Search results for: curve approximation

Authors: Serge B. Provost, Yishan Zhang

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A moment-based adjustment to the saddlepoint approximation is introduced in the context of density estimation. First applied to univariate distributions, this methodology is extended to the bivariate case. It then entails estimating the density function associated with each marginal distribution by means of the saddlepoint approximation and applying a bivariate adjustment to the product of the resulting density estimates. The connection to the distribution of empirical copulas will be pointed out. As well, a novel approach is proposed for estimating the support of distribution. As these results solely rely on sample moments and empirical cumulant-generating functions, they are particularly well suited for modeling massive data sets. Several illustrative applications will be presented.

Keywords: empirical cumulant-generating function, endpoints identification, saddlepoint approximation, sample moments, density estimation

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Authors: Salisu ibrahim, Abdalla Rababah

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In this research, we use Weighted G2-Multi-degree reduction of Bezier curve of degree n to a Bezier curve of degree m, m < n. The degree reduction of Bezier curves is used to represent a given Bezier curve of n by a Bezier curve of degree m, m < n. Exact degree reduction is not possible, and degree reduction is approximate process in nature. We derive a weighted degree reducing method that is geometrically continuous at the end points. Different norms will be considered, several error minimizations will be given. The proposed methods produce error function that are less than the errors of existing methods.

Keywords: Bezier curves, multiple degree reduction, geometric continuity, error function

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Authors: Smita Sonker

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Various investigators have determined the degree of approximation of conjugate signals (functions) of functions belonging to different classes Lipα, Lip(α,p), Lip(ξ(t),p), W(Lr,ξ(t), (β ≥ 0)) by matrix summability means, lower triangular matrix operator, product means (i.e. (C,1)(E,1), (C,1)(E,q), (E,q)(C,1) (N,p,q)(E,1), and (E,q)(N,pn) of their conjugate trigonometric Fourier series. In this paper, we shall determine the degree of approximation of 2π-periodic function conjugate functions of f belonging to the function classes Lipα and W(Lr; ξ(t); (β ≥ 0)) by (C1.T) -means of their conjugate trigonometric Fourier series. On the other hand, we shall review above-mentioned work in the light of Lenski.

Keywords: signals, trigonometric fourier approximation, class W(L^r, \xi(t), conjugate fourier series

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Authors: Ying Li, Yan Li

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A new algorithm for single hidden layer feedforward neural networks (SLFN), Orthogonal Basis Extreme Learning (OBEL) algorithm, is proposed and the algorithm derivation is given in the paper. The algorithm can decide both the NNs parameters and the neuron number of hidden layer(s) during training while providing extreme fast learning speed. It will provide a practical way to develop NNs. The simulation results of function approximation showed that the algorithm is effective and feasible with good accuracy and adaptability.

Keywords: neural network, orthogonal basis extreme learning, function approximation

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Authors: D. Sigirli

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The Receiver Operating Characteristic (ROC) curve is a commonly used statistical tool for evaluating the diagnostic performance of screening and diagnostic test with continuous or ordinal scale results which aims to predict the presence or absence probability of a condition, usually a disease. When the test results were measured as numeric values, sensitivity and specificity can be computed across all possible threshold values which discriminate the subjects as diseased and non-diseased. There are infinite numbers of possible decision thresholds along the continuum of the test results. The ROC curve presents the trade-off between sensitivity and the 1-specificity as the threshold changes. The empirical ROC curve which is a non-parametric estimator of the ROC curve is robust and it represents data accurately. However, especially for small sample sizes, it has a problem of variability and as it is a step function there can be different false positive rates for a true positive rate value and vice versa. Besides, the estimated ROC curve being in a jagged form, since the true ROC curve is a smooth curve, it underestimates the true ROC curve. Since the true ROC curve is assumed to be smooth, several smoothing methods have been explored to smooth a ROC curve. These include using kernel estimates, using log-concave densities, to fit parameters for the specified density function to the data with the maximum-likelihood fitting of univariate distributions or to create a probability distribution by fitting the specified distribution to the data nd using smooth versions of the empirical distribution functions. In the present paper, we aimed to propose a smooth ROC curve estimation based on the boundary corrected kernel function and to compare the performances of ROC curve smoothing methods for the diagnostic test results coming from different distributions in different sample sizes. We performed simulation study to compare the performances of different methods for different scenarios with 1000 repetitions. It is seen that the performance of the proposed method was typically better than that of the empirical ROC curve and only slightly worse compared to the binormal model when in fact the underlying samples were generated from the normal distribution.

