Search results for: differential filters

Authors: Somveer Singh, Vineet Kumar Singh

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This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Keywords: legendre wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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Authors: Youssef Abdelli, Rachid Nasri

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The large amplitude free vibration analysis of three-layered symmetric sandwich beams is carried out using two different approaches. The governing nonlinear partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two nonlinear partial differential equations that are coupled both in axial and binding deformations. In the first approach, the method of multiple scales is applied directly to the governing equation that is a nonlinear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained by two approaches; they are compared with the solutions obtained numerically by the finite difference method.

Keywords: finite difference method, large amplitude vibration, multiple scales, nonlinear vibration

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza Khalili, Davood Domiri Danji

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In this conference, our aims are accuracy, capabilities and power at solving of the complicated non-linear partial differential. Our purpose is to enhance the ability to solve the mentioned nonlinear differential equations at basic science and engineering field and similar issues with a simple and innovative approach. As we know most of engineering system behavior in practical are nonlinear process (especially basic science and engineering field, etc.) and analytical solving (no numeric) these problems are difficult, complex, and sometimes impossible like (Fluids and Gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure an innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical method (Runge-Kutta 4th). Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear partial differential equations, with help of that there is no difficulty for solving all nonlinear differential equations. Advantages and ability of this method (AGM) as follow: (a) Non-linear Differential equations (ODE, PDE) are directly solvable by this method. (b) In this method (AGM), most of the time, without any dimensionless procedure, we can solve equation(s) by any boundary or initial condition number. (c) AGM method always is convergent in boundary or initial condition. (d) Parameters of exponential, Trigonometric and Logarithmic of the existent in the non-linear differential equation with AGM method no needs Taylor expand which are caused high solve precision. (e) AGM method is very flexible in the coding system, and can solve easily varieties of the non-linear differential equation at high acceptable accuracy. (f) One of the important advantages of this method is analytical solving with high accuracy such as partial differential equation in vibration in solids, waves in water and gas, with minimum initial and boundary condition capable to solve problem. (g) It is very important to present a general and simple approach for solving most problems of the differential equations with high non-linearity in engineering sciences especially at civil engineering, and compare output with numerical method (Runge-Kutta 4th) and Exact solutions.

Keywords: new approach, AGM, sets of coupled nonlinear differential equation, exact solutions, numerical

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Authors: Adetunji A. Adeyanju., Mathew O. Omeike, Johnson O. Adeniran, Biodun S. Badmus

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In this paper, we discuss certain conditions for uniform asymptotic stability and uniform ultimate boundedness of solutions to some systems of Aizermann-type of differential equations by means of second method of Lyapunov. In achieving our goal, some Lyapunov functions are constructed to serve as basic tools. The stability results in this paper, extend some stability results for some Aizermann-type of differential equations found in literature. Also, we prove some results on uniform boundedness and uniform ultimate boundedness of solutions of systems of equations study.

Keywords: Aizermann, boundedness, first order, Lyapunov function, stability

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Authors: Janjira Triped, Wipada Sanongraj, Wipawee Khamwichit

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The research work covered in this study includes the morphological structure and optical properties of TiO2-coated silk fibroin (SF) filters at 2.5% wt. TiO2/vol. PVA solution. SEM micrographs revealed the fibrous morphology of the TiO2-coated SF filters. An average diameter of the SF fiber was estimated to be approximately 10µm. Also, it was confirmed that TiO2 can be adhered more on SF filter surface at higher TiO2 dosages. The activity of semiconductor materials was studied by UV-VIS spectrophotometer method. The spectral data recorded shows the strong cut off at 390 nm. The calculated band-gap energy was about 3.19 eV. The photocatalytic activity of the filter was tested for gaseous formaldehyde removal in a modeling room with the total volume of 2.66 m3. The highest removal efficiency (54.72 ± 1.75%) was obtained at the initial formaldehyde concentration of about 5.00 ± 0.50ppm.

