In this paper, we investigate the relationship between a meromorphic function f(z) and its difference operator when they share two sets, and give some interesting results.

We show that the quotient of a Hom-finite triangulated category C by the kernel of the functor HomC(T, −), where T is a rigid object, is preabelian. We further show that the class of regular morphisms in the quotient admit a calculus of left and right fractions. It follows that the Gabriel-Zisman localisation of the quotient at the class of regular morphisms is abelian. We show that it is equiv...

The Faculty of Engineering & Surveying Technical Reports serve as a mechanism for disseminating results from certain of its research and development activities. The scope of reports in this series includes (but is not restricted to): literature reviews, designs, analyses, scientific and technical findings, commissioned research, and descriptions of software and hardware produced by staff of the...

The recently proposed high-order central difference schemes for conservation laws have a tendency of smearing linear discontinuities. In principle, Harten’s artificial compression method (ACM) could be used to improve resolution. We analyze why this approach has not yet been used successfully and derive a more powerful version of the ACM based on a rigorous estimate of the total variation. We d...