Keywords: empirical estimator, kernel function, smoothing, receiver operating characteristic curve

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Authors: Dariusz Jacek Jakóbczak

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Mathematics and computer science are interested in methods of 2D curve interpolation and extrapolation using the set of key points (knots). A proposed method of Hurwitz- Radon Matrices (MHR) is such a method. This novel method is based on the family of Hurwitz-Radon (HR) matrices which possess columns composed of orthogonal vectors. Two-dimensional curve is interpolated via different functions as probability distribution functions: polynomial, sinus, cosine, tangent, cotangent, logarithm, exponent, arcsin, arccos, arctan, arcctg or power function, also inverse functions. It is shown how to build the orthogonal matrix operator and how to use it in a process of curve reconstruction.

Keywords: 2D data interpolation, hurwitz-radon matrices, MHR method, probabilistic modeling, curve extrapolation

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Authors: B. Bahloul, K. Babesse, A. Dkhira, Y. Bahloul, L. Amirouche

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Structural and electronic properties of the rock-salt BaxSr1−xS are calculated using the first-principles calculations based on the density functional theory (DFT) within the generalized gradient approximation (GGA), the local density approximation (LDA) and the virtual-crystal approximation (VCA). The calculated lattice parameters at equilibrium volume for x=0 and x=1 are in good agreement with the literature data. The BaxSr1−xS alloys are found to be an indirect band gap semiconductor. Moreoever, for the composition (x) ranging between [0-1], we think that our results are well discussed and well predicted.

Keywords: semiconductor, Ab initio calculations, rocksalt, band structure, BaxSr1−xS

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Authors: S. B. Provost, Susan Sheng

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An alternative bivariate density estimation methodology is introduced in this presentation. The proposed approach involves estimating the density function associated with the marginal distribution of each of the two variables by means of the saddlepoint approximation technique and applying a bivariate polynomial adjustment to the product of these density estimates. Since the saddlepoint approximation is utilized in the context of density estimation, such estimates are determined from empirical cumulant-generating functions. In the univariate case, the saddlepoint density estimate is itself adjusted by a polynomial. Given a set of observations, the coefficients of the polynomial adjustments are obtained from the sample moments. Several illustrative applications of the proposed methodology shall be presented. Since this approach relies essentially on a determinate number of sample moments, it is particularly well suited for modeling massive data sets.

Keywords: density estimation, empirical cumulant-generating function, moments, saddlepoint approximation

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Authors: Cyril Hrncar, Jozef Bujko, Widya P. B. Putra

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The growth curve of poultry is important to evaluate the farming management system. This study was aimed to estimate the growth curve of body weight in goose. The growth curve in this study was estimated with non-linear Gompertz model through CurveExpert 1.4. software. Three Slovak mixed-sex goose breeds of Landes (L), Pomeranian (P) and Steinbacher (S) were used in this study. Total of 28 geese (10 L, 8 P and 10 S) were used to estimate the growth curve. Research showed that the asymptotic weight (A) in those geese were reached of 5332.51 g (L), 6186.14 g (P) and 5048.27 g (S). Thus, the maturing rate (k) in each breed were similar (0.05 g/day). The weight of inflection was reached of 1960.48 g (L), 2274.32 g (P) and 1855.98 g (S). The time of inflection (ti) was reached of 25.6 days (L), 26.2 days (P) and 27.80 days (S). The maximum growth rate (MGR) was reached of 98.02 g/day (L), 113.72 g/day (P) and 92.80 g/day (S). Hence, the coefficient of determination (R2) in Gompertz model was 0.99 for each breed. It can be concluded that Pomeranian geese had highest of growth trait than the other breeds.

