Centricity

The two exponential tenns are complex conjugates of one another, so that all structure amplitudes must be real and their phases can therefore be only zero or n. (Nearly 40% of all known structures belong to monoclinic space group Pl c. The systematic absences of (OlcO) reflections when A is odd and of (liOl) reflections when / is odd identify this space group and show tiiat it is centrosyimnetric.) Even in the absence of a definitive set of systematic absences it is still possible to infer the (probable) presence of a centre of synnnetry. A J C Wilson [21] first observed that the probability distribution of the magnitudes of the structure amplitudes would be different if the amplitudes were constrained to be real from that if they could be complex. Wilson and co-workers established a procedure by which the frequencies of suitably scaled values of F could be compared with the tlieoretical distributions for centrosymmetric and noncentrosymmetric structures. (Note that Wilson named the statistical distributions centric and acentric. These were not intended to be synonyms for centrosyimnetric and noncentrosynnnetric, but they have come to be used that way.)... 

Typical electrostrictive materials include such compounds as lead manganese niobate lead titanate (PMN PT) and lead lanthanium 2irconate titanate (PLZT). Electrostriction is a fourth-rank tensor property observed in both centric and acentric insulators (14,15). 

Germany, Bitterfeld 1920 two-stage rotary kilns heated internally using intermediate grinding of roast oxidation completed within 3—4 h cylindrical monopolar ceUs, 4 m volume undivided con-centric Ni anodes, rod-shaped Fe cathodes unfiltered electrolyte batch operation KMnO crystallizes in ceU electrolysis energy consumption about 700 kWh/1 4,000 27,113... 

Zentrifuge,/. centrifuge sling, zentrifugieren, v.t. centrifuge, centrifugalize. zentrisch, a. centric central concentric. Zentrizitat,/. centricity. 

For this reason we want to determine the number of centric and bicentric trees separately. Numbers of centric trees will be distinguished from those of bicentric trees by primes and double primes, respectively. Of the p, a, T, respectively, free trees are... 

We call PjjQj the number of topologically distinct free C-H trees with n vertices of degree 4, which have exactly a asymmetric points. Suppose PjJqj are centric and PjJ are bicentric, such that... 

Let 5 be a centric tree, whose center Af is a vertex of degree k, and 02 branches originating in M. Each of the branches carries the number the edge is assigned to in the corona of M. We consider the configuration... 

Similar arguments as in Sec. 39 lead to the following result Two centric trees are congruent if and only if the same number of branches originates from their centers and the configurations of these branches are equivalent with respect to the group associated with the corona of the center. 

Let m be the maximum number of nodes of a branch which originates in the center of a centric tree with n vertices. In other words, m is the integer which satisfies the double inequality... 

We consider free centric C-H trees with n vertices of degree 4, that is, with a total of 3 + 2 points [Sec. 36(a)]. Some branch with V vertices of degree 4 has a total of 3v + 1 nodes [Sec. 36(a)]. Thus, we have for a branch originating in the center... 

Now we get to the determination of the number of topologically different free centric trees with n vertices. Select those among the trees whose center carries s branches. The number of such trees is, according to the preceding discussion, equal to the number of nonequivalent configurations of s planted trees with respect to 3. It is the coefficient of in the expression we obtain by replacing f(x,y,z) in (1.12) by... 

We are about to enter what is, to many, a mysterious world—the world of factor spaces and the factor based techniques, Principal Component Analysis (PCA, sometimes known as Factor Analysis) and Partial Least-Squares (PLS) in latent variables. Our goal here is to thoroughly explore these topics using a data-centric approach to dispell the mysteries. When you complete this chapter, neither factor spaces nor the rhyme at the top of this page will be mysterious any longer. As we will see, it s all in your point of view. 

Metaphase Metaphase offers a Web-centric information infrastructure that harnesses its customers intellectual capital to drive product innovation and manage the complete product life cycle. 

