Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 17725

Search results for: derivative free method

17725 Using Derivative Free Method to Improve the Error Estimation of Numerical Quadrature

Authors: Chin-Yun Chen


Numerical integration is an essential tool for deriving different physical quantities in engineering and science. The effectiveness of a numerical integrator depends on different factors, where the crucial one is the error estimation. This work presents an error estimator that combines a derivative free method to improve the performance of verified numerical quadrature.

Keywords: numerical quadrature, error estimation, derivative free method, interval computation

Procedia PDF Downloads 369
17724 A Hybrid Derivative-Free Optimization Method for Pass Schedule Calculation in Cold Rolling Mill

Authors: Mohammadhadi Mirmohammadi, Reza Safian, Hossein Haddad


This paper presents an innovative solution for complex multi-objective optimization problem which is a part of efforts toward maximizing rolling mill throughput and minimizing processing costs in tandem cold rolling. This computational intelligence based optimization has been applied to the rolling schedules of tandem cold rolling mill. This method involves the combination of two derivative-free optimization procedures in the form of nested loops. The first optimization loop is based on Improving Hit and Run method which focus on balance of power, force and reduction distribution in rolling schedules. The second loop is a real-coded genetic algorithm based optimization procedure which optimizes energy consumption and productivity. An experimental result of application to five stand tandem cold rolling mill is presented.

Keywords: derivative-free optimization, Improving Hit and Run method, real-coded genetic algorithm, rolling schedules of tandem cold rolling mill

Procedia PDF Downloads 585
17723 A Class of Third Derivative Four-Step Exponential Fitting Numerical Integrator for Stiff Differential Equations

Authors: Cletus Abhulimen, L. A. Ukpebor


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

Procedia PDF Downloads 171
17722 A Family of Second Derivative Methods for Numerical Integration of Stiff Initial Value Problems in Ordinary Differential Equations

Authors: Luke Ukpebor, C. E. Abhulimen


Stiff initial value problems in ordinary differential equations are problems for which a typical solution is rapidly decaying exponentially, and their numerical investigations are very tedious. Conventional numerical integration solvers cannot cope effectively with stiff problems as they lack adequate stability characteristics. In this article, we developed a new family of four-step second derivative exponentially fitted method of order six for the numerical integration of stiff initial value problem of general first order differential equations. In deriving our method, we employed the idea of breaking down the general multi-derivative multistep method into predator and corrector schemes which possess free parameters that allow for automatic fitting into exponential functions. The stability analysis of the method was discussed and the method was implemented with numerical examples. The result shows that the method is A-stable and competes favorably with existing methods in terms of efficiency and accuracy.

Keywords: A-stable, exponentially fitted, four step, predator-corrector, second derivative, stiff initial value problems

Procedia PDF Downloads 175
17721 A Variant of Newton's Method with Free Second-Order Derivative

Authors: Young Hee Geum


In this paper, we present the iterative method and determine the control parameters to converge cubically for solving nonlinear equations. In addition, we derive the asymptotic error constant.

Keywords: asymptotic error constant, iterative method, multiple root, root-finding, order of convergent

Procedia PDF Downloads 184
17720 Fractional Euler Method and Finite Difference Formula Using Conformable Fractional Derivative

Authors: Ramzi B. Albadarneh


In this paper, we use the new definition of fractional derivative called conformable fractional derivative to derive some finite difference formulas and its error terms which are used to solve fractional differential equations and fractional partial differential equations, also to derive fractional Euler method and its error terms which can be applied to solve fractional differential equations. To provide the contribution of our work some applications on finite difference formulas and Euler Method are given.

Keywords: conformable fractional derivative, finite difference formula, fractional derivative, finite difference formula

Procedia PDF Downloads 320
17719 A Dynamical Study of Fractional Order Obesity Model by a Combined Legendre Wavelet Method

Authors: Hakiki Kheira, Belhamiti Omar


In this paper, we propose a new compartmental fractional order model for the simulation of epidemic obesity dynamics. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. We also present some fractional differential illustrative examples to demonstrate the applicability and efficiency of the method. The fractional derivative is described in the Caputo sense.

