Search results for: Split Step Method.

Authors: Yanan Yang, Zhigang Wang, Xiang Chen

Abstract:

This paper presents the use of Legendre pseudospectral method for the optimization of finite-thrust orbital transfer for spacecrafts. In order to get an accurate solution, the System-s dynamics equations were normalized through a dimensionless method. The Legendre pseudospectral method is based on interpolating functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This is used to transform the optimal control problem into a constrained parameter optimization problem. The developed novel optimization algorithm can be used to solve similar optimization problems of spacecraft finite-thrust orbital transfer. The results of a numerical simulation verified the validity of the proposed optimization method. The simulation results reveal that pseudospectral optimization method is a promising method for real-time trajectory optimization and provides good accuracy and fast convergence.

Keywords: Finite-thrust, Orbital transfer, Legendre pseudospectral method

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Authors: Hailong Zhu, Zhaoxiang Li, Kejun Zhuang

Abstract:

By means of Contractor Iteration Method, we solve and visualize the Lane-Emden(-Fowler) equation Δu + up = 0, in Ω, u = 0, on ∂Ω. It is shown that the present method converges quadratically as Newton’s method and the computation of Contractor Iteration Method is cheaper than the Newton’s method.

Keywords: Positive solutions, newton's method, contractor iteration method, Eigenpairs.

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Authors: Osamu Igawa, Hiroshi Kouchiwa, Yuji Ito

Abstract:

In recent years, a reconstruction project for sewer  pipelines has been progressing in Japan with the aim of renewing old  sewer culverts. However, it is difficult to secure a sufficient base area  for shafts in an urban area because many streets are narrow with a  complex layout. As a result, construction in such urban areas is  generally very demanding.  In urban areas, there is a strong requirement for a safe, reliable and  economical construction method that does not disturb the public’s  daily life and urban activities. With this in mind, we developed a new  construction method called the “shield switching type micro-tunneling  method,” which integrates the micro-tunneling method and shield  method.  In this method, pipeline is constructed first for sections that are  gently curved or straight using the economical micro-tunneling  method, and then the method is switched to the shield method for  sections with a sharp curve or a series of curves without establishing  an intermediate shaft.  This paper provides the information, features and construction  examples of this newly developed method.

 

Keywords: Micro-tunneling method, Secondary lining applied RC segment, Sharp curve, Shield method, Switching type.

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Authors: Ju Young Lee, Jung-Seok Yang, Jaeyoung Choi

Abstract:

The purpose of this paper primarily intends to develop GIS interface for estimating sequences of stream-flows at ungauged stations based on known flows at gauged stations. The integrated GIS interface is composed of three major steps. The first, precipitation characteristics using statistical analysis is the procedure for making multiple linear regression equation to get the long term mean daily flow at ungauged stations. The independent variables in regression equation are mean daily flow and drainage area. Traditionally, mean flow data are generated by using Thissen polygon method. However, method for obtaining mean flow data can be selected by user such as Kriging, IDW (Inverse Distance Weighted), Spline methods as well as other traditional methods. At the second, flow duration curve (FDC) is computing at unguaged station by FDCs in gauged stations. Finally, the mean annual daily flow is computed by spatial interpolation algorithm. The third step is to obtain watershed/topographic characteristics. They are the most important factors which govern stream-flows. In summary, the simulated daily flow time series are compared with observed times series. The results using integrated GIS interface are closely similar and are well fitted each other. Also, the relationship between the topographic/watershed characteristics and stream flow time series is highly correlated.

Keywords: Integrated GIS interface, spatial interpolation algorithm, FDC.

