Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2336

Search results for: electric differential

2336 Modelling and Technical Assessment of Multi-Motor for Electric Vehicle Drivetrains by Using Electric Differential

Authors: Mohamed Abdel-Monem, Gamal Sowilam, Omar Hegazy


This paper presents a technical assessment of an electric vehicle with two independent rear-wheel motor and an improved traction control system. The electric differential and the control strategy have been implemented to assure that in a straight trajectory, the two rear-wheels run exactly at the same speed, considering the same/different road conditions under the left and right side of the wheels. In case of turning to right/left, the difference between the two rear-wheels speeds assures a vehicle trajectory without sliding, thanks to a harmony between the electric differential and the control strategy. The present article demonstrates a complete model and analysis of a traction control system, considering four different traction scenarios, for two independent rear-wheels motors for electric vehicles. Furthermore, the vehicle model, including wheel dynamics, load forces, electric differential, and control strategy, is designed and verified by using MATLAB/Simulink environment.

Keywords: electric vehicle, energy saving, multi-motor, electric differential, simulation and control

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2335 Research on Control Strategy of Differential Drive Assisted Steering of Distributed Drive Electric Vehicle

Authors: J. Liu, Z. P. Yu, L. Xiong, Y. Feng, J. He


According to the independence, accuracy and controllability of the driving/braking torque of the distributed drive electric vehicle, a control strategy of differential drive assisted steering was designed. Firstly, the assisted curve under different speed and steering wheel torque was developed and the differential torques were distributed to the right and left front wheels. Then the steering return ability assisted control algorithm was designed. At last, the joint simulation was conducted by CarSim/Simulink. The result indicated: the differential drive assisted steering algorithm could provide enough steering drive-assisted under low speed and improve the steering portability. Along with the increase of the speed, the provided steering drive-assisted decreased. With the control algorithm, the steering stiffness of the steering system increased along with the increase of the speed, which ensures the driver’s road feeling. The control algorithm of differential drive assisted steering could avoid the understeer under low speed effectively.

Keywords: differential assisted steering, control strategy, distributed drive electric vehicle, driving/braking torque

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2334 Noncommutative Differential Structure on Finite Groups

Authors: Ibtisam Masmali, Edwin Beggs


In this paper, we take example of differential calculi, on the finite group A4. Then, we apply methods of non-commutative of non-commutative differential geometry to this example, and see how similar the results are to those of classical differential geometry.

Keywords: differential calculi, finite group A4, Christoffel symbols, covariant derivative, torsion compatible

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2333 Development of Extended Trapezoidal Method for Numerical Solution of Volterra Integro-Differential Equations

Authors: Fuziyah Ishak, Siti Norazura Ahmad


Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations

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2332 New Kinetic Effects in Spatial Distribution of Electron Flux and Excitation Rates in Glow Discharge Plasmas in Middle and High Pressures

Authors: Kirill D. Kapustin, Mikhail B. Krasilnikov, Anatoly A. Kudryavtsev


Physical formation mechanisms of differential electron fluxes is high pressure positive column gas discharge are discussed. It is shown that the spatial differential fluxes of the electrons are directed both inward and outward depending on the energy relaxation law. In some cases the direction of energy differential flux at intermediate energies (5-10eV) in whole volume, except region near the wall, appeared to be down directed, so electron in this region dissipate more energy than gain from axial electric field. Paradoxical behaviour of electron flux in spatial-energy space is presented.

Keywords: plasma kinetics, electron distribution function, excitation and radiation rates, local and nonlocal EDF

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2331 Advanced Simulation of Power Consumption of Electric Vehicles

Authors: Ilya Kavalchuk, Hayrettin Arisoy, Alex Stojcevski, Aman Maun Than Oo


Electric vehicles are one of the most complicated electric devices to simulate due to the significant number of different processes involved in electrical structure of it. There are concurrent processes of energy consumption and generation with different onboard systems, which make simulation tasks more complicated to perform. More accurate simulation on energy consumption can provide a better understanding of all energy management for electric transport. As a result of all those processes, electric transport can allow for a more sustainable future and become more convenient in relation to the distance range and recharging time. This paper discusses the problems of energy consumption simulations for electric vehicles using different software packages to provide ideas on how to make this process more precise, which can help engineers create better energy management strategies for electric vehicles.

