Search results for: Complex finite strip
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3075

Search results for: Complex finite strip

1935 Optimization of Technical and Technological Solutions for the Development of Offshore Hydrocarbon Fields in the Kaliningrad Region

Authors: Pavel Shcherban, Viktoria Ivanova, Alexander Neprokin, Vladislav Golovanov

Abstract:

Currently, LLC «Lukoil-Kaliningradmorneft» is implementing a comprehensive program for the development of offshore fields of the Kaliningrad region. This is largely associated with the depletion of the resource base of land in the region, as well as the positive results of geological investigation surrounding the Baltic Sea area and the data on the volume of hydrocarbon recovery from a single offshore field are working on the Kaliningrad region – D-6 «Kravtsovskoye».The article analyzes the main stages of the LLC «Lukoil-Kaliningradmorneft»’s development program for the development of the hydrocarbon resources of the region's shelf and suggests an optimization algorithm that allows managing a multi-criteria process of development of shelf deposits. The algorithm is formed on the basis of the problem of sequential decision making, which is a section of dynamic programming. Application of the algorithm during the consolidation of the initial data, the elaboration of project documentation, the further exploration and development of offshore fields will allow to optimize the complex of technical and technological solutions and increase the economic efficiency of the field development project implemented by LLC «Lukoil-Kaliningradmorneft».

Keywords: Offshore fields of hydrocarbons of the Baltic Sea, Development of offshore oil and gas fields, Optimization of the field development scheme, Solution of multi-criteria tasks in the oil and gas complex, Quality management of technical and technological processes.

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1934 A Comparison of Some Splines-Based Methods for the One-dimensional Heat Equation

Authors: Joan Goh, Ahmad Abd. Majid, Ahmad Izani Md. Ismail

Abstract:

In this paper, collocation based cubic B-spline and extended cubic uniform B-spline method are considered for solving one-dimensional heat equation with a nonlocal initial condition. Finite difference and θ-weighted scheme is used for time and space discretization respectively. The stability of the method is analyzed by the Von Neumann method. Accuracy of the methods is illustrated with an example. The numerical results are obtained and compared with the analytical solutions.

Keywords: Heat equation, Collocation based, Cubic Bspline, Extended cubic uniform B-spline.

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1933 Numerical Study of Flow around Flat Tube between Parallel Walls

Authors: Hamidreza Bayat, Arash Mirabdolah Lavasani, Meysam Bolhasani, Sajad Moosavi

Abstract:

Flow around a flat tube is studied numerically. Reynolds number is defined base on equivalent circular tube and it is varied in range of 100 to 300. Equations are solved by using finite volume method and results are presented in form of drag and lift coefficient. Results show that drag coefficient of flat tube is up to 66% lower than circular tube with equivalent diameter. In addition, by increasing l/D from 1 to 2, the drag coefficient of flat tube is decreased about 14-27%.

Keywords: Laminar flow, flat-tube, drag coefficient, cross-flow, heat exchanger.

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1932 Per Flow Packet Scheduling Scheme to Improve the End-to-End Fairness in Mobile Ad Hoc Wireless Network

Authors: K. Sasikala, R. S. D Wahidabanu

Abstract:

Various fairness models and criteria proposed by academia and industries for wired networks can be applied for ad hoc wireless network. The end-to-end fairness in an ad hoc wireless network is a challenging task compared to wired networks, which has not been addressed effectively. Most of the traffic in an ad hoc network are transport layer flows and thus the fairness of transport layer flows has attracted the interest of the researchers. The factors such as MAC protocol, routing protocol, the length of a route, buffer size, active queue management algorithm and the congestion control algorithms affects the fairness of transport layer flows. In this paper, we have considered the rate of data transmission, the queue management and packet scheduling technique. The ad hoc network is dynamic in nature due to various parameters such as transmission of control packets, multihop nature of forwarding packets, changes in source and destination nodes, changes in the routing path influences determining throughput and fairness among the concurrent flows. In addition, the effect of interaction between the protocol in the data link and transport layers has also plays a role in determining the rate of the data transmission. We maintain queue for each flow and the delay information of each flow is maintained accordingly. The pre-processing of flow is done up to the network layer only. The source and destination address information is used for separating the flow and the transport layer information is not used. This minimizes the delay in the network. Each flow is attached to a timer and is updated dynamically. Finite State Machine (FSM) is proposed for queue and transmission control mechanism. The performance of the proposed approach is evaluated in ns-2 simulation environment. The throughput and fairness based on mobility for different flows used as performance metrics. We have compared the performance of the proposed approach with ATP and the transport layer information is used. This minimizes the delay in the network. Each flow is attached to a timer and is updated dynamically. Finite State Machine (FSM) is proposed for queue and transmission control mechanism. The performance of the proposed approach is evaluated in ns-2 simulation environment. The throughput and fairness based on not mobility for different flows used as performance metrics. We have compared the performance of the proposed approach with ATP and MC-MLAS and the performance of the proposed approach is encouraging.

Keywords: ATP, End-to-End fairness, FSM, MAC, QoS.

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1931 Viscoelastic Modeling of Brain MRE Data Using FE Method

Authors: H. Ajabi Naeeni, M. Haghpanahi

Abstract:

Dynamic shear test on simulated phantom can be used to validate magnetic resonance elastography (MRE) measurements. Phantom gel has been usually utilized for the cell culture of cartilage and soft tissue and also been used for mechanical property characterization using imaging systems. The viscoelastic property of the phantom would be important for dynamic experiments and analyses. In this study, An axisymmetric FE model is presented for determining the dynamic shear behaviour of brain simulated phantom using ABAQUS. The main objective of this study was to investigate the effect of excitation frequencies and boundary conditions on shear modulus and shear viscosity in viscoelastic media.

Keywords: Viscoelastic, MR Elastography, Finite Element, Brain.

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1930 Optimizing the Design of Radial/Axial PMSM and SRM used for Powered Wheel-Chairs

Authors: D. Fodorean, D.C. Popa, F. Jurca, M. Ruba

Abstract:

the paper presents the optimization results for several electrical machines dedicated for powered electric wheel-chairs. The optimization, using the Hook-Jeeves algorithm, was employed based on a design approach which takes into consideration the road conditions. Also, through numerical simulations (based on finite element method), the analytical approach was validated. The optimization approach gave satisfactory results and the best suited variant was chosen for the motorization of the wheel-chair.

Keywords: electrical machines, numerical validation, optimization, electric wheel chair.

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1929 Retrospective Reconstruction of Time Series Data for Integrated Waste Management

Authors: A. Buruzs, M. F. Hatwágner, A. Torma, L. T. Kóczy

Abstract:

The development, operation and maintenance of Integrated Waste Management Systems (IWMS) affects essentially the sustainable concern of every region. The features of such systems have great influence on all of the components of sustainability. In order to reach the optimal way of processes, a comprehensive mapping of the variables affecting the future efficiency of the system is needed such as analysis of the interconnections among the components and modeling of their interactions. The planning of a IWMS is based fundamentally on technical and economical opportunities and the legal framework. Modeling the sustainability and operation effectiveness of a certain IWMS is not in the scope of the present research. The complexity of the systems and the large number of the variables require the utilization of a complex approach to model the outcomes and future risks. This complex method should be able to evaluate the logical framework of the factors composing the system and the interconnections between them. The authors of this paper studied the usability of the Fuzzy Cognitive Map (FCM) approach modeling the future operation of IWMS’s. The approach requires two input data set. One is the connection matrix containing all the factors affecting the system in focus with all the interconnections. The other input data set is the time series, a retrospective reconstruction of the weights and roles of the factors. This paper introduces a novel method to develop time series by content analysis.

Keywords: Content analysis, factors, integrated waste management system, time series.