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Authors: H. Zarei, M. H. Fazel Zarandi, M. Karbasian

Abstract:

A Decision Support System/Expert System for stock portfolio selection presented where at first step, both technical and fundamental data used to estimate technical and fundamental return and risk (1st phase); Then, the estimated values are aggregated with the investor preferences (2nd phase) to produce convenient stock portfolio. In the 1st phase, there are two expert systems, each of which is responsible for technical or fundamental estimation. In the technical expert system, for each stock, twenty seven candidates are identified and with using rough sets-based clustering method (RC) the effective variables have been selected. Next, for each stock two fuzzy rulebases are developed with fuzzy C-Mean method and Takai-Sugeno- Kang (TSK) approach; one for return estimation and the other for risk. Thereafter, the parameters of the rule-bases are tuned with backpropagation method. In parallel, for fundamental expert systems, fuzzy rule-bases have been identified in the form of “IF-THEN" rules through brainstorming with the stock market experts and the input data have been derived from financial statements; as a result two fuzzy rule-bases have been generated for all the stocks, one for return and the other for risk. In the 2nd phase, user preferences represented by four criteria and are obtained by questionnaire. Using an expert system, four estimated values of return and risk have been aggregated with the respective values of user preference. At last, a fuzzy rule base having four rules, treats these values and produce a ranking score for each stock which will lead to a satisfactory portfolio for the user. The stocks of six manufacturing companies and the period of 2003-2006 selected for data gathering.

Keywords: Stock Portfolio Selection, Fuzzy Rule-Base ExpertSystems, Financial Decision Support Systems, Technical Analysis, Fundamental Analysis.

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Authors: Shigeaki Sakurai, Ryohei Orihara

Abstract:

This paper proposes a new method for analyzing textual data. The method deals with items of textual data, where each item is described based on various viewpoints. The method acquires 2- class classification models of the viewpoints by applying an inductive learning method to items with multiple viewpoints. The method infers whether the viewpoints are assigned to the new items or not by using the models. The method extracts expressions from the new items classified into the viewpoints and extracts characteristic expressions corresponding to the viewpoints by comparing the frequency of expressions among the viewpoints. This paper also applies the method to questionnaire data given by guests at a hotel and verifies its effect through numerical experiments.

Keywords: Text mining, Multiple viewpoints, Differential analysis, Questionnaire data

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Authors: A. Raminfard, S. M. Shahrtash

Abstract:

In this paper, a new efficient method for load balancing in low voltage distribution systems is presented. The proposed method introduces an improved Leap-frog method for optimization. The proposed objective function includes the difference between three phase currents, as well as two other terms to provide the integer property of the variables; where the latter are the status of the connection of loads to different phases. Afterwards, a new algorithm is supplemented to undertake the integer values for the load connection status. Finally, the method is applied to different parts of Tabriz low voltage network, where the results have shown the good performance of the proposed method.

Keywords: Load balancing, improved leap-frog method, optimization algorithm, low voltage distribution systems.

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Authors: D. Kuchar, T. Fukuta, M. Kubota, H. Matsuda

Abstract:

The selective recovery of heavy metals of Cu, Zn, Ni and Cr from a mixed plating sludge by sulfidation and oxidation treatment was targeted in this study. At first, the mixed plating sludge was simultaneously subjected to an extraction and Cu sulfidation process at pH=1.5 to dissolve heavy metals and to precipitate Cu2+ as CuS. In the next step, the sulfidation treatment of Zn was carried out at pH=4.5 and the residual solution was subjected to an oxidation treatment of chromium with H2O2 at pH=10.0. After the experiments, the selectivity of metal precipitation and the chromium oxidation ratio were evaluated. As results, it was found that the filter cake obtained after selective sulfidation of Cu was composed of 96.6% of Cu (100% equals to the sum of Cu, Zn, Ni and Cr contents). Such findings confirmed that almost complete extraction of heavy metals was achieved at pH=1.5 and also that Cu could be selectively recovered as CuS. Further, the filter cake obtained at pH=4.5 was composed of 91.5% Zn and 6.83% of Cr. Regarding the chromium oxidation step, the chromium oxidation ratio was found to increase with temperature and the addition of oxidation agent of H2O2, but only oxidation ratio of 59% was achieved at a temperature of 60°C and H2O2 to Cr3+ equivalent ratio of 180.

