scholarly journals A Comparison of the Accuracy of Semi-empirical PM3, PDDG and PM6 methods in Predicting Heats of Formation for Organic Compounds

2017 ◽  
Vol 58 (2) ◽  
Author(s):  
Yang-Yang Wu ◽  
Feng-Qi Zhao ◽  
Xue-Hai Ju
Keyword(s):  
Organic Compounds ◽  
Least Square Method ◽  
Least Square ◽  
Heats Of Formation ◽  
Regression Equations ◽  
Chemical Calculation ◽  
Average Deviation ◽  
Experimental Values ◽  
Isomerization Energy ◽  
Semi Empirical

<p>Gas phase heats of formation (HOF) of 18 kinds of 390 organic compounds were calculated by quantum chemical calculation using semi-empirical PM3, PDDG and PM6 methods. The calculated HOFs were compared with the experimental data to illustrate the accuracy for different kinds of organics. Furthermore, the calculated values were linearly fitted with experimental values using the least square method, and were afterward substituted into the fitted regression equations to obtain the calibrated ones. The results show that, for 10 kinds of the selected organics, PM6 is more accurate, and PDDG is more accurate for 7 kinds of organics, while PM3 is only good for amino acid. As a whole, PM6 predicts the HOFs more accurately, with its weighted total mean average deviation (WTMAD) being 0.4 kJ/mol and 2.4 kJ/mol smaller than those of PM3 and PDDG, respectively. On the other hand, our results show that PDDG is the best to differentiate the isomers, with its mean average deviation (MAD) for isomerization energy being 7.8 kJ/mol and 11.0 kJ/mol smaller than PM6 and PM3, respectively. After the calibration, the values of MADs from the PM3, PDDG and PM6 results for most organics are reduced by 0.1 to 18.2 kJ/mol, with exceptions of the PM3 for amines, PDDG for carboxylic acids, and PM6 for ethers.</p>

scholarly journals A Mathematical Model for Predicting the Winnowing Efficiency of Bambara Groundnut Sheller

2020 ◽  
Vol 5 (2) ◽  
pp. 225-228
Author(s):  
Inimfon Samuel Ossom ◽  
Akindele Folarin Alonge ◽  
Kingsley Charles Umani ◽  
Edidiong J. Bassey
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Moisture Content ◽  
Model Equation ◽  
Model Simulation ◽  
Least Square Method ◽  
Bambara Groundnut ◽  
Least Square ◽  
Predicted Model ◽  
Experimental Values

A mathematical model for predicting the winnowing efficiency of bambara groundnut sheller was developed. The regression equation for model simulation was developed using Least Square Method. The model was verified and validated by fitting it into established experimental data from winnowing efficiency of already existed Bambara groundnut sheller. The result revealed that the fitted model correlated well with the experimental data with R-square value of 0.99. The winnowing efficiency obtained from the predicted model was approximately the same values with the experimental values. Therefore, the model equation was considered to be reasonably good for predicting the winnowing efficiency of bambara groundnut sheller for known values of moisture content and blower speed.

scholarly journals Time Scale in Least Square Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Özgür Yeniay ◽  
Öznur İşçi ◽  
Atilla Göktaş ◽  
M. Niyazi Çankaya
Keyword(s):  
Least Squares ◽  
Time Scale ◽  
Least Squares Method ◽  
Least Square Method ◽  
Forward Direction ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Regression Equations ◽  
Nabla Derivative ◽  
Derivative Concept

Study of dynamic equations in time scale is a new area in mathematics. Time scale tries to build a bridge between real numbers and integers. Two derivatives in time scale have been introduced and called as delta and nabla derivative. Delta derivative concept is defined as forward direction, and nabla derivative concept is defined as backward direction. Within the scope of this study, we consider the method of obtaining parameters of regression equation of integer values through time scale. Therefore, we implemented least squares method according to derivative definition of time scale and obtained coefficients related to the model. Here, there exist two coefficients originating from forward and backward jump operators relevant to the same model, which are different from each other. Occurrence of such a situation is equal to total number of values of vertical deviation between regression equations and observation values of forward and backward jump operators divided by two. We also estimated coefficients for the model using ordinary least squares method. As a result, we made an introduction to least squares method on time scale. We think that time scale theory would be a new vision in least square especially when assumptions of linear regression are violated.

