Search results for: nonlinear mathematical model.

Authors: Amr Mansour Mohsen, Hesham Ahmed Hassan, Amira M. Idrees

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Emotions classification of text documents is applied to reveal if the document expresses a determined emotion from its writer. As different supervised methods are previously used for emotion documents’ classification, in this research we present a novel model that supports the classification algorithms for more accurate results by the support of TF-IDF measure. Different experiments have been applied to reveal the applicability of the proposed model, the model succeeds in raising the accuracy percentage according to the determined metrics (precision, recall, and f-measure) based on applying the refinement of the lexicon, integration of lexicons using different perspectives, and applying the TF-IDF weighting measure over the classifying features. The proposed model has also been compared with other research to prove its competence in raising the results’ accuracy.

Keywords: Emotion detection, TF-IDF, WEKA tool, classification algorithms.

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Authors: Nan Chen, Baoguang Tian

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In this paper, some relative efficiency have been discussed, including the LSE estimate with respect to BLUE in curve model. Four new kinds of relative efficiency have defined, and their upper bounds have been discussed.

Keywords: Relative efficiency, LSE estimate, BLUE estimate, Upper bound, Curve model.

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Authors: F. Soleymani, M. Sharifi

Abstract:

Most of the nonlinear equation solvers do not converge always or they use the derivatives of the function to approximate the root of such equations. Here, we give a derivative-free algorithm that guarantees the convergence. The proposed two-step method, which is to some extent like the secant method, is accompanied with some numerical examples. The illustrative instances manifest that the rate of convergence in proposed algorithm is more than the quadratically iterative schemes.

Keywords: Non-linear equation, iterative methods, derivative-free, convergence.

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Authors: Yongxin Yuan, Jiashang Jiang

Abstract:

A new numerical method for simultaneously updating mass and stiffness matrices based on incomplete modal measured data is presented. By using the Kronecker product, all the variables that are to be modified can be found out and then can be updated directly. The optimal approximation mass matrix and stiffness matrix which satisfy the required eigenvalue equation and orthogonality condition are found under the Frobenius norm sense. The physical configuration of the analytical model is preserved and the updated model will exactly reproduce the modal measured data. The numerical example seems to indicate that the method is quite accurate and efficient.

Keywords: Finite element model, model updating, modal data, optimal approximation.

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Authors: Dalvir Singh, Somnath Chattopadhyaya

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During welding or flame cutting of metals, the prediction of heat affected zone (HAZ) is critical. There is need to develop a simple mathematical model to calculate the temperature variation in HAZ and derivative analysis can be used for this purpose. This study presents analytical solution for heat transfer through conduction in mild steel plate. The homogeneous and nonhomogeneous boundary conditions are single variables. The full field analytical solutions of temperature measurement, subjected to local heating source, are derived first by method of separation of variables followed with the experimental visualization using infrared imaging. Based on the present work, it is suggested that appropriate heat input characteristics controls the temperature distribution in and around HAZ.

Keywords: Conduction Heat Transfer, Heat Affected Zone (HAZ), Infra-Red Imaging, Numerical Method, Orthogonal Function, Plasma Arc Cutting, Separation of Variables, Temperature Measurement.

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Authors: Foad Saadi, M. Jalali Azizpour, S.A. Zahedi

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The objective of this paper is to present a comparative study of Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Homotopy Analysis Method (HAM) for the semi analytical solution of Kortweg-de Vries (KdV) type equation called KdV. The study have been highlighted the efficiency and capability of aforementioned methods in solving these nonlinear problems which has been arisen from a number of important physical phenomenon.

Keywords: Variational Iteration Method (VIM), HomotopyPerturbation Method (HPM), Homotopy Analysis Method (HAM), KdV Equation.

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Authors: Takayuki Shiina

Abstract:

Mathematical programming has been applied to various problems. For many actual problems, the assumption that the parameters involved are deterministic known data is often unjustified. In such cases, these data contain uncertainty and are thus represented as random variables, since they represent information about the future. Decision-making under uncertainty involves potential risk. Stochastic programming is a commonly used method for optimization under uncertainty. A stochastic programming problem with recourse is referred to as a two-stage stochastic problem. In this study, we consider a stochastic programming problem with simple integer recourse in which the value of the recourse variable is restricted to a multiple of a nonnegative integer. The algorithm of a dynamic slope scaling procedure for solving this problem is developed by using a property of the expected recourse function. Numerical experiments demonstrate that the proposed algorithm is quite efficient. The stochastic programming model defined in this paper is quite useful for a variety of design and operational problems.

