Remarks on Equations of the Form p2=Aq2 + 1, and on the common Method of resolving them in whole Numbers

2011 ◽  
pp. 578-583
Author(s):  
Leonard Euler ◽  
John Hewlett
2021 ◽  
Vol 1022 ◽  
pp. 1-6
Author(s):  
Victoria S. Romanova ◽  
Viktor V. Gabov

The article addresses the features of rock disintegration based on the principles of selective and preferential destruction in high-frequency cone vibratory crushers with a free-turning inner cone. Based on the common method for determining the ultimate strength of rocks, a method for investigating the process of ore destruction under repeated and versatile influences has been proposed depending on the structure of the crushed material. The results of an experimental research of the destruction of rock samples on a press with limited force are given.


Author(s):  
Jing Zhao ◽  
Zhihong Liu ◽  
Chunlin Wei ◽  
Yongming Hu

Solving diffusion equations with the equivalence homogenization theory is the common method in reactor neutronics. But for some case, as for stronger absorbers, the diffusion equations will bring great errors and the transport method will be more suitable. The discontinuity factor theory has been successfully used in core diffusion computation programs and effectively reduced the homogenization error. The method of using the discontinuity factor in the transport method were studied. The result shows that higher accuracy was obtained from the discrete ordinates core transport computation program with discontinued factor.


Author(s):  
Gopindra S. Nair ◽  
Chandra R. Bhat ◽  
Ram M. Pendyala ◽  
Becky P. Y. Loo ◽  
William H. K. Lam

In consumer surveys, more information per response regarding preferences of alternatives may be obtained if individuals are asked to rank alternatives instead of being asked to select only the most-preferred alternative. However, the latter method continues to be the common method of preference elicitation. This is because of the belief that ranking of alternatives is cognitively burdensome. In addition, the limited research on modeling ranking data has been based on the rank ordered logit (ROL) model. In this paper, we show that a rank ordered probit (ROP) model can better utilize ranking data information, and that the prevalent view of ranking data as not being reliable (because of the attenuation of model coefficients with rank depth) may be traced to the use of a misspecified ROL model rather than to any cognitive burden considerations.


2020 ◽  
Vol 13 (21) ◽  
Author(s):  
Caiwen Shu ◽  
Guangming Tan ◽  
Yiwei Lv ◽  
Quanxi Xu

AbstractUsing experimental data of near-bed suspended sediment concentrations at five typical hydrometric stations of the Three Gorges Reservoir at the early reserving stage, the differences were investigated between the common method and improved method during flood seasons and non-flood seasons. The impact of taking measurements below 0.2 times the water depth on the results was discussed. The results show that the average discharges and velocities at each station calculated by the common method were slightly larger than those calculated by the improved method. Regarding the suspended sediment concentration at each station, the errors in the reservoir and downstream channels in dynamic equilibrium state were small, and the largest errors occurred where the river bed was strongly scoured in the downstream reach below the large dam. There was no significant relationship between water discharge and flow velocity, and the missed measurement phenomenon also occurred. The sediment discharge error was affected by the suspended sediment concentration, implying that errors usually occurred in channels with serious erosion during flood seasons. The correction coefficients (R2) of sediment discharge at each station were given during the experiment, which showed that the sediment discharges at the hydrometric stations where a large amount of sediment transport occurred near the river bottom, needed to be modified. Furthermore, the test methods proposed in this study were applied to calculate the sediment discharges of three rivers, and the results indicate that this method can narrow the gap between bathymetric comparisons and sediment load measurements.


1969 ◽  
Vol 16 (4) ◽  
pp. 242-243
Author(s):  
James E. Inskeep

The ancient Greeks sought and observed patterns in the world about them. The world seemed to be naturally arranged in a particular, predictable fashion. It is not strange that the earliest of the Greek mathematicians would also see patterns in the common counting numbers. Many of us have neglected these strong ideas of pattern and prediction in our presentation of number work to children. As you read this month's journal, you will surely be encouraged to try new methods in the teaching of whole numbers. The theme of whole numbers, operations, and ideas inherent in the system will be refreshing.


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