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1928 Positive Solutions of Initial Value Problem for the Systems of Second Order Integro-Differential Equations in Banach Space

Authors: Lv Yuhua

Abstract:

In this paper, by establishing a new comparison result, we investigate the existence of positive solutions for initial value problems of nonlinear systems of second order integro-differential equations in Banach space.We improve and generalize some results  (see[5,6]), and the results is new even in finite dimensional spaces.

Keywords: Systems of integro-differential equations, monotone iterative method, comparison result, cone.

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1927 A Numerical Model for Studying Convectional Lifting Processes in the Tropics

Authors: Chantawan Noisri, Robert Harold Buchanan Exell

Abstract:

A simple model for studying convectional lifting processes in the tropics is described in this paper with some tests of the model in dry air. The model consists of the density equation, the wind equation, the vertical velocity equation, and the temperature equation. The model domain is two-dimensional with length 100 km and height 17.5 km. Plan for experiments to investigate the effects of the heating surface, the deep convection approximation and the treatment of velocities at the boundaries are discussed. Equations for the simplified treatment of moisture in the atmosphere in future numerical experiments are also given.

Keywords: Numerical weather prediction, Finite differences, Convection lifting.

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1926 Development of Blower for Air Management System of Fuel Cell Modules

Authors: Joo-Han Kim, Jung-Moo Seo, Ha Gyeong Sung, Se Hyun Rhyu

Abstract:

This study presents a blower for air management system of fuel cell modules. A blower is composed of BLDC motor and impeller. Magnetic equivalent circuit model and finite element analysis are used to design the motor, and an improved structure is considered to reduce a mechanical loss induced from bearing units. Finally, air blower system combined with the motor and an impeller is manufactured and output properties, such as an air pressure and an amount of flowing air, are measured. Through the experimental results, a validity of the simulated one is confirmed.

Keywords: Fuel cell modules, BLDC motor, Impeller, Air management

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1925 Magnetohydrodynamic Mixed Convective Flow in a Cavity

Authors: R.YadollahiFarsani, B. Ghasemi

Abstract:

A magnetohydrodynamic mixed convective flow in a cavity was studied in this paper. The lower surface of cavity was heated from below whereas other walls of the cavity were thermally isolated. The governing two-dimensional flow equations have been solved by using finite volume code. The effects of magnetic field were studied on flow and temperature field and heat transfer performance at a wide range of parameters, Such as Hartmann (0≤Ha≤100) and Reynolds (1≤Re≤100) numbers. The results showed that as Hartman number increases the Nusselt number, representing heat transfer from the cavity decreases.

Keywords: Cavity, Magnetic Field, Mixed Convection, Magnetohydrodynamic

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1924 An Alternative Proof for the Topological Entropy of the Motzkin Shift

Authors: Fahad Alsharari, Mohd Salmi Md Noorani

Abstract:

A Motzkin shift is a mathematical model for constraints on genetic sequences. In terms of the theory of symbolic dynamics, the Motzkin shift is nonsofic, and therefore, we cannot use the Perron- Frobenius theory to calculate its topological entropy. The Motzkin shift M(M,N) which comes from language theory, is defined to be the shift system over an alphabet A that consists of N negative symbols, N positive symbols and M neutral symbols. For an x in the full shift, x will be in the Motzkin subshift M(M,N) if and only if every finite block appearing in x has a non-zero reduced form. Therefore, the constraint for x cannot be bounded in length. K. Inoue has shown that the entropy of the Motzkin shift M(M,N) is log(M + N + 1). In this paper, a new direct method of calculating the topological entropy of the Motzkin shift is given without any measure theoretical discussion.

Keywords: Motzkin shift, topological entropy.

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1923 Seismic Behavior of Thin Shear Wall under the Exerted Loads

Authors: Ali A. Ofoghi

Abstract:

While the shear walls are not economical in buildings, thin shear walls are widely used in the buildings. In the present study, the ratio of different loads to their plasticity and seismic behavior of the wall under different loads have been investigated. Modeling and analysis are carried out by the finite element analysis software ABAQUS. The results show that any increase in the exerted loads will have adverse effects on the seismic behavior of the thin shear walls and causes the wall to collapse by small displacements.

