Search results for: Direction angle

Authors: Prateek Maheshwari, Nitin Seth, Anoop Kumar Gupta

Abstract:

The objective of present research paper is to highlight the importance of measuring advertisement effectiveness in print media and to develop a conceptual model for advertisement effectiveness. The developed model is based on dimensions on which advertisement effectiveness depends and on the dimensions which are used to measure the effectiveness. An in-depth and extensive literature review is carried out to understand the concept of advertisement effectiveness and its various determinants in context of print media. Based on the insights gained, a conceptual framework for advertisement effectiveness is presented. The model is an attempt to uncover the relatively less explored area of advertisement effectiveness in Indian advertising scenario. It is believed that present work will encourage scholars and academicians to further explore the area and will offer conceptual assistance and a fresh direction in the domain of advertisement effectiveness.

Keywords: Advertisement Effectiveness, Conceptual Model, Effectiveness Dimensions, Print Media.

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Authors: I. Brandys, M. Levy, K. Harush, Y. Haim, M. Korngold

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Theoretical optimization of a copper-water negative inclination heat pipe with internal composite wick structure had been performed, regarding a new introduced parameter: the ratio between the coarse mesh wraps and the fine mesh wraps of the composite wick. Since in many cases, the design of a heat pipe matches specific thermal requirements and physical limitations, this work demonstrates the optimization of a 1m length, 8mm internal diameter heat pipe without an adiabatic section, at a negative inclination angle of -10º. The optimization is based on a new introduced parameter, LR: the ratio between the coarse mesh wraps and the fine mesh wraps.

Keywords: Heat pipe, inclination, optimization, ratio.

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Authors: A. Hossain, M. A. Gafur, F. Gulshan, A. S. W. Kurny

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Al-Si-Mg-Ni(-Cu) alloys are widely used in the automotive industry. They have the advantage of low weight associated with low coefficient of thermal expansion and excellent mechanical properties – mainly at high temperatures. The corrosion resistance of these alloys in coastal area, particularly sea water, however is not yet known. In this investigation, electrochemical impedance spectroscopy (EIS) and potentiodynamic polarization have been used to evaluate the corrosion resistance of Al-6Si-0.5Mg-2Ni (-2Cu) alloys in simulated sea water environments. The potentiodynamic polarization curves reveal that 2 wt% Cu content alloy (Alloy-2) is more prone to corrosion than the Cu free alloy (Alloy-1). But the EIS test results showed that corrosion resistance or charge transfer resistance (Rct) increases with the addition of Cu. Due to addition of Cu and thermal treatment, the magnitude of open circuit potential (OCP), corrosion potential (Ecorr) and pitting corrosion potential (Epit) of Al-6Si-0.5Mg-2Ni alloy in NaCl solution were shifted to the more noble direction.

Keywords: Al-Si alloy, potentiodynamic polarization, EIS, SEM.

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Authors: Tarek Mohammad

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The amplitude response of infrared (IR) sensors depends on the reflectance properties of the target. Therefore, in order to use IR sensor for measuring distances accurately, prior knowledge of the surface must be known. This paper describes the Phong Illumination Model for determining the properties of a surface and subsequently calculating the distance to the surface. The angular position of the IR sensor is computed as normal to the surface for simplifying the calculation. Ultrasonic (US) sensor can provide the initial information on distance to obtain the parameters for this method. In addition, the experimental results obtained by using LabView are discussed. More care should be taken when placing the objects from the sensors during acquiring data since the small change in angle could show very different distance than the actual one. Since stereo camera vision systems do not perform well under some environmental conditions such as plain wall, glass surfaces, or poor lighting conditions, the IR and US sensors can be used additionally to improve the overall vision systems of mobile robots.

Keywords: Distance Measurement, Infrared sensor, Surface properties, Ultrasonic sensor.

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Authors: H. Ettouney, A. AL-Haddad, S. Saqer

Abstract:

This paper focuses on assessment of air pollution in Umm-Alhyman, Kuwait, which is located south to oil refineries, power station, oil field, and highways. The measurements were made over a period of four days in March and July in 2001, 2004, and 2008. The measured pollutants included methanated and nonmethanated hydrocarbons (MHC, NMHC), CO, CO2, SO2, NOX, O3, and PM10. Also, meteorological parameters were measured, which includes temperature, wind speed and direction, and solar radiation. Over the study period, data analysis showed increase in measured SO2, NOX and CO by factors of 1.2, 5.5 and 2, respectively. This is explained in terms of increase in industrial activities, motor vehicle density, and power generation. Predictions of the measured data were made by the ISC-AERMOD software package and by using the ISCST3 model option. Finally, comparison was made between measured data against international standards.

