Exact image theory

In this chapter we present the backscatter polarization signals resulting from small particles located in the proximity of a planar interface. This system was treated by Lindell et al. [22] and Muinonen et al. [23] using Exact Image Theory (EIT). Simnltaneously, and in the same journal issue, Videen [24, 25]... 

Around the defect, enhanced scattering was observed and this loss of extinction is the origin of the name. The exact nature of the images can only be explained using dynamical diffraction theory and we will return to this in a later section. 

X-ray topography is the X-ray analogue of transmission election microscopy and as such provides a map of the strain distribution in a crystal. The theory of image formation is well established and image simulation is thus a powerful means of defect identification. Despite a reputation for being a slow and exacting technique, with modem detector technology and care to match spatial resolution of detector and experiment, it can be a powerful and economical quality-control tool for the semiconductor industry. 

The question, what conditions are to be fulfilled by a density matrix to be the image of a wave function, that is, to describe a real physical system is opened till today. The contracted Schrodinger-equations derived for different order reduced density matrices by H. Nakatsui [1] give opportunity to determine density matrices by a non-variational way. The equations contain density matrices of different order, and the relationships needed for the exact solutions are not yet known in spite of the intensive research activity [2,3]. Recently perturbation theory corrections were published for correcting the error of the energy obtained by minimizing the density matrix directly applying the known conditions of N-representability [4], and... 

As Soukup and Mayer have argued recently, "Without question, docimasy, namely, the analysis of ores and alloys of gold, silver, [and] copper, had great significance in Oberstockstall.. . . For anyone who had to examine ores or metal for coins, as well as for those who wanted to know whether their transmutations were finally crowned with success, exact balances, precise observations, and accurate computation were more important than wishes, conjectures, theories, and images." Ibid., 2. 

Proof. The lemma immediately shows the equivalence of (1) and (2) and of (4) and (6). Clearly (5) implies (2), and (2) implies (3) because Homk(/t, fc) Hom((/4 k, k). RecaU from field theory now that a finite L over k has at most dimk(L) maps to k, and has exactly that number iff it is separable. But a map from A to k also kills all but one of the factors of A and vanishes on nilpotents in that one. Thus (3) is equivalent to (4). If they hold, then all maps A - k have separable image and thus actually map to k,. The kernels of the corresponding maps A k,->ks are primes, and (5) must hold since the number of these primes equals the dimension. ... 

New graphical representations of the exact molecular orbitals for Hj that make it easier to visualize these orbitals and interpret their meanings. These images provide a foundation for developing MO theory for the first- and second-period diatomic molecules. 

In order to study the decoherence of quasi-particles within BEC, we use Bragg spectroscopy and Monte Carlo hydrodynamic simulations of the system [Castin 1996], and confirm recent theoretical predictions of the identical particle collision cross-section within a Bose-Einstein condensate. We use computerized tomography [Ozeri 2002] of the experimental images in determining the exact distributions. We then conduct both quantum mechanical and hydrodynamic simulation of the expansion dynamics, to model the distribution of the atoms, and compare theory and experiment [Katz 2002] (see Fig. 2). 

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