Keywords: Thin shear wall, nonlinear dynamic analysis, reinforced concrete, plasticity.

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1922 A New Self-stabilizing Algorithm for Maximal 2-packing

Authors: Zhengnan Shi

Abstract:

In the self-stabilizing algorithmic paradigm, each node has a local view of the system, in a finite amount of time the system converges to a global state with desired property. In a graph G = (V, E), a subset S C V is a 2-packing if Vi c V: IN[i] n SI <1. In this paper, an ID-based, constant space, self-stabilizing algorithm that stabilizes to a maximal 2-packing in an arbitrary graph is proposed. It is shown that the algorithm stabilizes in 0(n3) moves under any scheduler (daemon). Specifically, it is shown that the algorithm stabilizes in linear time-steps under a synchronous daemon where every privileged node moves at each time-step.

Keywords: self-stabilization, 2-packing, distributed computing, fault tolerance, graph algorithms

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1921 Expert Based System Design for Integrated Waste Management

Authors: A. Buruzs, M. F. Hatwágner, A. Torma, L. T. Kóczy

Abstract:

Recently, an increasing number of researchers have been focusing on working out realistic solutions to sustainability problems. As sustainability issues gain higher importance for organisations, the management of such decisions becomes critical. Knowledge representation is a fundamental issue of complex knowledge based systems. Many types of sustainability problems would benefit from models based on experts’ knowledge. Cognitive maps have been used for analyzing and aiding decision making. A cognitive map can be made of almost any system or problem. A fuzzy cognitive map (FCM) can successfully represent knowledge and human experience, introducing concepts to represent the essential elements and the cause and effect relationships among the concepts to model the behaviour of any system. Integrated waste management systems (IWMS) are complex systems that can be decomposed to non-related and related subsystems and elements, where many factors have to be taken into consideration that may be complementary, contradictory, and competitive; these factors influence each other and determine the overall decision process of the system. The goal of the present paper is to construct an efficient IWMS which considers various factors. The authors’ intention is to propose an expert based system design approach for implementing expert decision support in the area of IWMSs and introduces an appropriate methodology for the development and analysis of group FCM. A framework for such a methodology consisting of the development and application phases is presented.

Keywords: Factors, fuzzy cognitive map, group decision, integrated waste management system.

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1920 Multi-fidelity Fluid-Structure Interaction Analysis of a Membrane Wing

Authors: M. Saeedi, R. Wuchner, K.-U. Bletzinger

Abstract:

In order to study the aerodynamic performance of a semi-flexible membrane wing, Fluid-Structure Interaction simulations have been performed. The fluid problem has been modeled using two different approaches which are the vortex panel method and the numerical solution of the Navier-Stokes equations. Nonlinear analysis of the structural problem is performed using the Finite Element Method. Comparison between the two fluid solvers has been made. Aerodynamic performance of the wing is discussed regarding its lift and drag coefficients and they are compared with those of the equivalent rigid wing.

Keywords: CFD, FSI, Membrane wing, Vortex panel method.

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1919 Simulated Annealing Application for Structural Optimization

Authors: Farhad Kolahan, M. Hossein Abolbashari, Samaeddin Mohitzadeh

Abstract:

Several methods are available for weight and shape optimization of structures, among which Evolutionary Structural Optimization (ESO) is one of the most widely used methods. In ESO, however, the optimization criterion is completely case-dependent. Moreover, only the improving solutions are accepted during the search. In this paper a Simulated Annealing (SA) algorithm is used for structural optimization problem. This algorithm differs from other random search methods by accepting non-improving solutions. The implementation of SA algorithm is done through reducing the number of finite element analyses (function evaluations). Computational results show that SA can efficiently and effectively solve such optimization problems within short search time.

Keywords: Simulated annealing, Structural optimization, Compliance, C.V. product.