Keywords: Air pollution, Emission inventory, ISCST3 model, Modeling

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Authors: Ji-il Park, Donghan Koo, Hyungtae Seo, Jihyuk Park, Heewon Park, Sukyung Park, Kyung-Soo Kim, and Soohyun Kim

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In the paper, the energetic features of the loaded gait are newly analyzed depending on the trunk flexion change. To investigate the loaded gait, walking experiments are performed for five subjects and, the ground reaction forces and kinematic data are measured. Based on these information, we compute the impulse, momentum and mechanical works done on the center of body mass, through the trunk flexion change. As a result, it is shown that the trunk flexion change does not affect the impulses and momentums during the step-to-step transition as well. However, the direction of the pre-collision momentum does change depending on the trunk flexion change, which is degenerated just after (or during) the collision period.

Keywords: Loaded gait, collision, impulse, gravity, heel strike, push-off, gait analysis.

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Authors: Niloufar Ghoreishi, Ali Nekouzadeh

Abstract:

The stability of the flight during maneuvering and in response to probable perturbations is one of the most essential features of an aircraft that should be analyzed and designed for. In this study, we derived the non-linear governing equations of aircraft dynamics during the climb/descend phase and simulated a model aircraft. The corresponding force and moment dimensionless coefficients of the model and their variations with elevator angle and other relevant aerodynamic parameters were measured experimentally. The short-period mode and phugoid mode response were simulated by solving the governing equations numerically and then compared with the desired stability parameters for the particular level, category, and class of the aircraft model. To meet the target stability, a controller was designed and used. This resulted in significant improvement in the stability parameters of the flight.

Keywords: Flight stability, phugoid mode, short period mode, climb phase, damping coefficient.

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Authors: Eunji Choi, Borang Park, Youngjae Choi, Jinwoo Moon

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In this study, a predictive model for estimating the metabolism (MET) of human body was developed for the optimal control of indoor thermal environment. Human body images for indoor activities and human body joint coordinated values were collected as data sets, which are used in predictive model. A deep learning algorithm was used in an initial model, and its number of hidden layers and hidden neurons were optimized. Lastly, the model prediction performance was analyzed after the model being trained through collected data. In conclusion, the possibility of MET prediction was confirmed, and the direction of the future study was proposed as developing various data and the predictive model.

Keywords: Deep learning, indoor quality, metabolism, predictive model.

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Authors: Ogunsina Babatunde, Aregbesola Omotayo, Adebayo Adewale, Odunlami Johnson

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The physical properties of nine Nigerian staple food flours related to bulk handling and processing were investigated following standard procedures. The results showed that the moisture content, bulk density, angle of repose, water absorption capacity, swelling index, dispersability, pH and wettability of the flours ranged from 9.95 to 11.98%, 0.44 to 0.66 g/cm³, 31.43 to 39.65^o, 198.3 to 291.7 g of water/100 g of sample, 5.53 to 7.63, 60.3 to 73.8%, 4.43 to 6.70, and 11 to 150 s. The particle size analysis of the flour samples indicated significant differences (p<0.05). The least gelation concentration of the flour samples ranged from 6 to 14%. The colour of the flours fell between light and saturated, with the exception of cassava, millet and maize flours which appear dark and dull. The properties of food flours depend largely on the inherent property of the food material and may influence their functional behaviour as food materials.

Keywords: Properties, staple food flours, Nigeria, cereals, tuber, root crops, fruits.

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Authors: Bachir Chemani, Rachid Halfaoui

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The aim of work is to define the distribution density of winding yarn on cylindrical and conical bobbins. It is known that parallel winding gives greater density and more regular distribution, but the unwinding of yarn is much more difficult for following process. The conical spool has an enormous advantage during unwinding and may contain a large amount of yarns, but the density distribution is not regular because of difference in diameters. The variation of specific density over the reel height is explained generally by the sudden change of winding speed due to direction movement variation of yarn. We determined the conditions of uniform winding and developed a calculate model to the change of the specific density of winding wire over entire spool height.