Keywords: Caputo derivative, epidemiology, Legendre wavelet method, obesity

Procedia PDF Downloads 307
17718 Estimation and Validation of Free Lime Analysis of Clinker by Quantitative Phase Analysis Using X ray diffraction

Authors: Suresh Palla, Kalpna Sharma, Gaurav Bhatnagar, S. K. Chaturvedi, B. N. Mohapatra


Determining the content of free lime is especially important to judge reactivity of the raw materials and clinker quality. The free lime limit isn’t the same for all cements; it depends on several factors, especially the temperature reached during the cooking and the grain size distribution in cement after grinding. Estimation of free lime by conventional method is influenced by the presence of portlandite and misleads the actual free lime content in the clinker for quality check up conditions. To ensure the product quality according to the standard specifications in terms of within the quality limits or not, a reliable, precise, and very reproducible method to quantify the relative phase abundances in the Portland Cement clinker and Portland Cements is to use X-ray diffraction (XRD) in combination with the Rietveld method. In the present study, a methodology was proposed using XRD to validate the obtained results of free lime by conventional method. The XRD and TG/DTA results confirm the presence of portlandite in the clinker to take the decision on the obtained free lime results through conventional method.

Keywords: free lime, quantitative phase analysis, conventional method, x ray diffraction

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17717 Simultaneous Determination of Methotrexate and Aspirin Using Fourier Transform Convolution Emission Data under Non-Parametric Linear Regression Method

Authors: Marwa A. A. Ragab, Hadir M. Maher, Eman I. El-Kimary


Co-administration of methotrexate (MTX) and aspirin (ASP) can cause a pharmacokinetic interaction and a subsequent increase in blood MTX concentrations which may increase the risk of MTX toxicity. Therefore, it is important to develop a sensitive, selective, accurate and precise method for their simultaneous determination in urine. A new hybrid chemometric method has been applied to the emission response data of the two drugs. Spectrofluorimetric method for determination of MTX through measurement of its acid-degradation product, 4-amino-4-deoxy-10-methylpteroic acid (4-AMP), was developed. Moreover, the acid-catalyzed degradation reaction enables the spectrofluorimetric determination of ASP through the formation of its active metabolite salicylic acid (SA). The proposed chemometric method deals with convolution of emission data using 8-points sin xi polynomials (discrete Fourier functions) after the derivative treatment of these emission data. The first and second derivative curves (D1 & D2) were obtained first then convolution of these curves was done to obtain first and second derivative under Fourier functions curves (D1/FF) and (D2/FF). This new application was used for the resolution of the overlapped emission bands of the degradation products of both drugs to allow their simultaneous indirect determination in human urine. Not only this chemometric approach was applied to the emission data but also the obtained data were subjected to non-parametric linear regression analysis (Theil’s method). The proposed method was fully validated according to the ICH guidelines and it yielded linearity ranges as follows: 0.05-0.75 and 0.5-2.5 µg mL-1 for MTX and ASP respectively. It was found that the non-parametric method was superior over the parametric one in the simultaneous determination of MTX and ASP after the chemometric treatment of the emission spectra of their degradation products. The work combines the advantages of derivative and convolution using discrete Fourier function together with the reliability and efficacy of the non-parametric analysis of data. The achieved sensitivity along with the low values of LOD (0.01 and 0.06 µg mL-1) and LOQ (0.04 and 0.2 µg mL-1) for MTX and ASP respectively, by the second derivative under Fourier functions (D2/FF) were promising and guarantee its application for monitoring the two drugs in patients’ urine samples.

Keywords: chemometrics, emission curves, derivative, convolution, Fourier transform, human urine, non-parametric regression, Theil’s method

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17716 Calculating Stress Intensity Factor of Cracked Axis by Using a Meshless Method

Authors: S. Shahrooi, A. Talavari


Numeral study on the crack and discontinuity using element-free methods has been widely spread in recent years. In this study, for stress intensity factor calculation of the cracked axis under torsional loading has been used from a new element-free method as MLPG method. Region range is discretized by some dispersed nodal points. From method of moving least square (MLS) utilized to create the functions using these nodal points. Then, results of meshless method and finite element method (FEM) were compared. The results is shown which the element-free method was of good accuracy.