Keywords: electric vehicles, EV, power consumption, power management, simulation

Procedia PDF Downloads 377
2330 Electric Propulsion System Development for High Floor Trolley Bus

Authors: Asep Andi Suryandi, Katri Yulianto, Dewi Rianti Mandasari


The development of environmentally friendly vehicles increasingly attracted the attention of almost all countries in the world, including Indonesia. There are various types of environmentally friendly vehicles, such as: electric vehicles, hybrid, and fuel gas. The Electric vehicle has been developed in Indonesia, a private or public vehicle. But many electric vehicles had been developed using the battery as a power source, while the battery technology for electric vehicles still constraints in capacity, dimensions of the battery itself and charging system. Trolley bus is one of the electric buses with the main power source of the network catenary / overhead line with trolley pole as the point of contact. This paper will discuss the design and manufacture electrical system in Trolleybus.

Keywords: trolley bus, electric propulsion system, design, manufacture, electric vehicle

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2329 Existence Result of Third Order Functional Random Integro-Differential Inclusion

Authors: D. S. Palimkar


The FRIGDI (functional random integrodifferential inclusion) seems to be new and includes several known random differential inclusions already studied in the literature as special cases have been discussed in the literature for various aspects of the solutions. In this paper, we prove the existence result for FIGDI under the non-convex case of multi-valued function involved in it.Using random fixed point theorem of B. C. Dhage and caratheodory condition. This result is new to the theory of differential inclusion.

Keywords: caratheodory condition, random differential inclusion, random solution, integro-differential inclusion

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2328 Integral Image-Based Differential Filters

Authors: Kohei Inoue, Kenji Hara, Kiichi Urahama


We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.

Keywords: integral images, differential images, differential filters, image fusion

Procedia PDF Downloads 230
2327 On the Relation between λ-Symmetries and μ-Symmetries of Partial Differential Equations

Authors: Teoman Ozer, Ozlem Orhan


This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions.

Keywords: λ-symmetry, μ-symmetry, classification, invariant solution

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2326 Reduced Differential Transform Methods for Solving the Fractional Diffusion Equations

Authors: Yildiray Keskin, Omer Acan, Murat Akkus


In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations.

Keywords: fractional diffusion equations, Caputo fractional derivative, reduced differential transform method, partial

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2325 Nonhomogeneous Linear Second Order Differential Equations and Resonance through Geogebra Program

Authors: F. Maass, P. Martin, J. Olivares


The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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2324 The LIP’s Electric Propulsion Development for Chinese Spacecraft

Authors: Zhang Tianping, Jia Yanhui, Li Juan, Yang Le, Yang Hao, Yang Wei, Sun Xiaojing, Shi Kai, Li Xingda, Sun Yunkui


Lanzhou Institute of Physics (LIP) is the major supplier of electric propulsion subsystems for Chinese satellite platforms. The development statuses of these electric propulsion subsystems were summarized including the LIPS-200 ion electric propulsion subsystem (IEPS) for DFH-3B platform, the LIPS-300 IEPS for DFH-5 and DFH-4SP platform, the LIPS-200+ IEPS for DFH-4E platform and near-earth asteroid exploration spacecraft, the LIPS-100 IEPS for small satellite platform, the LHT-100 hall electric propulsion subsystem (HEPS) for flight test on XY-2 satellite, the LHT-140 HEPS for large LEO spacecraft, the LIPS-400 IEPS for deep space exploration mission and other EPS for other Chinese spacecraft.

Keywords: ion electric propulsion, hall electric propulsion, satellite platform, LIP

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2323 Generalization of Tau Approximant and Error Estimate of Integral Form of Tau Methods for Some Class of Ordinary Differential Equations

Authors: A. I. Ma’ali, R. B. Adeniyi, A. Y. Badeggi, U. Mohammed


An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples.

Keywords: approximant, error estimate, tau method, overdetermination

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2322 An Equivalence between a Harmonic Form and a Closed Co-Closed Differential Form in L^Q and Non-L^Q Spaces

Authors: Lina Wu, Ye Li


An equivalent relation between a harmonic form and a closed co-closed form is established on a complete non-compact manifold. This equivalence has been generalized for a differential k-form ω from Lq spaces to non-Lq spaces when q=2 in the context of p-balanced growth where p=2. Especially for a simple differential k-form on a complete non-compact manifold, the equivalent relation has been verified with the extended scope of q for from finite q-energy in Lq spaces to infinite q-energy in non-Lq spaces when with 2-balanced growth. Generalized Hadamard Theorem, Cauchy-Schwarz Inequality, and Calculus skills including Integration by Parts as well as Convergent Series have been applied as estimation techniques to evaluate growth rates for a differential form. In particular, energy growth rates as indicated by an appropriate power range in a selected test function lead to a balance between a harmonic differential form and a closed co-closed differential form. Research ideas and computational methods in this paper could provide an innovative way in the study of broadening Lq spaces to non-Lq spaces with a wide variety of infinite energy growth for a differential form.

