Error Estimation For The Methods Of Correlated colour Temperature Calculation

2021 ◽  
pp. 70-77
Author(s):  
Sergey V. Prytkov ◽  
Maxim V. Kolyadin
Keyword(s):  
Numerical Solutions ◽  
Search Algorithm ◽  
Absolute Error ◽  
National Standards ◽  
Software Developers ◽  
Colour Temperature ◽  
Universal Approach ◽  
Binary Search Algorithm ◽  
The Absolute

To date, a lot of methods have been developed for calculating correlated colour temperature (CCT). There are both numerical solutions (Robertson’s method, Yoshi Ohno method, binary search algorithm) and analytical (Javier Hernandez-Andres’s method, McCamy’s method). At the same time, the information about their accuracy is of a segmental fragmentary nature, therefore, it is very difficult to develop recommendations for the application of methods for certain radiators. In this connection, it seems extremely interesting to compare the error of the most well-known CCT calculating methods, using a single universal approach. The paper proposes an algorithm for researching the error of the methods for calculating correlated colour temperature, based on the method for plotting lines of constant CCT of a given length. Temperatures corresponding to these lines are taken as true, and the chromaticity lying on them are used as input data for the researched method. The paper proposes an approach when first the distribution of the error in the entire range of determination of CCT is determined, followed by bilinear interpolation for the required chromaticity. Using this approach, the absolute errors of the following methods for calculating CCT: McCamy, Javier Hernandez, Robertson, and Yoshi Ohno were estimated. The error was estimated in the range occupied by quadrangles of possible values from ANSI C78.377 chromaticity standard, developed by American National Standards Institute for LED lamps for indoor lightning. The tabular and graphical distribution of the absolute error for each investigated method was presented in the range of (2000–7000) K. In addition, to clarify the applicability of the methods for calculating CCT of the sky, the calculation of the distribution of the relative error up to 100000 K was performed. The results of the study can be useful for developers of standards and measurement procedures and for software developers of measuring equipment.

Automated Determination of Ethanol and Wine Extract with Precision Density Meter, Automatic Sampler, and Programmable Calculator

1986 ◽  
Vol 69 (4) ◽  
pp. 709-711
Author(s):  
Jerry R Ruppert
Keyword(s):  
Polynomial Equation ◽  
Absolute Error ◽  
Degree Polynomial ◽  
Programmable Calculator ◽  
Wine Sample ◽  
Automatic Sampler ◽  
Aoac Method ◽  
The Absolute ◽  
Automated Determination

Abstract Use of density meters has become the preferred method in many alcohol beverage laboratories to determine the concentration of ethanol in wines and spirits. Density converted to SG (20/20) is also the basis of an official AOAC method to determine extract of wine. Automation of the latter procedure is inhibited by the necessity to access AOAC Table 52.008 to convert SG (20/20) of the dealcoholized wine sample to percentage of sucrose by weight. The author reduced the most commonly used portion of that table (1-30% sucrose by weight) to a third degree polynomial, enabling the use of a density meter, an automatic sampler, and a computer or programmable calculator to automatically determine alcoholic content and wine extract from a sample of wine and its distillate. The absolute error between AOAC Table 52.008 and the author’s polynomial equation is less than ± 0.002 percentage of sucrose by weight for the range 1-30% sucrose by weight.

scholarly journals Rapid Determination of Methyl Salicylate and Menthol in Activating Collaterals Oil by Near Infrared Spectroscopy

2021 ◽  
Vol 292 ◽  
pp. 01040
Author(s):  
Yao Wanqing ◽  
Peng Mengxia ◽  
Chen Ziyun ◽  
Wang Yanxia ◽  
Lin Tao
Keyword(s):  
Relative Error ◽  
Methyl Salicylate ◽  
Near Infrared ◽  
Accurate Determination ◽  
Absolute Error ◽  
Partial Least Square ◽  
Least Square ◽  
Content Model ◽  
The Absolute

The near infrared spectra of 10 kinds of commercial collaterals oil samples were collected by liquid transmission analysis module, and the contents of methyl salicylate and menthol in collaterals oil were determined by gas chromatography-mass spectrometry (GC-MS). The quantitative analysis model of methyl salicylate content (model 1) and menthol content (model 2) was established by correlating spectral information with measured values by partial least square method (PLS) in chemometrics. Model 1 was used to detect the content of methyl salicylate in activating oil. The predicted results showed that the absolute error was in the range of -0.098~0.082%, and the relative error was in the range of -9.986~8.195%. Model 2 was used to detect menthol in activating collaterals oil. The predicted results showed that the absolute error was in the range of -0.173~0.194%, and the relative error was in the range of -7.25~9.69%. A new method for rapid and accurate determination of methyl salicylate and menthol in activating collaterals oil was established.

A different approach for the fractional chemical model

2021 ◽  
Vol 68 (1 Jan-Feb) ◽  
Author(s):  
Khaled Saad
Keyword(s):  
Numerical Solutions ◽  
Polynomial Interpolation ◽  
Absolute Error ◽  
Mass Action ◽  
Algebraic Equations ◽  
Mass Action Kinetics ◽  
Chemical Equations ◽  
Newton Polynomial ◽  
The Absolute ◽  
Raphson Method

This article analyzes and compares the two algorithms for the numerical solutions of the fractional isothermal chemical equations (FICEs) based on mass action kinetics for autocatalytic feedback, involving the conversion of a reactant in the Liouville-Caputo sense. The first method is based upon the spectral collocation method (SCM), where the properties of Legendre polynomials are utilized to reduce the FICEs to a set of algebraic equations. We then use the well-known method like Newton-Raphson method (NRM) to solve the set of algebraic equations. The second method is based upon the properties of Newton polynomial interpolation (NPI) and the fundamental theorem of fractional calculus. We utilize these methods to construct the numerical solutions of the FICEs. The accuracy and effectiveness of these methods is satisfied graphically by combining the numerical results and plotting the absolute error. Also, the absolute errors are tabulated, and a good agreementfound in all cases.

