Rings Theory

Keller JB. 1980. Liesegang rings theory of fast reaction and slow diffusion. In Stewart WE, Ray WH, Conley CC, eds. Dynamics and Modelling of Reactive Systems. New York Academic Press, 211-224. 

The number of two-polymer, multipolymer, and multimonomer systems reported in the scientific and patent literature continues to rise without an adequate nomenclature to describe the several materials. This chapter is divided into three parts. (1) A proposed nomenclature system which uses a short list of elements (polymers or polymer reaction products). These elements are reacted together in specific ways by binary operations which join the two polymers to form blends, grafts, blocks, crosslinked systems, or more complex combinations. (2) The relationship between the proposed nomenclature and the mathematics of ring theory (a form of the new math9 ) is discussed. (3) A few experimental examples now in the literature are mentioned to show how the new nomenclature scheme already has been used to discover new multipolymer systems. 

In the previous papers of this series, the concepts of mathematical group theory and then ring theory were brought to bear on the nomenclature and structure of multicomponent polymer materials (12,18,19). In each case, no proof of the existence of either a mathematical group or ring was offered, but rather only the notions or concepts were applied. 

In the proceeding, the notions of elements and binary operations were developed. An important part of the mathematics of ring theory involves the concept of functions. 

Kekule, the great chemist whose benzene ring theory is now the basic law of the chemistry of the aromatic compounds, worked exhaustively with nitrotoluene, and did much to clear the cloud caused by Jaworsky s contradiction of Deville s work. Kekule s work showed—to quote his words— At least it is quite probable that the substance hitherto regarded as nitro-... 

ABSTRACT Using the overburden rock fissure 0 -ring theory, and based on the three-dimensional stope Merry flow continuity equation, differential equations and gas migration momentum dispersion equation, combined with the similarity theory, the similarity criteria relationship of experimental model is established. Such design contains a variety of ways to build a three-dimensiond ventilation stope experimental model. Make use of this model as the basis for the test-bed U-shaped ventilation flow field experiment, then input obtained experimental data into MATLAB software for numerical analysis. Finally get the discipline of air leakage field under the U-type ventilation and gas field distribution, then take it as the basis to determine the principles of Spontaneous Combustion Prevention and gas control. 

Washington, D.C. (1979). Nomenclature for polymer blends, blocks, grafts, and IPNs. Ring theory application. 

L. H. Sperling, K. B. Ferguson, J. A. Manson, E. M. Corwin, and D. L. Siegfried, Isomeric Graft Copolymers and Interpenetrating Polymer Networks. Theory and Experiment, Macromolecules 9(5), 743 (1970). Application of ring theory concepts to IPN nomenclature. Decrosslinking of PS as example. 

While reviewing all of the applications of group and ring theory to multipolymer systems and compound crosslinking is beyond the scope of this paperl2,13 it is important to note that a number of theorems can be brought into play. Some of these deal with functions, which spell out the rules by which an element can be moved from one table to another, or to a different position within the table. For example. Table IV codified systems that are... 

Friedrich August Kekule announces his benzene ring theory. This makes it possible to draw the structural formulas of simple aromatic chemicals. 

Except for artificial alizarin, made from coal tar anthracene, practically all the early synthetic dyes were derived from, coal tar benzene and toluene. From the mid-1870s, however, interest turned to amino and nitro derivatives of the more abundant coal tar hydrocarbon naphthalene. These endeavours were assisted by the large body of theoretical, synthetic and analytical knowledge about aromatic chemistry that had become available during the decade following the announcement of Kekule s benzene ring theory (1865). Roussin s azo dyes were naphthalene derivatives. 

Single particle stellar orbital mechanics is not unlike planetary ring theory. Bodies move under the influence of a gravitational field created by the mutual interactions of all of the stellar masses in the system, a spatially extended and complicated potential. 

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