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.     

Combinatorial Characterizations of Authentication Codes II

For any authentication code for k source states and v messages having minimum possible deception probabilities (namely, % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9qq-f0-yqaqVeLsFr0-vr% 0-vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbWaaS% baaSqaaiaadsgaaeqaaOWaaSbaaSqaaiaaicdaaeqaaOGaeyypa0Za% aSGbaeaacaWGRbaabaGaamODaaaaaaa!3F28!\[P_d _0 = {k \mathord{\left/ {\vphantom {k v}} \right. \kern-\nulldelimiterspace} v}\] and % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9qq-f0-yqaqVeLsFr0-vr% 0-vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbWaaS% baaSqaaiaadsgaaeqaaOWaaSbaaSqaaiaaigdaaeqaaOGaeyypa0Ze% xLMBb50ujbqeguuDJXwAKbacfaGae8hkaGIaam4AaiabgkHiTiaaig% dacqWFPaqkcqWFVaWlcqWFOaakcqWF2bGDcqGHsislcaaIXaGae8xk% aKIae8xkaKcaaa!4CD1!\[P_d _1 = (k - 1)/(v - 1))\], we show that there must be at least v encoding rules. (This can be thought of as an authentication-code analogue of Fisher's Inequality.) We derive several properties that an extremal code must satisfy, and we characterize the extremal codes for equiprobable source states as arising from symmetric balanced incomplete block designs. We also present an infinite class of extremal codes, in which the source states are not equiprobable, derived from affine planes.Dedicated to Gus Simmons     

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.     

On the existence of MOLS with equal-sized holes

We consider a pair of MOLS (mutually orthogonal Latin squares) having holes, corresponding to missing sub-MOLS, which are disjoint and spanning It is shown that a pair of MOLS withn holes of sizeh exist forh 2 if and only ifn 4 For SOLS (self-orthogonal Latin squares) with holes, we have the same result, with two possible exceptions SOLS with 7 or 13 holes of size 6     

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.     

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.     

On resolvable Golomb rulers,symmetric configurations and progressive dinner parties

Journal of Algebraic Combinatorics - We define a new type of Golomb ruler, which we term a resolvable Golomb ruler. These are Golomb rulers that satisfy an additional “resolvability”...