Keywords: Textile, cylindrical bobbins, conical bobbins, parallel winding, cross winding.

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Authors: Srinath Shetty K., Shivashankar R., Rashmi P. Shetty

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Earth reinforcing techniques have become useful and economical to solve problems related to difficult grounds and provide satisfactory foundation performance. In this context, this paper uses radial basis function neural network (RBFNN) for predicting the bearing pressure of strip footing on reinforced granular bed overlying weak soil. The inputs for the neural network models included plate width, thickness of granular bed and number of layers of reinforcements, settlement ratio, water content, dry density, cohesion and angle of friction. The results indicated that RBFNN model exhibited more than 84 % prediction accuracy, thereby demonstrating its application in a geotechnical problem.

Keywords: Bearing pressure, granular bed, radial basis function neural network, strip footing.

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Authors: Hou Youfu, Wang Daoming, Meng Qingrui

Abstract:

To reveal the temperature field distribution of disc brake in downward belt conveyor, mathematical models of heat transfer for disc brake were established combined with heat transfer theory. Then, the simulation process was stated in detail and the temperature field of disc brake under conditions of dynamic speed and dynamic braking torque was numerically simulated by using ANSYS software. Finally the distribution and variation laws of temperature field in the braking process were analyzed. Results indicate that the maximum surface temperature occurs at a time before the brake end and there exist large temperature gradients in both radial and axial directions, while it is relatively small in the circumferential direction.

Keywords: Downward belt conveyor, Disc brake, Temperature field, Numerical simulation.

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Authors: Osama A. Marzouk

Abstract:

We propose a reduced-ordermodel for the instantaneous hydrodynamic force on a cylinder. The model consists of a system of two ordinary differential equations (ODEs), which can be integrated in time to yield very accurate histories of the resultant force and its direction. In contrast to several existing models, the proposed model considers the actual (total) hydrodynamic force rather than its perpendicular or parallel projection (the lift and drag), and captures the complete force rather than the oscillatory part only. We study and provide descriptions of the relationship between the model parameters, evaluated utilizing results from numerical simulations, and the Reynolds number so that the model can be used at any arbitrary value within the considered range of 100 to 500 to provide accurate representation of the force without the need to perform timeconsuming simulations and solving the partial differential equations (PDEs) governing the flow field.

Keywords: reduced-order model, wake oscillator, nonlinear, ODEsystem

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Authors: Olesya Bolkhovskaya, Alexey Davydov, Alexander Maltsev

Abstract:

In this paper two approaches to joint signal detection, time of arrival (ToA) and angle of arrival (AoA) estimation in multi-element antenna array are investigated. Two scenarios were considered: first one, when the waveform of the useful signal is known a priori and, second one, when the waveform of the desired signal is unknown. For first scenario, the antenna array signal processing based on multi-element matched filtering (MF) with the following non-coherent detection scheme and maximum likelihood (ML) parameter estimation blocks is exploited. For second scenario, the signal processing based on the antenna array elements covariance matrix estimation with the following eigenvector analysis and ML parameter estimation blocks is applied. The performance characteristics of both signal processing schemes are thoroughly investigated and compared for different useful signals and noise parameters.

Keywords: Antenna array, signal detection, ToA, AoA estimation.

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Authors: Sophia Fry, Mahir Irtiza, Alexa Hoffman, Yousef Sardahi

Abstract:

This study presents an intelligent control algorithm for a flexible robotic arm. Fuzzy control is used to control the motion of the arm to maintain the arm tip at the desired position while reducing vibration and increasing the system speed of response. The Fuzzy controller (FC) is based on adding the tip angular position to the arm deflection angle and using their sum as a feedback signal to the control algorithm. This reduces the complexity of the FC in terms of the input variables, number of membership functions, fuzzy rules, and control structure. Also, the design of the fuzzy controller is model-free and uses only our knowledge about the system. To show the efficacy of the FC, the control algorithm is implemented on the flexible joint manipulator (FJM) developed by Quanser. The results show that the proposed control method is effective in terms of response time, overshoot, and vibration amplitude.

Keywords: Fuzzy logic control, model-free control, flexible joint manipulators, nonlinear control.

