Convenient Asymmetric Syntheses of anti-beta-Amino Alcohols

Condensation of allylborane reagents 9 and 12 with aldehydes gave anti-3-[(diphenylmethylene)amino]-1-alken-4-ols 10 and 13 with high relative and absolute stereocontrol. Subsequent deprotection gave the corresponding free anti-3-amino-1-alken-4-ols 11 and 14. Alternatively, reaction of imines 13a, 13f, and 13g with trifluoromethanesulfonic anhydride and acidic methanol gave, via rearrangement, double inversion, and hydrolysis, the isomeric anti-4-amino-1-alken-3-ols 22, 38a, and 38b in good yield. The stereochemistry of the rearrangement products has been established by a single crystal X-ray study of compound 37 and by chemical correlation.     

A New Generation of "Cholaphanes": Steroid-Derived Macrocyclic Hosts with Enhanced Solubility and Controlled Flexibility

The macrocyclic "cholaphanes" 3a-c were synthesized from the inexpensive steroid cholic acid. Like earlier relatives they feature substantial cavities with inward-directed hydroxyl groups, suitable for binding polar molecules such as carbohydrates in nonpolar media. New features are the externally directed alkyl chains, promoting solubility in organic solvents, and (in the case of 3b/c) reduced conformational freedom resulting from truncation of the steroidal side-chain. In particular, modeling shows that the smallest macrocycle 3c possesses very little flexibility, preferring an open conformation which is also revealed in the X-ray crystal structure of its pentahydrate. NMR studies indicated that all three cholaphanes form 1:1 complexes with octyl beta-D-glucoside in CDCl(3), with K(a) = 600-1560 M(-)(1). Cholaphanes 3b/c proved able to extract methyl beta-D-glucoside from aqueous solutions into CHCl(3). The transport of methyl beta-D-glucoside across a chloroform barrier was also demonstrated for 3c.     

Synthesis of some benzimidazole‐, benzothiazole‐ and pyridine‐derived chelating agents

Procedures are given for the preparation of new linear bidentate, tetradentate and tripodal heptadentate ligands incorporating benzimidazole, benzothiazole and pyridyl groups. The compounds were characterized by their nmr, uv and mass spectra. The crystal and molecular structure is reported for a chiral benzothiazole derived from camphoric acid.     

Pulsed titration sensors: Part 1: A breath-by-breath CO2 sensor

A novel electrochemical sensor for the determination of CO₂ in expired breath is described. The sensor works by generating from the reduction of O₂ in dimethyl sulphoxide (DMSO) in a generating pulse. There is a rapid titration reaction between the and any CO₂ present. In the recovery pulse the amount of unreacted is determined. The larger the concentration of CO₂ the less is found in the recovery pulse. The solubilities and diffusion coefficients of O₂ and CO₂ in DMSO have been determined using rotating disc voltammetry and rotation speed step experiments. The stoichiometry, the product, and the rate constant of the titration reaction have been determined using ring—disc voltammetry and laser Raman spectroscopy. The operation and the effect of adventitious water on the sensor are described. Results are presented which show that the sensor can indeed measure the breath-by-breath rhythm of expired CO₂ from a human subject.     

Synthesis, structure, and kinetics and stereochemistry of base-catalyzed hydrolysis of meso- and rac-[Co2(tmpdtne)Cl2]4+, bis(pentaamine) complexes devoid of deprotonatable NH centers

The bis(pentadentate) ligand tmpdtne binds two Co(II) centers, and the entity is readily oxidized to the dicobalt(III) derivative [Co(2)(tmpdtne)Cl(2)](4+) which has been separated into two isomeric forms. NMR studies establish these as meso and rac isomers arising from the different or same absolute configurations for the asym configuration about each Co(III) center. Each dinuclear ion base hydrolyses to the dihydroxo derivative [Co(2)(tmpdtne)(OH)(2)](4+) with retained asym configurations about each metal ion and also retained rac or meso configurations. The kinetics for the stepwise loss of the two Cl(-) ligands is uniphasic, and data are presented to show that the loss of the first chloride is rate determining and is followed by very rapid intramolecular and loss of the second Cl(-) via a hydroxo-bridged species to yield the observed dihydroxo derivative. Meso and rac forms of the latter have been crystallized. The X-ray crystal structure of the rac-dihydroxo complex is reported, and it establishes the configurations of all the complexes reported. The (1)H NMR spectra for the hydroxo ions show very high field Co-OH resonances (ca. delta-0.5 ppm) not observed previously for such ions, and this result is discussed in the context of published (1)H NMR data for bridged Co-OH-Co species. The base hydrolysis kinetics for the dichloro ions are first order in [OH(-)], and deprotonation at an alpha-CH(2) center (alpha to a pyridyl) is identified as the source of the catalysis, since there is no NH center available for deprotonation on the ligand. These data further support the new pseudoaminate base hydrolysis mechanism first reported in 2003. The values of k(OH) for the second-order base-catalyzed reaction are ca. 4.0 M(-1) s(-1) for both the rac and meso isomers, and these results are discussed in terms of the increased acidities of these 4+ cations compared to their 2+ ion counterparts.     

Frobenius distributions of elliptic curves in short intervals on average

The Ramanujan Journal - For an elliptic curve $$E/{\mathbb {Q}}$$ , let $$a_p$$ denote the trace of its Frobenius endomorphism over $${\mathbb {F}}_p$$ , where p is a prime of good reduction for E....     

The nearest neighbor random walk on subspaces of a vector space and rate of convergence

LetX be the collection ofk-dimensional subspaces of ann-dimensional vector spaceV _n overGF(q). A metric may be defined onX by letting

Necessary conditions for characterization of laws via mixed sums

SupposeX andY are independent and identically distributed, and independent ofU which satisfies 0U1. Recent work has centered on finding the lawsL(X) for whichX U(X+Y) where denotes equality in law. We show that this equation corresponds to a certain projective invariance property under random rotations. Implicitly or explicitly, it has been assumed that the characteristic function ofX has an expansion property near the origin. We show that solutions may be admitted in the absence of this condition when –logU has a lattice law. A continuous version of the basic problem replaces sums with a Lévy process. Instead we consider self-similar processes, showing that a solution exists only whenU is constant, and then all processes of a given order are admitted.This research was in part supported by NSERC grant A-8466.