Let P be a simple polygon with n vertices. The dual graph T ∗ of a triangulation T of P is the graph whose vertices correspond to the bounded faces of T and whose edges connect those faces of T that share an edge. We consider triangulations of P that minimize or maximize the diameter of their dual graph. We show that both triangulations can be constructed in O(n3 log n) time using dynamic progr...

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Use of a repetition time similar to, or shorter than, metabolite T(1)s is common in NMR spectroscopy of biological samples to improve the signal-to-noise ratio. Conventionally, the partial saturation that results from this is corrected using saturation factors. However, this can lead to erroneous results in the presence of chemical exchange or nonconstant T(1)s. We describe an alternative appro...

in this paper, the notions of $(t,s)$-composition matrix and$(t,s)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(t,s)$ is a dual pair of triangular module. theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. furthermore, theirproperties and characterizations are presented. then a new methodbased on $tilde{...

Abstract. A formal notion of a Typ T of a self-dual linear code over a finite left Rmodule V is introduced which allows to give explicit generators of a finite complex matrix group, the associated Clifford-Weil group C(T ) ≤ GL|V |(C), such that the complete weight enumerators of self-dual isotropic codes of Type T span the ring of invariants of C(T ). This generalizes Gleason’s 1970 theorem to...

In this paper, we introduce a new interconnection network, the dual-cube, its topological properties, and the routing/broadcasting algorithms in the dual-cube. The advanced subjects such as fault-tolerant routing and constructing multiple disjoint paths in dual-cubes are also included in this paper. The binary hypercube, or r-cube, can connect 2r nodes. In contrast, a dual-cube with r links for...

We construct the dual Cantor set for a degree two expanding map f acting as cover of the circle T onto itself. Then we use the criterion for a continuous function on this Cantor set to be the scaling function of a uniformly asymptotically affine UAA expanding map to show that the scaling function for f descends to a continuous function on a dual circle T∗. We use this representation to view the...