Keywords: stochastic programming problem with recourse, simple integer recourse, dynamic slope scaling procedure

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Authors: S.Shokri, S.Zahedi, M.Ahmadi Marvast, B. Baloochi, H.Ganji

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In this research, a systematic investigation was carried out to determine the optimum conditions of HDS reactor. Moreover, a suitable model was developed for a rigorous RTO (real time optimization) loop of HDS (Hydro desulfurization) process. A systematic experimental series was designed based on CCD (Central Composite design) and carried out in the related pilot plant to tune the develop model. The designed variables in the experiments were Temperature, LHSV and pressure. However, the hydrogen over fresh feed ratio was remained constant. The ranges of these variables were respectively equal to 320-380ºC, 1- 21/hr and 50-55 bar. a power law kinetic model was also developed for our further research in the future .The rate order and activation energy , power of reactant concentration and frequency factor of this model was respectively equal to 1.4, 92.66 kJ/mol and k0=2.7*109 .

Keywords: Statistical model, Multiphase Reactors, Gas oil, Hydrodesulfurization, Optimization, Kinetics

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Authors: Alexey V. Klyuev, Arkady. V. Yakimov

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The 1/f noise investigation in nanoscale light-emitting diodes and lasers, based on GaAs and alloys, is presented here. Leakage and additional (to recombination through quantum wells and/or dots) nonlinear currents were detected and it was shown that these currents are the main source of the 1/f noise in devices studied.

Keywords: Lasers, light-emitting diodes, quantum dots, quantum wells, 1/f noise.

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Authors: Amir Mohammad Fathollahi Fard, Mostafa Hajiaghaei-Keshteli, Mohammad Mahdi Paydar

Abstract:

With increasing life expectancy in developed countries, the role of home care services is highlighted by both academia and industrial contributors in Home Health Care Supply Chain (HHCSC) companies. The main decisions in such supply chain systems are the location of pharmacies, the allocation of patients to these pharmacies and also the routing and scheduling decisions of nurses to visit their patients. In this study, for the first time, an integrated model is proposed to consist of all preliminary and necessary decisions in these companies, namely, location-allocation-routing model. This model is a type of NP-hard one. Therefore, an Imperialist Competitive Algorithm (ICA) is utilized to solve the model, especially in large sizes. Results confirm the efficiency of the developed model for HHCSC companies as well as the performance of employed ICA.

Keywords: Home health care supply chain, location-allocation-routing problem, imperialist competitive algorithm, optimization.

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Authors: Hazem M. El-Bakry, Ahmed A. Saleh, Taghreed T. Asfour

Abstract:

Adaptive e-learning today gives the student a central role in his own learning process. It allows learners to try things out, participate in courses like never before, and get more out of learning than before. In this paper, an adaptive e-learning model for logic design, simplification of Boolean functions and related fields is presented. Such model presents suitable courses for each student in a dynamic and adaptive manner using existing database and workflow technologies. The main objective of this research work is to provide an adaptive e-learning model based learners' personality using explicit and implicit feedback. To recognize the learner-s, we develop dimensions to decide each individual learning style in order to accommodate different abilities of the users and to develop vital skills. Thus, the proposed model becomes more powerful, user friendly and easy to use and interpret. Finally, it suggests a learning strategy and appropriate electronic media that match the learner-s preference.

Keywords: Adaptive learning, Learning styles, Teaching strategies.

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Authors: Jia-Jang Wu

Abstract:

This paper presents the scaling laws that provide the criteria of geometry and dynamic similitude between the full-size rotor-shaft system and its scale model, and can be used to predict the torsional vibration characteristics of the full-size rotor-shaft system by manipulating the corresponding data of its scale model. The scaling factors, which play fundamental roles in predicting the geometry and dynamic relationships between the full-size rotor-shaft system and its scale model, for torsional free vibration problems between scale and full-size rotor-shaft systems are firstly obtained from the equation of motion of torsional free vibration. Then, the scaling factor of external force (i.e., torque) required for the torsional forced vibration problems is determined based on the Newton’s second law. Numerical results show that the torsional free and forced vibration characteristics of a full-size rotor-shaft system can be accurately predicted from those of its scale models by using the foregoing scaling factors. For this reason, it is believed that the presented approach will be significant for investigating the relevant phenomenon in the scale model tests.

