Spin models for link invariants were introduced by Jones [7], and their connection to combinatorics was revealed first in [4]. Jaeger and Nomura [6] constructed nonsymmetric spin models for link invariants from Hadamard matrices, and showed that these models give link invariants which depend nontrivially on link orientation. These models are a modification of the Hadamard model originally const...

Let A be an association scheme on q ≥ 3 vertices. We show that the Bose-Mesner algebra of the generalized Hamming scheme H(n,A), for n ≥ 2, is not the Nomura algebra of a type II matrix. This result gives examples of formally self-dual Bose-Mesner algebras that are not the Nomura algebras of type II matrices.

We determine the Nomura algebras of the type-II matrices belonging to the Bose-Mesner algebra of a conference graph. 1 Type-II Matrices and Nomura Algebras We say that an n × n matrix W with complex entries is type II if W (j, i)(W)(i, j) = 1 n for i, j = 1, . . . , n. So a type-II matrix is invertible and has no zero entry. We use I and J to denote the identity matrix and the matrix of all one...

A Leonard pair is an ordered of diagonalizable linear maps on a finite-dimensional vector space, that each act eigenbasis for the other one in irreducible tridiagonal fashion. In present paper we consider type pair, said to have spin. The notion spin model was introduced by V.F.R. Jones construct link invariants. symmetric matrix over C satisfies two conditions, called II and III conditions. It...

‎in this paper‎, ‎the type-{rm ii} matrices on (negative) latin square graphs are considered and it is proved that‎, ‎under‎ ‎certain conditions‎, ‎the nomura algebras of such type-{rm ii} matrices are trivial‎. ‎in addition‎, ‎we construct type-{rm ii} matrices‎ ‎on doubly regular tournaments and show that the nomura algebras of such matrices are also trivial‎.

CEREBELLAR DEVELOPMENT AND EARLY POSTNATAL ATAXIA IN MICE Lixiang Wang, Masatoshi Nomura, Yutaka Goto, Kimitaka Tanaka, Ryuichi Sakamoto, Ichiro Abe, Shohei Sakamoto, Atsushi Shibata, Patricio L.M. Enciso, Masahiro Adachi, Keizo Ohnaka, Hisaya Kawate, Ryoichi Takayanagi From the Department of Medicine and Bioregulatory Science, Graduate School of Medical Science, Kyushu University, Maidashi 3-1...

A spin model is a square matrix W satisfying certain conditions which ensure that it yields an invariant of knots and links via a statistical mechanical construction of V. F. R. Jones. Recently F. Jaeger gave a topological construction for each spin model W of an association scheme which contains W in its Bose Mesner algebra. Shortly thereafter, K. Nomura gave a simple algebraic construction of...

The genus Sinotrisus Yin & Li, comprising four species, is redefined and revised. Members of Sinotrisus are often found with ants of the subfamily Formicinae, or in humid forest habitats. The type speciesand three new species are (re-)described and illustrated: Sinotrisus kishimotoi Yin & Nomura, sp. n. (China: Sichuan), Sinotrisus nomurai Yin, Li & Zhao (type species) (China: Zhejing), Sinotri...