scholarly journals A Comparative Study of the Fractional-Order Clock Chemical Model

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1436 ◽  
Author(s):  
Hari Mohan Srivastava ◽  
Khaled M. Saad
Keyword(s):  
Comparative Study ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Absolute Error ◽  
Chemical Model ◽  
Kutta Method ◽  
Integer Order ◽  
Runge Kutta Method ◽  
The Absolute ◽  
Better Than

In this paper, a comparative study has been made between different algorithms to find the numerical solutions of the fractional-order clock chemical model (FOCCM). The spectral collocation method (SCM) with the shifted Legendre polynomials, the two-stage fractional Runge–Kutta method (TSFRK) and the four-stage fractional Runge–Kutta method (FSFRK) are used to approximate the numerical solutions of FOCCM. Our results are compared with the results obtained for the numerical solutions that are based upon the fundamental theorem of fractional calculus as well as the Lagrange polynomial interpolation (LPI). Firstly, the accuracy of the results is checked by computing the absolute error between the numerical solutions by using SCM, TSFRK, FSFRK, and LPI and the exact solution in the case of the fractional-order logistic equation (FOLE). The numerical results demonstrate the accuracy of the proposed method. It is observed that the FSFRK is better than those by SCM, TSFRK and LPI in the case of an integer order. However, the non-integer orders in the cases of the SCM and LPI are better than those obtained by using the TSFRK and FSFRK. Secondly, the absolute error between the numerical solutions of FOCCM based upon SCM, TSFFRK, FSFRK, and LPI for integer order and non-integer order has been computed. The absolute error in the case of the integer order by using the three methods of the third order is considered. For the non-integer order, the order of the absolute error in the case of SCM is found to be the best. Finally, these results are graphically illustrated by means of different figures.

scholarly journals Solutions of First-Order Volterra Type Linear Integrodifferential Equations by Collocation Method

2017 ◽  
Vol 2017 ◽  
pp. 1-5 ◽  
Author(s):  
Olumuyiwa A. Agbolade ◽  
Timothy A. Anake
Keyword(s):  
Numerical Solutions ◽  
Finite Difference Methods ◽  
Absolute Error ◽  
Integrodifferential Equations ◽  
Analysis Method ◽  
Volterra Type ◽  
First Order ◽  
Collocation Points ◽  
Homotopy Analysis ◽  
The Absolute

The numerical solutions of linear integrodifferential equations of Volterra type have been considered. Power series is used as the basis polynomial to approximate the solution of the problem. Furthermore, standard and Chebyshev-Gauss-Lobatto collocation points were, respectively, chosen to collocate the approximate solution. Numerical experiments are performed on some sample problems already solved by homotopy analysis method and finite difference methods. Comparison of the absolute error is obtained from the present method and those from aforementioned methods. It is also observed that the absolute errors obtained are very low establishing convergence and computational efficiency.

Polarity Determination in Sphalerite and Wurtzite Structures

1990 ◽  
Vol 48 (2) ◽  
pp. 500-501
Author(s):  
Stuart McKernan ◽  
C. Barry Carter
Keyword(s):  
Opposite Polarity ◽  
Single Domain ◽  
Polar Material ◽  
Electron Microscopic ◽  
Dynamical Interaction ◽  
X Ray ◽  
Polarity Determination ◽  
The Absolute ◽  
Microscopic Techniques

The determination of the absolute polarity of a polar material is often crucial to the understanding of the defects which occur in such materials. Several methods exist by which this determination may be performed. In bulk, single-domain specimens, macroscopic techniques may be used, such as the different etching behavior, using the appropriate etchant, of surfaces with opposite polarity. X-ray measurements under conditions where Friedel’s law (which means that the intensity of reflections from planes of opposite polarity are indistinguishable) breaks down can also be used to determine the absolute polarity of bulk, single-domain specimens. On the microscopic scale, and particularly where antiphase boundaries (APBs), which separate regions of opposite polarity exist, electron microscopic techniques must be employed. Two techniques are commonly practised; the first [1], involves the dynamical interaction of hoLz lines which interfere constructively or destructively with the zero order reflection, depending on the crystal polarity. The crystal polarity can therefore be directly deduced from the relative intensity of these interactions.

Determination of Optimal Public Transportation Routes Using Firefly and Tabu Search Algorithms

2020 ◽  
Vol 4 (5) ◽  
pp. 884-891
Author(s):  
Salwa Salsabila Mansur ◽  
Sri Widowati ◽  
Mahmud Imrona
Keyword(s):  
Tabu Search ◽  
Public Transportation ◽  
Traffic Congestion ◽  
Search Algorithm ◽  
Urban Transportation ◽  
The Public ◽  
Comparison Results ◽  
Congestion Problems ◽  
Transportation Routes

Traffic congestion problems generally caused by the increasing use of private vehicles and public transportations. In order to overcome the situation, the optimization of public transportation’s route is required particularly the urban transportation. In this research, the performance analysis of Firefly and Tabu Search algorithm is conducted to optimize eleven public transportation’s routes in Bandung. This optimization aims to increase the dispersion of public transportation’s route by expanding the scope of route that are crossed by public transportation so that it can reach the entire Bandung city and increase the driver’s income by providing the passengers easier access to public transportations in order to get to their destinations. The optimal route is represented by the route with most roads and highest number of incomes. In this research, the comparison results between the reference route and the public transportation’s optimized route increasing the dispersion of public transportation’s route to 60,58% and increasing the driver’s income to 20,03%.

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