Search results for: integral method

Authors: Fayssal Amrane, Azeddine Chaiba, Bruno Francois

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In this paper, design and experimental study based on Direct Power Control (DPC) of DFIG is proposed for Stand-alone mode in Variable Speed Wind Energy Conversion System (VS-WECS). The proposed IDPC method based on robust IP (Integral-Proportional) controllers in order to control the Rotor Side Converter (RSC) by the means of the rotor current d-q axes components (Ird* and Irq*) of Doubly Fed Induction Generator (DFIG) through AC-DC-AC converter. The implementation is realized using dSPACE dS1103 card under Sub and Super-synchronous operations (means < and > of the synchronous speed “1500 rpm”). Finally, experimental results demonstrate that the proposed control using IP provides improved dynamic responses, and decoupled control of the wind turbine has driven DFIG with high performances (good reference tracking, short response time and low power error) despite for sudden variation of wind speed and rotor references currents.

Keywords: Direct Power Control (DPC), Doubly fed induction generator (DFIG), Wind Energy Conversion System (WECS), Experimental study.

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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: Renata Markiewicz-Żukowska, Patryk Nowakowski, Sylwia K. Naliwajko, Jakub M. Bołtryk, Katarzyna Socha, Anna Puścion-Jakubik, Jolanta Soroczyńska, Maria H. Borawska

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Selenium (Se) is an essential element for human health. As an integral part of glutathione peroxidase, it has antioxidant, anti-inflammatory and anticancer activities. Unfortunately, Se dietary intake is often insufficient, especially in regions where the soil is low in Se. Therefore, in search for good sources of Se, the content of this element in food products should be monitored. Food product can be considered as a source of Se when its standard portion covers above 15% of recommended daily allowance. In the case of nuts, 42g is recognized as the standard portion. The aim of this study was to determine the Se content in nuts and to answer the question of whether the studied nuts can be considered as a source of Se in the diet. The material for the study consisted of 10 types of nuts (12 samples of each one): almonds, Brazil nuts, cashews, hazelnuts, macadamia nuts, peanuts, pecans, pine nuts, pistachios and walnuts. The nuts were mineralized using microwave technique (Berghof, Germany). The content of Se was determined by atomic absorption spectrometry method with electrothermal atomization in a graphite tube with Zeeman background correction (Hitachi, Japan). The accuracy of the method was verified on certified reference material: Simulated Diet D. The statistical analysis was performed using Statistica v. 13.0 software. Statistical significance was determined at p < 0.05 level. The highest content of Se was found in Brazil nuts (4566.21 ± 3393.9 µg/kg) and the lowest in almonds (36.07 ± 18.8 µg/kg). A standard portion (42g) of almonds, brazil nuts, cashews, hazelnuts, macadamia nuts, peanuts, pecans, pine nuts, pistachios and walnuts covers the recommended daily allowance for Se respectively in: 2, 192, 28, 2, 16, 7, 4, 3, 12, 6%. Brazil nuts, cashews and macadamia nuts can be considered as a good source of Se in diet.

Keywords: atomic absorption spectrometry, diet, nuts, selenium

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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: Roger-Claude Liwanga

