Rotating method

The aim of factor analysis is to calculate a rotation matrix R which rotates the abstract factors (V) (principal components) into interpretable factors. The various algorithms for factor analysis differ in the criterion to calculate the rotation matrix R. Two classes of rotation methods can be distinguished (i) rotation procedures based on general criteria which are not specific for the domain of the data and (ii) rotation procedures which use specific properties of the factors (e.g. non-negativity). 

A powerful technique which allows to answer such questions is Generalized Procrustes Analysis (GPA). This is a generalization of the Procrustes rotation method to the case of more than two data sets. As explained in Chapter 36 Procrustes analysis applies three basic operations to each data set with the objective to optimize their similarity, i.e. to reduce their distance. Each data set can be seen as defining a configuration of its rows (objects, food samples, products) in a space defined by the columns (sensory attributes) of that data set. In geometrical terms the (squared) distance between two data sets equals the sum over the squared distances between the two positions (one for data set and one for Xg) for each object. 

From a comparison of various spot electron diffraction patterns of a given crystal, a three-dimensional system of axis in the reeiproeal lattice may be established. The reeiproeal unit cell may be eompletely determined, if all the photographs indexed. For this it is sufficient to have two electron diffraction patterns and to know the angle between the seetions of the reeiproeal lattice represented by them, or to have three patterns which do not all have a particular row of points in common (Fig.5). Crystals of any compound usually grow with a particular face parallel to the surface of the specimen support. Various sections of the reciprocal lattice may, in this case, be obtained by the rotation method (Fig.5). 

Figure 5. Interrelationship between three reciprocal lattice sections, i.e. between three ED patterns of different zones (a). Schematic representation of the rotation method. Period c is common for all ED patterns obtained by the rotation method. The other period of these patterns is determined by the structure of the net perpendicular to the axis of rotation (b).

Arndt, U. W., Wonacott, A. in The Rotation Method in Crystallography (Arndt and Wonacott eds.). North Holland Pubhshing Co., Amsterdam (1977)... 

The MOs in eq 5 are typically optimized using a reorthogonalization technique that has been described by Gianinetti et al.,(30) though they can also be obtained using a Jacobi rotation method that sequentially and iteratively optimizes each individual orbital.(28,37)... 

ASTM has the DIN abrader specified as D596356. It has the rotating and non-rotating methods and both standard rubbers but does not cater for the lower force for soft rubbers. The details are said to be equivalent to the 1985 version of ISO 4649 and there is no indication of why it has not been updated. 

Wonacott, A.J. in "The Rotation Method in Crystallography" Amsterdam, New York and Oxford North-Holland, 1977, Ch. 7. 

As with Ps , there is only one bound state of Ps2 but there exist Rydberg series of autodissociating states arising from the attractive interaction between one of the positrons and the residual Ps- (or between one of the electrons and the charge conjugate of Ps ). The positions and widths of several of these states were determined by Ho (1989) using the complex coordinate rotation method. To date Ps2 has not been observed in the laboratory. 

J. Simons, The complex coordinate rotation method and exterior scaling A simple example, Int. J. Quant. Chem. 14 (1980) 113. 

G.D. Doolen, J. Nuttal, R.W. Stagat, Electron-hydrogen resonance calculation by the coordinate-rotation method, Phys. Rev. A 10 (5) (1974) 1612. 

K.T. Chung, B.F. Davis, Saddle-point complex-rotation method for resonances, Phys. Rev. A 26 (1982) 3278. 

Rotational methods Concentric cylinder viscometers Non-Newtonian 6.2.2... 

Measurement of the flow properties of non-Newtonian fluids is typically accomplished via rotational techniques. The rotational methods fall into two basic types, concentric cylinder and cone and plate rheometers. In a concentric cylinder rheometer, a bob is placed inside a cylinder so that the fluid to be studied may be placed into the gap between the cylinders. This arrangement helps approximate a uniform shear rate throughout a sample by shearing only a thin film of sample fluid between... 

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