Keywords: Chromium recovery, oxidation, plating sludge, sulfidation.

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Authors: H. Fallah, Z. Naddaf Baghdadabadi

Abstract:

Planning of economic activities development has various dimensions one of which determines adequate capacity of economic activities in provinces regarding the government-s goals. Paralleling planning goals of economic activities development including subjects being focused on the view statement is effective to better realize the statement's goals. Current paper presents a native framework for economic activities development in provincial level. Triple steps within the framework are concordant with the view statement-s goals achievement. At first step of the proposed framework, economic activities are being prioritized in terms of employment indices, and secondly economic activities regarding to the province's relative advantages are being recognized. In the third step, desirable capacity of economic activities is determined with regards to the government's goals and effective constraints in economic activities development. Development of economic activities related to the provinces- relative advantages, contributes on regional balance and on equal development of economic activities. Furthermore, results of the framework enable more confident investment, affect employment development and remove unemployment concern as the main goals of the view statement.

Keywords: Development, economic activity, regional planning, view statement.

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Authors: Pongthep Bunrueng

Abstract:

This action research accentuates the outcome of a development in English pronunciation, using principles of phonetics for English major students at Loei Rajabhat University. The research is split into 5 separate modules: 1) Organs of Speech and How to Produce Sounds, 2) Monopthongs, 3) Diphthongs, 4) Consonant sounds, and 5) Suprasegmental Features. Each module followed a 4 step action research process, 1) Planning, 2) Acting, 3) Observing, and 4) Reflecting. The research targeted 2nd year students who were majoring in English Education at Loei Rajabhat University during the academic year of 2011. A mixed methodology employing both quantitative and qualitative research was used, which put theory into action, taking segmental features up to suprasegmental features. Multiple tools were employed which included the following documents: pre-test and post-test papers, evaluation and assessment papers, group work assessment forms, a presentation grading form, an observation of participants form and a participant self-reflection form.

All 5 modules for the target group showed that results from the post-tests were higher than those of the pre-tests, with 0.01 statistical significance. All target groups attained results ranging from low to moderate and from moderate to high performance. The participants who attained low to moderate results had to re-sit the second round. During the first development stage, participants attended classes with group participation, in which they addressed planning through mutual co-operation and sharing of responsibility. Analytic induction of strong points for this operation illustrated that learner cognition, comprehension, application, and group practices were all present whereas the participants with weak results could be attributed to biological differences, differences in life and learning, or individual differences in responsiveness and self-discipline.

Participants who were required to be re-treated in Spiral 2 received the same treatment again. Results of tests from the 5 modules after the 2^nd treatment were that the participants attained higher scores than those attained in the pre-test. Their assessment and development stages also showed improved results. They showed greater confidence at participating in activities, produced higher quality work, and correctly followed instructions for each activity. Analytic induction of strong and weak points for this operation remains the same as for Spiral 1, though there were improvements to problems which existed prior to undertaking the second treatment.

Keywords: Action research, English pronunciation, phonetics, segmental features, suprasegmental features.

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Authors: Changqing Yang, Jianhua Hou, Beibo Qin

Abstract:

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

Keywords: Hybrid functions, Riccati differential equation, Blockpulse, Chebyshev polynomials, Tau method, operational matrix.

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Authors: Lina Yan, Shiheng Wang, Ke Wang

Abstract:

A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp Mmatrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

Keywords: preconditioning, M-matrix, Jacobi method, fuzzy linear system (FLS).

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Authors: Muniyasamy Kalanchiam, Moorthy Chinnasamy

Abstract:

In the competitive environment of aircraft industries it becomes absolutely necessary to improve the efficiency, performance of the aircrafts to reduce the development and operating costs considerably, in order to capitalize the market. An important contribution to improve the efficiency and performance can be achieved by decreasing the aircraft weight through considerable usage of composite materials in primary aircraft structures. In this study, a type of composite material called Carbon Fiber Reinforced Plastic (CFRP) is explored for the usage is aircraft skin panels. Even though there were plenty of studies and research has been already carried out, here a practical example of an aircraft skin panel is taken and substantiated the benefits of composites material usage over the metallic skin panel. A crown skin panel of a commercial aircraft is designed using both metal and composite materials. Stress analysis has been carried out for both and margin of safety is estimated for the critical load cases. The skin panels are compared for manufacturing, tooling, assembly and cost parameters. Detail step by step comparison between metal and composite constructions are studied and results are tabulated for better understanding.