Keywords: Torsional vibration, full-size model, scale model, scaling laws.

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Authors: Amal A. Abdel-Sattar

Abstract:

The curriculum of architecture department in Prince Sultan University includes ‘Building Surveying’ course which is usually a part of civil engineering courses. As a fundamental requirement of the course, it requires a strong background in mathematics and physics, which are not usually preferred subjects to the architecture students and many of them are not giving the required and necessary attention to these courses during their preparation year before commencing their architectural study. This paper introduces the concept and the methodology of the student-centered learning approach in the course of building surveying for architects. One of the major outcomes is the improvement in the students’ involvement in the course and how this will cover and strength their analytical weak points and improve their mathematical skills. The study is conducted through three semesters with a total number of 99 students. The effectiveness of the student-centered learning approach is studied using the student survey at the end of each semester and teacher observations. This survey showed great acceptance of the students for these methods. Also, the teachers observed a great improvement in the students’ mathematical abilities and how keener they became in attending the classes which were clearly reflected on the low absence record.

Keywords: Architecture, building surveying, student-centered learning, teaching, and learning.

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Authors: Jung–Min Yang

Abstract:

Solvability of the model matching problem for input/output switched asynchronous sequential machines is discussed in this paper. The control objective is to determine the existence condition and design algorithm for a corrective controller that can match the stable-state behavior of the closed-loop system to that of a reference model. Switching operations and correction procedures are incorporated using output feedback so that the controlled switched machine can show the desired input/output behavior. A matrix expression is presented to address reachability of switched asynchronous sequential machines with output equivalence with respect to a model. The presented reachability condition for the controller design is validated in a simple example.

Keywords: Asynchronous sequential machines, corrective control, model matching, input/output control.

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Authors: Rabah Haoui

Abstract:

This work presents a numerical simulation of the interaction of an incident shock wave propagates from the left to the right with a cone placed in a tube at shock. The Mathematical model is based on a non stationary, viscous and axisymmetric flow. The Discretization of the Navier-stokes equations is carried out by the finite volume method in the integral form along with the Flux Vector Splitting method of Van Leer. Here, adequate combination of time stepping parameter, CFL coefficient and mesh size level is selected to ensure numerical convergence. The numerical simulation considers a shock tube filled with air. The incident shock wave propagates to the right with a determined Mach number and crosses the cone by leaving behind it a stationary detached shock wave in front of the nose cone. This type of interaction is observed according to the time of flow.

Keywords: Supersonic flow, viscous flow, finite volume, cone body

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Authors: Hussain Syed Asad, Richard Kwok Kit Yuen, Gongsheng Huang

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Real-time optimization has been considered an effective approach for improving energy efficient operation of heating, ventilation, and air-conditioning (HVAC) systems. In model-based real-time optimization, model mismatches cannot be avoided. When model mismatches are significant, the performance of the real-time optimization will be impaired and hence the expected energy saving will be reduced. In this paper, the model mismatches for chiller plant on real-time optimization are considered. In the real-time optimization of the chiller plant, simplified semi-physical or grey box model of chiller is always used, which should be identified using available operation data. To overcome the model mismatches associated with the chiller model, hybrid Genetic Algorithms (HGAs) method is used for online real-time training of the chiller model. HGAs combines Genetic Algorithms (GAs) method (for global search) and traditional optimization method (i.e. faster and more efficient for local search) to avoid conventional hit and trial process of GAs. The identification of model parameters is synthesized as an optimization problem; and the objective function is the Least Square Error between the output from the model and the actual output from the chiller plant. A case study is used to illustrate the implementation of the proposed method. It has been shown that the proposed approach is able to provide reliability in decision making, enhance the robustness of the real-time optimization strategy and improve on energy performance.

Keywords: Energy performance, hybrid adaptive modeling, hybrid genetic algorithms, real-time optimization, heating, ventilation, and air-conditioning.

