Search results for: rolling sphere method

Authors: Haijie Li, Xuping Zhang

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This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: flexible manipulator, transfer matrix method, linearization, finite segment method

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Authors: Ahmed Guerine, Ali El Hafidi, Bruno Martin, Philippe Leclaire

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In this paper, we propose a method for the dynamic response of multi-storey structures with uncertain-but-bounded parameters. The effectiveness of the proposed method is demonstrated by a numerical example of three-storey structures. This equation is integrated numerically using Newmark’s method. The numerical results are obtained by the proposed method. The simulation accounting the interval analysis method results are compared with a probabilistic approach results. The interval analysis method provides a mean curve that is between an upper and lower bound obtained from the probabilistic approach.

Keywords: multi-storey structure, dynamic response, interval analysis method, random parameters

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Authors: Somaya Adwan, Rasha Majed, Lamya'a Majed, Hamzah Arof

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In order to produce images with whole body parts, X-ray of different portions of the body parts is assembled using image stitching methods. A new method for image stitching that exploits mutually feature based method and direct based method to identify and merge pairs of X-ray medical images is presented in this paper. The performance of the proposed method based on this hybrid approach is investigated in this paper. The ability of the proposed method to stitch and merge the overlapping pairs of images is demonstrated. Our proposed method display comparable if not superior performance to other feature based methods that are mentioned in the literature on the standard databases. These results are promising and demonstrate the potential of the proposed method for further development to tackle more advanced stitching problems.

Keywords: image stitching, direct based method, panoramic image, X-ray

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Authors: M. O. Olayiwola

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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Isabel L. Guidote

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Continued advancements and innovation in the technological arena may yield both beneficial and detrimental effects to market competition in the Philippines. This paper discusses recent developments in the digital sphere which have resulted in improved access to the Philippine market for both producers and consumers. Acknowledging that these developments are likely to disrupt or alter prevailing market conditions, this paper likewise tackles competition theories of harm that may arise as a result of such technological innovations, with reference to cases decided by foreign competition authorities and the European Commission. As the Philippine moves closer to the digital frontier, it is imperative that producers, consumers, and regulators alike be well-equipped to address the risks and challenges posed by these rapid advancements in technology.

Keywords: antitrust, competition law, market competition, technology

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Authors: Mohammad Ahmad, Dayalan Kasilingam

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In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using the spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The study focuses on the application of SD-FMM to one-dimensional (1D) and two-dimensional (2D) electric field integral equation (EFIE). The case of perfectly conducting strip, circular and square cylinders are numerically analyzed and compared with the results from the standard method of moments (MoM).

Keywords: electric field integral equation, fast multipole method, method of moments, wave scattering, spectral domain

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Authors: Alkaben Patel

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The proposed RP-HPLC method is easy, rapid, economical, precise and accurate stability indicating RP-HPLC method for simultaneous estimation of Astorvastatin and Methylcobalamine in their combined dosage form has been developed.The separation was achieved by LC-20 AT C18(250mm*4.6mm*2.6mm)Colum and water (pH 3.5): methanol 70:30 as mobile phase, at a flow rate of 1ml/min. wavelength of this dosage form is 215nm.The drug is related to stress condition of hydrolysis, oxidation, photolysis and thermal degradation.

Keywords: RP- HPLC, atorvastatin, methylcobalamine, method, development, validation

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Authors: M. Osipova

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Thanks to informational technologies development every sphere of economics is becoming more and more data-centralized as people are generating huge datasets containing information on any aspect of their life. Applying research of such data to human resources management allows getting scarce statistics on labor market state including salary expectations and potential employees’ typical career behavior, and this information can become a reliable basis for management decisions. The following article presents results of career behavior research based on freely accessible resume data. Information used for study is much wider than one usually uses in human resources surveys. That is why there is enough data for statistically significant results even for subgroups analysis.

