Regular elements

Lockyer s studies of the solar spectrum revealed to him that the sun is a miasma of chemical elements. Where did they come from In 1873 Lockyer developed the theory, later expounded in his Chemistry of the Sun (1887), that in the hottest (blue-white) stars the stellar matter is broken apart into the constituents of atoms themselves subatomieparticles, the protyle discussed by Dumas. Then, as the stars cooled, these particles combined to form regular elements - including some, like helium, not (then) known on Earth. 

Due to the relevance and the complexity of proteins, some descriptors were defined to represent amino acid side chains, these being responsible for the packing of the regular elements of secondary structure and then for the tertiary structure of a protein. As a consequence, the structure of a protein can be expressed quantitatively by means of side chain amino add properties. Starting from the pioneering work of Sneath, who described peptide sequences by semiquantitative experimental parameters of the 20 coded amino acids [Sneath, 1966], several amino acid descriptors have been proposed that contain information about properties of side chains of amino adds. 

We now discuss two ways of introducing regular elements to equation (16) ... 

Secondary structures are regular elements such as a-helices and p-pleated sheets, which are formed between relatively small parts of the protein sequence. These structural domains are determined by the conformation of the peptide backbone, the influence of side-chains is not taken into account for secondary structures. 

Irregular elements should be separated from regular elements. 

Notice that the finite difference method can also be related to the particular finite element method with linear shape functions (see below) and regular element distribution [l2S]. 

Proof of the theorem Fix an arbitrary element of general position a eG. Consider a regular element x E G. Let /i,..., /ib be a complete set of local invariants at the point x E G. The completeness means that at the point x the differentials generate Annx, where Annx = 6 Gjad x = 0. The... 

Proof Let ( 6 G be a regular element, that is, such an element that an orbit passing through it has maximal dimension. Then for a set Xi of linear coordinate... 

Despite the compelling need for spacecraft autonomy and the feasibility demonstrated by the successful missions described above, obstacles remain to the use of autonomous systems as regular elements of spacecraft flight software. Two kinds of requirements for spacecraft autonomy must be satisfied (1) functional requirements, which represent attributes the software must objectively satisfy for it to be acceptable and (2) perceived requirements, which are not all grounded in real mission requirements but weigh heavily in subjective evaluations of autonomous systems. Both types of requirements must be satisfied for the widespread use of autonomous systems. 

Analysis of known protein stmctures has demonstrated that regular elements can exist in combined forms. Examples are the coiled-coil a-helix (Fig. 1.25, a), chain segments with antiparallel P-stmctures (P-meander stmcture Fig. 1.25, b) and combinations of a-helix and P-stmcture (e. g., PaPaP Fig. 1.25 c). 

Fig. 3. Generalized phase diagram for the regular lanthanides and regular intra-lanthanide alloys at low temperatures (OK), taken with slight modifictions from Kruger et al. (1990). The region covered by experiments on the regular elements is marked by thin vertical lines. The anomalous regions for the elements Ce, Eu, and Yb, as well as Pr, bid, and Sm, under higher pressures are marked by heavy vertical bars. Dashed lines represent extrapolations.

---