By H.; Beckert, H. Schumann
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Extra info for 100 Jahre Mathematisches Seminar der Karl-Marx-Universitaet Leipzig
5 Projection of the gyroid along the a-axis. 7 Projection of D along a cubic space diagonal. 6 Projection of the gyroid along a space diagonal. 8 Projection of D along a cubic face diagonal. 4. 9 but with larger boundaries. 2 Nodal Surfaces and Planes The w a y we describe the nodal surfaces is particularly useful to study some of their properties. 1 cos A + cos B + cos C + cos E + cos D... = 0, one term, cosA, is an infinite number of parallel planes. 2. ) = 0 Similarly the terms cosA+cosB, or cosA+cosB+cosC, are two sets of intersecting planes that via the addition of a constant become parallel rod systems.
Lidin, and S. T. Hyde, J. Phys. France 48, 15 (1987). S. Lidin, J. Phys. France 49, 421 (1988). anorg. This Page Intentionally Left Blank Nodal Surfaces, Planes, Rods and Transformations 47 4 Nodal Surfaces, Planes, Rods and Transformations In the actual three-dimensional case we have nodal surfaces, nodal planes and spheres, instead of nodal lines [Bom,1]. We show how the cubic nodal surfaces are derived from the permutation of variables in space. We study how parallel planes transform into surfaces.
8, and 1. A=I is of course the P-surface. For lower A:s, curvature is given to the plane and gradually, as A increases, the planes are joined via catenoids and the transformation to the P-surface is obvious. 6. 2. 7 we demonstrate that it is possible to use a plane that does not belong to the surface. These mathematics are used to describe the structural changes in the Endoplasmic Reticulum in chapter 8. 6. 6. 6. 6. 6. 7. 7. 7. 7. We redo the calculations with the D-surface and the plane, cos(x+y+z).