scholarly journals Singularities of solutions of equations with noninvolutive characteristics-I; the case of second order Fuchsian equations

1993 ◽  
Vol 45 (2) ◽  
pp. 215-251 ◽  
Author(s):  
Sunao ŌUCHI
Keyword(s):  
Second Order ◽  
Solutions Of Equations ◽  
Fuchsian Equations

On Monodromy Groups of Second-Order Fuchsian Equations

1990 ◽  
Vol 21 (6) ◽  
pp. 1642-1652 ◽  
Author(s):  
A. Baider ◽  
R. C. Churchill
Keyword(s):  
Second Order ◽  
Monodromy Groups ◽  
Fuchsian Equations

10.—The Area-function for Non-linear Second-order Oscillations

1974 ◽  
Vol 72 (2) ◽  
pp. 135-147
Author(s):  
F. V. Atkinson
Keyword(s):  
Second Order ◽  
Oscillatory Solutions ◽  
Area Function ◽  
Rate Of Growth ◽  
Non Linear ◽  
Solutions Of Equations ◽  
Image Position ◽  
Fowler Equation

This paper is concerned with the rate of growth or decline as t → ∞ of oscillatory solutions of equations of the formwe have in mind equations which resemble in some degree the Lane-Emden-Fowler equationwhere n ≧ is integral, and σ is either positive, or if negative is not too large, so that oscillatory solutions exist.

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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