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Authors: T. J. Jemi Jeya, V. Sriram

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Pile Supported Caisson breakwater is an ecofriendly breakwater very useful in coastal zone protection. The model is developed by considering the advantages of both caisson breakwater and pile supported breakwater, where the top portion is a vertical or quarter circle caisson and the bottom portion consists of a pile supported breakwater defined as Vertical Pile Supported Breakwater (VPSCB) and Quarter-circle Pile Supported Breakwater (QPSCB). The study mainly focuses on comparison of run up over VPSCB and QPSCB under oblique waves. The experiments are carried out in a shallow wave basin under different water depths (d = 0.5 m & 0.55 m) and under different oblique regular waves (0⁰, 15⁰, 30⁰). The run up over the surface is measured by placing two run up probes over the surface at 0.3 m on both sides from the centre of the model. The results show that the non-dimensional shoreward run up shows slight decrease with respect to increase in angle of wave attack.

Keywords: Caisson breakwater, pile supported breakwater, quarter circle breakwater, vertical breakwater.

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Authors: Nour Charara, Hussein Charara, Omar Abou Khaled, Hani Abdallah, Elena Mugellini

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In this paper, we present a human behavior modeling approach in videos scenes. This approach is used to model the normal behaviors in the conference halls. We exploited the Probabilistic Latent Semantic Analysis technique (PLSA), using the 'Bag-of-Terms' paradigm, as a tool for exploring video data to learn the model by grouping similar activities. Our term vocabulary consists of 3D spatio-temporal patch groups assigned by the direction of motion. Our video representation ensures the spatial information, the object trajectory, and the motion. The main importance of this approach is that it can be adapted to detect abnormal behaviors in order to ensure and enhance human security.

Keywords: Activity modeling, clustering, PLSA, video representation.

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Authors: J. Dzugan, M. Spaniel, P. Konopík, J. Ruzicka, J. Kuzelka

Abstract:

The modeling of inelastic behavior of plastic materials requires measurements providing information on material response to different multiaxial loading conditions. Different triaxiality conditions and values of Lode parameters have to be covered for complex description of the material plastic behavior. Samples geometries providing material plastic behavoiur over the range of interest are proposed with the use of FEM analysis. Round samples with 3 different notches and smooth surface are used together with butterfly type of samples tested at angle ranging for 0 to 90°. Identification of ductile damage parameters is carried out on the basis of obtained experimental data for austenitic stainless steel. The obtained material plastic damage parameters are subsequently applied to FEM simulation of notched CT normally samples used for fracture mechanics testing and results from the simulation are compared with real tests.

Keywords: baqus, austenitic steel, computer simulation, ductile damage, triaxiality

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Authors: G. N. Sekhar, P. G. Siddheshwar, G. Jayalatha, R. Prakash

Abstract:

The problem of thermal convection in temperature and magnetic field sensitive Newtonian ferromagnetic liquid is studied in the presence of uniform vertical magnetic field and throughflow. Using a combination of Galerkin and shooting techniques the critical eigenvalues are obtained for stationary mode. The effect of Prandtl number (Pr > 1) on onset is insignificant and nonlinearity of non-buoyancy magnetic parameter M3 is found to have no influence on the onset of ferroconvection. The magnetic buoyancy number, M1 and variable viscosity parameter, V have destabilizing influences on the system. The effect of throughflow Peclet number, Pe is to delay the onset of ferroconvection and this effect is independent of the direction of flow.

Keywords: Ferroconvection, throughflow, temperature dependent viscosity, magnetic field dependent viscosity.

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Authors: Defne Akay, Bekir S. Kandemir

Abstract:

In this paper, we investigate the low-lying energy levels of the two-dimensional parabolic graphene quantum dots (GQDs) in the presence of topological defects with long range Coulomb impurity and subjected to an external uniform magnetic field. The low-lying energy levels of the system are obtained within the framework of the perturbation theory. We theoretically demonstrate that a valley splitting can be controlled by geometrical parameters of the graphene quantum dots and/or by tuning a uniform magnetic field, as well as topological defects. It is found that, for parabolic graphene dots, the valley splitting occurs due to the introduction of spatial confinement. The corresponding splitting is enhanced by the introduction of a uniform magnetic field and it increases by increasing the angle of the cone in subcritical regime.

Keywords: Coulomb impurity, graphene cones, graphene quantum dots, topological defects.

