This short survey article reviews our current state of understanding of the structure of noetherian Hopf algebras. The focus is on homological properties. A number of open problems are listed. To the memory of my teacher and friend Brian Hartley

Discrete transforms such as the discrete Fourier transform (DFT) or the discrete Hartley transform (DHT) furnish an indispensable tool in signal processing. The successful application of transform techniques relies on the existence of the so-called fast transforms. In this paper some fast algorithms are derived which meet the lower bound on the multiplicative complexity of the DFT/DHT. The appr...

We introduce the chiral domain of an arrangement cameras $$\mathcal {A} = \{A_1,..., A_m\}$$ which is subset $$\mathbb {P}^3$$ visible in {A}$$ . It generalizes classical definition chirality to include all and offers a unifying framework for studying multiview chirality. give algebraic description allows us define describe version Triggs’ joint image. then use re-derive extend prior results on...

In this paper, we propose a class of Hartley-Ross type unbiased estimators for estimating the finite population mean of the study variable under ranked set sampling (RSS), when population mean of the auxiliary variable is known. The variances of the proposed class of unbiased estimators are obtained to first degree of approximation. Both theoretically and numerically, the proposed estimators ar...

An efficient approach to the design of a VLSI array for a prime-length type III generalized discrete Hartley transform (GDHT) is presented. The design makes use of an appropriate decomposition of the GDHT into two half-length circular correlation structures having the same length and form that can be concurrently computed and implemented on a single linear systolic array using some of the known...

An algorithm based on Fast Hartley Transform (FHT) that uses a digital voltmeter for measuring the harmonic parameters of low-frequency signals with negligible leakage is presented. The algorithm was compared favorably in speed with a previous one based on discrete Fourier transforms.

The role of finite centralizers involutions in pseudo-finite groups is analyzed. It shown that a group admitting definable involutory automorphism fixing only finitely many elements finite-by-abelian-by-finite. As consequence, we give model-theoretic proof result for periodic due to Hartley and Meixner. Furthermore, it any has an infinite abelian subgroup.