Keywords: photocatalytic oxidation process, formaldehyde (HCHO), silk fibroin (SF), titanium dioxide (TiO2)

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Authors: Zuhier Altawallbeh

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This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

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Authors: Clarinda Vitorino Nhangumbe, Ercília Sousa

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Weather derivatives are financial products used to cover non catastrophic weather events with a weather index as the underlying asset. The rainfall weather derivative pricing model is modeled based in the assumption that the rainfall dynamics follows Ornstein-Uhlenbeck process, and the partial differential equation approach is used to derive the convection-diffusion two dimensional time dependent partial differential equation, where the spatial variables are the rainfall index and rainfall depth. To compute the approximation solutions of the partial differential equation, the appropriate boundary conditions are suggested, and an explicit numerical method is proposed in order to deal efficiently with the different choices of the coefficients involved in the equation. Being an explicit numerical method, it will be conditionally stable, then the stability region of the numerical method and the order of convergence are discussed. The model is tested for real precipitation data.

Keywords: finite differences method, ornstein-uhlenbeck process, partial differential equations approach, rainfall derivatives

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Authors: S. A. M. Yatim, Z. B. Ibrahim, K. I. Othman, M. Suleiman

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The method of solving second order stiff ordinary differential equation (ODEs) that is based on backward differentiation formula (BDF) is considered in this paper. We derived the method by increasing the order of the existing method using an improved strategy in choosing the step size. Numerical results are presented to compare the efficiency of the proposed method to the MATLAB’s suite of ODEs solvers namely ode15s and ode23s. The method was found to be efficient to solve second order ordinary differential equation.

Keywords: backward differentiation formulae, block backward differentiation formulae, stiff ordinary differential equation, variable step size

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Authors: Mustafa Ekici

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Natural convection is a basic process which is important in a wide variety of practical applications. In essence, a heated fluid expands and rises from buoyancy due to decreased density. Numerous papers have been written on natural or mixed convection in vertical ducts heated on the side. These equations have been proved to be valuable tools for the modelling of many phenomena such as fluid dynamics. Finding solutions to such equations or system of equations are in general not an easy task. We propose a method, which is called differential transform method, of solving a non-linear equations and compare the results with some of the other techniques. Illustrative examples shows that the results are in good agreement.

Keywords: differential transform method, momentum, energy equation, boundry value problem

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Authors: Tarek S. Jamil, Ahmed M. Shaban, Eman S. Mansor, Ahmed A. Karim, Azza M. Abdel Aty

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In this manuscript, 35 m³/d NF unit was designed and applied for surface water treatment of river Nile water. Intake of Embaba drinking water treatment plant was selected to install that unit at since; it has the lowest water quality index value through the examined 6 sites in greater Cairo area. The optimized operating conditions were feed and permeate flow, 40 and 7 m³/d, feed pressure 2.68 bar and flux rate 37.7 l/m2.h. The permeate water was drinkable according to Egyptian Ministerial decree 458/2007 for the tested parameters (physic-chemical, heavy metals, organic, algal, bacteriological and parasitological). Single and double sand filters were used as pretreatment for NF membranes, but continuous clogging for sand filters moved us to use UF membrane as pretreatment for NF membrane.

Keywords: River Nile, NF membrane, pretreatment, UF membrane, water quality

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Authors: Himanshu Dehra

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This paper presents a paradigm for characterization and checking of human noise behavior. The definitions of ‘Noise’ and ‘Noise Behavior’ are devised. The concept of characterization and examining of Noise Behavior is obtained from the proposed paradigm of Psychoacoustics. The measurement of human noise behavior is discussed through definitions of noise sources and noise measurements. The noise sources, noise measurement equations and noise filters are further illustrated through examples. The theory and significance of solar energy acoustics is presented for life and its activities. Human comfort and health are correlated with human brain through physiological responses and noise protection. Examples of heat stress, intense heat, sweating and evaporation are also enumerated.

Keywords: human brain, noise behavior, noise characterization, noise filters, physiological responses, psychoacoustics

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Authors: Razieh Khalafi

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The brain is the information processing centre of the human body. Stimuli in the form of information are transferred to the brain and then brain makes the decision on how to respond to them. In this research, we propose a new partial differential equation which analyses the EEG signals and make a relationship between the incoming stimuli and the brain response to them. In order to test the proposed model, a set of external stimuli applied to the model and the model’s outputs were checked versus the real EEG data. The results show that this model can model the EEG signal well. The proposed model is useful not only for modelling of EEG signal in case external stimuli but it can be used for modelling of brain response in case of internal stimuli.

