Numerical solution of a first-order conservation equation by a least square method

1982 ◽  
Vol 2 (2) ◽  
pp. 209-219 ◽  
Author(s):  
J. J. Chattot ◽  
J. Guiu-Roux ◽  
J. Lamine
Keyword(s):  
Numerical Solution ◽  
Least Square Method ◽  
Conservation Equation ◽  
Least Square ◽  
First Order

scholarly journals Minimization of Deviations of Gear Real Tooth Surfaces Determined by Coordinate Measurements

1993 ◽  
Vol 115 (4) ◽  
pp. 995-1001 ◽  
Author(s):  
F. L. Litvin ◽  
C. Kuan ◽  
J. C. Wang ◽  
R. F. Handschuh ◽  
J. Masseth ◽  
...  
Keyword(s):  
Linear Equations ◽  
Least Square Method ◽  
Least Square ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Overdetermined System ◽  
Entire Surface ◽  
First Order ◽  
Tooth Surfaces ◽  
Coordinate Measurements

The deviations of a gear’s real tooth surface from the theoretical surface are determined by coordinate measurements at the grid of the surface. A method has been developed to transform the deviations from Cartesian coordinates to those along the normal at the measurement locations. Equations are derived that relate the first order deviations with the adjustment to the manufacturing machine tool settings. The deviations of the entire surface are minimized. The minimization is achieved by application of the least-square method for an overdetermined system of linear equations. The proposed method is illustrated with a numerical example for hypoid gear and pinion.

scholarly journals Statistical Analysis of Nigeria’s Price Sector: An Econometric Approach

2021 ◽  
pp. 29-40
Author(s):  
D. M. O. Omebo ◽  
T. D. Ailobhio ◽  
G. I. Fanen
Keyword(s):  
Predictive Performance ◽  
Least Square Method ◽  
Least Square ◽  
Explanatory Variables ◽  
Ordinary Least Square ◽  
First Order ◽  
Overall Performance ◽  
Econometric Approach ◽  
Good Predictive Performance ◽  
High Measure

This study analyzed Nigeria’s price sector using a formulated model for the price sector of the Nigeria economy. A set of simultaneous equations were used to reflect the implicit gross domestic product deflators for each of the sectors of the Nigeria economy and was found to be over identified under the order condition for identification. The model was estimated by ordinary least square method and two stage least square methods. All the variables have expected signs and as indicated by the F –statistic, the overall performance of the entire regression is significant.  The high measure of R2 and Ṝ2, in each case indicates that the explanatory variables included in the equation jointly account for the entire variation. The small RMSE also indicates that the equations have good fit. Durbin –Watson statistics shows that there is no positive first order autocorrelation. The small value of the Theil’s inequality indicates that the equation has good predictive performance. The researcher therefore recommends that government should employ the model so as to be able to monitor price of each of the sectors of the economy and put proper mechanism in place to control those sectors that affect the overall price sector of the economy.

scholarly journals Minimization of Deviations of Gear Real Tooth Surfaces Determined by Coordinate Measurements

1992 ◽  
Author(s):  
F. L. Litvin ◽  
C. Kuan ◽  
J.-C. Wang ◽  
Robert F. Handschuh ◽  
J. Masseth ◽  
...  
Keyword(s):  
Linear Equations ◽  
Least Square Method ◽  
Least Square ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Overdetermined System ◽  
Entire Surface ◽  
First Order ◽  
Tooth Surfaces ◽  
Coordinate Measurements

Abstract The deviations of a gear’s real tooth surface from the theoretical surface are determined by coordinate measurements at the grid of the surface. A method has been developed to transform the deviations from Cartesian coordinates to those along the normal at the measurement locations. Equations are derived that relate the first order deviations with the adjustment to the manufacturing machine-tool settings. The deviations of the entire surface are minimized. The minimization is achieved by application of the least-square method for an overdetermined system of linear equations. The proposed method is illustrated with a numerical example for hypoid gear and pinion.

Final Results of Establishment of the Geodetic Vertical Second Order Network of Lithuania

2017 ◽  
Author(s):  
Rosita Birvydienė ◽  
Algirdas Butkus ◽  
Arūnas Būga ◽  
Ramunas Dedela ◽  
Ricardas Kolosovskis ◽  
...  
Keyword(s):  
Least Square Method ◽  
Second Order ◽  
Least Square ◽  
Observation Data ◽  
Gps Receivers ◽  
Accuracy Estimation ◽  
First Order ◽  
Height System ◽  
Rms Error ◽  
Digital Levels

The methodology of all kinds of geodetic measurements of the Geodetic Vertical Second Order Network, the information on the observation data received and main results of the accuracy estimation and adjustment of the network are presented. In 2006 the development of the Geodetic Vertical First Order Network of Lithuania was completed. It was the basis to adopt the Height System of Lithuania (LAS07). The densification of the Geodetic Vertical First Order Network started in 2010 by development of the Geodetic Vertical Second Order Network. The Second Order Network consists of 74 levelling lines, and total length of them is 3087 km. In the period of 2010–2013 the 16 levelling lines (814 km) were observed. Rest of levelling lines were observed in 2013–2016. Total number of benchmarks is 2099. The levelling was executed by digital levels Trimble DiNi12 and coded rods Nedo LD13. All ground benchmarks were positioned by GPS receivers Trimble 5700 and Trimble Zephyr Geodetic antennas. LitPOS stations served as fiducial points. The gravity accelerations at all benchmarks were observed by gravimeters Scintrex CG-5. The levellings of the Second Order Network carried out is characterized by high precision: the double run of one kilometre levelling RMS error does not exceeds 0.7 mm. The adjustments of the second order levelling lines applying least square method were executed separately in each region outlined by the First Order network lines and border of a country.

First-Order Nonlinear Pseudo-Beat Vibration Model Identification of High Rise Buildings

2010 ◽  
Vol 163-167 ◽  
pp. 3925-3934
Author(s):  
Dong Mei Huang ◽  
Le Dong Zhu ◽  
Qiu Fen Wang
Keyword(s):  
Harmonic Wave ◽  
Least Square Method ◽  
Nonlinear Damping ◽  
Least Square ◽  
Damping Force ◽  
Aerodynamic Parameter ◽  
First Order ◽  
High Rise ◽  
High Rise Building ◽  
Vibration Responses

With vibration amplitude increasing, the super high-rise building appears obvious pseudo-beat vibration under the combination of vortex-induced force and nonlinear damping force. Therefore, based on Scanlan nonlinear empirical model the first-order nonlinear pseudo-beat vibration responses of the super high-rise building are deduced with KBM method. And then the aerodynamic parameters and vortex-induced force can be identified with least square method. By using the aeroelastic model wind tunnel test of a certain super high-rise building, the wind-induced displacement vibration responses are gathered. By the least square method, each aerodynamic parameter is identified. It shows by analysis that the pseudo-beat vibration force is mainly offered by linear and nonlinear damping forces but secondary offered by linear stiffness force and periodic excitation force. The pseudo-beat vibration force calculated by KBM approximation has the predominant frequency like that of beat vibration response as well as high-order harmonic wave.

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.

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