Keywords: body weight, growth curve, inflection, Slovak geese, Gompertz model

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Authors: Jamilatuzzahro, Rezzy Eko Caraka

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The yield curve is the plot of the yield to maturity of zero-coupon bonds against maturity. In practice, the yield curve is not observed but must be extracted from observed bond prices for a set of (usually) incomplete maturities. There exist many methodologies and theory to analyze of yield curve. We use two methods (the Nelson-Siegel Method, the Svensson Method, and the SVR method) in order to construct and compare our zero-coupon yield curves. The objectives of this research were: (i) to study the adequacy of NSS model and SVR to Indonesian government bonds data, (ii) to choose the best optimization or estimation method for NSS model and SVR. To obtain that objective, this research was done by the following steps: data preparation, cleaning or filtering data, modeling, and model evaluation.

Keywords: support vector regression, Nelson-Siegel-Svensson, yield curve, Indonesian government

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Authors: Petter Eklund, Jonathan Sjölund, Sandra Eriksson, Mats Leijon

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The spoke type rotor can be used to obtain magnetic flux concentration in permanent magnet machines. This allows the air gap magnetic flux density to exceed the remanent flux density of the permanent magnets but gives problems with leakage fluxes in the magnetic circuit. The end leakage flux of one spoke type permanent magnet rotor design is studied through measurements and finite element simulations. The measurements are performed in the end regions of a 12 kW prototype generator for a vertical axis wind turbine. The simulations are made using three dimensional finite elements to calculate the magnetic field distribution in the end regions of the machine. Also two dimensional finite element simulations are performed and the impact of the two dimensional approximation is studied. It is found that the magnetic leakage flux in the end regions of the machine is equal to about 20% of the flux in the permanent magnets. The overestimation of the performance by the two dimensional approximation is quantified and a curve-fitted expression for its behavior is suggested.

Keywords: end effects, end leakage flux, permanent magnet machine, spoke type rotor

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Authors: M. Bassoui, M. Ferfra, M. Chrayagne

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This paper presents a qualitative modeling for the nonlinear B-H curve of the saturable magnetic materials for a transformer with shunts used in the power supply for the magnetron. This power supply is composed of a single phase leakage flux transformer supplying a cell composed of a capacitor and a diode, which double the voltage and stabilize the current, and a single magnetron at the output of the cell. A procedure consisting of a fuzzy clustering method and a rule processing algorithm is then employed for processing the constructed fuzzy modeling rules to extract the qualitative properties of the curve.

Keywords: B(H) curve, fuzzy clustering, magnetron, power supply

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Authors: Edlira Donefski, Lorenc Ekonomi, Tina Donefski

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Edgeworth approximation is one of the most important statistical methods that has a considered contribution in the reduction of the sum of standard deviation of the independent variables’ coefficients in a Quantile Regression Model. This model estimates the conditional median or other quantiles. In this paper, we have applied approximating statistical methods in an economical problem. We have created and generated a quantile regression model to see how the profit gained is connected with the realized sales of the cosmetic products in a real data, taken from a local business. The Linear Regression of the generated profit and the realized sales was not free of autocorrelation and heteroscedasticity, so this is the reason that we have used this model instead of Linear Regression. Our aim is to analyze in more details the relation between the variables taken into study: the profit and the finalized sales and how to minimize the standard errors of the independent variable involved in this study, the level of realized sales. The statistical methods that we have applied in our work are Edgeworth Approximation for Independent and Identical distributed (IID) cases, Bootstrap version of the Model and the Edgeworth approximation for Bootstrap Quantile Regression Model. The graphics and the results that we have presented here identify the best approximating model of our study.

