We examine corresponding Cauchy-Riemann equations by using the non-commutativity for the product on split-biquaternions. Additionally, we describe the regularity of functions and properties of their differential equations on split-biquaternions. We investigate representations and calculations of the derivatives of functions of split-biquaternionic variables. c ©2016 all rights reserved.

In one of his early papers Claude Berge proved a Helly-type theorem, which replaces the usual “nonempty intersection” condition with a “convex union” condition. Inspired by this we prove a fractional Helly-type result, where we assume that many (d+1)-tuples of a family of convex sets have a star-shaped union, and the conclusion is that many of the sets have a common point. We also investigate s...

This paper discusses evaluation in the context of public art and specifically of interactive digital art. The study reported is of ‘Light Logic’, an exhibition of retrospective and current drawings, paintings and interactive digital works by the second author. The study was conducted by Site Gallery Sheffield in association with UK and Australian researchers. A survey of evaluation practice amo...

During gene transcription, RNA polymerase (Pol) II encounters obstacles, including lesions in the DNA template. Here, we review a recent structure-function analysis of Pol II transcribing DNA with a bulky photo-lesion in the template strand. The study provided the molecular basis for recognition of a damaged DNA by Pol II, which is the first step in transcription-coupled DNA repair (TCR). The r...

Given the increasing number of mobile platforms, a key technical challenge is how to provide an optimal photo browsing experience given the limited screen size available on mobile devices. This paper proposes a novel technique for intelligent mobile image categorization to reduce computation complexity on the Android mobile platform. In this technique, captured images are analyzed directly in J...

Integrating a silicon solar cell with a recently developed cobalt-based water-splitting catalyst (Co-Pi) yields a robust, monolithic, photo-assisted anode for the solar fuels process of water splitting to O(2) at neutral pH. Deposition of the Co-Pi catalyst on the Indium Tin Oxide (ITO)-passivated p-side of a np-Si junction enables the majority of the voltage generated by the solar cell to be u...

Catalytic oxidative C-H bond functionalization reactions that proceed without requiring stoichiometric amounts of external oxidants or pre-functionalized oxidizing reagents could maximize the atom- and step-economy in chemical syntheses. However, such a transformation remains elusive. Here, we report that a photo-driven catalytic process enables decarboxylative C-H trifluoromethylation of (hete...

abstract aims: the application of photocatalytic processes to remove heavy metals in aqueous solutions and industrial wastewater are regarded as extremely effective, clean and without producing waste methods. the goal of the present study was to investigate the photocatalytic activity of zno based on h-zsm-5 zeolite support. materials & methods: zno/h-zsm-5 composite synthesized by impregnation...

tungsten trioxide nanoparticles with two different sizes (average particle sizes about 50 and 80 nm) were prepared by the spray pyrolysis method. photo degradation of congo red (azo dye) showed that photo catalytic property of the as-prepared wo3 nanoparticles with average size about 80 nm is higher than the sample with average size about 50 nm. photo degradation of rhodamine b (cationic triary...

We describe a new variant of the well known Baby-Step Giant-Step algorithm in the case of some discrete logarithms with a special structure. More precisely, we focus on discrete logarithms equal to products in groups of unknown order. As an example of application, we show that this new algorithm enables to cryptanalyse a variant of the GPS scheme proposed by Girault and Lefranc at CHES 2004 con...