Number pattern

R. E. Williams, Coordination number-pattern recognition theory of carborane structures, Adv. Incrg. Chem. Radiochem. 18, 67-142 (1976). R. E. Williams, Chap. 2 in G. A. Olah, K. Wade and R. E. Williams (eds.). Electron Deficient Boron and Carbon Clusters, Wiley, New York, 1991, pp. 11-93. 

The tetracyclines are valuable orally active broad-spectrum antibiotics prepared by isolation from the fermentation liquors of various strains of Streptomyces or by chemical transformation of fermentation-derived substances. The basic ring system and numbering pattern is as follows ... 

The carbon number distribution of technical secondary alkanesulfonates determined by pyrolysis gas chromatography and mass spectrometry (GC-MS) is shown in Fig. 13 together with the corresponding carbon number pattern of the raw material paraffins obtained by GC [16]. Pyrolysis was performed in a crucible-modified SGE pyrojector after covering the mixture with quartz wool. The presence of up to 10 wt % of disulfonates in technical alkanesulfonates is demonstrated by fast atom bombardment and mass spectrometry (FAB-MS) (Fig. 14) [24],... 

Coordination Number Pattern Recognition Theory of Carborane Structures Robert E. Williams... 

COORDINATION NUMBER PATTERN RECOGNITION THEORY OF CARBORANE STRUCTURES ... 

B. History of Coordination Number Pattern Becognition Theory... 

This paper subscribes to the third viewpoint, and is based on an empirical approach that involves coordination number pattern recognition (CNPR). It is a simplistic approach, yet it apparently accommodates most if not all carborane and borane structures. For compounds that are still controversial and for compounds that have not yet been discovered or characterized, the CNPR thesis frequently predicts different structures, or at least fewer candidates, than do any of the theoretical treatments. 

The movie is notable in that, as mentioned above, it s about a mathematical genius named Max who is obsessed with numbers. Max rarely leaves his apartment and sees numbers and number patterns in everything around him. When his computer displays the mystical 216-digit number, it crashes and a strange adventure ensues. Perhaps the number even makes the computer conscious. The audience is never sure. Max decides that the 216-digit number is responsible for his own ill health, and the movie closes as he drills a hole in his own skull as a cure. Weird ending ... 

Fig. 4.25 The determinants corresponding to different numbering patterns can seem to differ, but on expansion they give the same polynomial...

Like elemental periodicity, which is a function of electron configuration, an empirical periodic function for nucleons, known as the magic-number pattern, has been derived. The reason why this function has been less successful... 

This section presents the structure of the boron hybrides and is arranged in accordance with the relationship defined by Wade s Rules and expressed by Williams and Rudolph. Thus for the boranes containing six or more pairs of skeletal bonding electrons, the relationship between the structures of the closo-, nido-, arachno-and hypho-species is described. In cases where the parent borane does not exist, examples from heteroboranes with the correctly predicted structure based on Williams coordination number pattern recognition theory (CNPR) of borane structures will be described 70. Treated separately will be mono- and diborane species and also species with more than 12 boron atoms. Although there have been several reviews on the structures of the boranes in recent years none have used the current approach89. ... 

Magic Numbers — Number Patterns Associated with the Hierarchy... 

The persistent correlation that recurs between number patterns and physical structures indicates a similarity between the structure of space-time and number. Like numbers and chiral growth, matter has a symmetry-related conjugate counterpart. The mystery about this antimatter is its whereabouts in the universe. By analogy with numbers, the two chiral forms of fermionic matter may be located on opposite sides of an achiral bosonic interface. In the case of numbers this interface is the complex plane, in the physical world it is the vacuum. An equivalent mapping has classical worlds located in the two surfaces and the quantum world, which requires complex formulation, in the interface. 

What is the missing term in the number pattern below ... 

When the central atoms linked through bridges exhibit a tetrahedral distribution of bonds rather than a planar one, the following numbering pattern applies ... 

Clearly, Eq. (4.84) ignores correlations in the occupation-number patterns (i.e., the configurations of the lattice fluid). This (independent) assumption is, however, required to be consistent with the mean-field ansatein Eq. (4.77). 

Throughout history, mathematicians have studied number patterns. Research Pascal s Triangle, Fibonacci and the Fibonacci Sequence, and the Golden Mean that was used by the Greeks in building the Parthenon. 

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