Search results for: Mohammad Tahaye Abadi
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 587

Search results for: Mohammad Tahaye Abadi

587 Influence of Fiber Packing on Transverse Plastic Properties of Metal Matrix Composites

Authors: Mohammad Tahaye Abadi

Abstract:

The present paper concerns with the influence of fiber packing on the transverse plastic properties of metal matrix composites. A micromechanical modeling procedure is used to predict the effective mechanical properties of composite materials at large tensile and compressive deformations. Microstructure is represented by a repeating unit cell (RUC). Two fiber arrays are considered including ideal square fiber packing and random fiber packing defined by random sequential algorithm. The micromechanical modeling procedure is implemented for graphite/aluminum metal matrix composite in which the reinforcement behaves as elastic, isotropic solids and the matrix is modeled as an isotropic elastic-plastic solid following the von Mises criterion with isotropic hardening and the Ramberg-Osgood relationship between equivalent true stress and logarithmic strain. The deformation is increased to a considerable value to evaluate both elastic and plastic behaviors of metal matrix composites. The yields strength and true elastic-plastic stress are determined for graphite/aluminum composites.

Keywords: Fiber packing, metal matrix composites, micromechanics, plastic deformation, random

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586 Extend Three-wave Method for the (3+1)-Dimensional Soliton Equation

Authors: Somayeh Arbabi Mohammad-Abadi, Maliheh Najafi

Abstract:

In this paper, we study (3+1)-dimensional Soliton equation. We employ the Hirota-s bilinear method to obtain the bilinear form of (3+1)-dimensional Soliton equation. Then by the idea of extended three-wave method, some exact soliton solutions including breather type solutions are presented.

Keywords: Three-wave method, (3+1)-dimensional Soliton equation, Hirota's bilinear form.

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585 A Family of Affine Projection Adaptive Filtering Algorithms With Selective Regressors

Authors: Mohammad Shams Esfand Abadi, Nader Hadizadeh Kashani, Vahid Mehrdad

Abstract:

In this paper we present a general formalism for the establishment of the family of selective regressor affine projection algorithms (SR-APA). The SR-APA, the SR regularized APA (SR-RAPA), the SR partial rank algorithm (SR-PRA), the SR binormalized data reusing least mean squares (SR-BNDR-LMS), and the SR normalized LMS with orthogonal correction factors (SR-NLMS-OCF) algorithms are established by this general formalism. We demonstrate the performance of the presented algorithms through simulations in acoustic echo cancellation scenario.

Keywords: Adaptive filter, affine projection, selective regressor.

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584 Mean-Square Performance of Adaptive Filter Algorithms in Nonstationary Environments

Authors: Mohammad Shams Esfand Abadi, John Hakon Husøy

Abstract:

Employing a recently introduced unified adaptive filter theory, we show how the performance of a large number of important adaptive filter algorithms can be predicted within a general framework in nonstationary environment. This approach is based on energy conservation arguments and does not need to assume a Gaussian or white distribution for the regressors. This general performance analysis can be used to evaluate the mean square performance of the Least Mean Square (LMS) algorithm, its normalized version (NLMS), the family of Affine Projection Algorithms (APA), the Recursive Least Squares (RLS), the Data-Reusing LMS (DR-LMS), its normalized version (NDR-LMS), the Block Least Mean Squares (BLMS), the Block Normalized LMS (BNLMS), the Transform Domain Adaptive Filters (TDAF) and the Subband Adaptive Filters (SAF) in nonstationary environment. Also, we establish the general expressions for the steady-state excess mean square in this environment for all these adaptive algorithms. Finally, we demonstrate through simulations that these results are useful in predicting the adaptive filter performance.

Keywords: Adaptive filter, general framework, energy conservation, mean-square performance, nonstationary environment.

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583 Advances on LuGre Friction Model

Authors: Mohammad Fuad Mohammad Naser, Faycal Ikhouane

Abstract:

LuGre friction model is an ordinary differential equation that is widely used in describing the friction phenomenon for mechanical systems. The importance of this model comes from the fact that it captures most of the friction behavior that has been observed including hysteresis. In this paper, we study some aspects related to the hysteresis behavior induced by the LuGre friction model.

