The antipode and primitive elements in the Hopf monoid of supercharacters

From a recent paper, we recall the Hopf monoid structure on the supercharacters of the unipotent uppertriangular groups over a finite field. We give cancellation-free formula for the antipode applied to the bases of class functions and power sum functions, giving new cancellation-free formulae for the standard Hopf algebra of supercharacters and symmetric functions in noncommuting variables. We also give partial results for the antipode on the supercharacter basis, and explicitly describe the primitives of this Hopf monoid.     

Racemisation in Chemistry and Biology

The two enantiomers of a compound often have profoundly different biological properties and thus their liability to racemisation in aqueous solutions is an important piece of information. The authors reviewed the available data concerning the process of racemisation in vivo, in the presence of biological molecules (e.g., racemase enzymes, serum albumin, cofactors and derivatives) and under purely chemical but aqueous conditions (acid, base and other aqueous systems). Mechanistic studies are described critically in light of reported kinetic data. The types of experimental measurement that can be used to effectively determine rate constants of racemisation in various conditions are discussed and the data they provide is summarised. The proposed origins of enzymatic racemisation are presented and suggest ways to promote the process that are different from processes taking place in bulk water. Experimental and computational studies that provide understanding and quantitative predictions of racemisation risk are also presented.     

A Minimal Framework for Non-Commutative Quantum Mechanics

Deformation quantisation is applied to ordinary Quantum Mechanics by introducing the star product in a configuration space combining a Riemannian structure with a Poisson one. A Hilbert space compatible with such a configuration space is designed. The dynamics is expressed by a Hermitian Hamiltonian containing a scalar potential and a one-form potential. As a simple illustration, it is shown how a particular type of non-commutativity of the star product is interpretable as generating the Zeeman effect of ordinary Quantum Mechanics.     

Total Synthesis of (6R,10R,13R,14R,16R,17R,19S,20R,21R,24S, 25S,28S,30S,32R,33R,34R,36S,37S,39R)‐Azaspiracid‐3 Reveals Non‐Identity with the Natural Product

A convergent and stereoselective total synthesis of the previously assigned structure of azaspiracid‐3 has been achieved by a late‐stage Nozaki–Hiyama–Kishi coupling to form the C21?C22 bond with the C20 configuration unambiguously established from l ‐(+)‐tartaric acid. Postcoupling steps involved oxidation to an ynone, modified Stryker reduction of the alkyne, global deprotection, and oxidation of the resulting C1 primary alcohol to the carboxylic acid. The synthetic product matched naturally occurring azaspiracid‐3 by mass spectrometry, but differed both chromatographically and spectroscopically.     

Preparation of N(G)-substituted L-arginine analogues suitable for solid phase peptide synthesis

A high-yielding and concise preparation of N(G)-substituted L-arginine analogues, suitably protected for use in solid phase peptide synthesis, is reported. The synthesis of each analogue employed an activated thiourea intermediate that was converted under mild conditions to the desired L-arginine analogue (10 examples, each in near quantitative yield). Subsequent allyl group removal provided each analogue in a form ideally suited for use in solid phase peptide synthesis.     

Atmospheric chemistry of 3-pentanol: kinetics, mechanisms, and products of Cl atom and OH radical initiated oxidation in the presence and absence of NOX

Smog chamber/FTIR techniques were used to study the atmospheric chemistry of 3-pentanol and determine rate constants of k(Cl+3-pentanol) = (2.03 +/- 0.23) x 10 (-10) and k(OH+3-pentanol) = (1.32 +/- 0.15) x 10 (-11) cm (3) molecule (-1) s (-1) in 700 Torr of N 2/O 2 diluent at 296 +/- 2 K. The primary products of the Cl atom initiated oxidation of 3-pentanol in the absence of NO were (with molar yields) 3-pentanone (26 +/- 2%), propionaldehyde (12 +/- 2%), acetaldehyde (13 +/- 2%) and formaldehyde (2 +/- 1%). The primary products of the Cl atom initiated oxidation of 3-pentanol in the presence of NO were (with molar yields) 3-pentanone (51 +/- 4%), propionaldehyde (39 +/- 2%), acetaldehyde (44 +/- 4%) and formaldehyde (4 +/- 1%). The primary products of the OH radical initiated oxidation of 3-pentanol in the presence of NO were (with molar yields) 3-pentanone (58 +/- 3%), propionaldehyde (28 +/- 2%), and acetaldehyde (37 +/- 2%). In all cases the product yields were independent of oxygen concentration over the partial pressure range 10-700 Torr. The reactions of Cl atoms and OH radicals with 3-pentanol proceed 26 +/- 2 and 58 +/- 3%, respectively, via attack on the 3-position to give an alpha-hydroxyalkyl radical, which reacts with O 2 to give 3-pentanone. The results are discussed with respect to the literature data and atmospheric chemistry of 3-pentanol.     

Length-based encoding of binary data in DNA

We developed a system to encode digital information in DNA polymers based on the partial restriction digest (PRD). Our encoding method relies on the length of the fragments obtained by the PRD rather than the actual content of the nucleotide sequence, thus eliminating the need for expensive sequencing machinery. In this letter, we report on the encoding of 12 bits of data in a DNA fragment of 110 nucleotides and the process of recovering the data.