Keywords: stress intensity factor, crack, torsional loading, meshless method

Procedia PDF Downloads 459
17715 The Improved Element Free Galerkin Method for 2D Heat Transfer Problems

Authors: Imen Debbabi, Hédi BelHadjSalah


The Improved Element Free Galerkin (IEFG) method is presented to treat the steady states and the transient heat transfer problems. As a result of a combination between the Improved Moving Least Square (IMLS) approximation and the Element Free Galerkin (EFG) method, the IEFG's shape functions don't have the Kronecker delta property and the penalty method is used to impose the Dirichlet boundary conditions. In this paper, two heat transfer problems, transient and steady states, are studied to improve the efficiency of this meshfree method for 2D heat transfer problems. The performance of the IEFG method is shown using the comparison between numerical and analytic results.

Keywords: meshfree methods, the Improved Moving Least Square approximation (IMLS), the Improved Element Free Galerkin method (IEFG), heat transfer problems

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17714 Assessment of Pre-Processing Influence on Near-Infrared Spectra for Predicting the Mechanical Properties of Wood

Authors: Aasheesh Raturi, Vimal Kothiyal, P. D. Semalty


We studied mechanical properties of Eucalyptus tereticornis using FT-NIR spectroscopy. Firstly, spectra were pre-processed to eliminate useless information. Then, prediction model was constructed by partial least squares regression. To study the influence of pre-processing on prediction of mechanical properties for NIR analysis of wood samples, we applied various pretreatment methods like straight line subtraction, constant offset elimination, vector-normalization, min-max normalization, multiple scattering. Correction, first derivative, second derivatives and their combination with other treatment such as First derivative + straight line subtraction, First derivative+ vector normalization and First derivative+ multiplicative scattering correction. The data processing methods in combination of preprocessing with different NIR regions, RMSECV, RMSEP and optimum factors/rank were obtained by optimization process of model development. More than 350 combinations were obtained during optimization process. More than one pre-processing method gave good calibration/cross-validation and prediction/test models, but only the best calibration/cross-validation and prediction/test models are reported here. The results show that one can safely use NIR region between 4000 to 7500 cm-1 with straight line subtraction, constant offset elimination, first derivative and second derivative preprocessing method which were found to be most appropriate for models development.

Keywords: FT-NIR, mechanical properties, pre-processing, PLS

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17713 Application of a SubIval Numerical Solver for Fractional Circuits

Authors: Marcin Sowa


The paper discusses the subinterval-based numerical method for fractional derivative computations. It is now referred to by its acronym – SubIval. The basis of the method is briefly recalled. The ability of the method to be applied in time stepping solvers is discussed. The possibility of implementing a time step size adaptive solver is also mentioned. The solver is tested on a transient circuit example. In order to display the accuracy of the solver – the results have been compared with those obtained by means of a semi-analytical method called gcdAlpha. The time step size adaptive solver applying SubIval has been proven to be very accurate as the results are very close to the referential solution. The solver is currently able to solve FDE (fractional differential equations) with various derivative orders for each equation and any type of source time functions.

Keywords: numerical method, SubIval, fractional calculus, numerical solver, circuit analysis

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17712 Semilocal Convergence of a Three Step Fifth Order Iterative Method under Hölder Continuity Condition in Banach Spaces

Authors: Ramandeep Behl, Prashanth Maroju, S. S. Motsa


In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equation of the second kind.

Keywords: Holder continuity condition, Frechet derivative, fifth order convergence, recurrence relations

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17711 On a Univalent Function and the Integral Means of Its Derivative

Authors: Shatha S. Alhily


The purpose of this research paper is to show all the possible values of the pth power of the integrable function which make the integral means of the derivative of univalent function existing and finite.

Keywords: derivative, integral means, self conformal maps, univalent function

Procedia PDF Downloads 447
17710 Chemometric-Based Voltammetric Method for Analysis of Vitamins and Heavy Metals in Honey Samples