Keywords: Hysteresis, LuGre model, operator, (strong) consistency.

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582 Adaptive Car Safety System

Authors: Shahram Jafari, Mohammad-Ali Nikouei Mahani, Mohammad Arabnezhad, Mahdi Sharifi

Abstract:

Car accident is one of the major causes of death in many countries. Many researchers have attempted to design and develop techniques to increase car safety in the past recent years. In spite of all the efforts, it is still challenging to design a system adaptive to the driver rather than the automotive characteristics. In this paper, the adaptive car safety system is explained which attempts to find a balance.

Keywords: Analog to Digital Converter (ADC), AdaptiveCar Safety System, Multi-Media Card (MMC).

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581 New Exact Solutions for the (3+1)-Dimensional Breaking Soliton Equation

Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

Abstract:

In this work, we obtain some analytic solutions for the (3+1)-dimensional breaking soliton after obtaining its Hirota-s bilinear form. Our calculations show that, three-wave method is very easy and straightforward to solve nonlinear partial differential equations.

Keywords: (3+1)-dimensional breaking soliton equation, Hirota'sbilinear form.

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580 Some Complexiton Type Solutions of the (3+1)-Dimensional Jimbo-Miwa Equation

Authors: Mohammad Taghi Darvishi, Mohammad Najafi

Abstract:

By means of the extended homoclinic test approach (shortly EHTA) with the aid of a symbolic computation system such as Maple, some complexiton type solutions for the (3+1)-dimensional Jimbo-Miwa equation are presented.

Keywords: Jimbo-Miwa equation, painleve analysis, Hirota's bilinear form, computerized symbolic computation.

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579 New Application of EHTA for the Generalized(2+1)-Dimensional Nonlinear Evolution Equations

Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

Abstract:

In this paper, the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (shortly CBS) equations are investigated. We employ the Hirota-s bilinear method to obtain the bilinear form of CBS equations. Then by the idea of extended homoclinic test approach (shortly EHTA), some exact soliton solutions including breather type solutions are presented.

Keywords: EHTA, (2+1)-dimensional CBS equations, (2+1)-dimensional breaking solution equation, Hirota's bilinear form.

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578 Analysis of Creative City Indicators in Isfahan City, Iran

Authors: Reza Mokhtari Malek Abadi, Mohsen Saghaei, Fatima Iman

Abstract:

This paper investigates the indices of a creative city in Isfahan. Its main aim is to evaluate quantitative status of the creative city indices in Isfahan city, analyze the dispersion and distribution of these indices in Isfahan city. Concerning these, this study tries to analyze the creative city indices in fifteen area of Isfahan through secondary data, questionnaire, TOPSIS model, Shannon entropy and SPSS. Based on this, the fifteen areas of Isfahan city have been ranked with 12 factors of creative city indices. The results of studies show that fifteen areas of Isfahan city are not equally benefiting from creative indices and there is much difference between the areas of Isfahan city.

Keywords: Grading, creative city, creative city evaluation indicators, regional planning model.

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577 Some Exact Solutions of the (2+1)-Dimensional Breaking Soliton Equation using the Three-wave Method

Authors: Mohammad Taghi Darvishi, Mohammad Najafi

Abstract:

This paper considers the (2+1)-dimensional breaking soliton equation in its bilinear form. Some exact solutions to this equation are explicitly derived by the idea of three-wave solution method with the assistance of Maple. We can see that the new idea is very simple and straightforward.

Keywords: Soliton solution, computerized symbolic computation, painleve analysis, (2+1)-dimensional breaking soliton equation, Hirota's bilinear form.

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576 The Impact of e-Learning and e-Teaching

Authors: Mohammad Mohammad

Abstract:

With the exponential progress of technological development comes a strong sense that events are moving too quickly for our schools and that teachers may be losing control of them in the process. This paper examines the impact of e-learning and e-teaching in universities, from both the student and teacher perspective. In particular, it is shown that e-teachers should focus not only on the technical capacities and functions of IT materials and activities, but must attempt to more fully understand how their e-learners perceive the learning environment. From the e-learner perspective, this paper indicates that simply having IT tools available does not automatically translate into all students becoming effective learners. More evidence-based evaluative research is needed to allow e-learning and e-teaching to reach full potential.