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1918 Cooling of Fresh Vegetable Farm Produce: Experimental and Numerical Studies

Authors: Hala Yassine, Hervé Noel, Pascal Le Bideau, Patrick Glouannec

Abstract:

Following harvest, fresh produce needs to be cooled immediately in a room where the air temperature and the relative air humidity are controlled to maintain the produce quality. In this paper, an experimental study for forced air cooling of fresh produce (cauliflower) is performed using a pilot developed within our laboratory. Furthermore, a numerical simulation of spherical produces, taking into account the aerodynamic aspect and also the heat transfer in the produce and in the air, was carried out using a finite element method. At the end of this communication, experimental results are presented and compared with the simulation.

Keywords: Cauliflower, Forced air cooling, Heat transfer, Numerical model, Tunnel of air.

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1917 Performance Comparison of Different Regression Methods for a Polymerization Process with Adaptive Sampling

Authors: Florin Leon, Silvia Curteanu

Abstract:

Developing complete mechanistic models for polymerization reactors is not easy, because complex reactions occur simultaneously; there is a large number of kinetic parameters involved and sometimes the chemical and physical phenomena for mixtures involving polymers are poorly understood. To overcome these difficulties, empirical models based on sampled data can be used instead, namely regression methods typical of machine learning field. They have the ability to learn the trends of a process without any knowledge about its particular physical and chemical laws. Therefore, they are useful for modeling complex processes, such as the free radical polymerization of methyl methacrylate achieved in a batch bulk process. The goal is to generate accurate predictions of monomer conversion, numerical average molecular weight and gravimetrical average molecular weight. This process is associated with non-linear gel and glass effects. For this purpose, an adaptive sampling technique is presented, which can select more samples around the regions where the values have a higher variation. Several machine learning methods are used for the modeling and their performance is compared: support vector machines, k-nearest neighbor, k-nearest neighbor and random forest, as well as an original algorithm, large margin nearest neighbor regression. The suggested method provides very good results compared to the other well-known regression algorithms.

Keywords: Adaptive sampling, batch bulk methyl methacrylate polymerization, large margin nearest neighbor regression, machine learning.

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1916 Study the Behavior of Different Composite Short Columns (DST) with Prismatic Sections under Bending Load

Authors: V. Sadeghi Balkanlou, M. Reza Bagerzadeh Karimi, A. Hasanbakloo, B. Bagheri Azar

Abstract:

In this paper, the behavior of different types of DST columns has been studied under bending load. Briefly, composite columns consist of an internal carbon steel tube and an external stainless steel wall that the between the walls are filled with concrete. Composite columns are expected to combine the advantages of all three materials and have the advantage of high flexural stiffness of CFDST columns. In this research, ABAQUS software is used for finite element analysis then the results of ultimate strength of the composite sections are illustrated.

Keywords: DST, Stainless steel, carbon steel, ABAQUS, Straigh Columns, Tapered Columns.

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1915 Effect of Band Contact on the Temperature Distribution for Dry Friction Clutch

Authors: Oday I. Abdullah, J. Schlattmann

Abstract:

In this study, the two dimensional heat conduction problem for the dry friction clutch disc is modeled mathematically analysis and is solved numerically using finite element method, to determine the temperature field when band contacts occurs between the rubbing surfaces during the operation of an automotive clutch. Temperature calculation have been made for contact area of different band width and the results obtained compared with these attained when complete contact occurs. Furthermore, the effects of slipping time and sliding velocity function are investigated as well. Both single and repeated engagements made at regular interval are considered.

Keywords: Band contact, dry friction clutch, frictional heating, temperature field, 2D FEM.

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1914 Absorption Spectra of Artificial Atoms in Presence of THz Fields

Authors: B. Dahiya, K.Batra, V.Prasad

Abstract:

Artificial atoms are growing fields of interest due to their physical and optoelectronicapplications. The absorption spectra of the proposed artificial atom inpresence of Tera-Hertz field is investigated theoretically. We use the non-perturbativeFloquet theory and finite difference method to study the electronic structure of ArtificialAtom. The effect of static electric field on the energy levels of artificial atom is studied.The effect of orientation of static electric field on energy levels and diploe matrix elementsis also highlighted.