Authors: Marwa A. A. Ragab, Amira F. El-Yazbi, Amr El-Hawiet


The analysis of heavy metals in honey samples is crucial. When found in honey, they denote environmental pollution. Some of these heavy metals as lead either present at low or high concentrations are considered to be toxic. Other heavy metals, for example, copper and zinc, if present at low concentrations, they considered safe even vital minerals. On the contrary, if they present at high concentrations, they are toxic. Their voltammetric determination in honey represents a challenge due to the presence of other electro-active components as vitamins, which may overlap with the peaks of the metal, hindering their accurate and precise determination. The simultaneous analysis of some vitamins: nicotinic acid (B3) and riboflavin (B2), and heavy metals: lead, cadmium, and zinc, in honey samples, was addressed. The analysis was done in 0.1 M Potassium Chloride (KCl) using a hanging mercury drop electrode (HMDE), followed by chemometric manipulation of the voltammetric data using the derivative method. Then the derivative data were convoluted using discrete Fourier functions. The proposed method allowed the simultaneous analysis of vitamins and metals though their varied responses and sensitivities. Although their peaks were overlapped, the proposed chemometric method allowed their accurate and precise analysis. After the chemometric treatment of the data, metals were successfully quantified at low levels in the presence of vitamins (1: 2000). The heavy metals limit of detection (LOD) values after the chemometric treatment of data decreased by more than 60% than those obtained from the direct voltammetric method. The method applicability was tested by analyzing the selected metals and vitamins in real honey samples obtained from different botanical origins.

Keywords: chemometrics, overlapped voltammetric peaks, derivative and convoluted derivative methods, metals and vitamins

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17709 A Comparative Study on a Tilt-Integral-Derivative Controller with Proportional-Integral-Derivative Controller for a Pacemaker

Authors: Aysan Esgandanian, Sabalan Daneshvar


The study is done to determine the comparison between proportional-integral-derivative controller (PID controller) and tilt-integral-derivative (TID controller) for cardiac pacemaker systems, which can automatically control the heart rate to accurately track a desired preset profile. The controller offers good adaption of heart to the physiological needs of the patient. The parameters of the both controllers are tuned by particle swarm optimization (PSO) algorithm which uses the integral of time square error as a fitness function to be minimized. Simulation results are performed on the developed cardiovascular system of humans and results demonstrate that the TID controller produces superior control performance than PID controllers. In this paper, all simulations were performed in Matlab.

Keywords: integral of time square error, pacemaker systems, proportional-integral-derivative controller, PSO algorithm, tilt-integral-derivative controller

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17708 Certain Results of a New Class of Meromorphic Multivalent Functions Involving Ruscheweyh Derivative

Authors: Kassim A. Jassim


In the present paper, we introduce and discuss a new class Kp(λ,α) of meromorphic multivalent functions in the punctured unit disk U*={z∈¢:0<|z|<1} defined by Ruscheweyh derivative. We obtain some sufficient conditions for the functions belonging to the class Kp(λ,α).

Keywords: meromorphic multivalent function, Ruscheweyh derivative, hadamard product

Procedia PDF Downloads 239
17707 A New Approach for Generalized First Derivative of Nonsmooth Functions Using Optimization

Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor


In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.

Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions

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17706 Out-of-Plane Free Vibrations of Circular Rods

Authors: Faruk Firat Çalim, Nurullah Karaca, Hakan Tacettin Türker


In this study, out-of-plane free vibrations of a circular rods is investigated theoretically. The governing equations for naturally twisted and curved spatial rods are obtained using Timoshenko beam theory and rewritten for circular rods. Effects of the axial and shear deformations are considered in the formulations. Ordinary differential equations in scalar form are solved analytically by using transfer matrix method. The circular rods of the mass matrix are obtained by using straight rod of consistent mass matrix. Free vibrations frequencies obtained by solving eigenvalue problem. A computer program coded in MATHEMATICA language is prepared. Circular beams are analyzed through various examples for free vibrations analysis. Results are compared with ANSYS results based on finite element method and available in the literature.

Keywords: circular rod, out-of-plane free vibration analysis, transfer matrix method

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17705 Versatile Variation of Fischer Indolization in Green Synthesis of Nitro Substituted Tetrahydrocarbazole

Authors: Zubi Sadiq, Ghazala Yaqub, Almas Hamid


We wish to report herein a very stimulating variation in Fischer indole reaction by adopting solvent and catalyst free conditions. A concise synthesis of dinitro tetrahydrocarbazole derivative 3 was introduced without the use of any accelerating agent at ambient temperature with fairly good yield. Product was fully corroborated by UV, FTIR, 1H NMR, 13C NMR, MS, and CHN analysis.