Keywords: e-learning, e-teaching, distance learning, education

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575 Fuzzy Control of a Three Phase ThyristorizedInduction Motor

Authors: Abolfazl Jalilvand, Mohammad Reza Feyzi, Sohrab Khanmohammad, Mohammad Bagher Bana Sharifian, Ali Sajjadi

Abstract:

Nowadays the control of stator voltage at a constant frequency is one of the traditional and low expense methods in order to control the speed of induction motors near its nominal speed. The torque of induction motor is a nonlinear function of the firing angle, phase angle and speed. In this paper the speed control of induction motor regarding various load torque and under different conditions will be investigated based on a fuzzy controller with inverse training.

Keywords: Three phase induction motor, AC converter, speedcontrol, fuzzy control.

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574 Quantitative Analysis of PCA, ICA, LDA and SVM in Face Recognition

Authors: Liton Jude Rozario, Mohammad Reduanul Haque, Md. Ziarul Islam, Mohammad Shorif Uddin

Abstract:

Face recognition is a technique to automatically identify or verify individuals. It receives great attention in identification, authentication, security and many more applications. Diverse methods had been proposed for this purpose and also a lot of comparative studies were performed. However, researchers could not reach unified conclusion. In this paper, we are reporting an extensive quantitative accuracy analysis of four most widely used face recognition algorithms: Principal Component Analysis (PCA), Independent Component Analysis (ICA), Linear Discriminant Analysis (LDA) and Support Vector Machine (SVM) using AT&T, Sheffield and Bangladeshi people face databases under diverse situations such as illumination, alignment and pose variations.

Keywords: PCA, ICA, LDA, SVM, face recognition, noise.

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573 A Review of Control Schemes for Active Power Filters in Order to Power Quality Improvement

Authors: Mohammad Hasan Raouf, Azim Nowbakht, Mohammad Bagher Haddadi, Mohammad Reza Tabatabaei

Abstract:

Power quality has become a very important issue recently due to the impact on electricity suppliers, equipment manufacturers and customers. Power quality is described as the variation of voltage, current and frequency in a power system. Voltage magnitude is one of the major factors that determine the quality of power. Indeed, custom power technology, the low-voltage counterpart of the more widely known flexible ac transmission system (FACTS) technology, aimed at high-voltage power transmission applications, has emerged as a credible solution to solve many problems relating to power quality problems. There are various power quality problems such as voltage sags, swells, flickers, interruptions and harmonics etc. Active Power Filter (APF) is one of the custom power devices and can mitigate harmonics, reactive power and unbalanced load currents originating from load side. In this study, an extensive review of APF studies, the advantages and disadvantages of each introduced methods are presented. The study also helps the researchers to choose the optimum control techniques and power circuit configuration for APF applications.

Keywords: Power Quality, Custom Power, Active Filter, Control Approach.

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572 Stabilization of the Lorenz Chaotic Equations by Fuzzy Controller

Authors: Behrooz Rezaie, Zahra Rahmani Cherati, Mohammad Reza Jahed Motlagh, Mohammad Farrokhi

Abstract:

In this paper, a fuzzy controller is designed for stabilization of the Lorenz chaotic equations. A simple Mamdani inference method is used for this purpose. This method is very simple and applicable for complex chaotic systems and it can be implemented easily. The stability of close loop system is investigated by the Lyapunov stabilization criterion. A Lyapunov function is introduced and the global stability is proven. Finally, the effectiveness of this method is illustrated by simulation results and it is shown that the performance of the system is improved.

Keywords: Chaotic system, Fuzzy control, Lorenz equation.

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571 Comparison of the Existing Methods in Determination of the Characteristic Polynomial

Authors: Mohammad Saleh Tavazoei, Mohammad Haeri

Abstract:

This paper presents comparison among methods of determination of the characteristic polynomial coefficients. First, the resultant systems from the methods are compared based on frequency criteria such as the closed loop bandwidth, gain and phase margins. Then the step responses of the resultant systems are compared on the basis of the transient behavior criteria including overshoot, rise time, settling time and error (via IAE, ITAE, ISE and ITSE integral indices). Also relative stability of the systems is compared together. Finally the best choices in regards to the above diverse criteria are presented.

