Skein related links in 3-manifolds

This paper addresses two problems in the skein theory of homotopy spheres first posed by P. Traczyk. Solutions to both problems are obtained for a large class of manifolds and, since one of the basic techniques used requires the first homology group of the ambient manifold to be torsion free, the extent to which this hypothesis is actually necessary is further explored.     

Some New Results on Key Distribution Patterns and Broadcast Encryption

This paper concerns methods by which a trusted authority can distribute keys and/or broadcast a message over a network, so that each member of a privileged subset of users can compute a specified key or decrypt the broadcast message. Moreover, this is done in such a way that no coalition is able to recover any information on a key or broadcast message they are not supposed to know. The problems are studied using the tools of information theory, so the security provided is unconditional (i.e., not based on any computational assumption).In a recent paper st95a, Stinson described a method of constructing key predistribution schemes by combining Mitchell-Piper key distribution patterns with resilient functions; and also presented a construction method for broadcast encryption schemes that combines Fiat-Naor key predistribution schemes with ideal secret sharing schemes. In this paper, we further pursue these two themes, providing several nice applications of these techniques by using combinatorial structures such as orthogonal arrays, perpendicular arrays, Steiner systems and universal hash families.     

The isolation and structure determination of cryptomisrine,a novel indolo[3,2-b]quinoline dimeric alkaloid from cryptolepis sanguinolenta

The isolation and structure determination of cryptomisrine, a novel indolo[3,2-b]quinoline dimeric alkaloid obtained from extracts of the roots of the Ghanaian medicinal plant Cryptolepis sanguinolenta is reported. The structure determination was made via a consideration of the spectral data, including uv, ir, nmr, and mass spectra. In particular, one-dimensional proton/carbon nmr, one-dimensional nOe difference nmr, and a series of homonuclear (COSY) and inverse-detected heteronuclear two-dimensional (HMQC, HMBC) experiments were utilized, as well as high resolution FABMS. Cryptomisrine is most unusual in that its two monomeric parts apparently exist in such a C₂ symmetric environment that only one set of proton and carbon nmr resonances are observed. Cryptomisrine is the first example of a dimeric indolo-[3,2-b]quinoline alkaloid to have been isolated from nature.     

The Role of Oxygen in the Antiviral Activity of Hypericin and Hypocrellin

The light-induced antiviral activity of hypericin and hypocrellin in the presence and absence of oxygen was examined under experimental conditions where the effect of oxygen depletion could be quantified. There was a significant reduction of light-induced antiviral activity of hypericin and hypocrellin under hypoxic conditions. Interestingly, antiviral activity of hypocrellin was not observed at low oxygen levels at which hypericin retained measurable virucidal activity. This suggests that additional pathways, such as the generation of protons from excited states of hypericin, may enhance the biological activity of activated oxygen species.     

Salvinicins A and B, new neoclerodane diterpenes from Salvia divinorum

[reaction: see text] Two new neoclerodane diterpenes, salvinicins A (4) and B (5), were isolated from the dried leaves of Salvia divinorum. The structures of these compounds were elucidated by spectroscopic techniques, including (1)H and (13)C NMR, NOESY, HMQC, and HMBC. The absolute stereochemistry of these compounds was assigned on the basis of single-crystal X-ray crystallographic analysis of salvinicin A (4) and a 3,4-dichlorobenzoate derivative of salvinorin B.     

Synthesis of substituted imidazoles via organocatalysis

A one-pot synthesis of substituted imidazoles is described. The cornerstone of this methodology involves the thiazolium-catalyzed addition of an aldehyde to an acyl imine to generate the corresponding alpha-ketoamide in situ followed by ring closure to the imidazole in a one-pot sequence. The extension of this methodology to the one-pot synthesis of substituted oxazoles and thiazoles is also described. [reaction: see text]     

Aluminium alkyl and aryloxide complexes of pyrazine and bipyridines: synthesis and structure

The reaction of AlMe(3) and [((t)Bu)(2)Al(micro-OPh)](2) with pyrazine (pyz), 4,4'-bipyridine (4-4'-bipy), 1,2-bis(4-pyridyl)ethane (bpetha) and 1,2-bis(4-pyridyl)ethylene (bpethe) yields (Me(3)Al)(2)(micro-pyz)(1), (Me(3)Al)(2)(micro-4,4'-bipy)(2), (Me(3)Al)(2)(micro-bpetha)(3), (Me(3)Al)(2)(micro-bipethe)(4), Al((t)Bu)(2)(OPh)(pyz)(5), [((t)Bu)(2)Al(OPh)](2)(micro-4,4-bipy)(6a), [((t)Bu)(2)Al(OPh)](2)(micro-bpetha)(7a), [((t)Bu)(2)Al(OPh)](2)(micro-bipethe)(8a). Compounds 1-4, 6a and 7a have been confirmed by X-ray crystallography. In solution compounds 1-4 undergo a rapid ligand-dissociation equilibrium resulting in a time-average spectrum in the (1)H NMR. In contrast, the solution equilibria for compounds 5-8a are sufficiently slow such that the mono-aluminium compounds may be observed by (1)H NMR spectroscopy: Al((t)Bu)(2)(OPh)(4,4-bipy)(6b), Al((t)Bu)(2)(OPh)(bpetha)(7b) and Al((t)Bu)(2)(OPh)(bpethe)(8b). The inability to isolate [((t)Bu)(2)Al(OPh)](2)(micro-pyz) and the relative stability of each complex is discussed with respect to the steric interactions across the bridging ligand (L) and the electronic effect on one Lewis acid-base interaction by the second Lewis acid-base interaction on the same ligand.     

Autocorrelation Functions as Translation Invariants in L1 and L2

The Adler-Konheim theorem [Proc. Amer. Math. Soc. 13 (1962), 425-428] states that the collection of nth-order autocorrelation functions is a complete set of translation invariants for real-valued L¹ functions on a locally compact abelian group. It is shown here that there are proper subsets of that also form a complete set of translation invariants, and these subsets are characterized. Specifically, a subset is complete if and only if it contains infinitely many even-order autocorrelation functions. In addition, any infinite subset of is complete up to a sign. While stated here for functions on the proofs presented hold for functions on any locally compact abelian group that is not compact, in particular, on and the integer lattice      

Determination of pyrithione in natural waters by cathodic stripping voltammetry

A method was developed to determine the biocide pyrithione in natural waters. The method is based on cathodic stripping voltammetry (CSV) in the presence of Triton-X-100, which is used to separate the peak from interfering thiol compounds. Optimised conditions include a Triton-X-100 concentration of 4 ppm and a pH adjusted to 9 using ammonia buffer. The adsorption potential for pyrithione was −0.10 V and the peak occurred at −0.2 to −0.3 V. Detection was by differential-pulse CSV. The detection limit in UV-digested seawater was 1.5 nM for a deposition time of 60 s. In principle, this limit of detection could be lowered by extending the adsorption time, but in practice this may not be possible due to interferences by other organic compounds (surfactants and thiol compounds) in natural waters.