scholarly journals Hereditary model of loose mined rock layer deformation in disintegrators

2018 ◽  
Vol 60 ◽  
pp. 00033 ◽  
Author(s):  
Volodymyr Nadutyi ◽  
Oleksandr Tytov ◽  
Ivan Cheberiachko
Keyword(s):  
Applied Pressure ◽  
Least Square Method ◽  
Least Square ◽  
Initial Porosity ◽  
Rock Layer ◽  
Thrust Coefficient ◽  
Fine Grained ◽  
Experimental Values ◽  
Hereditary Character ◽  
Experimental Researches

The objective of this work is to substantiate the hereditary character of the stresses and deformations accumulation in loose mined rock during the disintegrators working surfaces convergence. It is shown, in particular, that the layer porosity after compression and the side thrust coefficient depend not only on the applied pressure, but also on the initial porosity. It is substantiated the mechanism of interrelation between the stresses and deformations of a layer. The experimental researches on fine– grained granite compression in a rigid matrix have been fulfilled. The approximation of obtained results by polynomial functions has been carried out. The coefficients have been determined by the least-square method. The close agreement of the analytical and the experimental values has been recorded. The initial porosity parameter was put into the equation of dependences of the current porosity and the side thrust coefficient on pressure. The mechanism of the forces distribution on separate particles contacts has been explained in terms of the material compacting hystory. The practical value of the research is in calculating the disintegrators operating parts parameters with account of the mined rock layer condition prior to the act of crushing.

scholarly journals A National Reference Curve for Assaying Factor VIII Inhibitors

1977 ◽  
Author(s):  
G. Mariani ◽  
F. Serbanescu ◽  
Z.M. Ruggeri ◽  
P.M. Mannucoi
Keyword(s):  
Factor Viii ◽  
Least Square Method ◽  
Least Square ◽  
Factor Viii Inhibitor ◽  
Reference Curve ◽  
National Reference ◽  
Fviii Inhibitor ◽  
Experimental Values ◽  
The Individual ◽  
Degree Equation

The results of FVIII inhibitor assays obtained in different laboratories are of difficult comparison, and the dose—response curve from which the inhibitor potency is read in units appears to be one of the main variables. Differences in inhibitor kinetic behaviour make difficult to adopt as a reference the curve of a single patient. On the other hand, the use of individual curves for each patient is laborious and time consuming. We have evaluated whether the adoption of a single reference curve obtained from the mathematical elaboration of the individual experimental points of the curves of 33 inhibitors was statically acceptable and could be proposed as a national reference curve for factor VIII inhibitor assay. The experimental data have been used to make statistical series from which theoretical points were calculated by the least square method resulting in a second degree equation curve. Observed experimental values corresponded to the theoretical points of the calculated curve within a variation of ± 50%, resulting in a variation of the calculated inhibitor potency of ± 20% compared with those read on each individual inhibitor curve. A national trial to confirm the applicability of such reference curve is presently in progress.