Keywords: human resources management, salary expectations, statistics, turnover

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Authors: Yosra M. Badiei, Evelyn Ortiz, Marisa Portenti, David Szalda

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Water-oxidation half-reaction is a critical reaction that can be driven by a sustainable energy source (e.g., solar or wind) and be coupled with a chemical fuel making reaction which stores the released electrons and protons from water (e.g., H₂ or methanol). The use of molecular water-oxidation catalysts (WOC) allow the rationale design of redox active metal centers and provides a better understanding of their structure-activity-relationship. Herein, the structure of a Ru(III) complex bearing a doubly deprotonated N,N'-bis(aryl)pyridine-2,6-dicarboxamide ligand which contains a water molecule in its primary coordination sphere was elucidated by single-crystal X-ray diffraction. Further spectroscopic experimental data and pH-dependent electrochemical studies reveal its water-oxidation reactivity. Emphasis on mechanistic details for O₂ formation of this complex will be addressed.

Keywords: water-oxidation, catalysis, ruthenium, artificial photosynthesis

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Authors: Veeresham Mokali

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Recrystallization microstructure and grain growth studies of Ta₀.₅Nb₀.₅Hf₀.₅ZrTi₁.₅ refractory high entropy alloy have been explored in the present work. The as-cast Ta₀.₅Nb₀.₅Hf₀.₅ZrTi₁.₅ alloy was cold-rolled to 90% in several passes at room temperature and further subjected to annealing treatment for recrystallization at 800°C, 1000°C, 1250°C, and 1400°C temperatures for one hour. However, the characterization of heavily cold-rolled and annealed condition specimens was done using scanning electron microscopy (SEM-EBSD). The cold-rolled specimens showed the development of an inhomogeneous microstructure. Upon annealing, recrystallized microstructures were achieved; in addition to that, the coarsening of microstructure with raising annealing temperature noticed in the range of 800°C – 1400°C annealed temperatures.

Keywords: refractory high entropy alloys, cold-rolling, recrystallization, microstructure

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Authors: Sumachaya Harnsukworapanich, Tetsuo Ichimori

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The apportionment method is used by many countries, to calculate the distribution of seats in political bodies. For example, this method is used in the United States (U.S.) to distribute house seats proportionally based on the population of the electoral district. Famous apportionment methods include the divisor methods called the Adams Method, Dean Method, Hill Method, Jefferson Method and Webster Method. Sometimes the results from the implementation of these divisor methods are unfair and include errors. Therefore, it is important to examine the optimization of this method by using a bias measurement to figure out precise and fair results. In this research we investigate the bias of divisor methods in the U.S. Houses of Representatives toward large and small states by applying the Stolarsky Mean Method. We compare the bias of the apportionment method by using two famous bias measurements: The Balinski and Young measurement and the Ernst measurement. Both measurements have a formula for large and small states. The Third measurement however, which was created by the researchers, did not factor in the element of large and small states into the formula. All three measurements are compared and the results show that our measurement produces similar results to the other two famous measurements.

