Structure of the principal genus for second-order integral matrix rings

Author(s):  
V. M. Turchin
1967 ◽  
Vol 2 (2) ◽  
pp. 564-566
Author(s):  
Yu. A. Drozd ◽  
V. M. Turchin

Fractals ◽  
2005 ◽  
Vol 13 (02) ◽  
pp. 147-156 ◽  
Author(s):  
PAUL E. FISHBACK ◽  
MATTHEW D. HORTON

We describe the quadratic dynamics in certain three-component number systems, which like the complex numbers, can be expressed as rings of real matrices. This description is accomplished using the properties of the real quadratic family and its various first- and second-order phase and parameter derivatives. We demonstrate that the fundamental dichotomy of defining the Mandelbrot set either in terms of filled Julia sets or in terms of the orbit of the origin extends to these ternary number systems.


Author(s):  
W. L. Bell

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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