Keywords: Absorption spectra, Artificial atom, Floquet Theory, THz fields

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1913 Investigating the Capacity of Ultimate Torsion of Concrete Prismatic Beams with Transverse Spiral Bars

Authors: Hadi Barghlame, M. A. Lotfollahi-Yaghin

Abstract:

In this paper, the torsion capacity of ultimate point on rectangular beams with spiral reinforcements in the torsion direction and its anti-direction are investigated. Therefore, models of above-mentioned beams have been numerically analyzed under various loads using ANSYS software. It was observed that, spirallyreinforced prismatic beam and beam with spiral links, show lower torsion capacity than beam with normal links also in anti-direction. The result is that the concrete regulations are violated in this case.

Keywords: RC beam, ultimate torsion, finite element, prismatic beams, spirally tie.

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1912 Analysis and Preservation of Lime-Kilns in Corsica

Authors: A. Papalou, K. Vozikis

Abstract:

The aim of this paper is the analysis and preservation of lime kilns, focusing on the structure, construction, and functionality of vertical shaft lime kilns of the Cap Corse in Corsica. Plans and sections of two lime kilns are presented in detail, providing an overall picture of this specific industrial heritage. The potential damage areas are identified performing structural analysis of a lime kiln using the finite element method. A restoration and strengthening technique that satisfies the directions of the Charter of Venice is presented using post-tensioning tendons. Recommendations are given to preserve and promote these important historical structures integrating them into the custom footpath.

Keywords: industrial heritage, lime kilns, post-tensioning, preservation

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1911 Back Analysis of Tehran Metro Tunnel Construction Using FLAC-3D

Authors: M. Mahdi, N. Shariatmadari

Abstract:

An important aspect of planning for shallow tunneling under urban areas is the determination of likely surface movements and interaction with existing structures. Back analysis of built tunnels that their settlements magnitude is available, could aid the designers to have a more accuracy in future projects.

In this paper, one single Tehran Metro Tunnel (at west of Hor square, Jang University Street) was selected. At first, surface settlements of this tunnel were measured in situ. Then this tunnel was modeled using the commercial finite deference software FLAC-3D. Finally, Results of modeling and in situ measurements compared for verification.

Keywords: Shallow Tunnel, Back Analysis, Surface Movement, Numerical Modeling.

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1910 Numerical Modelling of Crack Initiation around a Wellbore Due to Explosion

Authors: Meysam Lak, Mohammad Fatehi Marji, Alireza Yarahamdi Bafghi, Abolfazl Abdollahipour

Abstract:

A wellbore is a hole that is drilled to aid in the exploration and recovery of natural resources including oil and gas. Occasionally, in order to increase productivity index and porosity of the wellbore and reservoir, the well stimulation methods have been used. Hydraulic fracturing is one of these methods. Moreover, several explosions at the end of the well can stimulate the reservoir and create fractures around it. In this study, crack initiation in rock around the wellbore has been numerically modeled due to explosion. One, two, three, and four pairs of explosion have been set at the end of the wellbore on its wall. After each stage of the explosion, results have been presented and discussed. Results show that this method can initiate and probably propagate several fractures around the wellbore.

Keywords: Crack initiation, explosion, finite difference modelling, well productivity.