Keywords: apportionment, bias, divisor, fair, measurement

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Authors: Merina Islam

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The feminists have identified the traditional western ethical theories as basically male centered. Feminists are committed to develop a critique showing how the traditional western ethics together with traditional philosophy, irrespective of the claim for gender neutrality, all throughout remained gender-biased. This exclusion of women’s experiences from the moral discourse is justified on the ground that women cannot be moral agents, since they are not rational. By way of entailment, we are thus led to the position that virtues of traditional ethics, so viewed, can nothing but rational and hence male. The ears of traditional Western ethicists have been attuned to male rather than female ethical voices. Right from the Plato, Aristotle, Augustine, Aquinas, Rousseau, Kant, Hegel and even philosophers like Freud, Schopenhauer, Nietzsche and many others the dualism between reason-passion or mind and body started gaining prominence. These, according to them, have either intentionally excluded women or else have used certain male moral experience as the standard for all moral experiences, thereby resulting once again in exclusion of women’s experiences. Men are identified with rationality and hence contrasted with women whose sphere is believed to be that of emotion and feeling. This act of exclusion of women’s experience from moral discourse has given birth to a tradition that emphasizes reason over emotion, universal over the particular, and justice over caring. That patriarchy’s use of gender distinctions in the realm of Ethics has resulted in gender discriminations is an undeniable fact. Hence women’s moral agency is said to have often been denied, not simply by the act of exclusion of women from moral debate or sheer ignorance of their contributions, but through philosophical claims to the effect that women lack moral reason. Traditional or mainstream ethics cannot justify its claim for universality, objectivity and gender neutrality the standards from which were drawn the legitimacy of the various moral maxims or principles of it. Right from the Platonic and Aristotelian period the dualism between reason-passion or mind and body started gaining prominence. Men are identified with rationality and hence contrasted with women whose sphere is believed to be that of emotion and feeling. Through the Association of the masculine values with reason (the feminine with irrational), was created the standard prototype of moral virtues The feminists’ critique of the traditional mainstream Ethics is based on this charge that because of its inherent gender bias, in the name of gender distinctions, Ethics has so far been justifying discriminations. In this paper, attempt would make upon the gender biased-ness of traditional ethics. But Feminists are committed to develop a critique showing how the traditional ethics together with traditional philosophy, irrespective of the claim for gender neutrality, all throughout remained gender-biased. We would try to show to what extent traditional ethics is male centered and consequentially fails to justify its claims for universality and gender neutrality.

Keywords: ethics, gender, male-centered, traditional

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Authors: Mei-Jie Xu, Yang Zhong

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Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system

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Authors: William C. Alexander

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The oscillating water column (OSC) wave energy converter (WEC) with deep water reactance (DWR) consists of a large hollow sphere filled with seawater at the base, referred to as the ‘stabilizer’, a hollow cylinder at the top of the device, with a said cylinder having a bottom open to the sea and a sealed top save for an orifice which leads to an air turbine, and a long, narrow rod connecting said stabilizer with said cylinder. A small amount of ballast at the bottom of the stabilizer and a small amount of floatation in the cylinder keeps the device upright in the sea. The floatation is set such that the mean water level is nominally halfway up the cylinder. The entire device is loosely moored to the seabed to keep it from drifting away. In the presence of ocean waves, seawater will move up and down within the cylinder, producing the ‘oscillating water column’. This gives rise to air pressure within the cylinder alternating between positive and negative gauge pressure, which in turn causes air to alternately leave and enter the cylinder through said top-cover situated orifice. An air turbine situated within or immediately adjacent to said orifice converts the oscillating airflow into electric power for transport to shore or elsewhere by electric power cable. Said oscillating air pressure produces large up and down forces on the cylinder. Said large forces are opposed through the rod to the large mass of water retained within the stabilizer, which is located deep enough to be mostly free of any wave influence and which provides the deepwater reactance. The cylinder and stabilizer form a spring-mass system which has a vertical (heave) resonant frequency. The diameter of the cylinder largely determines the power rating of the device, while the size (and water mass within) of the stabilizer determines said resonant frequency. Said frequency is chosen to be on the lower end of the wave frequency spectrum to maximize the average power output of the device over a large span of time (such as a year). The upper portion of the device (the cylinder) moves laterally (surge) with the waves. This motion is accommodated with minimal loading on the said rod by having the stabilizer shaped like a sphere, allowing the entire device to rotate about the center of the stabilizer without rotating the seawater within the stabilizer. A full-scale device of this type may have the following dimensions. The cylinder may be 16 meters in diameter and 30 meters high, the stabilizer 25 meters in diameter, and the rod 55 meters long. Simulations predict that this will produce 1,400 kW in waves of 3.5-meter height and 12 second period, with a relatively flat power curve between 5 and 16 second wave periods, as will be suitable for an open-ocean location. This is nominally 10 times higher power than similar-sized WEC spar buoys as reported in the literature, and the device is projected to have only 5% of the mass per unit power of other OWC converters.

