The r-mean curvature and rigidity of compact hypersurfaces in the Euclidean space

Annals of Global Analysis and Geometry - In this paper, we characterize round spheres in the Euclidean space under some suitable conditions on the r-mean curvature.     

Mosaics of combinatorial designs for information-theoretic security

Designs, Codes and Cryptography - We study security functions which can serve to establish semantic security for the two central problems of information-theoretic security: the wiretap channel, and...     

N7-DNA: Synthesis and Base Pairing of Oligonucleotides containing 7-(2-Deoxy-β -D-erythro-pentofuranosyl)adenine (N7Ad)

The synthesis of oligonucleotides containing 7-(2-deoxy-β -D -erythro-pentofuranosyl)adenine (N⁷A_d; 1 ) is described. Compound 1 was obtained from the precursor 4-amino-1H -imidazole-5-carbonitrile 2-deoxyribonucleoside 6 and was found to be much more labile than A_d. The N⁶-benzoyl protecting group (see 8 ) destabilized the N-glycosylic bond further and was difficult to remove by NH₃-catalyzed hydrolysis. Therefore, a (dimethyl-amino)methylidene residue was introduced (→ 9 ). Amidine 9 was blocked at OH? C(5′) with the dimethoxytrityl residue ((MeO)₂Tr), and phosphonate 4 as well as phosphoramidite 5 were prepared under standard conditions. Phosphonate 4 was employed in solid-phase oligonucleotide synthesis. Homooligonucleotides as well as self-complementary oligonucleotides were prepared. The oligomer d[(N⁷A)₁₁-A] ( 11 ) formed a duplex with d(T₁₂) ( 13 ). Antiparallel chain polarity and reverse Watson-Crick base pairing was deduced from duplex formation of the self-complementary d[(N⁷A)₈-T₈] ( 14 ).     

Synthesis of β -Cyperone via Fungal Hydroxylation of thujone-derived tricyclic cyclopropanes

Synthesis of optically active sesquiterpenes with a eudesmane C-skeleton from the chiral starting material thujone involves transformation of a tricyclic intermediate (1R,2R,4S)-1,7-dimethyl-4-(1-methylethyl)tricyclo[4.4.0.0^2,4]dec-6-en-8-one ( 2 ) into the bicyclic compound β -cyperone ( 5 ). Hydroxylation of 2 at C(5) or C(11) permits subsequent opening of the cyclopropane ring and rearrangement to β -cyperone. In this publication, studies involving hydroxylation of 2 by fungal cultures are presented. The resultant products are useful intermediates in efficient synthesis of eudesmane sesquiterpenes. Of five fungi tested, Rhizopus oryzae ATCC 11145 proved most versatile. It hydroxylates at the exocyclic C(11) position in high yield (70%) and, to a lesser extent, at C(5) (5%). Enzymatic activity appears at the end of growth phase and at least 2.2 g of 2 per liter can be metabolized without significant loss of product yield. A second fungus, Cunninghamella echinulata ATCC 9244, proved most useful for hydroxylation of derivatives of 2 for the preparation of derivatives of β -cyperone, although product yields were low (2–20%), some derivatives were nonreactive, and hydroxylation at C(9) occurred. The relationship between precursor structure and enzyme affinity is discussed.     

Characterization of low molecular weight hydrocarbon oligomers by laser desorption/ionization time-of-flight mass spectrometry using a solvent-free sample preparation method.

A new solvent-free sample preparation method using silver trifluoroacetate (AgTFA) was developed for the analysis of low molecular weight paraffins and microcrystalline waxes by laser desorption/ionization time-of-flight mass spectrometry (LDI-TOFMS). Experiments show that spectral quality can be enhanced by dispersing AgTFA directly in liquid paraffins without the use of additional solvents. This preparation mixture is applied directly to the MALDI probe. Solid waxes could be examined by melting prior to analysis. The method also provides sufficiently reproducible spectra that peak area ratios between mono- and bicyclic alkane peaks indicated variations in the cycloalkane content of paraffin samples. Dehydrogenation of hydrocarbons observed during the desorption/ionization process was studied by analysis of alkane standards.     

Design of neutral, mono- or di-cationic water-soluble trihydrazidophosphoradamantanes

The versatile behavior of a trihydrazidophosphoradamantane allowing the synthesis of a variety of neutral, mono- or di-cationic water-soluble molecules of potential interest for biphasic catalysis is reported.     

On the geometry of infinite cyclic subgroups

In this paper we construct an example of a word metric on an infinite cyclic subgroup. This example shows that subexponential distortion does not obstruct non-trivial growth of connected radii. This answers a question of Gromov [6]. The constructed metric has other pathological properies. Specifically, its asymptotic cone depends on the choice of ultrafilter and scaling sequence. The work has been partially supported by the Swiss National Science Foundation.     

IFS attractors and Cantor sets

We build a metric space which is homeomorphic to a Cantor set but cannot be realized as the attractor of an iterated function system. We give also an example of a Cantor set K in R³ such that every homeomorphism f of R³ which preserves K coincides with the identity on K.