Keywords: Characteristic Polynomial, Transient Response, Filters, Stability.

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570 Interest Rate of Managers and Tourism Officials over e-Tourism (Electronic Tourism) Development (Case Study of Lenjan City)

Authors: Akram Shahriyari, Reza Mokhtari Malek Abadi

Abstract:

E-tourism is among the issues that have recently been entered into the field of tourism. In order to achieve this type of tourism, Information and Communications Technology or ICT infrastructures as well as Co-governmental organizations and tourism resources are important. In this study, the opinions of managers and tourism officials about the e-tourism in Lenjan city were measured; it also surveyed the impact of level of digital literacy of managers and tourism officials on attracting tourists in Lenjan city. This study was conducted in Lenjan, one of the environs of the Esfahan province. This study is a documentary – survey and the sources include library resources and also questionnaires. The results obtained indicate that if managers use ICT, it may help E-tourism to be developed in the region, and increasing managers’ beliefs on e-tourism and upgrading their level of digital literacy may affect e-tourism development.

Keywords: ICT, e-tourism, opinion of managers and officials.

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569 Exact Three-wave Solutions for High Nonlinear Form of Benjamin-Bona-Mahony-Burgers Equations

Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

Abstract:

By means of the idea of three-wave method, we obtain some analytic solutions for high nonlinear form of Benjamin-Bona- Mahony-Burgers (shortly BBMB) equations in its bilinear form.

Keywords: Benjamin-Bona-Mahony-Burgers equations, Hirota's bilinear form, three-wave method.

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568 Preparation and Evaluation of New Nanocatalysts for Selective Oxidation of H2S to Sulfur

Authors: Mohammad Rezaee, Mohammad Kazemeini, Ali Morad Rashidi, Moslem Fattahi

Abstract:

Selective oxidation of H2S to elemental sulfur in a fixed bed reactor over newly synthesized alumina nanocatalysts was physio-chemically investigated and results compared with a commercial Claus catalyst. Amongst these new materials, Al2O3- supported sodium oxide prepared with wet chemical technique and Al2O3 nanocatalyst prepared with spray pyrolysis method were the most active catalysts for selective oxidation of H2S to elemental sulfur. Other prepared nanocatalysts were quickly deactivated, mainly due to the interaction with H2S and conversion into sulfides.

Keywords: H2S, Claus process, Al2O3, Spray pyrolysis method, Wet chemical technique

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567 Micromechanical Modeling of Fiber-Matrix Debonding in Unidirectional Composites

Authors: M. Palizvan, M. T. Abadi, M. H. Sadr

Abstract:

Due to variations in damage mechanisms in the microscale, the behavior of fiber-reinforced composites is nonlinear and difficult to model. To make use of computational advantages, homogenization method is applied to the micro-scale model in order to minimize the cost at the expense of detail of local microscale phenomena. In this paper, the effective stiffness is calculated using the homogenization of nonlinear behavior of a composite representative volume element (RVE) containing fiber-matrix debonding. The damage modes for the RVE are considered by using cohesive elements and contacts for the cohesive behavior of the interface between fiber and matrix. To predict more realistic responses of composite materials, different random distributions of fibers are proposed besides square and hexagonal arrays. It was shown that in some cases, there is quite different damage behavior in different fiber distributions. A comprehensive comparison has been made between different graphs.

Keywords: Homogenization, cohesive zone model, fiber-matrix debonding, RVE.

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566 Flood Scenarios for Hydrological and Hydrodynamic Modelling

Authors: Md. Sharif Imam Ibne Amir, Mohammad Masud Kamal khan, Mohammad Golam Rasul, Raj H Sharma, Fatema Akram

Abstract:

Future flood can be predicted using the probable maximum flood (PMF). PMF is calculated using the historical discharge or rainfall data considering the other climatic parameters remaining stationary. However climate is changing globally and the key climatic variables are temperature, evaporation, rainfall and sea level rise are likely to change. To develop scenarios to a basin or catchment scale these important climatic variables should be considered. Nowadays scenario based on climatic variables is more suitable than PMF. Six scenarios were developed for a large Fitzroy basin and presented in this paper.