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Authors: V. K. Jagadeesh, K. V. Naveen, P. Muthuchidambaranathan

Abstract:

Recently, there is a lot of interest in the field of under water optical wireless communication for short range because of its high bandwidth. But in most of the previous works line of sight propagation or single scattering of photons only considered. In practical case this is not applicable because of beam blockage in underwater and multiple scattering also occurred during the photons propagation through water. In this paper we consider a non-line of sight underwater wireless optical communication system with multiple scattering and examine the performance of the system using monte carlo simulation. The distribution scattering angle of photons are modeled by Henyey-Greenstein method. The average bit error rate is calculated using on-off keying modulation for different water types.

Keywords: Non line of sight under Water optical wireless communication, Henyey-Greenstein model, Multiple scattering, Monte-Carlo simulation.

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Authors: Teerayout Wattanasupachoke

Abstract:

This research project is developed in order to study managerial styles of modern Thai executives. The thorough understanding will lead to continuous improvement and efficient performance of Thai business organizations. Regarding managerial skills, Thai executives focus heavily upon human skills. Also, the negotiator roles are most emphasis in their management. In addition, Thai executives pay most attention to the fundamental management principles including Harmony and Unity of Direction of the organizations. Moreover, the management techniques, consisting of Team work and Career Planning are of their main concern. Finally, Thai executives wish to enhance their firms- image and employees- morale through conducting the ethical and socially responsible activities. The major tactic deployed to stimulate employees- ethical behaviors and mindset is Code of Ethics development.

Keywords: Management, Managerial Styles, Asian Executives, Thailand.

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Authors: R.Goudarzizadeh, S.H.Mousavi Jahromi, N.Hedayat

Abstract:

This paper analytically investigates the 3D flow pattern at the confluences of two rectangular channels having 900 angles using Navier-Stokes equations based on Reynolds Stress Turbulence Model (RSM). The equations are solved by the Finite- Volume Method (FVM) and the flow is analyzed in terms of steadystate (single-phased) conditions. The Shumate experimental findings were used to test the validity of data. Comparison of the simulation model with the experimental ones indicated a close proximity between the flow patterns of the two sets. Effects of the discharge ratio on separation zone dimensions created in the main-channel downstream of the confluence indicated an inverse relation, where a decrease in discharge ratio, will entail an increase in the length and width of the separation zone. The study also found the model as a powerful analytical tool in the feasibility study of hydraulic engineering projects.

Keywords: 900 confluence angle, flow separation zone, numerical modeling, turbulent flow.

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Authors: Hao Wu, Jonathan L. Shapiro

Abstract:

The Bayesian Optimization Algorithm (BOA) is an algorithm based on the estimation of distributions. It uses techniques from modeling data by Bayesian networks to estimating the joint distribution of promising solutions. To obtain the structure of Bayesian network, different search algorithms can be used. The key point that BOA addresses is whether the constructed Bayesian network could generate new and useful solutions (strings), which could lead the algorithm in the right direction to solve the problem. Undoubtedly, this ability is a crucial factor of the efficiency of BOA. Varied search algorithms can be used in BOA, but their performances are different. For choosing better ones, certain suitable method to present their ability difference is needed. In this paper, a greedy search algorithm and a stochastic search algorithm are used in BOA to solve certain optimization problem. A method using Kullback-Leibler (KL) Divergence to reflect their difference is described.

Keywords: Bayesian optimization algorithm, greedy search, KL divergence, stochastic search.

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Authors: S. A. Ahmadi, S. Sharif, R. Jamshidi

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In this article, the flow behavior around a NACA 0012 airfoil which is oscillating with different Reynolds numbers and in various amplitudes has been investigated numerically. Numerical simulations have been performed with ANSYS software. First, the 2- D geometry has been studied in different Reynolds numbers and angles of attack with various numerical methods in its static condition. This analysis was to choose the best turbulent model and comparing the grids to have the optimum one for dynamic simulations. Because the analysis was to study the blades of wind turbines, the Reynolds numbers were not arbitrary. They were in the range of 9.71e5 to 22.65e5. The angle of attack was in the range of -41.81° to 41.81°. By choosing the forward wind speed as the independent parameter, the others like Reynolds and the amplitude of the oscillation would be known automatically. The results show that the SST turbulent model is the best choice that leads the least numerical error with respect the experimental ones. Also, a dynamic stall phenomenon is more probable at lower wind speeds in which the lift force is less.

