PHANTOM

The first release of the high-energy 3D-CT will only deal with circular trajectories. Therefor the Ftldkamp algorithm has been implemented. Figure 3 shows the reconstruction of an ellipse phantom. From its design other trajectories should be possible and will be taken into account in further stages of development. 

Reconstructed Phantom of Ellipses with different size and absorption... 

Chiral Center. The chiral center, which is the chiral element most commonly met, is exemplified by an asymmetric carbon with a tetrahedral arrangement of ligands about the carbon. The ligands comprise four different atoms or groups. One ligand may be a lone pair of electrons another, a phantom atom of atomic number zero. This situation is encountered in sulfoxides or with a nitrogen atom. Lactic acid is an example of a molecule with an asymmetric (chiral) carbon. (See Fig. 1.13b.)... 

MicrobaUoons have been used for gap filling, where the spheres dampen sound or vibration in the stmcture. In the medical area, microbaUoons have been evaluated as a skin replacement for bum victims and phantom tissue for radiation studies. An important appHcation is in nitroglycerin-based explosives, in which microbaUoons permit a controUed sequential detonation not possible with glass spheres. 

Thyroid Uptake Systems. Studies involving absolute thyroid uptake can be performed without imaging using small amounts of or and a simple scintillation probe. This is caUbrated using a phantom, ie, a model of a portion of the human body, loaded with the isotope being used. This instmment is also useful for assaying thyroid exposure to radioiodine among personnel. 

When a stereogenic center is tricoordinate, as is the case for sulfoxides, sulfbnium salts, and phosphines, then a phantom atom of atomic number zero is taken to occupy... 

An achiral reagent cannot distinguish between these two faces. In a complex with a chiral reagent, however, the two (phantom ligand) electron pairs are in different (enantiotopic) environments. The two complexes are therefore diastereomeric and are formed and react at different rates. Two reaction systems that have been used successfully for enantioselective formation of sulfoxides are illustrated below. In the first example, the Ti(0-i-Pr)4-f-BuOOH-diethyl tartrate reagent is chiral by virtue of the presence of the chiral tartrate ester in the reactive complex. With simple aryl methyl sulfides, up to 90% enantiomeric purity of the product is obtained. 

Since, in contrast to experiment, the simulation knows in detail what the connectivity looks hke, how long the strands are, and how the network loops are distributed, one can attribute this behavior to the non-crossability of the chains. Actually, one can even go further by allowing the chains to cross each other but still keep the excluded volume. Such a technical trick, which is only possible in simulations, allows one to isolate the effect of entanglement and non-crossability in such a case. As one would expect, if one allows chains to cross through each other one recovers the so-called phantom network result. 

Gespenstf n. specter, ghost, phantom. Gesperr(e), n. locking device, catch, ratchet, gespieen, p.p. (of speien) spat vomited. Gespinst, n. spun yarn spun goods thread (textile) fabric web cocoon, -faser, /. textile fiber, -pflanze,/. textile plant fiber plant. 

Trug, m. deception, fraud, -bild, n. phantom, illusion. 

These structures occur in branched chains of low DP. Particularly interesting is unit 24 which predominates in polymers prepared at —20 °C with trifluoroacetic acid these products are in fact phantom polymers108 in which everything seems to have gone the wrong way. 

During reaction, the number of potential nuclei-forming sites present at time t, Ni(t), progressively diminishes from the initial value N0, at t = 0, as N(t) of them form existing nuclei and N2(t) are eliminated by ingestion (i.e. converted to phantom nuclei). Now... 

A canonical set of structures for a system with more orbits than electrons is obtained by arranging all the orbits (including phantom orbits for 5>0) in a ring and then drawing non-intersecting bonds to a number determined by the number of electrons and the multiplicity. If two electrons occupy the same orbit, forming an unshared pair, a loop is drawn with its ends at the orbit. 

In carrying out he calculations we use essentially the same procedure as in the case of benzene and naphthalene. As an additional simplification, however, we neglect entirely all the excited states of the molecule, since their contribution to the total energy is comparatively small, and since they would complicate the calculations tremendously if retained. Another slight modification of the procedure is necessitated by the fact that a free radical possesses an odd number of electrons, one of which must remain unpaired. This is taken care of formally by introducing a phantom orbit X with an accompanying phantom electron which is paired with the odd electron.4 In the subsequent... 

Staverman, A.J. Properties of Phantom Networks and Real Networks. Vol. 44, pp. 73-102. 

Double and triple bonds are counted as if they were split into two or three single bonds, respectively, as in the examples in Table 4.1 (note the treatment of the phenyl group). Note that in a C=C double bond, the two carbon atoms are each regarded as being connected to two carbon atoms and that one of the latter is counted as having three phantom substituents. 

So far, we have not introduced a specific model of the polymer network chains. This problem can be rigorously solved for cross-linked polymer networks consisting of phantom chains [13], or even in the more general case of filled networks where the chains interact, additionally, with spherical hard filler particles [15]. 

Equations 22.3-22.14 represent the simplest formulation of filled phantom polymer networks. Clearly, specific features of the fractal filler structures of carbon black, etc., are totally neglected. However, the model uses chain variables R(i) directly. It assumes the chains are Gaussian the cross-links and filler particles are placed in position randomly and instantaneously and are thereafter permanent. Additionally, constraints arising from entanglements and packing effects can be introduced using the mean field approach of harmonic tube constraints [15]. 

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