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Authors: Spyridon Nikolaidis

Abstract:

A modeling approach for CMOS gates is presented based on the use of the equivalent inverter. A new model for the inverter has been developed using a simplified transistor current model which incorporates the nanoscale effects for the planar technology. Parametric expressions for the output voltage are provided as well as the values of the output and supply current to be compatible with the CCS technology. The model is parametric according the input signal slew, output load, transistor widths, supply voltage, temperature and process. The transistor widths of the equivalent inverter are determined by HSPICE simulations and parametric expressions are developed for that using a fitting procedure. Results for the NAND gate shows that the proposed approach offers sufficient accuracy with an average error in propagation delay about 5%.

Keywords: CMOS gate modeling, Inverter modeling, transistor current model, timing model.

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Authors: Mohammad Reza Oftadeh

Abstract:

The purpose of the article is to describe project objective structure (POS) concept that was developed on research activities and experiences about project management, Balanced Scorecard (BSC) and European Foundation Quality Management Excellence Model (EFQM Excellence Model). Furthermore, this paper tries to define a balanced, systematic, and integrated measurement approach to meet project objectives and project strategic goals based on a process-oriented model. In this paper, POS is suggested in order to measure project performance in the project life cycle. After using the POS model, the project manager can ensure in order to achieve the project objectives on the project charter. This concept can help project managers to implement integrated and balanced monitoring and control project work.

Keywords: Project objectives, project performance management, PMBOK, key performance indicators, integration management.

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Authors: Dariusz Dymek, Leszek Kotulski

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Modeling of the distributed systems allows us to represent the whole its functionality. The working system instance rarely fulfils the whole functionality represented by model; usually some parts of this functionality should be accessible periodically. The reporting system based on the Data Warehouse concept seams to be an intuitive example of the system that some of its functionality is required only from time to time. Analyzing an enterprise risk associated with the periodical change of the system functionality, we should consider not only the inaccessibility of the components (object) but also their functions (methods), and the impact of such a situation on the system functionality from the business point of view. In the paper we suggest that the risk attributes should be estimated from risk attributes specified at the requirements level (Use Case in the UML model) on the base of the information about the structure of the model (presented at other levels of the UML model). We argue that it is desirable to consider the influence of periodical changes in requirements on the enterprise risk estimation. Finally, the proposition of such a solution basing on the UML system model is presented.

Keywords: Risk assessing, software maintenance, UML, graph grammars.

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Authors: Malika Fekih, Mohamed Saighi

Abstract:

Many methods exist for either measuring or estimating evaporation from free water surfaces. Evaporation pans provide one of the simplest, inexpensive, and most widely used methods of estimating evaporative losses. In this study, the rate of evaporation starting from a water surface was calculated by modeling with application to dams in wet, arid and semi arid areas in Algeria. We calculate the evaporation rate from the pan using the energy budget equation, which offers the advantage of an ease of use, but our results do not agree completely with the measurements taken by the National Agency of areas carried out using dams located in areas of different climates. For that, we develop a mathematical model to simulate evaporation. This simulation uses an energy budget on the level of a vat of measurement and a Computational Fluid Dynamics (Fluent). Our calculation of evaporation rate is compared then by the two methods and with the measures of areas in situ.

Keywords: Evaporation, Energy budget, Surface water temperature, CFD, Dams

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Authors: Engin Yesil, Leon Urbas

Abstract:

Modeling of complex dynamic systems, which are very complicated to establish mathematical models, requires new and modern methodologies that will exploit the existing expert knowledge, human experience and historical data. Fuzzy cognitive maps are very suitable, simple, and powerful tools for simulation and analysis of these kinds of dynamic systems. However, human experts are subjective and can handle only relatively simple fuzzy cognitive maps; therefore, there is a need of developing new approaches for an automated generation of fuzzy cognitive maps using historical data. In this study, a new learning algorithm, which is called Big Bang-Big Crunch, is proposed for the first time in literature for an automated generation of fuzzy cognitive maps from data. Two real-world examples; namely a process control system and radiation therapy process, and one synthetic model are used to emphasize the effectiveness and usefulness of the proposed methodology.

Keywords: Big Bang-Big Crunch optimization, Dynamic Systems, Fuzzy Cognitive Maps, Learning.

