Search results for: Active method
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8792

Search results for: Active method

8462 Adomian Method for Second-order Fuzzy Differential Equation

Authors: Lei Wang, Sizong Guo

Abstract:

In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability.

Keywords: Fuzzy-valued function, fuzzy initial value problem, strongly generalized differentiability, adomian decomposition method.

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8461 Design of an Authentication Protocol for Secure Electronic Seals

Authors: Seongsoo Park, Mun-Kyu Lee, Dong Kyue Kim, Kunsoo Park, Yousung Kang, Sokjoon Lee, Howon Kim, Kyoil Chung

Abstract:

Electronic seal is an electronic device to check the authenticity and integrity of freight containers at the point of arrival. While RFID-based eSeals are gaining more acceptances and there are also some standardization processes for these devices, a recent research revealed that the current RFID-based eSeals are vulnerable to various attacks. In this paper, we provide a feasible solution to enhance the security of active RFID-based eSeals. Our approach is to use an authentication and key agreement protocol between eSeal and reader device, enabling data encryption and integrity check. Our protocol is based on the use of block cipher AES, which is reasonable since a block cipher can also be used for many other security purposes including data encryption and pseudo-random number generation. Our protocol is very simple, and it is applicable to low-end active RFID eSeals.

Keywords: Authentication, Container Security, Electronic seal, RFID

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8460 Multilevel Arnoldi-Tikhonov Regularization Methods for Large-Scale Linear Ill-Posed Systems

Authors: Yiqin Lin, Liang Bao

Abstract:

This paper is devoted to the numerical solution of large-scale linear ill-posed systems. A multilevel regularization method is proposed. This method is based on a synthesis of the Arnoldi-Tikhonov regularization technique and the multilevel technique. We show that if the Arnoldi-Tikhonov method is a regularization method, then the multilevel method is also a regularization one. Numerical experiments presented in this paper illustrate the effectiveness of the proposed method.

Keywords: Discrete ill-posed problem, Tikhonov regularization, discrepancy principle, Arnoldi process, multilevel method.

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8459 Proximal Parallel Alternating Direction Method for Monotone Structured Variational Inequalities

Authors: Min Sun, Jing Liu

Abstract:

In this paper, we focus on the alternating direction method, which is one of the most effective methods for solving structured variational inequalities(VI). In fact, we propose a proximal parallel alternating direction method which only needs to solve two strongly monotone sub-VI problems at each iteration. Convergence of the new method is proved under mild assumptions. We also present some preliminary numerical results, which indicate that the new method is quite efficient.

Keywords: structured variational inequalities, proximal point method, global convergence

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8458 A Method for Improving Dental Crown Fit-Increasing the Robustness

Authors: Kero T., Söderberg R., Andersson M., Lindkvist L.

Abstract:

The introduction of mass-customization has enabled new ways to treat patients within medicine. However, the introduction of industrialized treatments has also meant new obstacles. The purpose of this study was to introduce and theoretically test a method for improving dental crown fit. The optimization method allocates support points in order to check the final variation for dental crowns. Three different types of geometries were tested and compared. The three geometries were also divided into three sub-geometries: Current method, Optimized method and Feasible method. The Optimized method, using the whole surface for support points, provided the best results. The results support the objective of the study. It also seems that the support optimization method can dramatically improve the robustness of dental crown treatments.

Keywords: Bio-medicine, Dentistry, Mass-customization, Optimization and Robust design.

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8457 Analytical Solution for the Zakharov-Kuznetsov Equations by Differential Transform Method

Authors: Saeideh Hesam, Alireza Nazemi, Ahmad Haghbin

Abstract:

This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.

Keywords: Zakharov-Kuznetsov equation, differential transform method, closed form solution.

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8456 Design of Thermal Control Subsystem for TUSAT Telecommunication Satellite

Authors: N. Sozbir, M. Bulut, M.F.Oktem, A.Kahriman, A. Chaix

Abstract:

TUSAT is a prospective Turkish Communication Satellite designed for providing mainly data communication and broadcasting services through Ku-Band and C-Band channels. Thermal control is a vital issue in satellite design process. Therefore, all satellite subsystems and equipments should be maintained in the desired temperature range from launch to end of maneuvering life. The main function of the thermal control is to keep the equipments and the satellite structures in a given temperature range for various phases and operating modes of spacecraft during its lifetime. This paper describes the thermal control design which uses passive and active thermal control concepts. The active thermal control is based on heaters regulated by software via thermistors. Alternatively passive thermal control composes of heat pipes, multilayer insulation (MLI) blankets, radiators, paints and surface finishes maintaining temperature level of the overall carrier components within an acceptable value. Thermal control design is supported by thermal analysis using thermal mathematical models (TMM).