Keywords: fischer indole reaction, neutral medium, solvent free synthesis, tetrahydrocarbazole

Procedia PDF Downloads 259
17704 Prospective Mathematics Teachers' Content Knowledge on the Definition of Limit and Derivative

Authors: Reyhan Tekin Sitrava


Teachers should have robust and comprehensive content knowledge for effective mathematics teaching. It was explained that content knowledge includes knowing the facts, truths, and concepts; explaining the reasons behind these facts, truths and concepts, and making relationship between the concepts and other disciplines. By virtue of its importance, it will be significant to explore teachers and prospective teachers’ content knowledge related to variety of topics in mathematics. From this point of view, the purpose of this study was to investigate prospective mathematics teachers’ content knowledge. Particularly, it was aimed to reveal the prospective teachers’ knowledge regarding the definition of limit and derivate. To achieve the purpose and to get in-depth understanding, a qualitative case study method was used. The data was collected from 34 prospective mathematics teachers through a questionnaire containing 2 questions. The first question required the prospective teachers to define the limit and the second one required to define the derivative. The data was analyzed using content analysis method. Based on the analysis of the data, although half of the prospective teachers (50%) could write the definition of the limit, nine prospective teachers (26.5%) could not define limit. However, eight prospective teachers’ definition was regarded as partially correct. On the other hand, twenty-seven prospective teachers (79.5%) could define derivative, but seven of them (20.5%) defined it partially. According to the findings, most of the prospective teachers have robust content knowledge on limit and derivative. This result is important because definitions have a virtual role in learning and teaching of mathematics. More specifically, definition is starting point to understand the meaning of a concept. From this point of view, prospective teachers should know the definitions of the concepts to be able to teach them correctly to the students. In addition, they should have knowledge about the relationship between limit and derivative so that they can explain these concepts conceptually. Otherwise, students may memorize the rules of calculating the derivative and the limit. In conclusion, the present study showed that most of the prospective mathematics teachers had enough knowledge about the definition of derivative and limit. However, the rest of them should learn their definition conceptually. The examples of correct, partially correct, and incorrect definition of both concepts will be presented and discussed based on participants’ statements. This study has some implications for instructors. Instructors should be careful about whether students learn the definition of these concepts or not. In order to this, the instructors may give prospective teachers opportunities to discuss the definition of these concepts and the relationship between the concepts.

Keywords: content knowledge, derivative, limit, prospective mathematics teachers

Procedia PDF Downloads 135
17703 Ultrasonic Investigation as Tool for Study of Molecular Interaction of 2-Hydroxy Substituted Pyrimidine Derivative at Different Concentrations

Authors: Shradha S. Binani, P. S. Bodke, R. V. Joat


Recent decades have witnessed an exponential growth in the field of acoustical parameters and ultrasound on solid, liquid and gases. Ultrasonic propagation parameters yield valuable information regarding the behavior of liquid systems because intra and intermolecular association, dipolar interaction, complex formation and related structural changes affecting the compressibility of the system which in turn produces variations in the ultrasonic velocity. The acoustic and thermo dynamical parameters obtained in ultrasonic study show that ion-solvation is accompanied by the destruction or enhancement of the solvent structure. In the present paper the ultrasonic velocity (v), density (ρ), viscosity(η) have been measured for the pharmacological important compound 2-hydroxy substituted phenyl pyrimidine derivative (2-hydroxy-4-(4’-methoxy phenyl)-6-(2’-hydroxy-4’-methyl-5’-chlorophenyl)pyrimidine) in ethanol as a solvent by using different concentration at constant room temperature. These experimental data have been used to estimate physical parameter like adiabatic compressibility, intermolecular free length, relaxation time, free volume, specific acoustic impedance, relative association, Wada’s constant, Rao’s constant etc. The above parameters provide information in understanding the structural and molecular interaction between solute-solvent in the drug solution with respect to change in concentration.

Keywords: acoustical parameters, ultrasonic velocity, density, viscosity, 2-hydroxy substituted phenyl pyrimidine derivative

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17702 Development and Validation of First Derivative Method and Artificial Neural Network for Simultaneous Spectrophotometric Determination of Two Closely Related Antioxidant Nutraceuticals in Their Binary Mixture”