Keywords: brain, stimuli, partial differential equation, response, EEG signal

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Authors: Jong-Jy Shyu, Soo-Chang Pei, Yun-Da Huang

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In this paper, design of wide-range variable fractional-delay (WR-VFD) finite impulse response (FIR) digital filters is proposed. With respect to the conventional VFD filter which is designed such that its delay is adjustable within one unit, the proposed VFD FIR filter is designed such that its delay can be tunable within a wider range. By the traces of coefficients of the fractional-delay FIR filter, it is found that the conventional method of polynomial substitution for filter coefficients no longer satisfies the design demand, and the circuits perform the sinc function (sinc converter) are added to overcome this problem. In this paper, least-squares method is adopted to design WR-VFD FIR filter. Throughout this paper, several examples will be proposed to demonstrate the effectiveness of the presented methods.

Keywords: digital filter, FIR filter, variable fractional-delay (VFD) filter, least-squares approximation

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Authors: Roman Kalvin, Anam Nadeem, Shahab Khushnood

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Differential is an integral part of four wheeled vehicle, and its main function is to transmit power from drive shaft to wheels. Differential assembly allows both rear wheels to turn at different speed along curved paths. It consists of four gears which are assembled together namely pinion, ring, spider and bevel gears. This research focused on the spider gear and its static structural analysis using ANSYS. The main aim was to evaluate the distribution of stresses on the teeth of the spider gear. This study also analyzed total deformation that may occur during its working along with bevel gear that is meshed with spider gear. Structural steel was chosen for spider gear in this research. Modeling and assembling were done on SolidWorks for both spider and bevel gear. They were assembled exactly same as in a differential assembly. This assembly was then imported to ANSYS. After observing results that maximum amount of stress and deformation was produced in the spider gear, it was concluded that structural steel material for spider gear possesses greater amount of strength to bear maximum stress.

Keywords: ANSYS, differential, spider gear, structural steel

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

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

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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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Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili

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In this paper, three complicated nonlinear differential equations(PDE,ODE) in the field of engineering and non-vibration have been analyzed and solved completely by new method that we have named it Akbari-Ganji's Method (AGM) . As regards the previous published papers, investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by Numerical Method. Based on the comparisons which have been made between the gained solutions by AGM and Numerical Method (Runge-Kutta 4th), it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. Furthermore, It is necessary to mention that a summary of the excellence of this method in comparison with the other approaches can be considered as follows: It is noteworthy that these results have been indicated that this approach is very effective and easy therefore it can be applied for other kinds of nonlinear equations, And also the reasons of selecting the mentioned method for solving differential equations in a wide variety of fields not only in vibrations but also in different fields of sciences such as fluid mechanics, solid mechanics, chemical engineering, etc. Therefore, a solution with high precision will be acquired. With regard to the afore-mentioned explanations, the process of solving nonlinear equation(s) will be very easy and convenient in comparison with the other methods. And also one of the important position that is explored in this paper is: Trigonometric and exponential terms in the differential equation (the method AGM) , is no need to use Taylor series Expansion to enhance the precision of the result.

Keywords: new method (AGM), complex non-linear partial differential equations, damping ratio, energy lost per cycle

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Authors: Trilok Mathur, Shivi Agarwal

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This paper deals with the solutions of fuzzy-fractional-order Riccati equations under Caputo-type fuzzy fractional derivatives. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhura difference and strongly generalized fuzzy differentiability. The Laplace-Adomian-Pade method is used for solving fractional Riccati-type initial value differential equations of fractional order. Moreover, we also displayed some examples to illustrate our methods.

Keywords: Caputo-type fuzzy fractional derivative, Fractional Riccati differential equations, Laplace-Adomian-Pade method, Mittag Leffler function

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Authors: Barenten Suciu

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An electrical generator able to harness energy from the water waves and designed as a double-cone geared motor-generator (DCGMG), is proposed and theoretically investigated. Similar to a differential gear mechanism, used in the transmission system of the auto vehicle wheels, an angular speed differential is created between the cones rolling on two concentric circular rails. Water wave acting on the floating DCGMG produces and a gear-box amplifies the speed differential to gain sufficient torque for power generation. A model that allows computation of the speed differential, torque, and power of the DCGMG is suggested. Influence of various parameters, regarding the construction of the DCGMG, as well as the contact between the double-cone and rails, on the electro-mechanical output, is emphasized. Results obtained indicate that the generated electrical power can be increased by augmenting the mass of the double-cone, the span of the rails, the apex angle of the cones, the friction between cones and rails, the amplification factor of the gear-box, and the efficiency of the motor-generator. Such findings are useful to formulate a design methodology for the proposed wave-powered generator.

