Topic
Character (mathematics)
About: Character (mathematics) is a research topic. Over the lifetime, 46723 publications have been published within this topic receiving 411412 citations.
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Book•
01 Jan 1998TL;DR: The character of logic in India as discussed by the authors, The character of Logic in India, and the character of India's character in logic in the 1990s, is a good starting point for our work.
Abstract: The character of logic in India / , The character of logic in India / , کتابخانه دیجیتال و فن آوری اطلاعات دانشگاه امام صادق(ع)
94 citations
93 citations
04 Mar 2009
TL;DR: Good character is important in the daily lives of individuals and families, in the workplace, in school, and in the larger community as discussed by the authors, and building and strengthening good character among children and youth have been universal goals for parenting and education.
Abstract: Good character is important in the daily lives of individuals and families, in the workplace, in
school, and in the larger community. For centuries, building and strengthening good character
among children and youth have been universal goals for parenting and education. Good character
is what parents look for in their children, what teachers look for in their students, what siblings
look for in their brothers and sisters, and what friends look for in each other. Character is critical
for lifelong optimal human development (Colby, James, & Hart, 1998). Despite the importance
of good character, psychology largely neglected this topic throughout much of the 20th century.
However, character has never gone away. It has gured in public discourse at least from the time of
Aristotle in the West (Aristotle, 2000), and Confucius in the East, and it remains a major societal
concern today (Hunter, 2000).
93 citations
TL;DR: It is concluded that Proteus and Necturus are probably not derived from a common ancestor which was a perennibranchiate salamander and there is no morphological, paleontological, or biogeographical evidence to favor either of these hypotheses over the other.
Abstract: The basis of all comparative biology is the determination of phylogenetic relationships and lineages. The most difficult question in the determination of lineage is whether the similarity between two forms is the result of monophyly, parallel evolution, or convergent evolution. The erection of a new phylogeny or the testing of a previously proposed phylogenetic grouping involves several steps: (1) the relation of characters and their homologous character states-the morphocline; (2) determination within the morphocline of its primitive and derived states and their polarities; (3) evaluation of the character states by means of weighting analysis; and (4) construction of the new phylogeny. In this paper we have concentrated on the third step, and we have formalized a method for character state weighting. The criterion for character state importance is the information contained within the character and its states. Character states may be designated in increasing value according to the following groups: (I) lo...
93 citations
Journal Article•
TL;DR: The character fields of the irreducible characters of cyclotomic Hecke algebras with complex reflection groups were studied in this paper, where it was shown that the character fields can be obtained by adjoining roots of monomials in the parameters to the ground field (Corollary 4.8 and Theorem 5.2).
Abstract: Let W be a finite complex reflection group, and H = H(W,u) the corresponding generic (cyclotomic) Hecke algebra as introduced in [8] and [9]. In this paper we study the character fields of the irreducible characters of H. In the case that W is a Weyl group, hence a reflection group over the field of rational numbers, it is well known that all other complex irreducible representations of W can also be realized over Q. The corresponding situation for the associated Iwahori-Hecke algebras was investigated by Benson and Curtis [5] and Alvis and Lusztig [1]. They determined the character fields of all absolutely irreducible representations of Iwahori-Hecke algebras. It turned out that sometimes certain square roots of monomials in the parameters have to be adjoined to the ground field. Furthermore they showed that all absolutely irreducible representations can actually be realized over such an extension of the ground field [5,13]. For a complex reflection group W let k denote the character field of the reflection representation of W . It is a result of Benard [4] and Bessis [6] that again all absolutely irreducible complex representations of W can be realized over k and in particular have their character field contained in k. Here we determine the character fields of all generic cyclotomic Hecke algebras associated to complex reflection groups (under a certain assumption known to hold for all but finitely many irreducible types and conjectured to be always true). Partial results in this direction were already obtained in [8] for those complex reflection groups occurring as cyclotomic Weyl groups. Our results show that again the character fields and a splitting field for H can be obtained by adjoining roots of certain monomials in the parameters to the ground field (Corollary 4.8 and Theorem 5.2). Our methods are similar to those employed in [5, 6, 8]. As in all of the above references, we use a case-by-case analysis, handling each isomorphism
93 citations