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Authors: S. M. Abbas, M. A. Hannan, S. A. Samad, A. Hussain

Abstract:

This paper presented a modified efficient inductive powering link based on ASK modulator and proposed efficient class- E power amplifier. The design presents the external part which is located outside the body to transfer power and data to the implanted devices such as implanted Microsystems to stimulate and monitoring the nerves and muscles. The system operated with low band frequency 10MHZ according to industrial- scientific – medical (ISM) band to avoid the tissue heating. For external part, the modulation index is 11.1% and the modulation rate 7.2% with data rate 1 Mbit/s assuming Tbit = 1us. The system has been designed using 0.35-μm fabricated CMOS technology. The mathematical model is given and the design is simulated using OrCAD P Spice 16.2 software tool and for real-time simulation, the electronic workbench MULISIM 11 has been used.

Keywords: Implanted devices, ASK techniques, Class-E power amplifier, Inductive powering and low-frequency ISM band.

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Authors: Shafiq R. Qureshi, Syed Noman Danish, Muhammad Saeed Khalid

Abstract:

Fossil fuels are the major source to meet the world energy requirements but its rapidly diminishing rate and adverse effects on our ecological system are of major concern. Renewable energy utilization is the need of time to meet the future challenges. Ocean energy is the one of these promising energy resources. Threefourths of the earth-s surface is covered by the oceans. This enormous energy resource is contained in the oceans- waters, the air above the oceans, and the land beneath them. The renewable energy source of ocean mainly is contained in waves, ocean current and offshore solar energy. Very fewer efforts have been made to harness this reliable and predictable resource. Harnessing of ocean energy needs detail knowledge of underlying mathematical governing equation and their analysis. With the advent of extra ordinary computational resources it is now possible to predict the wave climatology in lab simulation. Several techniques have been developed mostly stem from numerical analysis of Navier Stokes equations. This paper presents a brief over view of such mathematical model and tools to understand and analyze the wave climatology. Models of 1st, 2nd and 3rd generations have been developed to estimate the wave characteristics to assess the power potential. A brief overview of available wave energy technologies is also given. A novel concept of on-shore wave energy extraction method is also presented at the end. The concept is based upon total energy conservation, where energy of wave is transferred to the flexible converter to increase its kinetic energy. Squeezing action by the external pressure on the converter body results in increase velocities at discharge section. High velocity head then can be used for energy storage or for direct utility of power generation. This converter utilizes the both potential and kinetic energy of the waves and designed for on-shore or near-shore application. Increased wave height at the shore due to shoaling effects increases the potential energy of the waves which is converted to renewable energy. This approach will result in economic wave energy converter due to near shore installation and more dense waves due to shoaling. Method will be more efficient because of tapping both potential and kinetic energy of the waves.

Keywords: Energy Utilizing, Wave Shoaling Phenomenon

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Authors: Mostafa.A. Fellani, Dawo.E. Abaid

Abstract:

This paper presents a controller design technique for Synchronous Reluctance Motor to improve its dynamic performance with fast response and high accuracy. The sliding mode control is the most attractive and suitable method to use for this purpose, since it is simple in design and for its insensitivity to parameter variations or external disturbances. When this method implemented it yields fast dynamic response without overshoot and a zero steady-state error. The current loop control with decentralized sliding mode is presented in this paper. The mathematical model for the synchronous machine, the inverter and the controller is developed. The stability of the sliding mode controller is analyzed. Simulation of synchronous reluctance motor and the controller with PWM-inverter has been curried out, using the SIMULINK software package of MATLAB. Simulation results are presented to show the effectiveness of the approach.

Keywords: Dynamic Simulation, MATLAB, PWM-inverter, Reluctance Machine, Sliding-mode.

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Authors: N.Pourmahmoud, S.Akhesmeh

Abstract:

This work has been carried out in order to provide an understanding of the physical behaviors of the flow variation of pressure and temperature in a vortex tube. A computational fluid dynamics model is used to predict the flow fields and the associated temperature separation within a Ranque–Hilsch vortex tube. The CFD model is a steady axisymmetric model (with swirl) that utilizes the standard k-ε turbulence model. The second–order numerical schemes, was used to carry out all the computations. Vortex tube with a circumferential inlet stream and an axial (cold) outlet stream and a circumferential (hot) outlet stream was considered. Performance curves (temperature separation versus cold outlet mass fraction) were obtained for a specific vortex tube with a given inlet mass flow rate. Simulations have been carried out for varying amounts of cold outlet mass flow rates. The model results have a good agreement with experimental data.