Authors: Mohamed Korany, Azza Gazy, Essam Khamis, Marwa Adel, Miranda Fawzy


Background: Two new, simple and specific methods; First, a Zero-crossing first-derivative technique and second, a chemometric-assisted spectrophotometric artificial neural network (ANN) were developed and validated in accordance with ICH guidelines. Both methods were used for the simultaneous estimation of the two closely related antioxidant nutraceuticals ; Coenzyme Q10 (Q) ; also known as Ubidecarenone or Ubiquinone-10, and Vitamin E (E); alpha-tocopherol acetate, in their pharmaceutical binary mixture. Results: For first method: By applying the first derivative, both Q and E were alternatively determined; each at the zero-crossing of the other. The D1 amplitudes of Q and E, at 285 nm and 235 nm respectively, were recorded and correlated to their concentrations. The calibration curve is linear over the concentration range of 10-60 and 5.6-70 μg mL-1 for Q and E, respectively. For second method: ANN (as a multivariate calibration method) was developed and applied for the simultaneous determination of both analytes. A training set (or a concentration set) of 90 different synthetic mixtures containing Q and E, in wide concentration ranges between 0-100 µg/mL and 0-556 µg/mL respectively, were prepared in ethanol. The absorption spectra of the training sets were recorded in the spectral region of 230–300 nm. A Gradient Descend Back Propagation ANN chemometric calibration was computed by relating the concentration sets (x-block) to their corresponding absorption data (y-block). Another set of 45 synthetic mixtures of the two drugs, in defined range, was used to validate the proposed network. Neither chemical separation, preparation stage nor mathematical graphical treatment were required. Conclusions: The proposed methods were successfully applied for the assay of Q and E in laboratory prepared mixtures and combined pharmaceutical tablet with excellent recoveries. The ANN method was superior over the derivative technique as the former determined both drugs in the non-linear experimental conditions. It also offers rapidity, high accuracy, effort and money saving. Moreover, no need for an analyst for its application. Although the ANN technique needed a large training set, it is the method of choice in the routine analysis of Q and E tablet. No interference was observed from common pharmaceutical additives. The results of the two methods were compared together

Keywords: coenzyme Q10, vitamin E, chemometry, quantitative analysis, first derivative spectrophotometry, artificial neural network

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17701 Solutions of Fractional Reaction-Diffusion Equations Used to Model the Growth and Spreading of Biological Species

Authors: Kamel Al-Khaled


Reaction-diffusion equations are commonly used in population biology to model the spread of biological species. In this paper, we propose a fractional reaction-diffusion equation, where the classical second derivative diffusion term is replaced by a fractional derivative of order less than two. Based on the symbolic computation system Mathematica, Adomian decomposition method, developed for fractional differential equations, is directly extended to derive explicit and numerical solutions of space fractional reaction-diffusion equations. The fractional derivative is described in the Caputo sense. Finally, the recent appearance of fractional reaction-diffusion equations as models in some fields such as cell biology, chemistry, physics, and finance, makes it necessary to apply the results reported here to some numerical examples.

Keywords: fractional partial differential equations, reaction-diffusion equations, adomian decomposition, biological species

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17700 Free Vibration and Buckling of Rectangular Plates under Nonuniform In-Plane Edge Shear Loads

Authors: T. H. Young, Y. J. Tsai


A method for determining the stress distribution of a rectangular plate subjected to two pairs of arbitrarily distributed in-plane edge shear loads is proposed, and the free vibration and buckling of such a rectangular plate are investigated in this work.  The method utilizes two stress functions to synthesize the stress-resultant field of the plate with each of the stress functions satisfying the biharmonic compatibility equation. The sum of stress-resultant fields due to these two stress functions satisfies the boundary conditions at the edges of the plate, from which these two stress functions are determined. Then, the free vibration and buckling of the rectangular plate are investigated by the Galerkin method. Numerical results obtained by this work are compared with those appeared in the literature, and good agreements are observed.

Keywords: stress analysis, free vibration, plate buckling, nonuniform in-plane edge shear

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17699 An Improved Total Variation Regularization Method for Denoising Magnetocardiography

