When maths really is rocket science

Two problems in projectiles are discussed which generate interestingloci.     

One cannot hear orbifold isotropy type

We show that the isotropy types of the singularities of Riemannian orbifolds are not determined by the Laplace spectrum. Indeed, we construct arbitrarily large families of mutually isospectral orbifolds with different isotropy types. Finally, we show that the corresponding singular strata of two isospectral orbifolds may not be homeomorphic. Received: 6 October 2005     

Crystal and molecular structure of crenatine carbonate

The crystal and molecular structure of 1-ethyl-4-methoxy-9H-pyrido[3,4b]indole (crenatine) carbonate C₁₄H₁₄N₂O·H₂CO₃, (MS, m/z 226)M _R 288.3, a-carboline alkaloid, has been determined from X-ray diffraction data. The compound crystallizes in the space group Pbca with cell parameters:a=11.616(4),b=18.450(8),c=12.992(5)Å,V=2784(2)ų,Z=8,D _calc=1.375 g cm^–3, (MoK)=0.71069Å,(Mo K)=0.94 cm^–1,F(000)=1216,R/R _w =8.2/10.3% for 1099 reflections. The ring system of the-carboline nucleus is planar. The title compound shows a two center hydrogen bond between the indole N-H group and the oxygen atom of a carbonate group. The structure does not display hydrogen bonding between-carboline groups but rather a bonding network involving the carbonate group.     

New Chiral Kemp's Acid Diamides for Chiral Amine Recognition by 1 H NMR

Two Kemp's acid diamides were synthesized and applied to chiral amine recognition using ¹H NMR analysis. One derivative based on 1-(1-naphthyl)ethylamine had good chiral recognition of six amines and was useful to determine the optical purity for three amines, i.e., methylbenzylamine, 1-(1-naphthyl)ethylamine and 1- henylpropylamine,however, the cyclohexylethylamine derivative showed little discrimination for the amines studied. Together with the results for alkylamines, it was shown that aromatic structure was important for aromatic shielding anisotropy and –– interactions between host and guest. The structure of the 1-(1-naphthyl)ethylamine derivative in solution was also considered based on ¹H NMR data and computer simulation.     

‘Sacrificial’ supramolecular assembly and pressure-induced polymerization: toward sequence-defined functionalized nanothreads

Limited supramolecular strategies have been utilized to synthesize sequence-defined polymers, despite the prominence of noncovalent interactions in materials design. Herein, we illustrate the utility of ‘sacrificial’ aryl-perfluoroaryl supramolecular synthons to synthesize sp³-hybridized nanothreads from sp²-enriched reactants. Our strategy features A–B reactant pairs in the form of a phenol:pentafluorophenol co-crystal that is preorganized for an electronically-biased and sequence-defined polymerization. The polymerization, initiated at 12 GPa, affords an alternating copolymer featuring exogenous –OH functionalities. The external substitution is confirmed through IR spectroscopy. Importantly, the inclusion of the functional unit provides the first experimental glimpse at reaction mechanism: keto–enol tautomerization that can only occur during cycloaddition is observed through IR spectroscopy. Our approach realizes the first example of a functionalized nanothread and attains sequence definition through sacrificial supramolecular preorganization and presents a further approach for de novo design of complex nanothreads.

Supramolecular synthons are exploited to synthesize –OH functionalized sp³-rich sequence-defined nanothreads using pressure-induced polymerization of a phenol:pentafluorophenol co-crystal.      

