approaches; 1) geometric-based and 2) appearance-based. The two classification approaches are used for two tasks: multi-class and intra-class vehicle classifications. For the evaluation purpose of the proposed classification approaches’ performance and the identification of the most effective yet efficient one, 10-fold cross-validation technique is used with a large dataset. The proposed approaches are distinguishable from previous research on vehicle classification in which: i) they consider both geometric and appearance attributes of vehicles, and ii) they perform remarkably well in both multi-class and intra-class vehicle classification. Experimental results exhibit promising potentials implementations of the proposed vehicle classification approaches into real-world applications.

Keywords: Appearance attributes, Geometric attributes, Support vector machine, Vehicle classification.

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Authors: Fuyang Peng, Bo Deng, Chao Qi

Abstract:

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: M. Phankokkruad, K. Woraratpanya

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This paper proposes a Web service and serviceoriented architecture (SOA) for a computer-adaptive testing (CAT) process on e-learning systems. The proposed architecture is developed to solve an interoperability problem of the CAT process by using Web service. The proposed SOA and Web service define all services needed for the interactions between systems in order to deliver items and essential data from Web service to the CAT Webbased application. These services are implemented in a XML-based architecture, platform independence and interoperability between the Web service and CAT Web-based applications.

Keywords: Web service, service-oriented architecture, computer-adaptive testing, e-learning, interoperability

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Authors: Nathar Shah

Abstract:

Concurrency and synchronization are becoming big issues as every new PC comes with multi-core processors. A major reason for Object-Oriented Programming originally was to enable easier reuse: encode your algorithm into a class and thoroughly debug it, then you can reuse the class again and again. However, when we get to concurrency and synchronization, this is often not possible. Thread-safety issues means that synchronization constructs need to be entangled into every class involved. We contributed a detailed literature review of issues and challenges in concurrent programming and present a methodology that uses the Aspect- Oriented paradigm to address this problem. Aspects will allow us to extract the synchronization concerns as schemes to be “weaved in" later into the main code. This allows the aspects to be separately tested and verified. Hence, the functional components can be weaved with reusable synchronization schemes that are robust and scalable.

Keywords: Aspect-orientation, development methodologysoftware concurrency, synchronization.

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Authors: Tshaudi Motsima

Abstract:

Class attendance is key at all levels of education. At tertiary level many students develop a tendency of not attending all classes without being aware of the repercussions of not attending all classes. It is important for all students to attend all classes as they can receive first-hand information and they can benefit more. The student who attends classes is likely to perform better academically than the student who does not. The aim of this paper is to assess the relationship between class attendance and academic performance of industrial engineering students. The data for this study were collected through the attendance register of students and the other data were accessed from the Integrated Tertiary Software and the Higher Education Data Analyzer Portal. Data analysis was conducted on a sample of 93 students. The results revealed that students with medium predicate scores (OR = 3.8; p = 0.027) and students with low predicate scores (OR = 21.4, p < 0.001) were significantly likely to attend less than 80% of the classes as compared to students with high predicate scores. Students with examination performance of less than 50% were likely to attend less than 80% of classes than students with examination performance of 50% and above, but the differences were not statistically significant (OR = 1.3; p = 0.750).

Keywords: Class attendance, examination performance, final outcome, logistic regression.

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Authors: Ling Zhang, Ting-Zhu Huang

Abstract:

A P0-matrix is a real square matrix all of whose principle minors are nonnegative. In this paper, we consider the class of P0-matrix. Our main aim is to determine which sign pattern matrices are admissible for this class of real matrices.

Keywords: Sign pattern matrices, P0 matrices, graph, digraph.

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Authors: Gyoutae Park, Woosuk Kim, Sangguk Ahn, Seungmo Kim, Minjun Kim, Jinhan Lee, Youngdo Jo, Jongsam Moon, Hiesik Kim

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In this research, we designed a remote system to test parameters of gas detectors such as gas concentration and initial response time. This testing system is available to measure two gas instruments simultaneously. First of all, we assembled an experimental jig with a square structure. Those parts are included with a glass flask, two high-quality cameras, and two Ethernet modems for transmitting data. This remote gas detector testing system extracts numerals from videos with continually various gas concentrations while LCDs show photographs from cameras. Extracted numeral data are received to a laptop computer through Ethernet modem. And then, the numerical data with gas concentrations and the measured initial response speeds are recorded and graphed. Our remote testing system will be diversely applied on gas detector’s test and will be certificated in domestic and international countries.

Keywords: Gas leakage detector, inspection instrument, extracting numerals, concentration.

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Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang

Abstract:

This paper investigates the problem of designing a robust state-feedback controller for a class of uncertain Markovian jump nonlinear systems that guarantees the L2-gain from an exogenous input to a regulated output is less than or equal to a prescribed value. First, we approximate this class of uncertain Markovian jump nonlinear systems by a class of uncertain Takagi-Sugeno fuzzy models with Markovian jumps. Then, based on an LMI approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear systems to have an H performance are derived. An illustrative example is used to illustrate the effectiveness of the proposed design techniques.

Keywords: Robust H, Fuzzy Control, Markovian Jump Systems, LMI.

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Authors: Sukrit Shankar, Chetana Shanta Patsa, Jaydev Sharma

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Fractional Fourier Transform is a generalization of the classical Fourier Transform which is often symbolized as the rotation in time- frequency plane. Similar to the product of time and frequency span which provides the Uncertainty Principle for the classical Fourier domain, there has not been till date an Uncertainty Principle for the Fractional Fourier domain for a generalized class of finite energy signals. Though the lower bound for the product of time and Fractional Fourier span is derived for the real signals, a tighter lower bound for a general class of signals is of practical importance, especially for the analysis of signals containing chirps. We hence formulate a mathematical derivation that gives the lower bound of time and Fractional Fourier span product. The relation proves to be utmost importance in taking the Fractional Fourier Transform with adaptive time and Fractional span resolutions for a varied class of complex signals.

Keywords: Fractional Fourier Transform, uncertainty principle, Fractional Fourier Span, amplitude, phase.

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Authors: Norlyda Mohamed, Daud Mohamad, Shaharuddin Cik Soh

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Let Gα ,β (γ ,δ ) denote the class of function f (z), f (0) = f ′(0)−1= 0 which satisfied e δ {αf ′(z)+ βzf ′′(z)}> γ i Re in the open unit disk D = {z ∈ı : z < 1} for some α ∈ı (α ≠ 0) , β ∈ı and γ ∈ı (0 ≤γ <α ) where δ ≤ π and α cosδ −γ > 0 . In this paper, we determine some extremal properties including distortion theorem and argument of f ′( z ) .

Keywords: Argument of f ′(z) , Carathéodory Function, Closeto- convex Function, Distortion Theorem, Extremal Properties

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