Keywords: amplification of angular speed differential, circular concentric rails, double-cone, wave-powered electrical generator

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Authors: Shu-Yu Hsu, Chen-Chien Hsu, Wei-Yen Wang

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Color segmentation is a basic and simple way for recognizing the visual markers in a robotic tracking system. In this paper, we propose a new method for color segmentation by incorporating differential evolution algorithm and connected component labeling to autonomously preset the HSV threshold of visual markers. To evaluate the effectiveness of the proposed algorithm, a ROBOTIS OP2 humanoid robot is used to conduct the experiment, where five most commonly used color including red, purple, blue, yellow, and green in visual markers are given for comparisons.

Keywords: color segmentation, differential evolution, connected component labeling, humanoid robot

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Authors: Shigeyuki Haruyama, Ken Kaminishi, Junji Kaneko, Tadayuki Kyoutani, Siti Ruhana Omar, Oke Oktavianty

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This study is used as a definition method to the value and function in manufacturing sector. In concurrence of discussion about present condition of modeling method, until now definition of 1D-CAE is ambiguity and not conceptual. Across all the physics fields, those methods are defined with the formulation of differential algebraic equation which only applied time derivation and simulation. At the same time, we propose semi-acausal modeling concept and differential algebraic equation method as a newly modeling method which the efficiency has been verified through the comparison of numerical analysis result between the semi-acausal modeling calculation and FEM theory calculation.

Keywords: system model, physical models, empirical models, conservation law, differential algebraic equation, object-oriented

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Authors: Sajidullah Khan, Najeeb Ullah, Wang Yin Chai, Chai Soo See

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In this paper, we propose an approach to remove impulse and Poisson noise from X-ray images. Many filters have been used for impulse noise removal from color and gray scale images with their own strengths and weaknesses but X-ray images contain Poisson noise and unfortunately there is no intelligent filter which can detect impulse and Poisson noise from X-ray images. Our proposed filter uses the upgraded layer discrimination approach to detect both Impulse and Poisson noise corrupted pixels in X-ray images and then restores only those detected pixels with a simple efficient and reliable one line equation. Our Proposed algorithms are very effective and much more efficient than all existing filters used only for Impulse noise removal. The proposed method uses a new powerful and efficient noise detection method to determine whether the pixel under observation is corrupted or noise free. Results from computer simulations are used to demonstrate pleasing performance of our proposed method.

Keywords: X-ray image de-noising, impulse noise, poisson noise, PRWF

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Authors: Kun-Peng Jin, Jin Liang, Ti-Jun Xiao

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In this work, we are concerned with the dynamic behaviors of solutions to some coupled systems with infinite memory, which consist of two partial differential equations where only one partial differential equation has damping. Such coupled systems are good mathematical models to describe the deformation and stress characteristics of some viscoelastic materials affected by temperature change, external forces, and other factors. By using the theory of operator semigroups, we give wellposedness results for the Cauchy problem for these coupled systems. Then, with the help of some auxiliary functions and lemmas, which are specially designed for overcoming difficulties in the proof, we show that the solutions of the coupled systems decay to zero in a strong way under a few basic conditions. The results in this dynamic analysis of coupled systems are generalizations of many existing results.

Keywords: dynamic analysis, coupled system, infinite memory, damping.

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Authors: Yacine Arioua

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In this paper, we investigate the existence and uniqueness of solutions for a coupled system of nonlinear Caputo-type Katugampola fractional differential equations with integral boundary conditions. Based upon a contraction mapping principle, Schauders fixed point theorems, some new existence and uniqueness results of solutions for the given problems are obtained. For application, some examples are given to illustrate the usefulness of our main results.

Keywords: fractional differential equations, coupled system, Caputo-Katugampola derivative, fixed point theorems, existence, uniqueness

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Authors: Luis Miguel Méndez Díaz

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In this article, a mathematics teaching-learning strategy will be presented, specifically differential calculus in one variable, in a fun and competitive space in which the action on the part of the student is manifested and not only the repetition of information on the part of the teacher. Said action refers to motivating, problematizing, summarizing, and coordinating a game of dominoes whose thematic cards are designed around the basic and main contents of differential calculus. The strategies for teaching this area are diverse and precisely the game of dominoes is one of the most used strategies in the practice of mathematics because it stimulates logical reasoning and mental abilities. The objective on this investigation is to identify the way in which the game of dominoes affects the learning and understanding of fundamentals concepts of differential calculus in one variable through experimentation carried out on students of the first semester of the School of Engineering and Sciences of the Technological Institute of Monterrey Campus Querétaro. Finally, the results of this study will be presented and the use of this strategy in other topics around mathematics will be recommended to facilitate logical and meaningful learning in students.

