Pseudo-element

A methyl group may be shown in a structural representation as CH3 or Me, and similar pseudo-elemental symbols are used for ethyl, propyl and butyl side chains. It is cortrmon to represent a phenyl group as either Ph or as a hexagon with a circle irtscribed within it. This circle is meant to represent electron density that lies above and beneath the main plane of the molecule. However, when faced with... 

A typical Zintl phase is a compound like NaSi [12]. It is described by the formulation Na Si . The anion Si" has to be triply bonded, which is expressed by the symbol (3b) [13]. Si" is isoelectronic with phosphorus and arsenic (diagonal relationship) and it is, therefore, according to Klemm, a pseudo element of group 15. This means it should accomodate a structure which is typical for group 15 elements. In NaSi (3b)Sr anions form [SiJ " tetrahedra, like phosphorus and arsenic do in white phosphorus and yellow arsenic, respectively. In CaSi2, a comparable situation oecurs. According to the formulation Ca (Si )2, anions (3b)Si" are expected as well. 

SubMat binary descriptors are a set of binary descriptors of different substructure groups covering a large diversity of organic molecules [Scsibrany, Karlovits et al, 2003 Varmuza, Demuth et al, 2005]. The different kinds of substructure groups are collected in Table S19, giving a total number of 1365 substructures. These descriptors are restricted to the most common elements C, N, O, S, P, F, Cl, Br, I, B, and Si. Moreover, two pseudo-elements have... 

The first finite element schemes for differential viscoelastic models that yielded numerically stable results for non-zero Weissenberg numbers appeared less than two decades ago. These schemes were later improved and shown that for some benchmark viscoelastic problems, such as flow through a two-dimensional section with an abrupt contraction (usually a width reduction of four to one), they can generate simulations that were qualitatively comparable with the experimental evidence. A notable example was the coupled scheme developed by Marchal and Crochet (1987) for the solution of Maxwell and Oldroyd constitutive equations. To achieve stability they used element subdivision for the stress approximations and applied inconsistent streamline upwinding to the stress terms in the discretized equations. In another attempt, Luo and Tanner (1989) developed a typical decoupled scheme that started with the solution of the constitutive equation for a fixed-flow field (e.g. obtained by initially assuming non-elastic fluid behaviour). The extra stress found at this step was subsequently inserted into the equation of motion as a pseudo-body force and the flow field was updated. These authors also used inconsistent streamline upwinding to maintain the stability of the scheme. 

Many binary and pseudo-binary compounds of the alkali metals are more conveniently treated within the context of the chemistry of the other element and for this reason discussion Is deferred to later chapters, e.g. borides (p. 145),... 

Turning finally to compounds with bonds from the heavier Group 14 elements to heavier Group 15 elements we may note compounds such as [Sn C(PMe2)3)2] which has the pseudo trigonal bipyramidal structure (6). This complex, which has Sn bonded exclusively to four P atoms, is formed as yellow crystals by the... 

The third structural possibility, the formulation of the compounds as pseudo-bases (445) was eliminated in the case of the anhydro-bases derived from p /r-iV -alkyl-l-methyl-3,4-dihydro-j8-carbolinium salts on the basis of their ultraviolet absorption spectra. A structure such as 445 demands indole-type absorption (A jax 280 mp) which was not encountered in the spectra of the anhydro-bases under discussion. This is in accord with general experience. Pseudo-bases are generally found only when dehydration to anhydro-bases is structurally impossible Indole-type absorption was indeed found in the case of the product obtained by treatment of 3,4-dihydro-)3-carboline methiodide (452 R = H) with alkali.In acid solution this compound gave the expected absorption (A jax 355 mp). In alkaline solution, however, an indole-type absorption (A jax 285 mp) was observed. On this basis formulation of the product as a derivative of 2-formylindole (454) ( max 315 mp) was rejected. Although the indole-type absorption is in accord with the pseudo-base structure 453 (R = H), the elemental analysis and molecular weight were not compatible with this formulation and the product was regarded as a dimeric anhydro-base (455). 

The concept of oxidation number is used to simplify the electron bookkeeping in redox reactions. For a monatomic ion (e.g., Na+, S2 ), the oxidation number is, quite simply, the charge of the ion (+1, —2). In a molecule or polyatomic ion, the oxidation number of an element is a pseudo-charge obtained in a rather arbitrary way, assigning bonding electrons to the atom with the greater attraction for electrons. 

In arriving at Eq. (11-249) we have made use of Eq. (11-241), of the (pseudo)vector character of the surface element dau(x) and of the invariance of the vacuum state expressed by Eq. (11-239). We now insert into the right-hand side of Eq. (11-249) the expansion of iftin(x) in terms of operators, and find... 

The novel element in these models is the introduction of a third phase in the Hashin-Rosen model, which lies between the two main phases (inclusions and matrix) and contributes to the progressive unfolding of the properties of the inclusions to those of the matrix, without discontinuities. Then, these models incoporate all transition properties of a thin boundary-layer of the matrix near the inclusions. Thus, this pseudo-phase characterizes the effectiveness of the bonding between phases and defines a adhesion factor of the composite. 

Scientiae / Robert Pring-Mill — Arbor Scientiae The Tree of the Elements / Charles Lohr — "Vegetare Seu Transmutare." The Vegetable Soul and Pseudo-Lullian Alchemy / Michela Pereira... 

At each stage of the refinement of a new set of parameters, the hat matrix diagonal elements were calculated in order to detect the influential observations following the criterium of Velleman and Welsh [8,9]. The inspection of the residues of such reflections revealed those which are aberrant but progressively, these aberrations disappeared when the pseudo-atoms model was used (introduction of multipoler coefficients). This fact confirms that the determination of the phases in acentric structures is improved by sophisticated models like the multipole density model. 

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