Is there stereoselectivity in spin trapping superoxide by 5-tert-butoxycarbonyl-5-methyl-1-pyrroline N-oxide?

[reaction: see text] Ester-containing nitrones, including 5-tert-butoxycarbonyl-5-methyl-1-pyrroline N-oxide 5, have been reported to be robust spin traps for superoxide (O2*-). Using a chiral column, we have been able to isolate the two enantiomers of nitrone 5. With enantiomerically pure nitrone 5a and 5b we explored whether one of these isomers was solely responsible for the EPR spectrum of aminoxyl 6. Data obtained demonstrate that the spin trapping of O2*- by nitrone 5a and nitrone 5b affords the identical EPR spectra and lifetimes in homogeneous aqueous solution and exhibits the same ratio of cis and trans isomers. Quantum chemical modeling in vacuo also finds no difference, aside from the expected optical activity, arising from the difference in stereochemistry.     

Hydrate inclusion compounds

There are three general classes of hydrate inclusion compounds: the gas hydrates, the per-alkyl onium salt hydrates, and the alkylamine hydrates. The first are clathrates, the second are ionic inclusion compounds, the third are semi-clathrates. Crystallization occurs because the H₂O molecules, like SiO₂, can form three-dimensional four-connected nets. With water alone, these are the ices. In the inclusion hydrates, nets with larger voids are stabilized by including other guest molecules. Anions and hydrogen-bonding functional groups can replace water molecules in these nets, in which case the guest species are cations or hydrophobic moieties of organic molecules. The guest must satisfy two criteria. One is dimensional, to ensure a comfortable fit within the voids. The other is functional. The guest molecules cannot have either a single strong hydrogen-bonding group, such as an amide or a carboxylate, or a number of moderately strong hydrogen-bonding groups, as in a polyol or a carbohydrate.The common topological feature of these nets is the pentagonal dodecahedra: i.e., 5¹²-hedron. These are combined with 5¹²6²-hedra, 5¹²6³-hedra, 5¹²6⁴-hedra and combinations of these polyhedra, to from five known nets. Two of these are the well-known 12 and 17 Å cubic gas hydrate structures,Pm3n, Fd3m; one is tetragonal,P4 ₂/mnm, and two are hexagonal,P6 ₃/mmc andP6/mmm. The clathrate hydrates provide examples of the two cubic and the tetragonal structures. The alkyl onium salt hydrates have distorted versions of thePm3n cubic, the tetragonal, and one of the hexagonal structures. The alkylamine hydrate structures hitherto determined provide examples of distorted versions of the two hexagonal structures.There are also three hydrate inclusion structures, represented by single examples, which do not involve the 5¹²-hedra. These are 4(CH₃)₃CHNH₂·39H₂O which is a clathrate; HPF₆·6H₂O and (CH₃)₄NOH·5H₂O which are ionic-water inclusion hydrates. In the monoclinic 6(CH₃CH₂CH₂NH₂)·105H₂O and the orthorhombic 3(CH₂CH₂)₂NH·26H₂O, the water structure is more complex. The idealization of these nets in terms of the close-packing of semi-regular polyhedra becomes difficult and artificial. There is an approach towards the complexity of the water salt structures found in the crystals of proteins.     

Jump discontinuities of semilinear,strictly hyperbolic systems in two variables: Creation and propagation

The creation and propagation of jump discontinuities in the solutions of semilinear strictly hyperbolic systems is studied in the case where the initial data has a discrete set, {x _i } _i ⁼¹ⁿ , of jump discontinuities. LetS be the smallest closed set which satisfies:

1. S is a union of forward characteristics.
2. S contains all the forward characteristics from the points {x _i } _i ⁼¹ⁿ .
3. if two forward characteristics inS intersect, then all forward characteristics from the point of intersection lie inS.

We prove that the singular support of the solution lies inS. We derive a sum law which gives a lower bound on the smoothness of the solution across forward characteristics from an intersection point. We prove a sufficient condition which guarantees that in many cases the lower bound is also an upper bound.     

The impact of cellulose structure on binding interactions with hemicellulose and pectin

Four cellulose substrates including highly crystalline cellulose nanowhiskers (CNWs) from Gluconacetobacter xylinus (cellulose Iα) or cotton (cellulose Iβ) and amorphous cellulose derived from CNWs (phosphoric acid swollen cellulose nanowhiskers, PASCNWs) were used to explore the interaction between cellulose and well-defined xyloglucan, xylan, arabinogalactan and pectin. The binding behavior was characterized by adsorption isotherm and Langmuir models. The maximum adsorption and the binding constant of xyloglucan, xylan and pectin to any CNWs were always higher than to PASCNWs derived from the same source. The binding affinity of xyloglucan, xylan and pectin to G. xylinus cellulose was generally higher than to cotton cellulose, showing that binding interactions depended on the biological origin of cellulose and associated differences in its structure. The surface area, porosity, crystal plane and degree of order of cellulose substrate may all impact the interactions.     

Nonvanishing theorems for L-functions of modular forms and their derivatives

Inventiones mathematicae -     

Stable in situ sorting and minimum data movement

In this paper, we describe an algorithm to stably sort an array ofn elements using only a linear number of data movements and constant extra space, albeit in quadratic time. It was not known previously whether such an algorithm existed. When the input contains only a constant number of distinct values, we present a sequence ofin situ stable sorting algorithms makingO(n lg^(k+1) n+kn) comparisons (lg^(K) means lg iteratedk times and lg* the number of times the logarithm must be taken to give a result 0) andO(kn) data movements for any fixed valuek, culminating in one that makesO(n lg*n) comparisons and data movements. Stable versions of quicksort follow from these algorithms.Research supported by Natural Sciences and Engineering Research Council of Canada grant No.A-8237 and the Information Technology Research Centre of Ontario.Supported in part by a Research Initiation Grant from the Virginia Engineering Foundation.     

Volumes and diophantine inequalities associated with decomposable forms

For homogeneous decomposable forms in n variables with real coefficients, we consider the associated volume of all real solutions to the inequality . We relate this to the number of integral solutions to the Diophantine inequality in the case where F has rational coefficients. We find quantities which bound the volume and which yield good upper bounds on the number of solutions to the Diophantine inequality in the rational case.     

Geometric Convergence Rates for Time-Sampled Markov Chains

We consider time-sampled Markov chain kernels, of the form P = _n n P ⁿ . We prove bounds on the total variation distance to stationarity of such chains. We are motivated by the analysis of near-periodic MCMC algorithms.