Keywords: Dynamic stall, Numerical simulation, Wind turbine, Turbulent Model

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Authors: Abo-El-Nour N. Abd-Alla, Fatimah A. Alsheikh

Abstract:

This study deals with the phenomena of reflection and transmission (refraction) of qSV-waves, for an incident of quasi transverse vertically waves, at a plane interface of two semi-infinite piezoelectric elastic media under the influence of the initial stresses. The relations governing the reflection and transmission coefficients of these reflected waves for various suitable boundary conditions are derived. We have shown analytically that reflection and transmission coefficients of (qP) and (qSV) waves depend upon the angle of incidence, the parameters of electric potential, the material constants of the medium as will as the initial stresses presented in the media. The numerical calculations of the reflection and transmission amplitude ratios for different values of initial stresses have been carried out by computer for different materials as examples and the results are given in the form of graphs. Finally, some of particular cases are considered.

Keywords: Quasi plane vertical transverse waves, reflection and transmission coefficients, initial stresses, PZT-5H Ceramic, Aluminum Nitride (AlN), Piezoelectricity

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Authors: Naser Ojaroudi Parchin, Atta Ullah, Haleh Jahanbakhsh Basherlou, Raed A. Abd-Alhameed, Peter S. Excell

Abstract:

A design of beam-steerable antenna array for the future cellular communication (5G) is presented. The proposed design contains eight elements of compact end-fire antennas arranged on the top edge of smartphone printed circuit board (PCB). Configuration of the antenna element consists of the conductive patterns on the top and bottom copper foil layers and a substrate layer with a via-hole. The simulated results including input-impedance and also fundamental radiation properties have been presented and discussed. The impedance bandwidth (S₁₁ ≤ -10 dB) of the antenna spans from 17.5 to 21 GHz (more than 3 GHz bandwidth) with a resonance at 19 GHz. The antenna exhibits end-fire (directional) radiation beams with wide-angle scanning property and could be used for the future 5G beam-forming. Furthermore, the characteristics of the array design in the vicinity of user-hand are studied.

Keywords: Beam-steering, end-fire radiation mode, mobile-phone antenna, phased array.

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Authors: A. Naga Rajesh, S. Chandralingam, T. Anjaneyulu, K. Satyanarayana

Abstract:

Assistive robotics are playing a vital role in advancing the quality of life for disable people. There exist wide range of systems that can control and guide autonomous mobile robots. The objective of the control system is to guide an autonomous mobile robot using the movement of eyes by means of EOG signal. The EOG signal is acquired using Ag/AgCl electrodes and this signal is processed by a microcontroller unit to calculate the eye gaze direction. Then according to the guidance control strategy, the control commands of the wheelchair are sent. The classification of different eye movements allows us to generate simple code for controlling the wheelchair. This work was aimed towards developing a usable and low-cost assistive robotic wheel chair system for disabled people. To live more independent life, the system can be used by the handicapped people especially those with only eye-motor coordination.

Keywords: Electrooculography, Microcontroller, Motors, Wheelchair.

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Authors: Eshagh Rasouli Sarabi, Mir Saeed Moosavi

Abstract:

Road transportation system is the most important method of transporting the goods. Considering the most suitable geographical situation of Iran to transport the goods between Europe and Asia and placement of this country in direction of international corridors (east- west) , (north-south) and Asian land transport to infrastructure development “A.L.T.I.D" and Transport corridor Europe - Caucasus - Asia “T.R.A.C.E.C.A", noticing the security of road transportation system in this country is so important. In this paper the main factors of accidents on the roads of Iran are categorized regarding the rate of accidents occurred. Then apart from studying the main reasons of accidents of every category, the main factors of these events are studied and its strategies in Iran are introduced.

Keywords: Road, Transportation, Accident, Factors

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Authors: Ali Dorostkar

Abstract:

In this paper, a basic schematic of fractional dimensional optimization problem is presented. As will be shown, a method is performed based on a relation between roots and tangent lines of function in fractional dimensions for an arbitrary initial point. It is shown that for each polynomial function with order N at least N tangent lines must be existed in fractional dimensions of 0 < α < N+1 which pass exactly through the all roots of the proposed function. Geometrical analysis of tangent lines in fractional dimensions is also presented to clarify more intuitively the proposed method. Results show that with an appropriate selection of fractional dimensions, we can directly find the roots. Method is presented for giving a different direction of optimization problems by the use of fractional dimensions.

Keywords: Tangent line, fractional dimension, root, optimization problem.

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