Authors: Yanping Liao, Congcong He, Ruigang Zhao


The application of magnetocardiography signals to detect cardiac electrical function is a new technology developed in recent years. The magnetocardiography signal is detected with Superconducting Quantum Interference Devices (SQUID) and has considerable advantages over electrocardiography (ECG). It is difficult to extract Magnetocardiography (MCG) signal which is buried in the noise, which is a critical issue to be resolved in cardiac monitoring system and MCG applications. In order to remove the severe background noise, the Total Variation (TV) regularization method is proposed to denoise MCG signal. The approach transforms the denoising problem into a minimization optimization problem and the Majorization-minimization algorithm is applied to iteratively solve the minimization problem. However, traditional TV regularization method tends to cause step effect and lacks constraint adaptability. In this paper, an improved TV regularization method for denoising MCG signal is proposed to improve the denoising precision. The improvement of this method is mainly divided into three parts. First, high-order TV is applied to reduce the step effect, and the corresponding second derivative matrix is used to substitute the first order. Then, the positions of the non-zero elements in the second order derivative matrix are determined based on the peak positions that are detected by the detection window. Finally, adaptive constraint parameters are defined to eliminate noises and preserve signal peak characteristics. Theoretical analysis and experimental results show that this algorithm can effectively improve the output signal-to-noise ratio and has superior performance.

Keywords: constraint parameters, derivative matrix, magnetocardiography, regular term, total variation

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17698 Lead Free BNT-BKT-BMgT-CoFe₂O₄ Magnetoelectric Nanoparticulate Composite Thin Films Prepared by Chemical Solution Deposition Method

Authors: A. K. Paul, Vinod Kumar


Lead free magnetoelectric (ME) nanoparticulate (1−x) BNT-BKT-BMgT−x CFO (x = 0, 0.1, 0.2, 0.3) composite films were synthesized using chemical solution deposition method. The X-ray diffraction and transmission electron microscope (TEM) reveal that CFO nanoparticles were well distributed in the matrix of BNT-BKT-BMgT. The nanocomposite films exhibit both good magnetic and ferroelectric properties at room temperature (R-T). It is concluded that the modulation in compositions of piezomagnetic/piezoelectric components plays a fundamental role in the magnetoelectric coupling in these nanoparticulate composite films. These ME composites provide a great opportunity as potential lead-free systems for ME devices.

Keywords: lead free multiferroic, nanocomposite, ferroelectric, ferromagnetic and magneto-electric properties

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17697 Design of a Cooperative Neural Network, Particle Swarm Optimization (PSO) and Fuzzy Based Tracking Control for a Tilt Rotor Unmanned Aerial Vehicle

Authors: Mostafa Mjahed


Tilt Rotor UAVs (Unmanned Aerial Vehicles) are naturally unstable and difficult to maneuver. The purpose of this paper is to design controllers for the stabilization and trajectory tracking of this type of UAV. To this end, artificial intelligence methods have been exploited. First, the dynamics of this UAV was modeled using the Lagrange-Euler method. The conventional method based on Proportional, Integral and Derivative (PID) control was applied by decoupling the different flight modes. To improve stability and trajectory tracking of the Tilt Rotor, the fuzzy approach and the technique of multilayer neural networks (NN) has been used. Thus, Fuzzy Proportional Integral and Derivative (FPID) and Neural Network-based Proportional Integral and Derivative controllers (NNPID) have been developed. The meta-heuristic approach based on Particle Swarm Optimization (PSO) method allowed adjusting the setting parameters of NNPID controller, giving us an improved NNPID-PSO controller. Simulation results under the Matlab environment show the efficiency of the approaches adopted. Besides, the Tilt Rotor UAV has become stable and follows different types of trajectories with acceptable precision. The Fuzzy, NN and NN-PSO-based approaches demonstrated their robustness because the presence of the disturbances did not alter the stability or the trajectory tracking of the Tilt Rotor UAV.

Keywords: neural network, fuzzy logic, PSO, PID, trajectory tracking, tilt-rotor UAV

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17696 A Study of Effective Stereo Matching Method for Long-Wave Infrared Camera Module

Authors: Hyun-Koo Kim, Yonghun Kim, Yong-Hoon Kim, Ju Hee Lee, Myungho Song


In this paper, we have described an efficient stereo matching method and pedestrian detection method using stereo types LWIR camera. We compared with three types stereo camera algorithm as block matching, ELAS, and SGM. For pedestrian detection using stereo LWIR camera, we used that SGM stereo matching method, free space detection method using u/v-disparity, and HOG feature based pedestrian detection. According to testing result, SGM method has better performance than block matching and ELAS algorithm. Combination of SGM, free space detection, and pedestrian detection using HOG features and SVM classification can detect pedestrian of 30m distance and has a distance error about 30 cm.

Keywords: advanced driver assistance system, pedestrian detection, stereo matching method, stereo long-wave IR camera

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