Oblique transformations

Essentially, the matrix K may be thought of as an "oblique transformation of the data. He must emphasize here that the U... 

The control has been performed by contact, in oblique transverse waves with an angle of 45°. In this test, we have inserted Hilbert transform for detecting envelops. 

Figure 2. Fonnation of ring and oblique texture patterns, a - several randomly rotated artificial crystallites and its Fourier transform (inset) b - reciprocal space with rings and zero tilt Ewald sphere c - 60° tilt of the Ewald sphere (reflection centers lie on the ellipse) d - the diffraction pattern as it is seen on the image plane.

When the microdensitometer data have been corrected for oblique incidence, they are in a form suitable for substitution into equation 18 for the specimen intensity transform. In practice, the correction is made as the integration is performed (see section 10.2). 

These criteria lead to different numeric transformation algorithms. The main distinction between them is orthogonal and oblique rotation. Orthogonal rotations save the structure of independent factors. Typical examples are the varimax, quartimax, and equi-max methods. Oblique rotations can lead to more useful information than orthogonal rotations but the interpretation of the results is not so straightforward. The rules about the factor loadings matrix explained above are not observed. Examples are oblimax and oblimin methods. 

The strain component S12 is usually the deformation of the body along axis 1, due to a force along axis 2 the strain tensor s is usually symmetrical, = s and thus, of the nine terms of s, at most six are unique. Both P and s can be represented as ellipsoids of stress and strain, respectively, and can be reduced to a diagonal form (e.g., P j along some preferred orthogonal system of axes, oblique to the laboratory frame or to the frame of the crystal, but characteristic for the solid the transformation to this diagonal form is a... 

As an example of obtaining a simpler core-array structure consider a (P, Q,R) Tucker3 model with P = Q x R. The core-array G can be rearranged as a two-way G (P x P) and, hence, is square. This means that premultipying G with S = G-1 (if this inverse exists) produces a (matricized) core-array that is the identity matrix. The transformation is oblique, thereby destroying the orthogonality of the component matrices. 

Tsipursky SI, Drits VA (1984) The distribution of octahedral cations in the 2 1 layers of dioctahedral smectites studied by oblique-texture electron diffraction. Clay Minerals 19 177-193 Tsipursky SI, Kameneva MYu, Drits VA (1985) Structural transformations of Fe -containing 2 1 dioctahedral phyllosihcates in the course of dehydroxylation. 5th Meet Eur Clay Groups, Prague, p 569-577... 

For an oblique rotation by multiplication with a transformation matrix, a matrix of the so-called factor structure, is obtained. This matrix contains correlation of common factors and features ... 

A polarizer is a device that transforms a linear polarized wave into a circular polarized wave, or vice versa. The common principle is simply to decompose the incident field into two components where the phase of one is advanced and the other is delayed such that their difference is 90° while their amplitudes are the same. It appears that Pakan [128] was the first to utilize this principle. Later improvements were introduced by Lemer [129]. These devices were not of the meander-line type, as will be discussed here. These seem to appear first in a paper by Young et al. [130] and were subsequently unproved by Epis [131]. Later, a paper by Terret et al. [132] discussed how to calculate the susceptance of a meander line. All of these contributions were primarily focused on normal angle of incidence while Chu and Lee [133] extended the calculation to include oblique angle of incidence. A recent contribution was supplied by Marino [134], It was apparent that meander-line polarizers gradually deteriorate for higher angles of incidence. The present appendix will demonstrate that introduction of a dielectric profile can greatly improve this calamity. 

The moment method can be formulated without reference to the Fourier transform of the flux. It can be regarded simply as a technique of constructing flux distribution functions from their (numerically calculated) moments. When information about the singularities of the flux transform is not utilized, the method becomes less well-founded theoretically, but it gains in flexibility and can be applied even when the singularities of the transform are not well understood. This situation arises in the case of the plane oblique source, as well as in connection with the penetration of fast neutrons whose attenuation coefficient may be a rapidly varying function of the energy with many maxima and minima. 

The effect of flexoelectricity is also considerable in the case of a.c. excitation. References [88] suggest that it is the flexoelectric effect which transforms chevrons, initially perpendicular to the director, into a set of oblique rolls at a field which is very slightly above the threshold value (Fig. 5.10). 

Figures (a) AFM phase image of a monolayer of an it-and st-PMMA mixture (it/st=1 2) deposited on mica at fOmNm". (b) Magnified image of the area indicated by the yellow square in (a) the pink lines represent the main-chain axes of the stereocomplex the yellow arrows indicate the antipodal oblique pendant helical arrangements with respect to the main-chain axes, (c) Typical Fourier transform of a section of (a). From Kumaki, J. Kawauchi, T. Okoshl, K. et al. Angew. Chem. Int. Ed. 2007,46,5348,- Rgure 3.

Particular care to the representation of the shape of the transmitted wave spectra was paid by Lamberti et al. The transmitted wave is reconstructed from the incident wave as the sum of the overtopped and filtered components. Incident waves transform seawards the structure into overtopping events and then regenerate, leeward the structure, due to perturbations caused by impulsive overtopping volumes. The overtopping and filtration discharges are added and converted into displacements of an ideal wave maker placed leeward the structure. A sample of the reconstructed transmitted wave spectrum with comparison of an experimental one is given in Fig. 22.9. The approach describes fairly the spectrum modification. Related to spectral change is the effect on obliquity described below. 

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