Gauss' Quadratic Formula with Twelve Ordinates

Biometrika ◽  
1938 ◽  
Vol 30 (1/2) ◽  
pp. 193
Author(s):  
B. De F. Bayly
Keyword(s):  
Quadratic Formula

Simultaneous source separation using a robust Radon transform

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. V1-V11 ◽  
Author(s):  
Amr Ibrahim ◽  
Mauricio D. Sacchi
Keyword(s):  
Radon Transform ◽  
Real Data ◽  
Radon Transforms ◽  
Accurate Data ◽  
Quadratic Formula ◽  
Penalty Term ◽  
Source Data ◽  
The Cost ◽  
Simultaneous Source ◽  
Incoherent Noise

We adopted the robust Radon transform to eliminate erratic incoherent noise that arises in common receiver gathers when simultaneous source data are acquired. The proposed robust Radon transform was posed as an inverse problem using an [Formula: see text] misfit that is not sensitive to erratic noise. The latter permitted us to design Radon algorithms that are capable of eliminating incoherent noise in common receiver gathers. We also compared nonrobust and robust Radon transforms that are implemented via a quadratic ([Formula: see text]) or a sparse ([Formula: see text]) penalty term in the cost function. The results demonstrated the importance of incorporating a robust misfit functional in the Radon transform to cope with simultaneous source interferences. Synthetic and real data examples proved that the robust Radon transform produces more accurate data estimates than least-squares and sparse Radon transforms.

Tasks That Make Connections through Representations

2012 ◽  
Vol 106 (4) ◽  
pp. 302-307 ◽  
Author(s):  
Joe Garofalo ◽  
Christine P. Trinter
Keyword(s):  
Quadratic Formula ◽  
Shortest Distance ◽  
Margin Of Error

Students think resiliently about using the quadratic formula, analyzing factors graphically, finding the shortest distance between two points, and finding margin of error.

Performance analysis of different turbulence models in impinging jet cooling

2020 ◽  
Vol 31 (04) ◽  
pp. 2050051
Author(s):  
Shashikant Pawar ◽  
Devendra Kumar Patel
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Transfer Problem ◽  
Impinging Jet ◽  
Experimental Results ◽  
Wall Jet ◽  
Quadratic Formula ◽  
Upward Direction ◽  
Number Formula ◽  
Text Model

The characteristics of heat transfer from a hot wall surface for the oblique impingement of a free turbulent slot jet have been investigated numerically. Different turbulent models — the [Formula: see text]-[Formula: see text], [Formula: see text]-[Formula: see text], SST [Formula: see text]-[Formula: see text], cubic [Formula: see text]-[Formula: see text] and quadratic [Formula: see text]-[Formula: see text] models — are used for the prediction of heat transfer and their results were compared with experimental results reported in the literature. The comparison shows that the [Formula: see text]-[Formula: see text], quadratic [Formula: see text]-[Formula: see text] and SST [Formula: see text]-[Formula: see text] models give more unsatisfactory results for the investigated configuration, while the cubic [Formula: see text]-[Formula: see text] model is capable of predicting the local Nusselt number in wall-jet region only. The [Formula: see text]-[Formula: see text] model exhibits the best agreement with the experimental results in both stagnation and wall-jet regions. Further, the [Formula: see text]-[Formula: see text] model is applied to analyze the obliquely impinging jet heat transfer problem. The parametric effects of the jet inclination ([Formula: see text], [Formula: see text] and [Formula: see text]), jet-to-surface distance ([Formula: see text], 6 and 8), Reynolds number ([Formula: see text], 15[Formula: see text]000 and 20[Formula: see text]000), and turbulent intensity ([Formula: see text], [Formula: see text] and [Formula: see text]) have been presented. The heat transfer on the upward direction is seen to decrease, while that on the downward direction it rises for the increasing angle. It is to be noted that as the value of [Formula: see text] decreases, the point of maximum Nusselt number ([Formula: see text]) displaces toward the upward direction from the geometric center point as well as its value reduces. The shifting of the [Formula: see text] is found to be independent of Re and [Formula: see text] within the range considered for the study.

A More Elegant Method of Deriving the Quadratic Formula

1975 ◽  
Vol 68 (5) ◽  
pp. 442-443
Author(s):  
Larry Hoehn
Keyword(s):  
Quadratic Formula ◽  
Elegant Method

Teachers of algebra should consider presenting this alternate method of deriving the quadratic formula to their students.

Computer-Oriented Mathematics: Quadratic Equations—Computer Style

1969 ◽  
Vol 62 (4) ◽  
pp. 305-309
Author(s):  
Walter Koetke ◽  
Thomas E. Kieren
Keyword(s):  
Quadratic Formula ◽  
Quadratic Equations ◽  
Modern Mathematics

ONE of the “old” topics that has been approached in a “new” way in modern mathematics is quadratic equations. No longer do students simply memorize the quadratic formula and do hundreds of exercises using it.

Another Look at the Quadratic Formula

1982 ◽  
Vol 75 (2) ◽  
pp. 146-152
Author(s):  
Dean D. Obermeyer
Keyword(s):  
Standard Method ◽  
Mathematics Teacher ◽  
Quadratic Formula ◽  
Interesting Article

In a particularly interesting article from the Mathematics Teacher (May 1975), Larry Hoehn gave an alternate method of deriving the quadratic formula. Hoehn’s step-by-step comparison of the standard method and the alternate method is found in table I.

Sharing Teaching Ideas: A Squeeze Play on Quadratic Equations

1982 ◽  
Vol 75 (2) ◽  
pp. 132-136
Keyword(s):  
High School ◽  
Mathematics Teacher ◽  
Quadratic Equation ◽  
Senior Year ◽  
Quadratic Formula ◽  
Mathematics Courses ◽  
Quadratic Equations ◽  
Teaching Ideas

As a mathematics teacher whose present assignment is to teach science, I was somewhat dismayed when my physics class wa unable to solve a nontrivial quadratic equation. These students are all enrolled in senior-year mathematics and had taken all lower level mathematics courses available in our small Western Kansas high school. They charged this inability to having forgotten the quadratic formula. To the e students the quadratic formula is a magic passkey to solving “unfactorable” quadratic equations. On further di scussion, l discovered that they vaguely remembered having heard of the method of completing the square, but they saw no connection between the quadratic formula and that method of solving a quadratic equation. They could solve simple quadratics by hit-and-miss factoring, but that was their only tool with which to attack this problem.

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