Keywords: Spacecraft thermal control, design of thermal control.

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8455 Two-Dimensional Solitary Wave Solution to the Quadratic Nonlinear Schrdinger Equation

Authors: Sarun Phibanchon

Abstract:

The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.

Keywords: soliton, iterative method, spectral method, plasma

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8454 The Reliability of the Improved e-N Method for Transition Prediction as Checked by PSE Method

Authors: Caihong Su

Abstract:

Transition prediction of boundary layers has always been an important problem in fluid mechanics both theoretically and practically, yet notwithstanding the great effort made by many investigators, there is no satisfactory answer to this problem. The most popular method available is so-called e-N method which is heavily dependent on experiments and experience. The author has proposed improvements to the e-N method, so to reduce its dependence on experiments and experience to a certain extent. One of the key assumptions is that transition would occur whenever the velocity amplitude of disturbance reaches 1-2% of the free stream velocity. However, the reliability of this assumption needs to be verified. In this paper, transition prediction on a flat plate is investigated by using both the improved e-N method and the parabolized stability equations (PSE) methods. The results show that the transition locations predicted by both methods agree reasonably well with each other, under the above assumption. For the supersonic case, the critical velocity amplitude in the improved e-N method should be taken as 0.013, whereas in the subsonic case, it should be 0.018, both are within the range 1-2%.

Keywords: Boundary layer, e-N method, PSE, Transition

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8453 Variational Iteration Method for the Solution of Boundary Value Problems

Authors: Olayiwola M.O., Gbolagade A .W., Akinpelu F. O.

Abstract:

In this work, we present a reliable framework to solve boundary value problems with particular significance in solid mechanics. These problems are used as mathematical models in deformation of beams. The algorithm rests mainly on a relatively new technique, the Variational Iteration Method. Some examples are given to confirm the efficiency and the accuracy of the method.

Keywords: Variational iteration method, boundary value problems, convergence, restricted variation.

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8452 1 kW Power Factor Correction Soft Switching Boost Converter with an Active Snubber Cell

Authors: Yakup Sahin, Naim Suleyman Ting, Ismail Aksoy

Abstract:

A 1 kW power factor correction boost converter with an active snubber cell is presented in this paper. In the converter, the main switch turns on under zero voltage transition (ZVT) and turns off under zero current transition (ZCT) without any additional voltage or current stress. The auxiliary switch turns on and off under zero current switching (ZCS). Besides, the main diode turns on under ZVS and turns off under ZCS. The output current and voltage are controlled by the PFC converter in wide line and load range. The simulation results of converter are obtained for 1 kW and 100 kHz. One of the most important feature of the given converter is that it has direct power transfer as well as excellent soft switching techniques. Also, the converter has 0.99 power factor with the sinusoidal input current shape.

Keywords: Power factor correction, direct power transfer, zero-voltage transition, zero-current transition, soft switching.

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8451 An Efficient Tool for Mitigating Voltage Unbalance with Reactive Power Control of Distributed Grid-Connected Photovoltaic Systems

Authors: Malinwo Estone Ayikpa

Abstract:

With the rapid increase of grid-connected PV systems over the last decades, genuine challenges have arisen for engineers and professionals of energy field in the planning and operation of existing distribution networks with the integration of new generation sources. However, the conventional distribution network, in its design was not expected to receive other generation outside the main power supply. The tools generally used to analyze the networks become inefficient and cannot take into account all the constraints related to the operation of grid-connected PV systems. Some of these constraints are voltage control difficulty, reverse power flow, and especially voltage unbalance which could be due to the poor distribution of single-phase PV systems in the network. In order to analyze the impact of the connection of small and large number of PV systems to the distribution networks, this paper presents an efficient optimization tool that minimizes voltage unbalance in three-phase distribution networks with active and reactive power injections from the allocation of single-phase and three-phase PV plants. Reactive power can be generated or absorbed using the available capacity and the adjustable power factor of the inverter. Good reduction of voltage unbalance can be achieved by reactive power control of the PV systems. The presented tool is based on the three-phase current injection method and the PV systems are modeled via an equivalent circuit. The primal-dual interior point method is used to obtain the optimal operating points for the systems.

Keywords: Photovoltaic generation, primal-dual interior point method, three-phase optimal power flow, unbalanced system.