Algorithms for descent along nodal straight lines in the problem of estimating regression equations using the least absolute deviations method

2021 ◽  
Vol 87 (5) ◽  
pp. 68-75
Author(s):  
A. N. Tyrsin
Keyword(s):  
Objective Function ◽  
Gradient Descent ◽  
Least Square Method ◽  
Least Square ◽  
Regression Equations ◽  
Exact Methods ◽  
Computational Costs ◽  
Least Absolute Deviations ◽  
Performance Reduction ◽  
Straight Lines

A problem of estimating linear regression equations by the least absolute deviations method is considered. The exact methods of implementation of the method are significantly inferior in performance to the least square method. The fastest algorithm based on coordinate descent along nodal straight lines has a computational complexity proportional to the square of the number of observations, which limits the practical application of the method to monitoring and diagnostic tasks. The goal of the study is to describe a faster version of the descent along the nodal straight lines, as well as to evaluate the performance. Reduction of the computational costs is achieved due to the fact that instead of calculating the values of the objective function at nodal points, we find the derivative of the objective function in the vicinity of these points along the nodal line. The computational efficiency of gradient descent along nodal straight lines is estimated. For a typical computer, a comparative analysis of the average calculation time for various algorithms of descent along nodal straight lines is performed. A simple example is given to illustrate the implementation of a gradient descent procedure. Along with reduction of the computational costs, we also eliminated the possibility of accumulating computational errors when determining the values of the objective function for large samples. Moreover, gradient descent is quite simple for implementation. This makes it possible to use the method of least absolute deviations as an alternative to the least square method in various practical applications.

Direct Assessment of Effective Renal Plasma Flow from Renoscintigraphy with a Gamma Camera and an On-Line Computer

1981 ◽  
Vol 20 (06) ◽  
pp. 274-278
Author(s):  
J. Liniecki ◽  
J. Bialobrzeski ◽  
Ewa Mlodkowska ◽  
M. J. Surma
Keyword(s):  
Count Rate ◽  
Renal Plasma Flow ◽  
Early Period ◽  
Least Square Method ◽  
Least Square ◽  
Uptake Coefficient ◽  
Positive Linear Correlation ◽  
On Line ◽  
Best Fit ◽  
Plasma Activity

A concept of a kidney uptake coefficient (UC) of 131I-o-hippurate was developed by analogy from the corresponding kidney clearance of blood plasma in the early period after injection of the hippurate. The UC for each kidney was defined as the count-rate over its ROI at a time shorter than the peak in the renoscintigraphic curve divided by the integral of the count-rate curve over the "blood"-ROI. A procedure for normalization of both curves against each other was also developed. The total kidney clearance of the hippurate was determined from the function of plasma activity concentration vs. time after a single injection; the determinations were made at 5, 10, 15, 20, 30, 45, 60, 75 and 90 min after intravenous administration of 131I-o-hippurate and the best-fit curve was obtained by means of the least-square method. When the UC was related to the absolute value of the clearance a positive linear correlation was found (r = 0.922, ρ > 0.99). Using this regression equation the clearance could be estimated in reverse from the uptake coefficient calculated solely on the basis of the renoscintigraphic curves without blood sampling. The errors of the estimate are compatible with the requirement of a fast appraisal of renal function for purposes of clinical diagknosis.

PENGARUH KNOWLEDGE MANAGEMENT, KOMPETENSI, MOTIVASI TERHADAP KINERJA KARYAWAN

2015 ◽  
Vol 5 (2) ◽  
pp. 1
Author(s):  
Miftahol Arifin
Keyword(s):  
Knowledge Management ◽  
Linear Regression ◽  
Significant Influence ◽  
Employee Performance ◽  
Least Square Method ◽  
Least Square ◽  
Analysis Tool ◽  
Ordinary Least Square ◽  
Competence Motivation ◽  
Performance Analyze

The purpose of this research is to analyze the influence of knowledge management on employee performance, analyze the effect of competence on employee performance, analyze the influence of motivation on employee performance). In this study, samples taken are structural employees PT.centris Kingdom Taxi Yogyakarta. The analysis tool in this study using multiple linear regression with Ordinary Least Square method (OLS). The conclusion of this study showed that the variables of knowledge management has a significant influence on employee performance, competence variables have an influence on employee performance, motivation variables have an influence on employee performance, The analysis showed that the variables of knowledge management, competence, motivation on employee performance.Keywords: knowledge management, competence, motivation, employee performance.

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