Keywords: Composites, CFRP, Aircraft Structure, Skin panel.

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Authors: Jafar Biazar, Behzad Ghanbari

Abstract:

In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.

Keywords: System of nonlinear equations.

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Authors: A. Soltani, M. Karimi Demneh

Abstract:

In this paper, modeling of an acoustic enclosed vehicle cabin has been carried out by using boundary element method. Also, the second purpose of this study is analyzing of linear wave equation in an acoustic field. The resultants of this modeling consist of natural frequencies that have been compared with resultants derived from finite element method. By using numerical method (boundary element method) and after solution of wave equation inside an acoustic enclosed cabin, this method has been progressed to simulate noise inside a simple vehicle cabin.

Keywords: Boundary element method, natural frequency, noise, vehicle cabin.

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Authors: B. S. Raghavendra, D. Narayana Dutt

Abstract:

In this paper, we have developed a method to compute fractal dimension (FD) of discrete time signals, in the time domain, by modifying the box-counting method. The size of the box is dependent on the sampling frequency of the signal. The number of boxes required to completely cover the signal are obtained at multiple time resolutions. The time resolutions are made coarse by decimating the signal. The loglog plot of total number of boxes required to cover the curve versus size of the box used appears to be a straight line, whose slope is taken as an estimate of FD of the signal. The results are provided to demonstrate the performance of the proposed method using parametric fractal signals. The estimation accuracy of the method is compared with that of Katz, Sevcik, and Higuchi methods. In addition, some properties of the FD are discussed.

Keywords: Box-counting, Fractal dimension, Higuchi method, Katz method, Parametric fractal signals, Sevcik method.

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Authors: Yiqin Lin, Liang Bao, Qinghua Wu, Liping Zhou

Abstract:

In this paper, we propose a direct method based on the real Schur factorization for solving the projected Sylvester equation with relatively small size. The algebraic formula of the solution of the projected continuous-time Sylvester equation is presented. The computational cost of the direct method is estimated. Numerical experiments show that this direct method has high accuracy.

Keywords: Projected Sylvester equation, Schur factorization, Spectral projection, Direct method.

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Authors: S. J. Hosseini Ghoncheh, M. Paripour

Abstract:

In this paper the Huang-s method for solving a m×n fuzzy linear system when, m≤ n, is considered. The method in detail is discussed and illustrated by solving some numerical examples.

Keywords: Fuzzy number, fuzzy linear systems, Huang's method.

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Authors: M. Zarebnia, R. Parvaz

Abstract:

In this paper, numerical solutions of the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation are obtained by a method based on collocation of cubic B-splines. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The L∞ and L2 in the solutions show the efficiency of the method computationally.

Keywords: Benjamin-Bona-Mahony-Burgers equation, Cubic Bspline, Collocation method, Finite difference.

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Authors: Erick López-Ornelas

Abstract:

As the world changes more rapidly, the demand for update information for resource management, environment monitoring, planning are increasing exponentially. Integration of Remote Sensing with GIS technology will significantly promote the ability for addressing these concerns. This paper presents an alternative way of update GIS applications using image processing and high resolution images. We show a method of high-resolution image segmentation using graphs and morphological operations, where a preprocessing step (watershed operation) is required. A morphological process is then applied using the opening and closing operations. After this segmentation we can extract significant cartographic elements such as urban areas, streets or green areas. The result of this segmentation and this extraction is then used to update GIS applications. Some examples are shown using aerial photography.

Keywords: GIS, Remote Sensing, image segmentation, feature extraction.