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1909 A Novel Hopfield Neural Network for Perfect Calculation of Magnetic Resonance Spectroscopy

Authors: Hazem M. El-Bakry

Abstract:

In this paper, an automatic determination algorithm for nuclear magnetic resonance (NMR) spectra of the metabolites in the living body by magnetic resonance spectroscopy (MRS) without human intervention or complicated calculations is presented. In such method, the problem of NMR spectrum determination is transformed into the determination of the parameters of a mathematical model of the NMR signal. To calculate these parameters efficiently, a new model called modified Hopfield neural network is designed. The main achievement of this paper over the work in literature [30] is that the speed of the modified Hopfield neural network is accelerated. This is done by applying cross correlation in the frequency domain between the input values and the input weights. The modified Hopfield neural network can accomplish complex dignals perfectly with out any additinal computation steps. This is a valuable advantage as NMR signals are complex-valued. In addition, a technique called “modified sequential extension of section (MSES)" that takes into account the damping rate of the NMR signal is developed to be faster than that presented in [30]. Simulation results show that the calculation precision of the spectrum improves when MSES is used along with the neural network. Furthermore, MSES is found to reduce the local minimum problem in Hopfield neural networks. Moreover, the performance of the proposed method is evaluated and there is no effect on the performance of calculations when using the modified Hopfield neural networks.

Keywords: Hopfield Neural Networks, Cross Correlation, Nuclear Magnetic Resonance, Magnetic Resonance Spectroscopy, Fast Fourier Transform.

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1908 Photonic Crystal Waveguide 1x3 Flexible Power Splitter for Optical Network

Authors: Jyothi Digge, B. U. Rindhe, S. K. Narayankhedkar

Abstract:

A compact 1x3 power splitter based on Photonic Crystal Waveguides (PCW) with flexible power splitting ratio is presented in this paper. Multimode interference coupler (MMI) is integrated with PCW. The device size reduction compared with the conventional MMI power splitter is attributed to the large dispersion of the PCW. Band Solve tool is used to calculate the band structure of PCW. Finite Difference Time Domain (FDTD) method is adopted to simulate the relevant structure at 1550nm wavelength. The device is polarization insensitive and allows the control of output (o/p) powers within certain percentage points for both polarizations.

Keywords: Dispersion, MMI Coupler, Photonic Bandgap, Power Splitter.

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1907 Developing Proof Demonstration Skills in Teaching Mathematics in the Secondary School

Authors: M. Rodionov, Z. Dedovets

Abstract:

The article describes the theoretical concept of teaching secondary school students proof demonstration skills in mathematics. It describes in detail different levels of mastery of the concept of proof-which correspond to Piaget’s idea of there being three distinct and progressively more complex stages in the development of human reflection. Lessons for each level contain a specific combination of the visual-figurative components and deductive reasoning. It is vital at the transition point between levels to carefully and rigorously recalibrate teaching to reflect the development of more complex reflective understanding. This can apply even within the same age range, since students will develop at different speeds and to different potential. The authors argue that this requires an aware and adaptive approach to lessons to reflect this complexity and variation. The authors also contend that effective teaching which enables students to properly understand the implementation of proof arguments must develop specific competences. These are: understanding of the importance of completeness and generality in making a valid argument; being task focused; having an internalised locus of control and being flexible in approach and evaluation. These criteria must be correlated with the systematic application of corresponding methodologies which are best likely to achieve success. The particular pedagogical decisions which are made to deliver this objective are illustrated by concrete examples from the existing secondary school mathematics courses. The proposed theoretical concept formed the basis of the development of methodological materials which have been tested in 47 secondary schools.

Keywords: Education, teaching of mathematics, proof, deductive reasoning, secondary school.

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1906 Fixed Point of Lipschitz Quasi Nonexpansive Mappings

Authors: M. Moosavi, H. Khatibzadeh

Abstract:

In this article, we study demiclosed and strongly quasi-nonexpansive of a sequence generated by the proximal point algorithm for a finite family of quasi-nonexpansive mappings in Hadamard spaces. Δ-convergence of iterations for the sequence of strongly quasi-nonexpansive mappings as well as the strong convergence of the Halpern type regularization of them to a common fixed point of sequence are also established. Our results generalize and improve several previously known results of the existing literature.

Keywords: Fixed point, Hadamard space, proximal point algorithm, quasi-nonexpansive sequence of mappings, resolvent.

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