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8450 Self-Sensing versus Reference Air Gaps

Authors: Alexander Schulz, Ingrid Rottensteiner, Manfred Neumann, Michael Wehse, Johann Wassermann

Abstract:

Self-sensing estimates the air gap within an electro magnetic path by analyzing the bearing coil current and/or voltage waveform. The self-sensing concept presented in this paper has been developed within the research project “Active Magnetic Bearings with Supreme Reliability" and is used for position sensor fault detection. Within this new concept gap calculation is carried out by an alldigital analysis of the digitized coil current and voltage waveform. For analysis those time periods within the PWM period are used, which give the best results. Additionally, the concept allows the digital compensation of nonlinearities, for example magnetic saturation, without degrading signal quality. This increases the accuracy and robustness of the air gap estimation and additionally reduces phase delays. Beneath an overview about the developed concept first measurement results are presented which show the potential of this all-digital self-sensing concept.

Keywords: digital signal analysis, active magnetic bearing, reliability, fault detection.

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8449 The Role of Blended Modality in Enhancing Active Learning Strategies in Higher Education: A Case Study of a Hybrid Course of Oral Production and Listening of French

Authors: Tharwat N. Hijjawi

Abstract:

Learning oral skills in an Arabic speaking environment is challenging. A blended course (material, activities, and individual/ group work tasks …) was implemented in a module of level B1 for undergraduate students of French as a foreign language in order to increase their opportunities to practice listening and speaking skills. This research investigates the influence of this modality on enhancing active learning and examines the effectiveness of provided strategies. Moreover, it aims at discovering how it allows teacher to flip the traditional classroom and create a learner-centered framework. Which approaches were integrated to motivate students and urge them to search, analyze, criticize, create and accomplish projects? What was the perception of students? This paper is based on the qualitative findings of a questionnaire and a focus group interview with learners. Despite the doubled time and effort both “teacher” and “student” needed, results revealed that the NTIC allowed a shift into a learning paradigm where learners were the “chiefs” of the process. Tasks and collaborative projects required higher intellectual capacities from them. Learners appreciated this experience and developed new life-long learning competencies at many levels: social, affective, ethical and cognitive. To conclude, they defined themselves as motivated young researchers, motivators and critical thinkers.

Keywords: Active learning, critical thinking, inverted classroom, learning paradigm, problem-based.

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8448 Haar Wavelet Method for Solving Fitz Hugh-Nagumo Equation

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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8447 Laser Transmission through Vegetative Material

Authors: Juliana A. Fracarolli, Adilson M. Enes, Inácio M. Dal Fabbro, Silvestre Rodrigues

Abstract:

The dynamic speckle or biospeckle is an interference phenomenon generated at the reflection of a coherent light by an active surface or even by a particulate or living body surface. The above mentioned phenomenon gave scientific support to a method named biospeckle which has been employed to study seed viability, biological activity, tissue senescence, tissue water content, fruit bruising, etc. Since the above mentioned method is not invasive and yields numerical values, it can be considered for possible automation associated to several processes, including selection and sorting. Based on these preliminary considerations, this research work proposed to study the interaction of a laser beam with vegetative samples by measuring the incident light intensity and the transmitted light beam intensity at several vegetative slabs of varying thickness. Tests were carried on fifteen slices of apple tissue divided into three thickness groups, i.e., 4 mm, 5 mm, 18 mm and 22 mm. A diode laser beam of 10mW and 632 nm wavelength and a Samsung digital camera were employed to carry the tests. Outgoing images were analyzed by comparing the gray gradient of a fixed image column of each image to obtain a laser penetration scale into the tissue, according to the slice thickness.

Keywords: Fruit, laser, laser transmission, vegetative tissue.

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8446 A Method for Measurement and Evaluation of Drape of Textiles

Authors: L. Fridrichova, R. Knížek, V. Bajzík

Abstract:

Drape is one of the important visual characteristics of the fabric. This paper is introducing an innovative method of measurement and evaluation of the drape shape of the fabric. The measuring principle is based on the possibility of multiple vertical strain of the fabric. This method more accurately simulates the real behavior of the fabric in the process of draping. The method is fully automated, so the sample can be measured by using any number of cycles in any time horizon. Using the present method of measurement, we are able to describe the viscoelastic behavior of the fabric.

Keywords: Drape, drape shape, automated drape meter.

