Using computers, Hanaki and I were classifying association schemes of small order for a past few years (Hanaki and Miyamoto (1998,1998,2000),Hanaki (1999)). In the present paper we will discuss about computing isomorphisms of association schemes. We compute isomorphisms of an association scheme using its relation matrix defined in the following section. A relation matrix can be seen an adjacenc...

We prove an S3-symmetry of the Jacobi identity for intertwining operator algebras. Since this Jacobi identity involves the braiding and fusing isomorphisms satisfying the genus-zero Moore–Seiberg equations, our proof uses not only the basic properties of intertwining operators, but also the properties of braiding and fusing isomorphisms and the genus-zero Moore–Seiberg equations. Our proof depe...

Taking the `1-completion and the topological dual of the singular chain complex gives rise to `1-homology and bounded cohomology respectively. Unlike `1-homology, bounded cohomology is quite well understood by the work of Gromov and Ivanov. We derive a mechanism linking isomorphisms on the level of homology of Banach chain complexes to isomorphisms on the level of cohomology of the dual Banach ...

Title of dissertation: CLASSICAL INVARIANTS OF PRINCIPAL SERIES AND ISOMORPHISMS OF ROOT DATA Robert Alexander McLean II Doctor of Philosophy, 2016 Dissertation directed by: Professor Jeffrey Adams Department of Mathematics We develop some new techniques to calculate the Schur indicator for selfdual irreducible Langlands quotients of the principal series representations. Using these techniques ...

Let N (l) be a continuous topological space. Recent developments in local calculus [19] have raised the question of whether every real, degenerate, semi-Kepler factor is linearly Noetherian. We show that every curve is pointwise semi-Hadamard, Thompson, almost surely ultra-reducible and non-continuously independent. It has long been known that every hyper-natural modulus equipped with a Pythago...

In [AS2] we classified a large class of finite-dimensional pointed Hopf algebras up to isomorphism. However the following problem was left open for Hopf algebras of of type A,D or E6, that is whose Cartan matrix is connected and allows a non-trivial automorphism of the corresponding Dynkin diagram. In this case we described the isomorphisms between two such Hopf algebras with the same Cartan ma...

Dependently typed programming uses precise variants of data structures to ensure program correctness in an economical way, but designing reusable libraries for all possible variants of data structures is a difficult problem. The authors addressed the problem by extending McBride’s ornaments to a framework of ornaments and refinements to support a modular structure for dependently typed librarie...

Following the work of Duistermaat-Singer [DS] on isomorphisms of algebras of global pseudodifferential operators, we classify isomorphisms of algebras of microlocally defined semiclassical pseudodifferential operators. Specifically, we show that any such isomorphism is given by conjugation by A = BF , where B is a microlocally elliptic semiclassical pseudodifferential operator, and F is a micro...

We propose to detect isomorphisms of algebraic modular speci cations, by representing speci cations as diagrams over a category C0 of base speci cations and speci cation morphisms. We start with a formulation of modular speci cations as terms, which are interpreted as diagrams. This representation has the advantage of being more abstract, i.e. less dependent of one speci c construction than ter...

Similarity of edge labeled graphs is considered in the sense of minimum squared distance between corresponding values. Vertex correspondences are established by isomorphisms if both graphs are of equal size and by subisomorphisms if one graph has fewer vertices than the other. Best fit isomorphisms and subisomorphisms amount to solutions of quadratic assignment problems and are computed exactly...