Keywords: oscillating water column, wave energy converter, spar bouy, stabilizer

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

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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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Authors: Dogan Ciloglu, Abdurrahim Bolukbasi, Harun Cifci

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In this study, the experiments were carried out to determine the best coolant for the quenching process among water-based silica, alumina, titania and copper oxide nanofluids (0.1 vol%). A sphere made up off brass material was used in the experiments. After the spherical test specimen was heated at high temperatures, it was suddenly plunged into the nanofluid suspensions. All experiments were performed at saturated conditions and under atmospheric pressure. Using the temperature-time data of the specimen, the cooling curves were obtained. The experimental results showed that the cooling performance of test specimen depended on the type of nanofluids. The silica nanoparticles enhanced the performance of boiling heat transfer and it is the best coolant for the quenching among other nanoparticles.

Keywords: quenching, nanofluid, pool boiling, heat transfer

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Authors: Alexander Matrosov, Guriy Shirunov

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A superposition method based on Lame's idea is used to get a general analytical solution to analyze a stress and strain state of a rectangular isotropjc elastic thick plate. The solution is built by using three solutions of the method of initial functions in the form of double trigonometric series. The results of bending of a thick plate under normal stress on its top face with two opposite sides clamped while others free of load are presented and compared with FEM modelling.

Keywords: general solution, method of initial functions, superposition method, thick isotropic plates

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Authors: Mahmood Otadi, Maryam Mosleh

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation

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Authors: Cletus Abhulimen, L. A. Ukpebor

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In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method.

Keywords: third derivative four-step, exponentially fitted, a-stable, stiff differential equations

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Authors: Guettal Djaouida, Ziadi Abdelkader

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In this paper, we study a coupling of the Alienor method with the algorithm of Piyavskii-Shubert. The classical multidimensional global optimization methods involves great difficulties for their implementation to high dimensions. The Alienor method allows to transform a multivariable function into a function of a single variable for which it is possible to use efficient and rapid method for calculating the the global optimum. This simplification is based on the using of a reducing transformation called Alienor.

Keywords: global optimization, reducing transformation, α-dense curves, Alienor method, Piyavskii-Shubert algorithm

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Authors: Avishkar Gawade, Omkar Bansode, Ketan Bhambure, Bhargav Deore

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In recent year wide range of business intelligence technology have been applied to different area in order to support decision making process BI enables extraction of knowledge from data store. BI tools usually used in public health field for financial and administrative purposes.BI uses a dashboard in presentation stage to deliver information to information to end users.In this paper,we intend to analyze some open source BI tools on the market and their applicability in the clinical sphere taking into consideration the general characteristics of the clinical environment.A pervasive BI platform was developed using a real case in order to prove the tool viability.Analysis of various BI Tools in done with the help of several parameters such as data security,data integration,data quality reporting and anlaytics,performance,scalability and cost effectivesness.

Keywords: CDSS, EHR, business intelliegence, tools

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Authors: Y. A. Yahaya, Ahmad Tijjani Asabe

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This paper focuses on the formulation of 3-step hybrid Adams type method for the solution of first order differential equation (ODE). The methods which was derived on both grid and off grid points using multistep collocation schemes and also evaluated at some points to produced Block Adams type method and Adams moulton method respectively. The method with the highest order was selected to serve as the corrector. The convergence was valid and efficient. The numerical experiments were carried out and reveal that hybrid Adams type methods performed better than the conventional Adams moulton method.

Keywords: adam-moulton type (amt), corrector method, off-grid, block method, convergence analysis

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Authors: Taiyo Matsumura, Kuninori Takahashi, Takashi Ono

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The purpose of this research is to improve the convenience of waiting for trains at level crossings and stations and to prevent accidents resulting from forcible entry into level crossings, by providing level crossing users and passengers with information that tells them when the next train will pass through or arrive. For this paper, we proposed methods for estimating operation by means of an average value method, variable response smoothing method, and exponential smoothing method, on the basis of open data, which has low accuracy, but for which performance schedules are distributed in real time. We then examined the accuracy of the estimations. The results showed that the application of an exponential smoothing method is valid.