Keywords: bootstrap, edgeworth approximation, IID, quantile

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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The Bessel function J₀(x) is very important in Electrodynamics and Physics, as well as its zeros. In this work, a method to obtain high accuracy approximation is presented through an application to that function. In most of the applications of this function, the values of the zeros are very important. In this work, analytic approximations for this function have been obtained valid for all positive values of the variable x, which have high accuracy for the function as well as for the zeros. The approximation is determined by the simultaneous used of the power series and asymptotic expansion. The structure of the approximation is a combination of two rational functions with elementary functions as trigonometric and fractional powers. Here us in Pade method, rational functions are used, but now there combined with elementary functions us fractional powers hyperbolic or trigonometric functions, and others. The reason of this is that now power series of the exact function are used, but together with the asymptotic expansion, which usually includes fractional powers trigonometric functions and other type of elementary functions. The approximation must be a bridge between both expansions, and this can not be accomplished using only with rational functions. In the simplest approximation using 4 parameters the maximum absolute error is less than 0.006 at x ∼ 4.9. In this case also the maximum relative error for the zeros is less than 0.003 which is for the second zero, but that value decreases rapidly for the other zeros. The same kind of behaviour happens for the relative error of the maximum and minimum of the functions. Approximations with higher accuracy and more parameters will be also shown. All the approximations are valid for any positive value of x, and they can be calculated easily.

Keywords: analytic approximations, asymptotic approximations, Bessel functions, quasirational approximations

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Authors: Lee Feng Koo, Tze Jin Wong, Pang Hung Yiu, Nik Mohd Asri Nik Long

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Greater common divisor (GCD) attack is an attack that relies on the polynomial structure of the cryptosystem. This attack required two plaintexts differ from a fixed number and encrypted under same modulus. This paper reports a security reaction of Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field under GCD attack. Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field was exposed mathematically to the GCD attack using GCD and Dickson polynomial. The result shows that the cryptanalyst is able to get the plaintext without decryption by using GCD attack. Thus, the study concluded that it is highly perilous when two plaintexts have a slight difference from a fixed number in the same Elliptic curve group over finite field.

Keywords: decryption, encryption, elliptic curve, greater common divisor

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Authors: Balachandra Kumaraswamy, P. G. Poonacha

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Automatic Music Information Retrieval has been one of the challenging topics of research for a few decades now with several interesting approaches reported in the literature. In this paper we have developed a pitch extraction method based on a finite Fourier series approximation to the given window of samples. We then estimate pitch as the fundamental period of the finite Fourier series approximation to the given window of samples. This method uses analysis of the strength of harmonics present in the signal to reduce octave as well as harmonic errors. The performance of our method is compared with three best known methods for pitch extraction, namely, Yin, Windowed Special Normalization of the Auto-Correlation Function and Harmonic Product Spectrum methods of pitch extraction. Our study with artificially created signals as well as music files show that Fourier Approximation method gives much better estimate of pitch with less octave and harmonic errors.

Keywords: pitch, fourier series, yin, normalization of the auto- correlation function, harmonic product, mean square error

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Authors: Diogo Silva, Fadul Rodor, Carlos Moraes

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This work compares the results of multidimensional function approximation using two algorithms: the classical Particle Swarm Optimization (PSO) and the Quantum Particle Swarm Optimization (QPSO). These algorithms were both tested on three functions - The Rosenbrock, the Rastrigin, and the sphere functions - with different characteristics by increasing their number of dimensions. As a result, this study shows that the higher the function space, i.e. the larger the function dimension, the more evident the advantages of using the QPSO method compared to the PSO method in terms of performance and number of necessary iterations to reach the stop criterion.

Keywords: PSO, QPSO, function approximation, AI, optimization, multidimensional functions

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Authors: Valeria Bondarenko

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We proposed algorithms for: estimation of parameters fBm (volatility and Hurst exponent) and for the approximation of random time series by functional of fBm. We proved the consistency of the estimators, which constitute the above algorithms, and proved the optimal forecast of approximated time series. The adequacy of estimation algorithms, approximation, and forecasting is proved by numerical experiment. During the process of creating software, the system has been created, which is displayed by the hierarchical structure. The comparative analysis of proposed algorithms with the other methods gives evidence of the advantage of approximation method. The results can be used to develop methods for the analysis and modeling of time series describing the economic, physical, biological and other processes.

