This work is a survey on decidable and undecidable problems in matrix theory. The problems studied are simply formulated, however most of them are undecidable. The method to prove undecidabilities is the one found by Paterson [Pat] in 1970 to prove that the mortality of nitely generated matrix monoids is undecidable. This method is based on the undecidability of the Post Correspondence Problem....

Background and Rationale The scientific infrastructure in support of cotton research and improvement took a ‘giant leap forward’ with the release of the first ‘gold-standard’ cotton reference genome sequence on 5 January 2012. Later in 2012, two independent publications (Paterson et al. 2012; Wang et al. 2012) provided initial descriptions of the basic genome of cotton, with one of these also r...

We revisit the work of Paterson and of Meijer & Hutton, which describes how to construct catamorphisms for recur-sive datatype deenitions that embed contravariant occurrences of the type being deened. Their construction requires , for each catamorphism, the deenition of an anamor-phism that has an inverse-like relationship to that cata-morphism. We present an alternative construction, which rep...

Recently, Al-Riyami and Paterson proposed a generic conversion from CL-PKE (Certificateless Public Key Encryption) to CBE (Certificate Based Encryption) and claimed that the derived CBE scheme is secure and even more efficient than the original scheme of Gentry. In this paper, we show that their conversion is wrong due to the flaw of the security proof. It leads the new concrete CBE scheme by A...

Surjective isometries between unital C*-algebras were classified in 1951 by Kadison [K]. In 1972 Paterson and Sinclair [PS] handled the nonunital case by assuming Kadison’s theorem and supplying some supplementary lemmas. Here we combine an observation of Paterson and Sinclair with variations on the methods of Yeadon [Y] and the author [S1], producing a fundamentally new proof of the structure ...

I was interested to read Rodríguez et al. (2012) on PCR to detect verrucosin producing fungi in food and cultures. However, their interpretation regarding mutated strains and internal amplification controls (IAC) appears to be incorrect, although they referred to our papers on the issue. It is worth restating to the wider scientific community that fungi may be mutated by self produced mutagens ...

The Goldman–Parker Conjecture classifies the complex hyperbolic C–reflection ideal triangle groups up to discreteness. We proved the Goldman–Parker Conjecture in [6] using a rigorous computer-assisted proof. In this paper we give a new and improved proof of the Goldman–Parker Conjecture. While the proof relies on the computer for extensive guidance, the proof itself is traditional. AMS Classifi...