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8445 Seat Assignment Model for Student Admissions Process at Saudi Higher Education Institutions

Authors: Mohammed Salem Alzahrani

Abstract:

In this paper, student admission process is studied to optimize the assignment of vacant seats with three main objectives. Utilizing all vacant seats, satisfying all programs of study admission requirements and maintaining fairness among all candidates are the three main objectives of the optimization model. Seat Assignment Method (SAM) is used to build the model and solve the optimization problem with help of Northwest Coroner Method and Least Cost Method. A closed formula is derived for applying the priority of assigning seat to candidate based on SAM.

Keywords: Admission Process Model, Assignment Problem, Hungarian Method, Least Cost Method, Northwest Corner Method, Seat Assignment Method (SAM).

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8444 Active Control for Reduction of Noise Passing through Enclosure and Optimization of Microphone Position

Authors: Han-wool Lee, Chin-suk Hong, Weui-bong Jung

Abstract:

In this study, noise characteristics of structure were analyzed in an effort to reduce noise passing through an opening of an enclosure surrounding the structure that generates noise. Enclosures are essential measure to protect noise propagation from operating machinery. Access openings of the enclosures are important path of noise leakage. First, noise characteristics of structure were analyzed and feed-forward noise control was performed using simulation in order to reduce noise passing through the opening of enclosure, which surrounds a structure generating noise. We then implemented a feed-forward controller to actively control the acoustic power through the opening. Finally, we conducted optimization of placement of the reference sensors for several cases of the number of sensors. Good control performances were achieved using the minimum number of microphones arranged an optimal placement.

Keywords: Active Noise Control, Feed-forward Control, Noise Attenuation, Position Optimization.

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8443 Zero-Dissipative Explicit Runge-Kutta Method for Periodic Initial Value Problems

Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

Abstract:

In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: Dissipation, Oscillatory solutions, Phase-lag, Runge- Kutta methods.

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8442 Selection Initial modes for Belief K-modes Method

Authors: Sarra Ben Hariz, Zied Elouedi, Khaled Mellouli

Abstract:

The belief K-modes method (BKM) approach is a new clustering technique handling uncertainty in the attribute values of objects in both the cluster construction task and the classification one. Like the standard version of this method, the BKM results depend on the chosen initial modes. So, one selection method of initial modes is developed, in this paper, aiming at improving the performances of the BKM approach. Experiments with several sets of real data show that by considered the developed selection initial modes method, the clustering algorithm produces more accurate results.

Keywords: Clustering, Uncertainty, Belief function theory, Belief K-modes Method, Initial modes selection.

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8441 Variational Iteration Method for Solving Systems of Linear Delay Differential Equations

Authors: Sara Barati, Karim Ivaz

Abstract:

In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.

Keywords: Variational iteration method, delay differential equations, multiple delays, Runge-Kutta method.

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8440 Comparison of Finite-Element and IEC Methods for Cable Thermal Analysis under Various Operating Environments

Authors: M. S. Baazzim, M. S. Al-Saud, M. A. El-Kady

Abstract:

In this paper, steady-state ampacity (current carrying capacity) evaluation of underground power cable system by using analytical and numerical methods for different conditions (depth of cable, spacing between phases, soil thermal resistivity, ambient temperature, wind speed), for two system voltage level were used 132 and 380 kV. The analytical method or traditional method that was used is based on the thermal analysis method developed by Neher-McGrath and further enhanced by International Electrotechnical Commission (IEC) and published in standard IEC 60287. The numerical method that was used is finite element method and it was recourse commercial software based on finite element method. 

Keywords: Cable ampacity, Finite element method, underground cable, thermal rating.

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8439 Numerical Solution of Linear Ordinary Differential Equations in Quantum Chemistry by Clenshaw Method

Authors: M. Saravi, F. Ashrafi, S.R. Mirrajei

Abstract:

As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.

Keywords: Chebyshev polynomials, Clenshaw method, ODEs, Spectral methods

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8438 Application of Homotopy Perturbation Method to Solve Steady Flow of Walter B Fluid A Vertical Channel In Porous Media

Authors: A.Memari

Abstract:

In this article, a simulation method called the Homotopy Perturbation Method (HPM) is employed in the steady flow of a Walter's B' fluid in a vertical channel with porous wall. We employed Homotopy Perturbation Method to derive solution of a nonlinear form of equation obtained from exerting similarity transforming to the ordinary differential equation gained from continuity and momentum equations of this kind of flow. The results obtained from the Homotopy Perturbation Method are then compared with those from the Runge–Kutta method in order to verify the accuracy of the proposed method. The results show that the Homotopy Perturbation Method can achieve good results in predicting the solution of such problems. Ultimately we use this solution to obtain the other terms of velocities and physical discussion about it.