The Claus centric structure, an old-quantum-theory found to make a less important contribution to the normal analogue of which was suggested several years ago by one state of benzene than do the Kekule structures. 

Fig. 17. Flow curve for various concentrations of polystyrene (Mw=2 106g/mol) in decalin solutions at 25 ° C obtained with a low-shear viscometer (A), a mechanical spectrometer ( ) and a high-shear con centric-cylinder viscometer (O)...

Fig. 3.4.3 (a) Two-dimensional k-space acquisition using SPI or SPRITE. The k-space data acquisition is indicated numerically. High magnetic field gradient amplitudes are applied at the extremities of k-space. (b) A generic two-dimensional centric scan SPRITE method. The... 

Cano Barrita [27] cast concrete specimens with w/c of 0.6, dried the specimens at 38 °C and 20% relative humidity, then measured the penetration of water in a capillary uptake type of experiment. A 3D centric scan SPRITE measurement was selected, as an image could be acquired in 150 s and the image would therefore be weighted only by the T2 decay. 3D images were acquired at various exposure times and the central 2D image slice was extracted from the data to measure the penetration depth with time. 

It is important to note that sodium and chlorine are both quadrupolar nuclei and Eq. (3.4.1) is therefore not true for SPI/SPRITE measurement of these species however, Eq. (3.4.2) is correct when centric scan SPRITE methods are employed. 

This provides one more illustration of the value of the centric scan SPRITE methods. 

The centric scan, one-dimensional, DHK SPRITE measurement was used to study the ingress of lithium. This measurement technique was selected due to the low absolute sensitivity of 7Li (27% of [36]), the small amounts that are present and the short signal lifetimes (bulk Tx of 10 ms and T2 of 120 ps). In addition to the robust, quantitative nature of this technique, lithium is a quadrupolar nucleus and interpretation of the image intensity is more complex than spin % nuclei. Once again Eq. (3.4.2) is quantitatively correct for even quadrupolar nuclei due to the fact the longitudinal steady state does not influence the image intensity. 

The SPI and SPRITE class of measurements for imaging short MR signal lifetimes are quantitative and have signal equations that are readily understood. The centric SPRITE methods are much faster and feature signal equations that are easier to interpret. This feature makes these measurements more readily density weighted and better suited to imaging quadrupolar nuclei. 

Under the simplifying assumption that the reflexions are independent of each other, K, can be written as a product over reflexions for which experimental structure factor amplitudes are available. For each of the reflexions, the likelihood gain takes different functional forms, depending on the centric or acentric character, and on the assumptions made for the phase probability distribution used in integrating over the phase circle for a discussion of the crystallographic likelihood functions we refer the reader to the description recently appeared in [51]. 

Blat Y, Kleckner N 1999 Cohesins bind to preferential sites along yeast chromosome III, with differential regulation along arms versus the centric region. Cell 98 249-259... 

The ordination of 23 taxa or groups of taxa in relation to the environmental predictors was examined by means of multivariate analyses. Nutrients (nitrates, total phosphate, and ammonia), conductivity, total suspended solids and water flow were retained by the redundancy analysis (RDA) (Fig. 4). The first RDA axis (RDA1 16.6% of the variance) showed a strong correlation between nutrients and suspended solids and (negatively) water flow. Large centric diatoms and Scenedesmus sp.pl. best defined this situation, which was characteristic of the meandering zone, mostly in autumn. Other taxa (Coelastrum microporum,... 

Differences in chlorophyll concentrations between present and past records in the lower part of the Ebro do not correspond with significant changes in the distribution of phytoplankton assemblages. The general trends in the distribution of phytoplankton communities appear to be consistent with those reported in previous surveys, at least in the lower part of the river. Centric diatoms such as Aulacoseira granulata, Cyclotella sp. and Stephanodiscus sp. were dominant in autumn, spring, and early summer 1989-1990, while Scenedesmus sp., Coelastrum sp., and Pediastrum sp. were most abundant in the summer of that period [7]. 

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