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Authors: S. H. Kazmi, T. Ahmed, K. Javed, A. Ghani

Abstract:

In this paper static scheme of under-frequency based load shedding is considered for chemical and petrochemical industries with islanded distribution networks relying heavily on the primary commodity to ensure minimum production loss, plant downtime or critical equipment shutdown. A simplistic methodology is proposed for in-house implementation of this scheme using underfrequency relays and a step by step guide is provided including the techniques to calculate maximum percentage overloads, frequency decay rates, time based frequency response and frequency based time response of the system. Case study of FFL electrical system is utilized, presenting the actual system parameters and employed load shedding settings following the similar series of steps. The arbitrary settings are then verified for worst overload conditions (loss of a generation source in this case) and comprehensive system response is then investigated.

Keywords: Islanding, under-frequency load shedding, frequency rate of change, static UFLS.

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Authors: H. Taghvafard, G. H. Erjaee

Abstract:

A method for solving linear and non-linear Goursat problem is given by using the two-dimensional differential transform method. The approximate solution of this problem is calculated in the form of a series with easily computable terms and also the exact solutions can be achieved by the known forms of the series solutions. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Several examples are given to demonstrate the reliability and the performance of the presented method.

Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.

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Authors: Hanifa Taher, Sulaiman Al-Zuhair, Ali H. Al-Marzouqi, Yousef Haik, Mohammed Farid

Abstract:

Biodiesel, as an alternative renewable fuel, has been receiving increasing attention due to the limited supply of fossil fuels and the increasing need for energy. Microalgae are promising source for lipids, which can be converted to biodiesel. The biodiesel production from microalgae lipids using lipase catalyzed reaction in supercritical CO2 medium has several advantages over conventional production processes. However, identifying the optimum microalgae lipid extraction and transesterification conditions is still a challenge. In this study, the quality of biodiesel produced from lipids extracted from Scenedesmus sp. and their enzymatic transesterification using supercritical carbon dioxide have been investigated. At the optimum conditions, the highest biodiesel production yield was found to be 82%. The fuel properties of the produced biodiesel, without any separation step, at optimum reaction condition, were determined and compared to ASTM standards. The properties were found to comply with the limits, and showed a low glycerol content, without any separation step.

Keywords: Biodiesel, fuel standards, lipase, microalgae, Supercritical CO2.

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Authors: Sumachaya Harnsukworapanich, Tetsuo Ichimori

Abstract:

The apportionment method is used by many countries, to calculate the distribution of seats in political bodies. For example, this method is used in the United States (U.S.) to distribute house seats proportionally based on the population of the electoral district. Famous apportionment methods include the divisor methods called the Adams Method, Dean Method, Hill Method, Jefferson Method and Webster Method. Sometimes the results from the implementation of these divisor methods are unfair and include errors. Therefore, it is important to examine the optimization of this method by using a bias measurement to figure out precise and fair results. In this research we investigate the bias of divisor methods in the U.S. Houses of Representatives toward large and small states by applying the Stolarsky Mean Method. We compare the bias of the apportionment method by using two famous bias measurements: the Balinski and Young measurement and the Ernst measurement. Both measurements have a formula for large and small states. The Third measurement however, which was created by the researchers, did not factor in the element of large and small states into the formula. All three measurements are compared and the results show that our measurement produces similar results to the other two famous measurements.

Keywords: Apportionment, Bias, Divisor, Fair, Simulation

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Authors: Amir Rastegarnia, Mohammad Ali Tinati, Azam Khalili

Abstract:

In this paper we consider the problem of distributed adaptive estimation in wireless sensor networks for two different observation noise conditions. In the first case, we assume that there are some sensors with high observation noise variance (noisy sensors) in the network. In the second case, different variance for observation noise is assumed among the sensors which is more close to real scenario. In both cases, an initial estimate of each sensor-s observation noise is obtained. For the first case, we show that when there are such sensors in the network, the performance of conventional distributed adaptive estimation algorithms such as incremental distributed least mean square (IDLMS) algorithm drastically decreases. In addition, detecting and ignoring these sensors leads to a better performance in a sense of estimation. In the next step, we propose a simple algorithm to detect theses noisy sensors and modify the IDLMS algorithm to deal with noisy sensors. For the second case, we propose a new algorithm in which the step-size parameter is adjusted for each sensor according to its observation noise variance. As the simulation results show, the proposed methods outperforms the IDLMS algorithm in the same condition.