Keywords: closed forms, co-closed forms, harmonic forms, L^q spaces, p-balanced growth, simple differential k-forms

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2321 Strict Stability of Fuzzy Differential Equations by Lyapunov Functions

Authors: Mustafa Bayram Gücen, Coşkun Yakar


In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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2320 Step Method for Solving Nonlinear Two Delays Differential Equation in Parkinson’s Disease

Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly


Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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2319 Volume Density of Power of Multivector Electric Machine

Authors: Aldan A. Sapargaliyev, Yerbol A. Sapargaliyev


Since the invention, the electric machine (EM) can be defined as oEM – one-vector electric machine, as it works due to one-vector inductive coupling with use of one-vector electromagnet. The disadvantages of oEM are large size and limited efficiency at low and medium power applications. This paper describes multi-vector electric machine (mEM) based on multi-vector inductive coupling, which is characterized by the increased surface area of ​​the inductive coupling per EM volume, with a reduced share of inefficient and energy-consuming part of the winding, in comparison with oEM’s. Particularly, it is considered, calculated and compared the performance of three different electrical motors and their power at the same volumes and rotor frequencies. It is also presented the result of calculation of correlation between power density and volume for oEM and mEM. The method of multi-vector inductive coupling enables mEM to possess 1.5-4.0 greater density of power per volume and significantly higher efficiency, in comparison with today’s oEM, especially in low and medium power applications. mEM has distinct advantages, when used in transport vehicles such as electric cars and aircrafts.

Keywords: electric machine, electric motor, electromagnet, efficiency of electric motor

Procedia PDF Downloads 217
2318 Existence of positive periodic solutions for certain delay differential equations

Authors: Farid Nouioua, Abdelouaheb Ardjouni


In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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2317 Periodicity of Solutions of a Nonlinear Impulsive Differential Equation with Piecewise Constant Arguments

Authors: Mehtap Lafcı


In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

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2316 Numerical Treatment of Block Method for the Solution of Ordinary Differential Equations

Authors: A. M. Sagir


Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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2315 Karachi Electric Power Technical and Financial Performance Evaluation after Privatization

Authors: Fawad Azeem


This paper deals with the comparative analysis of Karachi Electric before and after privatization. Technical as well as financial analysis has been done based on the available KE’s stats for last decade. Karachi Electric has evolved as a better entity in terms of its financial and technical achievements. On the other hand, human resources have been seriously affected due to mass firing of employees from the organizations. Study and analysis show that transparent and unbiased privatization practices on institutions like KE that were in serious trouble can upsurge the standards of the institution. Further, for the betterment of the social circle privatization must not affect the employment opportunities.

Keywords: Karachi Electric, power, energy, privatization

Procedia PDF Downloads 239
2314 New Series Input Parallel Output LLC DC/DC Converter with the Input Voltage Balancing Capacitor for the Electric System of Electric Vehicles

Authors: Kang Hyun Yi


This paper presents a new parallel output LLC DC/DC converter for electric vehicle. The electric vehicle has two batteries. One is a high voltage battery for the powertrain of the vehicle and the other is a low voltage battery for the vehicle electric system. The low voltage is charged from the high voltage battery and the high voltage input and the high current output DC/DC converter is needed. Therefore, the new LLC converter with the input voltage compensation is proposed for the high voltage input and the low voltage output DC/DC converter. The proposed circuit has two LLC converters with the series input voltage from the battery for the powertrain and the parallel output low battery voltage for the vehicle electric system because the battery voltage for the powertrain and the electric power for the vehicle become high. Also, the input series voltage compensation capacitor is used for balancing the input current in the two LLC converters. The proposed converter has an equal electric stress of the semiconductor parts and the reactive components, high efficiency and good heat dissipation.