Keywords: Climate change, rainfall, potential evaporation, scenario, sea level rise (SLR), sub-catchment.

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565 Detection of Legionella pneumophila in Cooling Water Systems of Hospitals and Nursing Homes of Kerman City, Iran by Semi- Nested PCR

Authors: Mohammad Ahmadinejad, Mohammad Reza Shakibaie, Kyvan Shams, Mohammad Khalili

Abstract:

Legionella pneumophila is involved in more than 95% cases of severe atypical pneumonia. Infection is mainly by inhalation the indoor aerosols through the water-coolant systems. Because some Legionella strains may be viable but not culturable, therefore, Taq polymerase, DNA amplification and semi-nested-PCR were carried out to detect Legionella-specific 16S-rDNA sequence. For this purpose, 1.5 litter of water samples from 77 water-coolant system were collected from four different hospitals, two nursing homes and one student hostel in Kerman city of Iran, each in a brand new plastic bottle during summer season of 2006 (from April to August). The samples were filtered in the sterile condition through the Millipore Membrane Filter. DNA was extracted from membrane and used for PCR to detect Legionella spp. The PCR product was then subjected to semi-nested PCR for detection of L. pneumophila. Out of 77 water samples that were tested by PCR, 30 (39%) were positive for most species of Legionella. However, L. pneumophila was detected from 14 (18.2%) water samples by semi-nested PCR. From the above results it can be concluded that water coolant systems of different hospitals and nursing homes in Kerman city of Iran are highly contaminated with L. pneumophila spp. and pose serious concern. So, we recommend avoiding such type of coolant system in the hospitals and nursing homes.

Keywords: Legionella pneumophila, water-coolant system, semi-nested -PCR.

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564 Dynamic Behaviour of Earth Dams for Variation of Earth Material Stiffness

Authors: Y. Parish, F. Najaei Abadi

Abstract:

This paper presents a numerical analysis of the seismic behaviour of earth dams. Analysis is conducted for the solid phase. It may correspond to the response of the dam before water filling. Analysis is conducted for a simple case which concerns the elastic response of the dam. Numerical analyses are conducted using the FLAC3D program. The behaviour of the Shell and core of the dam and the foundation behaviour is assumed to be elastic. Result shows the influence of the variation of the shear modulus of the core and shell on the seismic amplification of the dam. It can be observed that the variation of the shearing modulus of the core leads to a moderate increase in the dynamic amplification and the increase in the shell shearing modulus leads to a significant increase in the dynamic amplification.

Keywords: Numerical, earth dam, seismic, dynamic, core, FLAC3D.

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563 Low Nonlinear Effects Index-Guiding Nanostructured Photonic Crystal Fiber

Authors: S. Olyaee, M. Seifouri, A. Nikoosohbat, M. Shams Esfand Abadi

Abstract:

Photonic Crystal Fibers (PCFs) can be used in optical communications as transmission lines. For this reason, the PCFs with low confinement loss, low chromatic dispersion, and low nonlinear effects are highly suitable transmission media. In this paper, we introduce a new design of index-guiding nanostructured photonic crystal fiber (IG-NPCF) with ultra-low chromatic dispersion, low nonlinearity effects, and low confinement loss. Relatively low dispersion is achieved in the wavelength range of 1200 to 1600nm using the proposed design. According to the new structure of nanostructured PCF presented in this study, the chromatic dispersion slope is -30(ps/km.nm) and the confinement loss reaches below 10-7 dB/km. While in the wavelength range mentioned above at the same time an effective area of more than 50.2μm2 is obtained.

Keywords: Optical communication systems, nanostructured, index-guiding, dispersion, confinement loss, photonic crystal fiber.

