Characterization of Circuits Supporting Polynomial Systems with the Maximal Number of Positive Solutions

2017 ◽  
Vol 58 (2) ◽  
pp. 355-370
Author(s):  
Boulos El Hilany
Keyword(s):  
Positive Solutions ◽  
Polynomial Systems

scholarly journals A note on the Diophantine Equation x^2-kxy+ky^2+ly=0

Mathematica ◽  
2021 ◽  
Vol 63 (86) (2) ◽  
pp. 151-157
Author(s):  
Sakha A. Alkabouss ◽  
◽  
Boualem Benseba ◽  
Nacira Berbara ◽  
Simon Earp-Lynch ◽  
...  
Keyword(s):  
Positive Solutions ◽  
Diophantine Equation

We investigate the Diophantine equation x^2 −kxy + ky^2 + ly = 0 for integers k and l with k even. We give a characterization of the positive solutions of this equation in terms of k and l. We also consider the same equation for other values of k and l.

scholarly journals Existence of Positive Solutions for a Discrete Three-Point Boundary Value Problem

2007 ◽  
Vol 2007 ◽  
pp. 1-14
Author(s):  
Huting Yuan ◽  
Guang Zhang ◽  
Hongliang Zhao
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Positive Parameter ◽  
Point Boundary ◽  
Constant Number ◽  
Fixed Integer ◽  
Negative Numbers ◽  
Existence Of Positive Solutions

A discrete three-point boundary value problemΔ2xk−1+λfk(xk)=0,k=1,2,…,n, x0=0,axl=xn+1, is considered, where1≤l≤nis a fixed integer,ais a real constant number, andλis a positive parameter. A characterization of the values ofλis carried out so that the boundary value problem has the positive solutions. Particularly, in this paper the constantacan be negative numbers. The similar results are not valid for the three-point boundary value problem of differential equations.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

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