Keywords: Steady flow; Walter's B' Fluid;, vertical channel;porous media, Homotopy Perturbation Method (HPM), Numerical Solution (NS).

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8437 Realtime Lip Contour Tracking For Audio-Visual Speech Recognition Applications

Authors: Mehran Yazdi, Mehdi Seyfi, Amirhossein Rafati, Meghdad Asadi

Abstract:

Detection and tracking of the lip contour is an important issue in speechreading. While there are solutions for lip tracking once a good contour initialization in the first frame is available, the problem of finding such a good initialization is not yet solved automatically, but done manually. We have developed a new tracking solution for lip contour detection using only few landmarks (15 to 25) and applying the well known Active Shape Models (ASM). The proposed method is a new LMS-like adaptive scheme based on an Auto regressive (AR) model that has been fit on the landmark variations in successive video frames. Moreover, we propose an extra motion compensation model to address more general cases in lip tracking. Computer simulations demonstrate a fair match between the true and the estimated spatial pixels. Significant improvements related to the well known LMS approach has been obtained via a defined Frobenius norm index.

Keywords: Lip contour, Tracking, LMS-Like

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8436 An E-learning System Architecture based on Cloud Computing

Authors: Md. Anwar Hossain Masud, Xiaodi Huang

Abstract:

The massive proliferation of affordable computers, Internet broadband connectivity and rich education content has created a global phenomenon in which information and communication technology (ICT) is being used to transform education. Therefore, there is a need to redesign the educational system to meet the needs better. The advent of computers with sophisticated software has made it possible to solve many complex problems very fast and at a lower cost. This paper introduces the characteristics of the current E-Learning and then analyses the concept of cloud computing and describes the architecture of cloud computing platform by combining the features of E-Learning. The authors have tried to introduce cloud computing to e-learning, build an e-learning cloud, and make an active research and exploration for it from the following aspects: architecture, construction method and external interface with the model.

Keywords: Architecture, Cloud Computing, E-learning, Information Technology

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8435 Green, Smooth and Easy Electrochemical Synthesis of N-Protected Indole Derivatives

Authors: Sarah Fahad Alajmi, Tamer Ezzat Youssef

Abstract:

Here, we report a simple method for the direct conversion of 6-Nitro-1H-indole into N-substituted indoles via electrochemical dehydrogenative reaction with halogenated reagents under strongly basic conditions through N–R bond formation. The N-protected indoles have been prepared under moderate and scalable electrolytic conditions. The conduct of the reactions was performed in a simple divided cell under constant current without oxidizing reagents or transition-metal catalysts. The synthesized products have been characterized via UV/Vis spectrophotometry, 1H-NMR, and FTIR spectroscopy. A possible reaction mechanism is discussed based on the N-protective products. This methodology could be applied to the synthesis of various biologically active N-substituted indole derivatives.

Keywords: Green chemistry, 1H-indole, NH-containing heteroaromatic, organic electrosynthesis.

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8434 Texture Feature Extraction of Infrared River Ice Images using Second-Order Spatial Statistics

Authors: Bharathi P. T, P. Subashini

Abstract:

Ice cover County has a significant impact on rivers as it affects with the ice melting capacity which results in flooding, restrict navigation, modify the ecosystem and microclimate. River ices are made up of different ice types with varying ice thickness, so surveillance of river ice plays an important role. River ice types are captured using infrared imaging camera which captures the images even during the night times. In this paper the river ice infrared texture images are analysed using first-order statistical methods and secondorder statistical methods. The second order statistical methods considered are spatial gray level dependence method, gray level run length method and gray level difference method. The performance of the feature extraction methods are evaluated by using Probabilistic Neural Network classifier and it is found that the first-order statistical method and second-order statistical method yields low accuracy. So the features extracted from the first-order statistical method and second-order statistical method are combined and it is observed that the result of these combined features (First order statistical method + gray level run length method) provides higher accuracy when compared with the features from the first-order statistical method and second-order statistical method alone.

Keywords: Gray Level Difference Method, Gray Level Run Length Method, Kurtosis, Probabilistic Neural Network, Skewness, Spatial Gray Level Dependence Method.

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8433 A Method for Improving the Embedded Runge Kutta Fehlberg 4(5)

Authors: Sunyoung Bu, Wonkyu Chung, Philsu Kim

Abstract:

In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.

Keywords: Embedded Runge-Kutta-Fehlberg method, Initial value problem.

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