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562 Synthesis of Sterile and Pyrogen Free Biogenic Magnetic Nanoparticles: Biotechnological Potential of Magnetotactic Bacteria for Production of Nanomaterials

Authors: Saeid Ghorbanzadeh-Mashkani, Parisa Tajer-Mohammad-Ghazvini, Ahmad Nozad-Golikand, Rouha Kasra-Kermanshahi, Mohammad-Reza Davarpanah

Abstract:

Today, biogenic magnetite nanoparticles among magnetic nanoparticles have unique attracted attention because of their magnetic characteristics and potential applications in various fields such as therapeutic and diagnostic. A well known example of these biogenic nanoparticles is magnetosomes of magnetotactic bacteria. In this research, we used two different types of technique for the isolation and purification of magnetosome nanoparticles from the isolated magnetotactic bacterial cells, heat-alkaline treatment and sonication. Also we evaluated pyrogen content and sterility of synthesized the isolated individual magnetosome by the Limulus Amoebocyte Lysate test and direct impedimetric method respectively.

Keywords: Biogenic magnetic nanoparticles, Magnetosome, Magnetotactic bacteria, Nanobiotechnology

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561 Development Framework Based on Mobile Augmented Reality for Pre-Literacy Kit

Authors: Nazatul Aini Abd Majid, Faridah Yunus, Haslina Arshad, Mohammad Farhan Mohammad Johari

Abstract:

Mobile technology, augmented reality, and game-based learning are some of the key learning technologies that can be fully optimized to promote pre-literacy skills. The problem is how to design an effective pre-literacy kit that utilizes some of the learning technologies. This paper presents a framework based on mobile augmented reality for the development of pre-literacy kit. This pre-literacy kit incorporates three main components which are contents, design, and tools. A prototype of a mobile app based on the three main components was developed for promoting pre-literacy. The results show that the children and teachers gave positive feedbacks after using the mobile app for the pre-literacy.

Keywords: Framework, mobile technology, augmented reality, pre-literacy skills.

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560 Expression of Gen Extracellular Matrix and Cell Adhesion Molecule of Brain Embrio Mice at GD-10 By Real Time RT-PCR

Authors: Yulia Irnidayanti, Win Darmanto, Agus Abadi

Abstract:

research goal was to determine the expression levels cDNA of brain embrio at gestation days 10 (GD-10). The Electroforesis DNA results showed that GAPDH, Fibronectin1, Ncam1, Tenascin, Vimentin, Neurofilament heavy, Neurofilament medium and Neurofilament low were 447 bp, 462 bp, 293 bp. 416 bp, 327 bp, 301 bp, 398 bp and 289 bp. Result of real-time RT-PCR on brain Embryo at gestation days 10 showed that the expression of copy gen Fibronectin 36 copies, Ncam 21,708 copies; Tenascin 24,505 copies; Vimentin 538,554 copies; Neurofilament heavy 2,419 copies; Neurofilament medium 92,928 copies; Neurofilament low 125,809 copies. Vimentin expressed gene copies is very high compared with other gene copies. This condition are caused by Vimentin, that contribute to proliferate of brain development. The vimentin role to cell proliferation of brain.

Keywords: GAPDH, Fibronectin, Ncam, Tenascin, vimentin, Neurofilamen heavy, Neurofilament medium, Neurofilamen low.

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559 Modeling and Control of a 4DoF Robotic Assistive Device for Hand Rehabilitation

Authors: Christopher Spiewak, M. R. Islam, Mohammad Arifur Rahaman, Mohammad H. Rahman, Roger Smith, Maarouf Saad

Abstract:

For those who have lost the ability to move their hand, going through repetitious motions with the assistance of a therapist is the main method of recovery. We have been developed a robotic assistive device to rehabilitate the hand motions in place of the traditional therapy. The developed assistive device (RAD-HR) is comprised of four degrees of freedom enabling basic movements, hand function, and assists in supporting the hand during rehabilitation. We used a nonlinear computed torque control technique to control the RAD-HR. The accuracy of the controller was evaluated in simulations (MATLAB/Simulink environment). To see the robustness of the controller external disturbance as modelling uncertainty (±10% of joint torques) were added in each joints.

Keywords: Biorobotics, rehabilitation, nonlinear control, robotic assistive device, exoskeleton.

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558 Traveling Wave Solutions for the (3+1)-Dimensional Breaking Soliton Equation by (G'/G)- Expansion Method and Modified F-Expansion Method

Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

Abstract:

In this paper, using (G/G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.

Keywords: Exact solution, The (3+1)-dimensional breaking soliton equation, ( G G )-expansion method, Riccati equation, Modified Fexpansion method.

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