Keywords: electric vehicle, LLC DC/DC converter, input voltage balancing, parallel output

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2313 Weak Electric Fields Enhance Growth and Nutritional Quality of Kale

Authors: So-Ra Lee, Myung-Min Oh


Generally, plants growing on the earth are under the influence of natural electric fields and may even require exposure of the electric field to survive. Electric signals have been observed within plants and seem to play an important role on various metabolic processes, but their role is not fully understood. In this study, we attempted to explore the response of plants under external electric fields in kale (Brassica oleracea var. acephala). The plants were hydroponically grown for 28 days in a plant factory. Electric currents at 10, 50 and 100 mA were supplied to nutrient solution for 3 weeks. Additionally, some of the plants were cultivated in a Faraday cage to remove the natural electric field. Kale plants exposed to electric fields had higher fresh weight than the control and plants in Faraday cage. Absence of electric field caused a significant decrease in shoot dry weight and root growth. Leaf area also showed a similar response with shoot fresh weight. Supplying weak electric stimulation enhanced nutritional quality including total phenolic content and antioxidant capacity. This work provides basic information on the effects of electric fields on plants and is a meaningful attempt for developing a new economical technology to increase crop productivity and quality by applying an electric field. This work was supported by Korea Institute of Planning and Evaluation for Technology in Food, Agriculture, Forestry and Fisheries (IPET) through Agriculture, Food and Rural Affairs Research Center Support Program, funded by Ministry of Agriculture, Food and Rural Affairs (MAFRA) (717001-07-02-HD240).

Keywords: electroculture, electric signal, faraday cage, electric field

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2312 Series Solutions to Boundary Value Differential Equations

Authors: Armin Ardekani, Mohammad Akbari


We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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2311 11-Round Impossible Differential Attack on Midori64

Authors: Zhan Chen, Wenquan Bi


This paper focuses on examining the strength of Midori against impossible differential attack. The Midori family of light weight block cipher orienting to energy-efficiency is proposed in ASIACRYPT2015. Using a 6-round property, the authors implement an 11-round impossible differential attack on Midori64 by extending two rounds on the top and three rounds on the bottom. There is enough key space to consider pre-whitening keys in this attack. An impossible differential path that minimises the key bits involved is used to reduce computational complexity. Several additional observations such as partial abort technique are used to further reduce data and time complexities. This attack has data complexity of 2 ⁶⁹·² chosen plaintexts, requires 2 ¹⁴·⁵⁸ blocks of memory and 2 ⁹⁴·⁷ 11- round Midori64 encryptions.

Keywords: cryptanalysis, impossible differential, light weight block cipher, Midori

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2310 Differential Transform Method: Some Important Examples

Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen


In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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2309 An Explorative Research on the Electric and Electronic Officers Employment: Turkish Flagged Ship's Perspective

Authors: Mehmet Yahsi, Ozkan Ugurlu, Ercan Yuksekyildiz


Assistant department among the electric and electronic officers on ships, has an important place for the maintenance of electric and electronic devices. From this perspective, ships must be employed with a sufficient number of assistant department. In this study, in order to research on the Turkish-flagged ships electric and electronic officers employment; Our national manning regulation compared with international regulations. The data used in this study were collected via visiting of the ships. 3000 gross tonnage and above engaged in international voyages 181 Turkish-flagged ship’s crew lists were compared with Minimum Safety Manning Certificates. According to the findings; employment rate, %54 electric and electronic officers. According to the results of the study; Turkish-flagged ships, although it is not obliged to electric and electronic officers, were employed on ships.

Keywords: manning, electric officer, electronic officer, minimum safety manning certificate

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2308 Effect of Electric Stimulation on Characteristic Changes in Hot-Boned Beef Brisket of Different Potential Tenderness

Authors: Orose Rugchati, Kanita Thanacharoenchanaphas, Sarawut Wattanawongpitak


In this study, the effect of electric stimulation on the quality of hot-boned beef brisket muscles was evaluated, including the tenderness, pH, temperature change, and colorant. Muscles were obtained from steers in the local slaughter house. (3 steers for each muscle), removed from the carcasses 4-hour postmortem and variable time to treated with direct current electric 1 and 5 minutes, respectively. Six different electric intensities (direct current voltage of 50, 70 and 90 Volt, pulse with 10, 20 and 40 ms) plus a control were applied to each muscle to determine the optimum treatment conditions. Hot-boned beef brisket was found to get tender with increasing treatment direct current voltage and reduction in the shear force with pulsed with electric treatment. But in a long time to treated with electric current get fading in red color and temperature increase whereas pH quite different compared to non-treated control samples.

Keywords: electric stimulation, characteristic changes, hot-boned beef brisket, potential tenderness

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2307 Solution of Singularly Perturbed Differential Difference Equations Using Liouville Green Transformation

Authors: Y. N. Reddy


The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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