Computing the Determinant and the Algebraic Structure Count in Polygraphs

An algorithm for computing the algebraic structure count in polygraphs is presented. It expresses the related determinant of the adjacency matrix of a polygraph in terms of the determinants of monographs and bonding edges between the monographs. The algorithm is illustrated on a class of polygraphs with two bonding edges between monographs and computations for selected examples of polygraphs of this class are presented

Pojednostavljeni račun sparivanja u poligrafovima

Matching polynomial and perfect matchings for fasciagraphs, rotagraphs and twisted rotagraphs are treated in the paper. Classical transfer matrix approach makes it possible to get recursions for matching polynomial and perfect matchings, but the order of the matrix grows exponentially in the number of the linking edges between monographs. Novel transfer matrices are introduced whose order is much lower than that in classical transfer matrices. The virtue of the method introduced is especially pronounced when two or more linking edges end in the same terminal vertex of a monograph. An example of a polyacene polygraph with extended pairings is given where a novel matrix has only 16 entries as compared to 65536 entries in the classical transfer matrix. However, all pairings are treated here on equal footing, but the method introduced can be applied to selected types of pairings of interest in chemistry.U radu se razmatraju polinomi sparivanja i savršena sparivanja u fascia- i rotagrafovima te izvijenim rotagrafovima. Iako klasični postupak transfer matrice omogućava izvođenje rekurzija za polinom sparivanja i savršena sparivanja, red ove matrice eksponencijalno raste s brojem veza me|u monografovima. Ovdje su uvedene nove transfer matrice čiji je red mnogo ni`i od onoga za klasične transfer matrice, i to posebice kada jedna ili više veza me|u monografovima završava u jednom te istom čvoru. Postupak je ilustriran na primjeru poliacenskih poligrafova gdje ovdje uvedena matrica ima samo 16 elemenata u usporedbi s 65536 elemenata klasične transfer matrice. Iako se ovdje uvedeni postupak primjenjuje istovremeno na sva moguća sparivanja u poligrafovima, on je otvoren za primjenu na odabrana sparivanja od posebnoga kemijskoga interesa

A study of neologisms found in 'Le Monde' in 1955

A close study of every article in every number of the newspaper Le Monde which appeared in 1955 yielded 5,000 neologisms, that is words which are either completely new in the French language, or which, by their appearance in the newspaper, are emerging into the general language from the jargon or other limited area of the language to which they were earlier restricted. The words were compared with later dictionaries, and also with related studies.A method of classification based on the use of punch-cards was evolved to contain the words. It was found that the mode of formation was an important aspect of the neologisms, so these were studied under the headings of the modes of formation observed. Variation was found in the types of neologisms falling under the different headings, with respect to whether their formation was deliberate or unconscious, and to the usefulness and the durability of the words. Words formed by the use of suffixes tend to be deliberate and useful: those formed by the use of prefixes vary, A continuous progression was observed between formation by prefix, and the formation of compound words, with some link to formations by suffix.Different types of compound were found, varying in usefulness and in consciousness of formation. The validity of some compound forms as words was questioned, as these have some of the characteristics of syntactic groups rather than of words. Series of compounds were found to be sometimes more interestingThan individual formations. Relatively few creations by semantic change were found, but a large proportion of those found were useful and durable forms. Borrowings were found from many languages, the number from each language varying with closeness or importance to France of the people speaking it. A smaller proportion of borrowings was found than other studies led one to expect. Caiques followed a pattern similar to that of borrowings, and different types of caique were found. The findings were summed up in conclusion.<p

1976-1978 Xavier University College of Arts and Sciences, College of Business Administration, The College of Continuing Education, Graduate School Course Catalog

https://www.exhibit.xavier.edu/coursecatalog/1188/thumbnail.jp