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This article reflects on the normative aspects of the jurisprudence on the protection of human rights in times of war that the International Court of Justice (ICJ) developed in 2005 in the Case Concerning Armed Activities on the Territory of the Congo (Democratic Republic of Congo v. Uganda). The article focuses on theories raised in connection with the Democratic Republic of Congo (DRC)'s claim of the violation of human rights of its populations by Uganda as opposed to the violation of its territorial integrity claims. The article begins with a re-visitation of the doctrine of state extraterritorial responsibility for violations of human rights by suggesting that a state's accountability for the breach of its international obligations is not territorially confined but rather transcends the State's national borders. The article highlights the criteria of assessing the State's extraterritorial responsibility, including the circumstances: (1) where the concerned State has effective control over the territory of another State in the context of belligerent occupation, and (2) when the unlawful actions committed by the State's organs on the occupied territory can be attributable to that State. The article also analyzes the ICJ's opinions articulated in DRC v. Uganda with reference to the relationship between human rights law and humanitarian law, and it contends that the ICJ had revised the traditional interaction between these two bodies of law to the extent that human rights law can no longer be excluded from applying in times of war as both branches are complementary rather than exclusive. The article correspondingly looks at the issue of reparations for victims of human rights violations. It posits that reparations for victims of human rights violations should be integral (including restitution, compensation, rehabilitation, satisfaction, and guarantees of non-repetition). Yet, the article concludes by emphasizing that reparations for victims were not integral in DRC v. Uganda because: (1) the ICJ failed to set a reasonable timeframe for the negotiations between the DRC and Uganda on the amount of compensation, resulting in Uganda paying no financial reparation to the DRC since 2005; and (2) the ICJ did not request Uganda to domestically prosecute the perpetrators of human rights abuses.

Keywords: human rights law, humanitarian law, civilian protection, extraterritorial responsibility

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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: 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: 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: Salah Alrabeei, Mohammad Yousuf

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The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. Modeling option pricing by Black-School models with jumps guarantees to consider the market movement. However, only numerical methods can solve this model. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, the exponential time differencing (ETD) method is applied for solving partial integrodifferential equations arising in pricing European options under Merton’s and Kou’s jump-diffusion models. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). A partial fraction form of Pad`e schemes is used to overcome the complexity of inverting polynomial of matrices. These two tools guarantee to get efficient and accurate numerical solutions. We construct a parallel and easy to implement a version of the numerical scheme. Numerical experiments are given to show how fast and accurate is our scheme.

Keywords: Integral differential equations, , L-stable methods, pricing European options, Jump–diffusion model

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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: T. Al-Alawi, N. Shorbaji, E. Rashaidi, M.Alidrisi

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Purpose/Objective(s): The main purpose of this study is to analyze the planning of SBRT treatments for localized prostate cancer with 6FFF and 10FFF energies to see if there is a dosimetric difference between the two energies and how we can increase the plan efficiency and reduce its complexity. Also, to introduce a planning method in our department to treat prostate cancer by utilizing high energy photons without increasing patient toxicity and fulfilled all dosimetric constraints for OAR (an organ at risk). Then toevaluate the target 95% coverage PTV95, V5%, V2%, V1%, low dose volume for OAR (V1Gy, V2Gy, V5Gy), monitor unit (beam-on time), and estimate the values of homogeneity index HI, conformity index CI a Gradient index GI for each treatment plan.Materials/Methods: Two treatment plans were generated for15 patients with localized prostate cancer retrospectively using the CT planning image acquired for radiotherapy purposes. Each plan contains two/three complete arcs with two/three different collimator angle sets. The maximum dose rate available is 1400MU/min for the energy 6FFF and 2400MU/min for 10FFF. So in case, we need to avoid changing the gantry speed during the rotation, we tend to use the third arc in the plan with 6FFF to accommodate the high dose per fraction. The clinical target volume (CTV) consists of the entire prostate for organ-confined disease. The planning target volume (PTV) involves a margin of 5 mm. A 3-mm margin is favored posteriorly. Organs at risk identified and contoured include the rectum, bladder, penile bulb, femoral heads, and small bowel. The prescription dose is to deliver 35Gyin five fractions to the PTV and apply constraints for organ at risk (OAR) derived from those reported in references. Results: In terms of CI=0.99, HI=0.7, and GI= 4.1, it was observed that they are all thesame for both energies 6FFF and 10FFF with no differences, but the total delivered MUs are much less for the 10FFF plans (2907 for 6FFF vs.2468 for 10FFF) and the total delivery time is 124Sc for 6FFF vs. 61Sc for 10FFF beams. There were no dosimetric differences between 6FFF and 10FFF in terms of PTV coverage and mean doses; the mean doses for the bladder, rectum, femoral heads, penile bulb, and small bowel were collected, and they were in favor of the 10FFF. Also, we got lower V1Gy, V2Gy, and V5Gy doses for all OAR with 10FFF plans. Integral dosesID in (Gy. L) were recorded for all OAR, and they were lower with the 10FFF plans. Conclusion: High energy 10FFF has lower treatment time and lower delivered MUs; also, 10FFF showed lower integral and meant doses to organs at risk. In this study, we suggest usinga 10FFF beam for SBRTprostate treatment, which has the advantage of lowering the treatment time and that lead to lessplan complexity with respect to 6FFF beams.