Keywords: mathematical model, random process, Wiener process, fractional Brownian motion

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Authors: Sirapat Lookrak, Anol Paisal

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Space debris has numerous manifestations, including ferro-metalize and non-ferrous. The electric field will induce negative charges to split from positive charges inside the space debris. In this research, we focus only on conducting materials. The assumption is that the electric charge density of a conducting surface is proportional to the electric field on that surface due to Gauss's Law. We are trying to find the induced charge density from an external electric field perpendicular to a conducting spherical surface. An object is a sphere on which the external electric field is not uniform. The electric field is, therefore, considered locally. The localised spherical surface is a tangent plane, so the Gaussian surface is a very small cylinder, and every point on a spherical surface has its own cylinder. The electric field from a circular electrode has been calculated in near-field and far-field approximation and shown Explanation Touchless maneuvering space debris orbit properties. The electric charge density calculation from a near-field and far-field approximation is done.

Keywords: near-field approximation, far-field approximation, localized Gauss’s law, electric charge density

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Authors: Enea Danut Nicolae, Osman (Defta) Aurelia, Vidu Livia, Marginean Gheorghe, Defta Nicoleta, Moise Andrada

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Today, as a result of population growth, there is an increase in demand for animal products; milk and dairy products are an important part of this category. Maintaining production at maximum levels for as long as possible is one of the main objectives of dairy farmers. Over the course of lactation, a cow's milk production is not uniform. During the initial stage of lactation, the cow's milk production follows an upward slope, a plateau, and then a downward slope, which is a reflection of the lactation curve. The evolution of the lactation curve is influenced by numerous factors, which are genetic, exploitation, physiological, environmental and technological. The aim of this study was to observe the lactation curve of Holstein cows in Romania and determine the extent to which they conform to the expected pattern. In addition, there has been an analysis of the factors which have an influence on this curve and the extent of this influence. In order to be able to carry out the present study, data were collected from three farms located in three different geographical areas. To highlight the findings, the data collected was then statistically processed and graphically interpreted. All the farms have only Holstein cows, which are kept in free stalls.

Keywords: lactation curve, Holstein, milk production, influencing factors

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Authors: Preeti Sharma

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This paper deals with the Stancu type generalization of Lupaş-Durrmeyer operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, 1]. Also, Voronovskaja type theorem is studied.

Keywords: Lupas-Durrmeyer operators, polya distribution, weighted approximation, rate of convergence, modulus of continuity

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Authors: Muhammad Younis

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A ternary 4-point approximating non-stationary subdivision scheme has been introduced that generates the family of $C^2$ limiting curves. The theory of asymptotic equivalence is being used to analyze the convergence and smoothness of the scheme. The comparison of the proposed scheme has been demonstrated using different examples with the existing 4-point ternary approximating schemes, which shows that the limit curves of the proposed scheme behave more pleasantly and can generate conic sections as well.

Keywords: ternary, non-stationary, approximation subdivision scheme, convergence and smoothness

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Authors: Sofia Ayouche, Rachid Ellaia, Rajae Aboulaich

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Today, insurers may use the yield curve as an indicator evaluation of the profit or the performance of their portfolios; therefore, they modeled it by one class of model that has the ability to fit and forecast the future term structure of interest rates. This class of model is the Nelson-Siegel-Svensson model. Unfortunately, many authors have reported a lot of difficulties when they want to calibrate the model because the optimization problem is not convex and has multiple local optima. In this context, we implement a hybrid Particle Swarm optimization and Nelder Mead algorithm in order to minimize by least squares method, the difference between the zero-coupon curve and the NSS curve.

Keywords: optimization, zero-coupon curve, Nelson-Siegel-Svensson, particle swarm optimization, Nelder-Mead algorithm

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Authors: Mehdi Fuladipanah, Mehdi Jorabloo

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Water flow management is one of the most important parts of river engineering. Non-uniformity distribution of rainfall and various flow demand with unreasonable flow management will be caused destroyed of river ecosystem. Then, it is very serious to determine ecosystem flow requirement. In this paper, flow duration curve indices method which has hydrological based was used to evaluate environmental flow in Gharasou River, Ardabil, Iran. Using flow duration curve, Q90 and Q95 for different return periods were calculated. Their magnitude were determined as 1-day, 3-day, 7-day, and 30 day. According the second method, hydraulic alteration indices often had low and medium range. In order to maintain river at an acceptable ecological condition, minimum daily discharge of index Q95 is 0.7 m3.s-1.

