Errata: The Graphic Solution of Quadratic Equations

1927 ◽  
Vol 13 (188) ◽  
pp. 372
Keyword(s):  
Quadratic Equations ◽  
Graphic Solution

Historical Note: On the Graphic Solution of Quadratic Equations

1927 ◽  
Vol 13 (187) ◽  
pp. 318
Author(s):  
J. J. Milne
Keyword(s):  
Historical Note ◽  
Quadratic Equations ◽  
Graphic Solution

The Graphic Solution of Quadratic Equations

1927 ◽  
Vol 13 (187) ◽  
pp. 313
Author(s):  
Alfred Lodge
Keyword(s):  
Quadratic Equations ◽  
Graphic Solution

Extended Algorithm for Solving Underdefined Multivariate Quadratic Equations

2014 ◽  
Vol E97.A (6) ◽  
pp. 1418-1425 ◽  
Author(s):  
Hiroyuki MIURA ◽  
Yasufumi HASHIMOTO ◽  
Tsuyoshi TAKAGI
Keyword(s):  
Quadratic Equations

Solution of Quadratic Equations and Triangles by Machine

1951 ◽  
Vol 58 (2) ◽  
pp. 92
Author(s):  
J. P. Ballantine
Keyword(s):  
Quadratic Equations

scholarly journals Matrix zeros of quadratic equations

1988 ◽  
Vol 30 (1) ◽  
pp. 27-50 ◽  
Author(s):  
Galia Dafni ◽  
Leonid Vaserstein
Keyword(s):  
Quadratic Equations

Comparison of the Effect of Boron and Phosphorus Impurities on Solid Phase Epitaxial Regrowth of Amorphous Silicon

1989 ◽  
Vol 157 ◽  
Author(s):  
Young-Jin Jeon ◽  
M.F. Becker ◽  
R.M. Walser
Keyword(s):  
Amorphous Silicon ◽  
Isothermal Annealing ◽  
Solid Phase ◽  
Laser Interferometry ◽  
Electron Pairs ◽  
Quadratic Equations ◽  
Low Concentrations ◽  
Fractional Ionization ◽  
Reported Data

ABSTRACTThis work was concerned with comparing the relative effects of boron and phosphorus impurities on the solid phase epitaxial (SPE) regrowth rate of self-ion amorphized layers in silicon wafers with (100) orientation. We used previously reported data measured by in situ, high precision, cw laser interferometry during isothermal annealing for temperatures from 450°C to 590°C, and concentrations in the range from 7.8×1018 cm-3 to 5×l020 cm-3 for boron (NB), and from 5×l017 cm-3 to 3×1020 cm-3 for phosphorus (Np) impurities. The basis for the comparison was a recently developed model that extends the Spaepen-Turnbull model for silicon recrystallization to include ionization enhanced processes.The experimental data for bom boron and phosphorus exhibited the linear variation in regrowth rate expected for low concentrations of implanted hydrogenic impurities having a concentration-independent fractional ionization in amorphous silicon. In the linear range the relative enhanced regrowth rate produced by these impurities can be expressed as a product of their, relative fractional ionizations, and the relative amount the rate constant for reconstruction is altered by localizing an electron, or a hole, at the reconstruction site. Assuming that a localized hole and electron equally softened the potential barrier for reconstruction, the experimental results indicated that boron had an ?40 meV lower barrier to ionization in amorphous silicon than phosphorus.The variations in the SPE regrowth rates with higher concentrations of both implanted boron and phosphorus were well fit by quadratic equations, but with different curvatures (+ and - for B and P respectively). This result was interpreted to indicate that SPE regrowth was further enhanced by localized hole pairs, but retarded by localized electron pairs.

Great Circle Sailing (Graphic Solution)

Navigation ◽  
1968 ◽  
Vol 15 (1) ◽  
pp. 53-61
Author(s):  
WILLIAM M. FRASER
Keyword(s):  
Great Circle ◽  
Graphic Solution

Perturbation Analysis of Matrix Quadratic Equations

1990 ◽  
Vol 11 (6) ◽  
pp. 1159-1163 ◽  
Author(s):  
M. M. Konstantinov ◽  
P. Hr. Petkov ◽  
N. D. Christov
Keyword(s):  
Perturbation Analysis ◽  
Quadratic Equations

scholarly journals Simultaneous Additive Equations: Repeated and Differing Degrees

2017 ◽  
Vol 69 (02) ◽  
pp. 258-283 ◽  
Author(s):  
Julia Brandes ◽  
Scott T. Parsell
Keyword(s):  
Hybrid Systems ◽  
Existence Of Solutions ◽  
Square Root ◽  
Multiple Forms ◽  
Quadratic Equations ◽  
Asymptotic Formulae ◽  
Cubic Forms

Abstract We obtain bounds for the number of variables required to establish Hasse principles, both for the existence of solutions and for asymptotic formulæ, for systems of additive equations containing forms of differing degree but also multiple forms of like degree. Apart from the very general estimates of Schmidt and Browning–Heath–Brown, which give weak results when specialized to the diagonal situation, this is the first result on such “hybrid” systems. We also obtain specialized results for systems of quadratic and cubic forms, where we are able to take advantage of some of the stronger methods available in that setting. In particular, we achieve essentially square root cancellation for systems consisting of one cubic and r quadratic equations.

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