Klein four-group

Named after the Norwegian mathematician Niels Henrik Abel (1802-1829). This group is isomorphic to Felix Klein s four-group (yierergruppe). 

Gallium(III) arsenide (GaAs) is not naturally occurring, but it is manufactured and extensively used as a semiconductor (Chapter 5). The crystalline structure of GaAs resembles sphalerite (ZnS, isometric, F43m space group), where each arsenic atom is coordinated by four gallium atoms (Klein, 2002), 339 (Bloss,... 

As I did not scrutinize in this paper the contents of the chemical texts written by apothecary-chemists, I omit here epistemological criteria. Parenthetically, however, I would like to add that there is no way to sort out the books and journal articles on chemistry written by well-known German apothecary-chemists (my group four) and chemists educated at universities see Klein, Innovation. ... 

For the actual construction of the double group as a group of operators, we need a convention to connect the spatial operators to the spinor matrices. As we have seen in Sect. 7.2, the four possible parametric descriptions of a given rotation yield two different choices for the Cayley-Klein parameters. Hence, our convention should define how to characterize unequivocally the parameters of a rotation. It will consist of two criteria the rotation angle must be positive, and the pole from which the rotation is seen as counterclockwise must belong to the positive hemisphere in the nx,tiy, tiz parameter space. This is the hemisphere above the equatorial plane, i.e., with > 0. In the (rix, Wy)-plane, we include the half-circle of points with positive -value, i.e., with = 0, > 0, and also the point with ny = l,nx = 0, and... 

To overcome those problems, a computer-based group test system (GAP Assessment Group Assessment of Performance and Behaviour, Oubaid, 2007 Oubaid, Zinn and Klein, 2008) was developed in which behavior observations made by four experts (consisting of training captains and aviation psychologists) and objective behavior measures are integrated into an overall evaluation. The... 

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