Keywords: ardabil, environmental flow, flow duration curve, Gharasou river

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Authors: M. A. Ghebouli, H. Choutri, B. Ghebouli , M. Fatmi, L. Louail

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We employed the density-functional perturbation theory (DFPT) within the generalized gradient approximation (GGA), the local density approximation (LDA) and the virtual-crystal approximation (VCA) to study the effect of composition on the structure, stability, energy gaps, electron effective mass, the dynamic effective charge, optical and acoustical phonon frequencies and static and high dielectric constants of the rock-salt CaxMg1-xSe and CaxMg1-xTe alloys. The computed equilibrium lattice constant and bulk modulus show an important deviation from the linear concentration. From the Voigt-Reuss-Hill approximation, CaxMg1-xSe and CaxMg1-xTe present lower stiffness and lateral expansion. For Ca content ranging between 0.25-0.75, the elastic constants, energy gaps, electron effective mass and dynamic effective charge are predictions. The elastic constants and computed phonon dispersion curves indicate that these alloys are mechanically stable.

Keywords: CaxMg1-xSe, CaxMg1-xTe, band structure, phonon

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Authors: Rasaq Bello, Grace Akintola Sunday, Yemi Sikiru Onifade

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Groundwater is required for the continuity of life and sustainability of the ecosystem. Hence, this research was purposed to assess groundwater quality for domestic use in Kaltungo Local Government Area, Gombe State. The work was also aimed at determining the thickness and resistivity of the topsoil, areas suitable for borehole construction, quality and potentials of groundwater in the study area. The study area extends from latitude N10015’38” - E11008’01” and longitude N10019’29” - E11013’05”. The data was acquired using the Vertical Electrical Sounding (VES) method and processed using IP12win software. Twenty (20) Vertical Electrical Soundings were carried out with a maximum current electrode separation (AB) of 150m. The VES curves generated from the data reveal that all the VES points have five to six subsurface layers. The first layer has a resistivity value of 7.5 to 364.1 Ωm and a thickness ranging from 0.8 to 7.4m, and the second layer has a resistivity value of 1.8 to 600.3 Ωm thickness ranging from 2.6 to 31.4m, the third layer has resistivity value of 23.3 to 564.4 Ωm thickness ranging from 10.3 to 77.8m, the fourth layer has resistivity value of 19.7 to 640.2 Ωm thickness ranging from 8.2m to 120.0m, the fifth layer has resistivity value of 27 to 234 Ωm thickness ranging from 8.2 to 53.7m and the six-layer is the layer that extended beyond the probing depth. The VES curves generated from the data revealed KQHA curve type for VES 1, HKQQ curve for VES 4, HKQ curve for VES 5, KHA curve for VES 11, QQHK curve for VES 12, HAA curve for VES 6 and VES 19, HAKH curve for VES 7, VES 8, VES 10 and VES 18, HKH curve for VES 2, VES 3, VES 9, VES 13, VES 14, VES 15, VES 16, VES 17 and VES 20. Values of the Coefficient of Anisotropy, Reflection Coefficient, and Resistivity Contrast obtained from the Dar-Zarrouk parameters indicated good water prospects for all the VES points in this study, with VES points 4, 9 and 18 having the highest prospects for groundwater exploration.

Keywords: formation parameters, groundwater, resistivity, resistivity contrast, vertical electrical sounding

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Authors: Vinayak Malaghan, Digvijay Pawar

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Speed is the independent parameter which plays a vital role in the highway design. Design consistency of the highways is checked based on the variation in the operating speed. Often the design consistency fails to meet the driver’s expectation which results in the difference between operating and design speed. Literature reviews have shown that significant crashes take place in horizontal curves due to lack of design consistency. The paper focuses on continuous speed profile study on tangent to curve transition for both day and night daytime. Data is collected using GPS device which gives continuous speed profile and other parameters such as acceleration, deceleration were analyzed along with Tangent to Curve Transition. In this present study, models were developed to predict operating speed on tangents and horizontal curves as well as model indicating the speed reduction from tangent to curve based on continuous speed profile data. It is observed from the study that vehicle tends to decelerate from approach tangent to between beginning of the curve and midpoint of the curve and then accelerates from curve to tangent transition. The models generated were compared for both day and night and can be used in the road safety improvement by evaluating the geometric design consistency.