Keywords: collaborative learning, logical-mathematical intelligence, mathematical games, multiple intelligences

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Authors: Olusola Ezekiel Abolarin, Gift E. Noah

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This research work considered an innovative procedure to numerically approximate higher-order Initial value problems (IVP) of ordinary differential equations (ODE) using the Legendre polynomial as the basis function. The proposed method is a half-step, self-starting Block integrator employed to approximate fourth and fifth order IVPs without reduction to lower order. The method was developed through a collocation and interpolation approach. The basic properties of the method, such as convergence, consistency and stability, were well investigated. Several test problems were considered, and the results compared favorably with both exact solutions and other existing methods.

Keywords: initial value problem, ordinary differential equation, implicit off-grid block method, collocation, interpolation

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Authors: Ana B. Vivas, Antonia Ypsilanti, Aristea I. Ladas, Angeles F. Estevez

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Mild Cognitive Impairment (MCI) is considered an intermediate stage between normal and pathological aging, as a substantial percentage of people diagnosed with MCI converts later to dementia of the Alzheimer’s type. Memory is of the first cognitive processes to deteriorate in this condition. In the present study we employed the differential outcomes procedure (DOP) to improve visuospatial memory in a group of participants with MCI. The DOP requires the structure of a conditional discriminative learning task in which a correct choice response to a specific stimulus-stimulus association is reinforced with a particular reinforcer or outcome. A group of 10 participants with MCI, and a matched control group had to learn and keep in working memory four target locations out of eight possible locations where a shape could be presented. Results showed that participants with MCI had a statistically significant better terminal accuracy when a unique outcome was paired with a location (76% accuracy) as compared to a non differential outcome condition (64%). This finding suggests that the DOP is useful in improving working memory in MCI patients, which may delay their conversion to dementia.

Keywords: mild cognitive impairment, working memory, differential outcomes, cognitive process

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Authors: Sweta Sinha

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Rapid evolution of technology has changed language pedagogy as well as perspectives on language use, leading to strategic changes in discourse studies. We are now firmly embedded in a time when digital technologies have become an integral part of our daily lives. This has led to generalized approaches to English Language Teaching (ELT) which has raised two-pronged concerns in linguistically diverse settings: a) the diverse linguistic background of the learner might interfere/ intervene with the learning process and b) the differential level of already acquired knowledge of target language might make the classroom practices too easy or too difficult for the target group of learners. ELT needs a more systematic and differential pedagogical approach for greater efficiency and accuracy. The present research analyses the need of identifying learner groups based on different levels of target language proficiency based on a longitudinal study done on 150 undergraduate students. The learners were divided into five groups based on their performance on a twenty point scale in Listening Speaking Reading and Writing (LSRW). The groups were then subjected to varying durations of technology aided language learning sessions and their performance was recorded again on the same scale. Identifying groups and introducing differential teaching and learning strategies led to better results compared to generalized teaching strategies. Language teaching includes different aspects: the organizational, the technological, the sociological, the psychological, the pedagogical and the linguistic. And a facilitator must account for all these aspects in a carefully devised differential approach meeting the challenge of learner diversity. Apart from the justification of the formation of differential groups the paper attempts to devise framework to account for all these aspects in order to make ELT in multilingual setting much more effective.

Keywords: differential groups, English language teaching, language pedagogy, multilingualism, technology aided language learning

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Authors: A. Bentabet, A. Aydin, N. Fenineche

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In this work, we try to determine the best analytical approximation of differential cross sections, used generally in Monte Carlo simulation, to study the electron/positron slowing down in solid targets in the energy range up to 10 keV. Actually, our comparative study was carried out on the angular distribution of the scattering angle, the elastic total and the first transport cross sections which are the essential quantities used generally in the electron/positron transport study by using both stochastic and deterministic methods. Indeed, the obtained results using the relativistic partial wave expansion method and the backscattering coefficient experimental data are used as criteria to evaluate the used model.

Keywords: differential cross-section, backscattering coefficient, Rutherford cross-section, Vicanek and Urbassek theory

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