Carbocation-forming reactions in dimethyl sulfoxide

Mesylate derivatives of 3-aryl-3-hydroxy-beta-lactams and thiolactams react in DMSO-d(6) by first-order processes to give alcohol products. Substituent effect studies implicate carbocation intermediates (ion-pairs) that are captured by DMSO-d(6) to give transient oxosulfonium ions. Rapid reaction of the oxosulfonium ions with trace amounts of water leads to the alcohol product and regenerates DMSO-d(6). H(2)(17)O labeling studies show that (17)O is incorporated into the DMSO. The mesylate derivatives of endo- and exo-2-hydroxy-2-phenylbicyclo[2.2.1]heptan-3-one also react in DMSO-d(6) to give the alcohol products. Ion-pair intermediates that capture DMSO giving unstable oxosulfonium ions are again proposed. Exo-2-phenyl-endo-bicyclo[2.2.1]heptyl trifluoroacetate readily eliminates trifluoroacetic acid in DMSO-d(6) via a cationic mechanism involving loss of the endo-trifluoroacetate leaving group as well as an exo-hydrogen. The O-methyl oxime derivative of alpha-chloro-alpha,alpha-diphenylacetophenone reacts in DMSO-d(6) to give 1-methoxy-2,3-diphenylindole, a product derived from cyclization of a cationic intermediate. A common ion rate suppression provides further evidence for a cationic mechanism. The triflate derivative of pivaloin reacts by a cationic mechanism in DMSO-d(6) to give rearranged products. The rate is even faster than in highly ionizing solvents such as trifluoroethanol or trifluoroacetic acid. 1-Adamantyl mesylate reacts in DMSO-d(6) by a first-order process (Y(OMs) = -4.00) to give a long-lived oxosulfonium ion, 1-Ad-OS(CD(3))(2)(+), which can be characterized spectroscopically. This oxosulfonium ion reacts only slowly with water at elevated temperatures to give 1-adamantanol. DMSO is therefore a viable solvent for k(s), k(C), and k(Delta) cationic processes.     

Determination of organic carbon in water with a silver-catalyzed peroxydisulfate wet chemical oxidation method

The application of Ag(I) catalysis of S₂O₈^2? to the oxidation of organic carbon to CO₂ for determination of dissolved organic carbon in aqueous samples is described. The resulting method combines to a significant degree the speed of high-temperature combustion methods and the sensitivity of wet chemical oxidation. For some samples, a higher oxidation efficiency has been observed than with an uncatalyzed wet chemical oxidation method.     

Synthesis of polymer-bound hemoglobin samples

Dextran and hydroxyethyl starch have been chemically modified to give aldehyde-substituted polymers. These modified polymers were synthesised either by periodate oxidation of the starting polymer or by attachment of gluteraldehyde to amino-substituted side chains on the polymer. When such modified starches were allowed to react with hemoglobin soluble polymer-bound hemoglobins were formed. These were shown to be capable of binding oxygen but the observed oxygen-binding curves were shifted to the left relative to unbound hemoglobin. Heart perfusion experiments indicate that these polymer-bound hemoglobins are not suitable for use as blood substitutes     

On the High Viscosity of Aqueous Solution of Lysozyme Induced by Some Organic Solvents

A remarkably high viscosity has been induced in protein aqueous solutions by the addition of certain structurally related organic solvents. The effect has been observed for lysozyme aqueous solutions containing tetramethylurea (TMU), dimethylsulfoxide (DMSO), dimethylformamide, and hexamethylphosphortriamide. The effect has also been induced in ferrocytochrome c aqueous solutions by TMU. Critical concentrations for both the protein and organic solvent were verified for the onset of the viscosity increase. A common feature of the solvents which were able to induce the effect is a dipolar moiety (C=O, S → O and P → O) and a nonpolar region represented by the methyl groups. The resulting fluids show an extremely restricted flow and a typical non-Newtonian, pseudoplastic behavior. Use was made of¹H nuclear magnetic resonance (NMR) and Raman spectroscopy to characterize protein structural modifications and of¹³C NMR to investigate changes in relaxation times and chemical shifts in the solvent/water solutions. A systematic rheological characterization of the systems was undertaken for some of the solvents, and unusual patterns of viscous effects were identified for the solvent/water systems both with and without protein. The process was found to be at least partially reversible, as concluded from the recovered original solution rheological characteristics and the original protein¹H NMR spectrum, after eliminating the organic solvent by ultrafiltration. The whole process was characterized as consisting of two mutually independent stages. The first involves an extensive conformational transition of the polypeptide backbone, from a predominantly α-helical to increased random coiled and β-sheet structures, with the occurrence of nonorthodox protein secondary structures at regions above the solvent critical point. The second stage consists of short-lived interchain contacts leading to an entanglement of the macromolecular system as a whole. A microphase reversion in the organic solvent/water mixture, supported by¹³C NMR and rheological results, is proposed as the driving force causing the observed behavior.     

Expedient Diels-Alder assembly of 4-aryl-4-phenylsulfonyl cyclohexanones

The efficient preparation of 4-aryl-4-phenylsulfonyl cyclohexanones, containing a quaternary sulfone-bearing carbon centre, is described. Their synthesis proceeds in 38-78% overall yield by way of three steps: (i) sulfinate alkylation; (ii) methylenation; and (iii) regioselective Diels-Alder condensation with 2-trimethylsiloxybutadiene. The scope and limitations of the one-pot Mannich-type methylenation described were examined.