Keywords: operating speed, design consistency, continuous speed profile data, day and night time

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Authors: Thu Nhi Tran Caliste

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X-ray Bragg diffraction imaging (“topography”)entered into practical use when Lang designed an “easy” technical setup to characterise the defects / distortions in the high perfection crystals produced for the microelectronics industry. The use of this technique extended to all kind of high quality crystals, and deposited layers, and a series of publications explained, starting from the dynamical theory of diffraction, the contrast of the images of the defects. A quantitative version of “monochromatic topography” known as“Rocking Curve Imaging” (RCI) was implemented, by using synchrotron light and taking advantage of the dramatic improvement of the 2D-detectors and computerised image processing. The rough data is constituted by a number (~300) of images recorded along the diffraction (“rocking”) curve. If the quality of the crystal is such that a one-to-onerelation between a pixel of the detector and a voxel within the crystal can be established (this approximation is very well fulfilled if the local mosaic spread of the voxel is < 1 mradian), a software we developped provides, from the each rocking curve recorded on each of the pixels of the detector, not only the “voxel” integrated intensity (the only data provided by the previous techniques) but also its “mosaic spread” (FWHM) and peak position. We will show, based on many examples, that this new data, never recorded before, open the field to a highly enhanced characterization of the crystal and deposited layers. These examples include the characterization of dislocations and twins occurring during silicon growth, various growth features in Al203, GaNand CdTe (where the diffraction displays the Borrmannanomalous absorption, which leads to a new type of images), and the characterisation of the defects within deposited layers, or their effect on the substrate. We could also observe (due to the very high sensitivity of the setup installed on BM05, which allows revealing these faint effects) that, when dealing with very perfect crystals, the Kato’s interference fringes predicted by dynamical theory are also associated with very small modifications of the local FWHM and peak position (of the order of the µradian). This rather unexpected (at least for us) result appears to be in keeping with preliminary dynamical theory calculations.

Keywords: rocking curve imaging, X-ray diffraction, defect, distortion

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Authors: Najrullah Khan, Athar Ali Khan

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The Topp-Leone distribution was introduced by Topp- Leone in 1955. In this paper, an attempt has been made to fit Topp-Leone Generalized exponential (TPGE) distribution. A real survival data set is used for illustrations. Implementation is done using R and JAGS and appropriate illustrations are made. R and JAGS codes have been provided to implement censoring mechanism using both optimization and simulation tools. The main aim of this paper is to describe and illustrate the Bayesian modelling approach to the analysis of survival data. Emphasis is placed on the modeling of data and the interpretation of the results. Crucial to this is an understanding of the nature of the incomplete or 'censored' data encountered. Analytic approximation and simulation tools are covered here, but most of the emphasis is on Markov chain based Monte Carlo method including independent Metropolis algorithm, which is currently the most popular technique. For analytic approximation, among various optimization algorithms and trust region method is found to be the best. In this paper, TPGE model is also used to analyze the lifetime data in Bayesian paradigm. Results are evaluated from the above mentioned real survival data set. The analytic approximation and simulation methods are implemented using some software packages. It is clear from our findings that simulation tools provide better results as compared to those obtained by asymptotic approximation.

Keywords: Bayesian Inference, JAGS, Laplace Approximation, LaplacesDemon, posterior, R Software, simulation

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Authors: Zaid Jamal Saeed Almahmoud

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Smart grid is emerging as the future power grid, with smart techniques to optimize power consumption and electricity generation. Minimizing peak power consumption under a fixed delay requirement is a significant problem in the smart grid.For this problem, all appliances must be scheduled within a given finite time duration. We consider the problem of minimizing the peak demand under appliances constraints by scheduling power jobs with uniform release dates and deadlines. As the problem is known to be NP-hard, we analyze the performance of a version of the natural greedy heuristic for solving this problem. Our theoretical analysis and experimental results show that the proposed heuristic outperforms existing methods by providing a better approximation to the optimal solution.

Keywords: peak demand scheduling, approximation algorithms, smart grid, heuristics

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