Properties of a special class of doubly stochastic measures

Summary A measure on the unit squareI } I is doubly stochastic if(A } I) = (I } A) = the Lebesgue measure ofA for every Lebesgue measurable subsetA ofI = [0, 1]. By the hairpinL L ^–1, we mean the union of the graphs of an increasing homeomorphismL onI and its inverseL ^–1. By the latticework hairpin generated by a sequence {x _n :n Z} such thatx _n-1 < x_n (n Z), x _n = 0 and x _n = 1, we mean the hairpinL L ^–1 , whereL is linear on [x _n-1 ,x _n ] andL(n) =x _n-1 forn Z. In this note, a characterization of latticework hairpins which support doubly stochastic measures is given. This allows one to construct a variety of concrete examples of such measures. In particular, examples are given, disproving J. H. B. Kemperman's conjecture concerning a certain condition for the existence of doubly stochastic measures supported in hairpins.     

The measurement of nucleoside deaminases by high performance liquid chromatography and their use in clinical chemistry.

The measurement of the nucleoside deaminases--cytidine deaminase, guanosine deaminase and adenosine deaminase--by reversed phase high performance liquid chromatography is reviewed. The clinical value of assaying the enzyme activity is discussed for each of these enzymes. Both cytidine deaminase and adenosine deaminase measurements have proven clinical value, although the use of the assay of cytidine deaminase in the diagnosis of pre-eclampsia is probably not helpful.     

Rates of transport through a capsule membrane to attain Donnan equilibrium

The swelling of a capsule consisting of salt solution and polyelectrolyte, surrounded by a membrane, is studied. The membrane allows salt and water to pass, but is impermeable to polyelectrolyte molecules. Equilibrium swelling of the capsule is governed by Donnan equilibrium. Transport rates of a salt and water through the membrane are expressed in terms of a Darcy permeability and a salt diffusivity. The governing equations predict that the rate at which equilibrium is attained as the external salt concentration varies is controlled by the timescale for diffusion of salt, rather than by that for Darcy flow. Experiments were performed using capsules with membranes made of covalently linked HSA and alginate. The capsule volume varied with a single relaxation rate when the external salt concentration was changed, as predicted by theory. This constitutes the first step toward a simple method for determining the membrane properties of capsules by measuring rates of change of capsule volume.     

Scalable Hybrid Synthetic/Biocatalytic Route to Psilocybin

Psilocybin, the principal indole alkaloid of Psilocybe mushrooms, is currently undergoing clinical trials as a medication against treatment-resistant depression and major depressive disorder. The psilocybin supply for pharmaceutical purposes is met by synthetic chemistry. We replaced the problematic phosphorylation step during synthesis with the mushroom kinase PsiK. This enzyme was biochemically characterized and used to produce one gram of psilocybin from psilocin within 20 minutes. We also describe a pilot-scale protocol for recombinant PsiK that yielded 150 mg enzyme in active and soluble form. Our work consolidates the simplicity of tryptamine chemistry with the specificity and selectivity of enzymatic catalysis and helps provide access to an important drug at potentially reasonable cost.     

Frequency shifting through cascaded second-order processes in a N-(4-nitrophenyl)- L-prolinol crystal

We exploit the high second-order susceptibility of the organic crystal N-(4-nitrophenyl)-L-prolinol to accomplish, through a cascaded second-order process, wavelength conversion of a signal pulse (from 1.16 to 1.14 microm) under the action of a pump pulse (at 1.15 microm). In a 2.8-mm-thick crystal, wavelength conversion with unit gain was obtained with a pump peak intensity as low as 9 MW/cm(2) . At low intensities, in the limit of negligible conversion where the cascading effect can be described through an effective third-order susceptibility, we derive |(x)((3))(eff) | approximately 2.4 x 10(-17) m(2)/V(2), which is ~10(2) larger than the nonresonant (x)((3)) of conjugated polymers or semiconductors.