Keywords: FFF beam, SBRT prostate, VMAT, prostate cancer

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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: 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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Authors: Mohammed Salem Alzahrani

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In this paper, student admission process is studied to optimize the assignment of vacant seats with three main objectives. Utilizing all vacant seats, satisfying all program of study admission requirements and maintaining fairness among all candidates are the three main objectives of the optimization model. Seat Assignment Method (SAM) is used to build the model and solve the optimization problem with help of Northwest Coroner Method and Least Cost Method. A closed formula is derived for applying the priority of assigning seat to candidate based on SAM.

Keywords: admission process model, assignment problem, Hungarian Method, Least Cost Method, Northwest Corner Method, SAM

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Authors: J. S. Savier

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Real power is the component power which is converted into useful energy whereas reactive power is the component of power which cannot be converted to useful energy but it is required for the magnetization of various electrical machineries. If the reactive power is compensated at the consumer end, the need for reactive power flow from generators to the load can be avoided and hence the overall power loss can be reduced. In this scenario, this paper presents a succinct method called JSS method for allocation of reactive power losses to consumers connected to radial distribution networks in a deregulated environment. The proposed method has the advantage that no assumptions are made while deriving the reactive power loss allocation method.

Keywords: deregulation, reactive power loss allocation, radial distribution systems, succinct method

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Authors: S. Mousavian, A. Abedianpour, A. Khanmohammadi, S. Hematian, Gh. Eidi Veisi

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Distillation is one of the most important and utilized separation methods in the industrial practice. There are different ways to design of distillation column. One of these ways is short cut method. In short cut method, material balance and equilibrium are employed to calculate number of tray in distillation column. There are different methods that are classified in short cut method. One of these methods is Fenske-Underwood-Gilliland method. In this method, minimum reflux ratio should be calculated by underwood equation. Underwood proposed an equation that is useful for simple distillation column with one feed and one top and bottom product. In this study, underwood method is developed to predict minimum reflux ratio for column with one side stream upper than feed. The result of this model compared with McCabe-Thiele method. The result shows that proposed method able to calculate minimum reflux ratio with very small error.

Keywords: minimum reflux ratio, side stream, distillation, Underwood’s method

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Authors: Zarine Avetisyan

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The paradigm of Modern Linguistics incorporates disciplines which allow to analyze both language and discourse units and to demonstrate the multi-layeredness of lingo-cultural consciousness. By implementing lingo-cognitive approach to discourse and communication studies, the present paper tries to create the integral linguistic picture of the concept of joy and to analyze the lexico-semantic groups and relevant lexico-semantic variants of its realization in the context of Modern English fiction.

Keywords: concept of joy, lexico-semantic variant, semantic sign, cognition

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Authors: Nicolay Zarutskiy, Roman Bulkin

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The paper deals with the existing methods of force-torque sensor calibration with a number of components from one to six, analyzed their advantages and disadvantages, the necessity of introduction of a calibration method. Calibration method and its constructive realization are also described here. A calibration method allows performing automated force-torque sensor calibration both with selected components of the main vector of forces and moments and with complex loading. Thus, two main advantages of the proposed calibration method are achieved: the automation of the calibration process and universality.