Keywords: exponential smoothing method, open data, operation estimation, train schedule

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Authors: Maryam Khazaei Pool, Lori Lewis

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This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method, Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper, we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions, including Burgers equation, spline functions, and B-spline functions, are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided, and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

Keywords: Burgers’ equation, Septic B-spline, modified cubic B-spline differential quadrature method, exponential cubic B-spline technique, B-spline Galerkin method, quintic B-spline Galerkin method

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Authors: Juan F. P. Ramírez, Jésica A. L. Isaza, Benjamín A. Rojano

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This study proposes a novel use of a method to determine the mechanical properties of fruits by the use of the indentation tests. The method combines experimental results with a numerical finite elements model. The results presented correspond to a simplified numerical modeling of banana. The banana was assumed as one-layer material with an isotropic linear elastic mechanical behavior, the Young’s modulus found is 0.3Mpa. The method will be extended to multilayer models in further studies.

Keywords: finite element method, fruits, inverse analysis, mechanical properties

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Authors: Amara Prakasa Rao, N. V. S. N. Sarma

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This paper describes the synthesis of linear array geometry with minimum sidelobe level and null control using the Taguchi method. Based on the concept of the orthogonal array, Taguchi method effectively reduces the number of tests required in an optimization process. Taguchi method has been successfully applied in many fields such as mechanical, chemical engineering, power electronics, etc. Compared to other evolutionary methods such as genetic algorithms, simulated annealing and particle swarm optimization, the Taguchi method is much easier to understand and implement. It requires less computational/iteration processing to optimize the problem. Different cases are considered to illustrate the performance of this technique. Simulation results show that this method outperforms the other evolution algorithms (like GA, PSO) for smart antenna systems design.

Keywords: array factor, beamforming, null placement, optimization method, orthogonal array, Taguchi method, smart antenna system

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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: Kamaljeet Kaur, Vinod Kumari, Jatesh Kathpalia, Bas Kaur

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A gender bias towards girl child is pervasive across the world. It is seen in all the strata of the society and manifests in various forms. However nature and extent of these inequalities are not uniform. Generally these inequalities are more prevalent in patriarchal society. Despite emerging and increasing opportunities for women, there are still inequalities between men and women in each and every sphere like education, health, economy, polity and social sphere. Patriarchal ideology as a cultural norm enforces gender construction which is oriented toward hierarchical relations between the sexes and neglect of women in Indian society. Discrimination to girls may also vary by their age and be restricted to the birth order and sex composition of her elder surviving siblings. The present study was conducted to know the gender discrimination among rural children in India. The respondents were selected from three generations as per AICRP age group viz, 18-30 years (3rd generation), 31-60 years (2nd generation) and above 60 years (1st generation). A total sample size was 600 respondents from different villages of two districts of Haryana state comprising of half males and half females. Data were collected using personal interview schedule and analysed by SPSS software. Among the total births 46.35 per cent were girl child and 53.64 % were male child. Dropout rate was more in female children as compared to male children i.e. near about one third (31.09%) female children dropped school followed by 21.17 % male children. It was quite surprising that near about two-third (61.16%) female children and more than half (59.22%) of the male children dropped school. Cooking was mainly performed by adult female with overall mean scores 2.0 and ranked first which was followed by female child (1.7 mean scores) clearly indicating that cooking was the activity performed mainly by females while activity related to purchase of fruits and vegetable, cereals and pulses was mainly done by adult male. First preference was given to male child for serving of costly and special food. Regarding professional aspiration of children of the respondents’ families, it was observed that 20.10% of the male children wanted to become engineer, whereas only 3.89 % female children wanted to become engineer. Ratio of male children was high in both generations irrespective of the districts. School dropouts were more in case of female in both the 1st and 2 nd generations. The main reasons of school dropout were lack of interest, lack of resources and early marriage in both the generations. Female enrolment was more in faculty of arts, whereas in case of male percentage it was more in faculty of non-medical and medical which showed that female children were getting traditional type of education. It is suggested to provide equal opportunities to girls and boys in home as well as outside the home for smooth functioning of society.

Keywords: gender biasness, male child, female child, education, home

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Authors: Sunyoung Bu, Wonkyu Chung, Philsu Kim

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In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg 4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. This solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.

Keywords: embedded Runge-Kutta-Fehlberg method, initial value problem, EULR problem, integration step

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