A non-dualisable entropic algebra

We give an example of a five-element unary algebra which is entropic but does not admit a natural duality. Received September 26, 2000; accepted in final form April 4, 2001.     

Not every full duality is strong!

Is every full duality strong? We show that the answer is ‘no’, thereby answering a question that goes back to the earliest foundations of the theory of natural dualities. Received July 3, 2006; accepted in final form September 8, 2006.     

Considerations to prevent the breakdown and loss of fruit carotenoids during extraction and analysis in Musa

The impact of treatments aimed at improving the robustness of protocols for the analysis of carotenoids in fruit of banana and plantain were examined. Neither the inclusion of polyvinylpolypyrrolidine in the extraction buffer, nor vigorous homogenisation with glass beads influenced recoveries or chromatographic profiles. By contrast, heating lead to losses of up to 53% and to the formation of degradation products that are no longer detectable on our RP-HPLC system. Carotenoid extracts are unstable and most sensitive to exposure to light. However, even in the dark at −20 °C and in the presence of antioxidants breakdown rates of around 5% per day were observed.     

From Rectangular Bands to k -Primal Algebras

\noindent We begin by giving a new proof that every finite rectangular band is naturally dualisable. Motivated by the dualising structure arising from this proof, we call an algebra k-primal if it is (isomorphic to) a product of k independent primal algebras. For each k \geq 2 we exhibit a strong duality between the quasi-variety generated by a k -primal algebra and the topological quasi-variety \lilcat D _k of Boolean topological k -dimensional diagonal algebras. The category \lilcat D ₂ is the category of compact, totally disconnected rectangular bands. This duality extends Hu's duality for varieties generated by a primal algebra to the k -dimensional case. We find that Hu's ``uniqueness principle' for such varieties also extends to the k -dimensional case, namely, we show that a quasi-variety is equivalent as a category to the quasi-variety generated by a k -primal algebra if and only if it is itself generated by a k -primal algebra. June 18, 1999     

Photoconversion in the red fluorescent protein from the sea anemone Entacmaea quadricolor: is cis-trans isomerization involved?

Proteins from the family of the green fluorescent protein (GFP) are presently extensively used in molecular and cellular biology. Recent studies suggest that isomerization of the chromophore occurs upon excitation and is involved in nonradiative deactivation. Using Raman spectroscopy, we report on photoinduced cis-trans isomerization in the red fluorescent protein eqFP611 from the sea anemone Entacmaea quadricolor. The crystal structure of eqFP611 shows that the chemical structure of the chromophore, p-hydroxybenzylidene-imidazolinone with an extended -conjugated system, is nearly identical to the chromophore of other red fluorescent proteins such as DsRed and HcRed. However, the chromophore of eqFP611 has a trans configuration whereas the chromophore of DsRed has a cis configuration. Upon irradiation with 532-nm light, the absorption of eqFP611 peaking at 559 nm diminished, and concomitantly a drastic decrease in the quantum yield of fluorescence as well as more complex decay kinetics was observed. Upon irradiation, changes in the Raman spectrum of eqFP611 were observed, and the relative intensities and peak positions of the irradiated eqFP611 showed striking similarity with the peaks in the Raman spectrum of DsRed. These observations are tentatively interpreted as trans-to-cis isomerization of the chromophore taking place upon irradiation together with the opening of new, nonradiative pathways.