Keywords: automation, calibration, calibration device, calibration method, force-torque sensors

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Authors: Hari Prasad Nepal

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Research on lecture method issues confirm that this teaching method has been practiced from the very beginnings of schooling. Many teachers, lecturers and professors are convinced that lecture still represents main tool of contemporary instructional process. The central purpose of this study is to uncover the extent of using lecture method in the higher education. The study was carried out in Nepalese context with employing mixed method research design. To obtain the primary data this study employed a questionnaire involving items with close and open answers. 120 teachers, lecturers and professors participated in this study. The findings indicated that 75 percent of the respondents use the lecture method in their classroom teaching. The study reveals that there are advantages of using lecture method such as easy to practice, less time to prepare, high pass rate, high students’ satisfaction, little comments on instructors, appropriate to large classes and high level students. In addition, the study divulged the instructors’ reflections and measures to improve the lecture method. This research concludes that the practice of lecture method is still significantly applicable in colleges and universities in Nepalese contexts. So, there are no significant changes in the application of lecture method in the higher education classroom despite the emergence of new learning approaches and strategies.

Keywords: instructors, learning approaches, learning strategies, lecture method

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Authors: Lin Huo, Xianwei Liu, Jingxiong Zhou

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Recently, due to the existence of semantic gap between image visual features and human concepts, the semantic of image auto-annotation has become an important topic. Firstly, by extract low-level visual features of the image, and the corresponding Hash method, mapping the feature into the corresponding Hash coding, eventually, transformed that into a group of binary string and store it, image auto-annotation by search is a popular method, we can use it to design and implement a method of image semantic auto-annotation. Finally, Through the test based on the Corel image set, and the results show that, this method is effective.

Keywords: image auto-annotation, color correlograms, Hash code, image retrieval

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Authors: Anton A. Larenkov, Alesya Ya Maruk

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In the present study, highly effective iTLC single strip method for the determination of radiochemical purity (RCP) of ⁶⁸Ga-BCA-peptides was developed (with no double-developing, changing of eluents or other additional manipulation). In this method iTLC-SG strips and commonly used eluent TFA_aq. (3-5 % (v/v)) are used. The method allows determining each of the key radiochemical forms of ⁶⁸Ga (colloidal, bound, ionic) separately with the peaks separation being no less than 4 σ. Rf = 0.0-0.1 for ⁶⁸Ga-colloid; Rf = 0.5-0.6 for ⁶⁸Ga-BCA-peptides; Rf = 0.9-1.0 for ionic ⁶⁸Ga. The method is simple and fast: For developing length of 75 mm only 4-6 min is required (versus 18-20 min for pharmacopoeial method). The method has been tested on various compounds (including ⁶⁸Ga-DOTA-TOC, ⁶⁸Ga-DOTA-TATE, ⁶⁸Ga-NODAGA-RGD₂ etc.). The cross-validation work for every specific form of ⁶⁸Ga showed good correlation between method developed and control (pharmacopoeial) methods. The method can become convenient and much more informative replacement for pharmacopoeial methods, including HPLC.

Keywords: DOTA-TATE, 68Ga, quality control, radiochemical purity, radiopharmaceuticals, TLC

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Authors: Palwinder Singh, Munish Sandhir, Tejinder Singh

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The ordinary differential equations (ODE) represent a natural framework for mathematical modeling of many real-life situations in the field of engineering, control systems, physics, chemistry and astronomy etc. Such type of differential equations can be solved by analytical methods or by numerical methods. If the solution is calculated using analytical methods, it is done through calculus theories, and thus requires a longer time to solve. In this paper, we compare the numerical accuracy of the solutions given by the three main types of one-step initial value solvers: Taylor’s Series Method, Euler’s Method and Runge-Kutta Fourth Order Method (RK4). The comparison of accuracy is obtained through comparing the solutions of ordinary differential equation given by these three methods. Furthermore, to verify the accuracy; we compare these numerical solutions with the exact solutions.

Keywords: Ordinary differential equations (ODE), Taylor’s Series Method, Euler’s Method, Runge-Kutta Fourth Order Method

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