Keywords: Distributes estimation, sensor networks, adaptive filter, IDLMS.

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Authors: Zhenyu Zhao, Lei You

Abstract:

The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.

Keywords: Analytic continuation, ill-posed problem, regularization method Fourier spectral method, the discrepancy principle.

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

Abstract:

In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet together with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: Collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation.

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Authors: Z. Asadgol, A. Nadali, H. Arfaeinia, M. Khalifeh Gholi, R. Fateh, M. Fahiminia

Abstract:

The present investigation was conducted to detect the type and concentrations of bacterial and fungal bioaerosols in one room (bedroom) of each selected residential building located in different regions of Qom during February 2015 (n=9) to July 2016 (n=11). Moreover, we evaluated the efficiency of negative air ions (NAIs) in bioaerosol reduction in indoor air in residential buildings. In the first step, the mean concentrations of bacterial and fungal in nine sampling sites evaluated in winter were 744 and 579 colony forming units (CFU)/m³, while these values were 1628.6 and 231 CFU/m³ in the 11 sampling sites evaluated in summer, respectively. The most predominant genera between bacterial and fungal in all sampling sites were detected as Micrococcus spp. and Staphylococcus spp. and also, Aspergillus spp. and Penicillium spp., respectively. The 95% and 45% of sampling sites have bacterial and fungal concentrations over the recommended levels, respectively. In the removal step, we achieved a reduction with a range of 38% to 93% for bacterial genera and 25% to 100% for fungal genera by using NAIs. The results suggested that NAI is a highly effective, simple and efficient technique in reducing the bacterial and fungal concentration in the indoor air of residential buildings.

Keywords: Bacterial, fungal, negative air ions, indoor air, Iran.

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Authors: V. Ghadamyari, F. Samadi, F. Kowsary

Abstract:

An inverse geometry problem is solved to predict an unknown irregular boundary profile. The aim is to minimize the objective function, which is the difference between real and computed temperatures, using three different versions of Conjugate Gradient Method. The gradient of the objective function, considered necessary in this method, obtained as a result of solving the adjoint equation. The abilities of three versions of Conjugate Gradient Method in predicting the boundary profile are compared using a numerical algorithm based on the method. The predicted shapes show that due to its convergence rate and accuracy of predicted values, the Powell-Beale version of the method is more effective than the Fletcher-Reeves and Polak –Ribiere versions.

Keywords: Boundary elements, Conjugate Gradient Method, Inverse Geometry Problem, Sensitivity equation.

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Authors: M. Rodionov, N. Sharapova, Z. Dedovets

Abstract:

The article describes methods of preparation of future teachers that includes the entire diversity of traditional and computer-oriented methodological approaches. The authors reveal how, in the specific educational environment, a teacher can choose the most effective combination of educational technologies based on the nature of the learning task. The key conditions that determine such a choice are that the methodological approach corresponds to the specificity of the problem being solved and that it is also responsive to the individual characteristics of the students. The article refers to the training of students in the proper use of mathematical electronic tools for educational purposes. The preparation of future mathematics teachers should be a step-by-step process, building on specific examples. At the first stage, students optimally solve problems aided by electronic means of teaching. At the second stage, the main emphasis is on modeling lessons. At the third stage, students develop and implement strategies in the study of one of the topics within a school mathematics curriculum. The article also recommended the implementation of this strategy in preparation of future teachers and stated the possible benefits.

Keywords: Computer-oriented approach, traditional approach, future teachers, mathematics, lesson, students, education.

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