Character (mathematics)

About: Character (mathematics) is a research topic. Over the lifetime, 46723 publications have been published within this topic receiving 411412 citations.

Characters of irreducibleG-modules and cohomology ofG/P for the lie supergroupG=Q(N)

Abstract: We prove a character formula for any finite-dimensional irreducible representationV of the “queer” Lie superalgebra g=q(n). It expresses chV in terms of the multiplicities of the irreducible g-subquotients of the cohomology groups of certain dominant g-bundles on the Π-symmetric projective spaces (i.e., on the homogeneous superspacesG/P whose reduced space is a projective space, whereG=Q(n)). We also establish recurrent relations for the above multiplicities, and this enables us to compute explicitly chV for any givenV. This provides a complete solution to the Kac character problem for the Lie superalgebraq(n). Finally, we consider the particular cases ofq(2), q(3), andq(4) in which we compare the new character formula with the generic character formula of [12].

Methods and systems for implementing approximate string matching within a database

Abstract: A computer-based method for character string matching of a candidate character string with a plurality of character string records stored in a database is described. The method includes a) identifying a set of reference character strings in the database, the reference character strings identified utilizing an optimization search for a set of dissimilar character strings, b) generating an n-gram representation for one of the reference character strings in the set of reference character strings, c) generating an n-gram representation for the candidate character string, d) determining a similarity between the n-gram representations, e) repeating steps b) and d) for the remaining reference character strings in the set of identified reference character strings, and f) indexing the candidate character string within the database based on the determined similarities between the n-gram representation of the candidate character string and the reference character strings in the identified set.

The Inappropriateness of the Correlation Coefficient as a Measure of Taxonomic Resemblance

Abstract: three operational taxonomic units (OTU's): C, E, and G. The characters are presumed to be standardized and entirely independent of each other (i.e., not biased by a common factor such as size). C and E are taken from Sokal and Sneath (1963:296) with characters 5 and 6 omitted because there was no comparison for these characters. G and C are identical except for character 2. C agrees with E in character 2, but G does not. Therefore, the resemblance between C and E is obviously greater than the resemblance between E and G. However, the correlation coefficients (r) would suggest the reverse, being 0.882 for the former and 0.922 for the latter. Table 2 shows characters (also presumed to be standardized and independent) of OTU's H, I, and J. The differences between H and I and