Keywords: Ranque–Hilsch vortex tube, Temperature separation, k–ε model, cold mass fraction.

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Authors: Dursun Aydın

Abstract:

In this paper, estimation of the linear regression model is made by ordinary least squares method and the partially linear regression model is estimated by penalized least squares method using smoothing spline. Then, it is investigated that differences and similarity in the sum of squares related for linear regression and partial linear regression models (semi-parametric regression models). It is denoted that the sum of squares in linear regression is reduced to sum of squares in partial linear regression models. Furthermore, we indicated that various sums of squares in the linear regression are similar to different deviance statements in partial linear regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the partial linear regression model. For this aim, it is made two different applications. A simulated and a real data set are considered to prove the claim mentioned here. In this way, this study is supported with a simulation and a real data example.

Keywords: Partial Linear Regression Model, Linear RegressionModel, Residuals, Deviance, Smoothing Spline.

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Authors: Francisca Grimón, Marylin Giugni, Josep Monguet F., Joaquín Fernández, Luis León G.

Abstract:

In blended learning environments, the Internet can be combined with other technologies. The aim of this research was to design, introduce and validate a model to support synchronous and asynchronous activities by managing content domains in an Adaptive Hypermedia System (AHS). The application is based on information recovery techniques, clustering algorithms and adaptation rules to adjust the user's model to contents and objects of study. This system was applied to blended learning in higher education. The research strategy used was the case study method. Empirical studies were carried out on courses at two universities to validate the model. The results of this research show that the model had a positive effect on the learning process. The students indicated that the synchronous and asynchronous scenario is a good option, as it involves a combination of work with the lecturer and the AHS. In addition, they gave positive ratings to the system and stated that the contents were adapted to each user profile.

Keywords: Blended Learning, System Adaptive, Model, Clustering Algorithms.

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Authors: G.Hariharan, K.Kannan

Abstract:

In this paper, we develop an accurate and efficient Haar wavelet method for well-known FitzHugh-Nagumo equation. The proposed scheme can be used to a wide class of nonlinear reaction-diffusion equations. The power of this manageable method is confirmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.

Keywords: FitzHugh-Nagumo equation, Haar wavelet method, adomain decomposition method, computationally attractive.

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Authors: Tian Hai, Yang Shengsheng, Jr., Wang Yi

Abstract:

Based on an analysis of the mechanism of degradation of optical characteristics of the ZnO-pigmented white paint by electron irradiation, a model of single molecular color centers is built. An equation that explains the relationship between the changes of variation of the ZnO-pigmented white paint-s spectrum absorptance and electron fluence is derived. The uncertain parameters in the equation can be calculated using the curve fitting by experimental data. The result indicates that the model can be applied to predict the degradation of optical characteristics of ZnO-pigmented white paint by electron radiation.

Keywords: ZnO-pigmented white pain, effects of electron radiation, optical characteristics degradation, prediction model.

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Authors: M. F. R. Zuthi, H. H. Ngo, W. S. Guo, S. S. Chen, N. C. Nguyen, L. J. Deng, T. D. C. Tran

Abstract:

Sustaining a desired rate of oxygen transfer for microbial activity is a matter of major concern for biological wastewater treatment (MBR). The study reported in the paper was aimed at assessing the effects of microbial products on the specific oxygen uptake rate (SOUR) in a conventional membrane bioreactor (CMBR) and that in a sponge submerged MBR (SSMBR). The production and progressive accumulation of soluble microbial products (SMP) and bound-extracellular polymeric substances (bEPS) were affecting the SOUR of the microorganisms which varied at different stages of operation of the MBR systems depending on the variable concentrations of the SMP/bEPS. The effect of bEPS on the SOUR was stronger in the SSMBR compared to that of the SMP, while relative high concentrations of SMP had adverse effects on the SOUR of the CMBR system. Of the different mathematical correlations analyzed in the study, logarithmic mathematical correlations could be established between SOUR and bEPS in SSMBR, and similar correlations could also be found between SOUR and SMP concentrations in the CMBR.

Keywords: Microbial products, Microbial activity, Specific oxygen uptake rate, Membrane bioreactor.

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