Fixed point and common fixed point theorems on ordered cone metric spaces

In the present work, some fixed point and common fixed point theorems for self-maps on ordered cone metric spaces, where the cone is not necessarily normal, are proved.     

Vertex-transitive expansions of (1, 3)-trees

A nonidentity automorphism of a graph is said to be semiregular if all of its orbits are of the same length. Given a graph X with a semiregular automorphism γ, the quotient of X relative to γ is the multigraph X/γ whose vertices are the orbits of γ and two vertices are adjacent by an edge with multiplicity r if every vertex of one orbit is adjacent to r vertices of the other orbit. We say that X is an expansion of X/γ. In [J.D. Horton, I.Z. Bouwer, Symmetric Y-graphs and H-graphs, J. Combin. Theory Ser. B 53 (1991) 114-129], Horton and Bouwer considered a restricted sort of expansions (which we will call ‘strong’ in this paper) where every leaf of X/γ expands to a single cycle in X. They determined all cubic arc-transitive strong expansions of simple (1, 3)-trees, that is, trees with all of their vertices having valency 1 or 3, thus extending the classical result of Frucht, Graver and Watkins (see [R. Frucht, J.E. Graver, M.E. Watkins, The groups of the generalized Petersen graphs, Proc. Cambridge Philos. Soc. 70 (1971) 211-218]) about arc-transitive strong expansions of K₂ (also known as the generalized Petersen graphs). In this paper another step is taken further by considering the possible structure of cubic vertex-transitive expansions of general (1,3)-multitrees (where vertices with double edges are also allowed); thus the restriction on every leaf to be expanded to a single cycle is dropped.     

Cross-reactive arrays based on three-way junctions

We report herein a novel system for the parallel processing of molecular recognition events utilizing arrays of oligonucleotide-based fluorescent sensors to characterize hydrophobic molecules in solution. The binding domains of the sensors were based on three-way junctions that utilize double helical stems as framework regions to reliably fold regardless of variations in or around the binding domain. A reporting domain was introduced by the specific substitution of a single phosphodiester group with a phosphorothioate, followed by selective functionalization with a fluorophore. The sensors were organized into cross-reactive arrays to yield characteristic fingerprints for samples containing hydrophobic molecules. The fingerprints can be used to characterize steroids in solution, including complex biologically important fluids. Arrays have the potential for clinical applications such as the detection of gross errors in steroidogenesis.     

Electrochemical behaviour of rosmanol 9-ethyl ether,a diterpene lactone antioxidant isolated from sage

The electrochemical behaviour and mechanism of the redox process of the natural antioxidant rosmanol 9-ethyl ether, isolated fromSaliva officinalis L., were studied. The cyclic voltammograms of rosmanol 9-ethyl ether (R9EE), at characteristic pH values, and the electrochemical parameters for all investigated pH values were measured. Three characteristic pH regions, each with different behaviour of R9EE, were identified. In regions of pH < 4 and pH > 5 only one anodic peak appeared, whereas in the solutions of pH 4–5 two anodic peaks could be noted. The overall oxidation mechanism at pH < 4 is an e.H.e.H. oxidation mechanism, which as a final product gives a quinonic molecule. The influence of pH on the second oxidation peak potential tends towards zero in accordance with the preceding dissociation of the one of phenolic groups, thus suggesting an e.e.H. mechanism at pH > 5. This means that at the pH values expected in plant cells, R9EE has an unexpected structure, making this substance a potent antioxidant. Electrochemical and spectrophotometric measurements enabled us to establish an extremely low pK _a value (4.35) for R9EE.     

Ene-type reaction of trisubstituted monoterpene alkenes with methyl sulfite and thionyl chloride

Trisubstituted methylalkenes react with methyl sulfite at 25°C in the presence of BF₃ · Et₂O in the ene-type fashion to give the corresponding methallyl sulfinates. Such compounds can also be prepared under considerably milder conditions by the Et₂AlCl-catalyzed reaction of thionyl chloride with mono- and dienes followed by methanolysis of intermediate alkyl sulfinyl chlorides. These reactions represent a new method for terminal functionalization of linear isoprenoids.Deceased Nov.1, 1992.Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 1, pp. 105–107, January, 1993.     

Synthesis and structure of tricyclic furanosesquiterpenoids related to pallescensin A

Electrophilic cyclization of (cyclo)farnesanes containing anexo-methylene group in the a-isoprenoid unit smoothly gives regio- and stereoisomeric octalins subsequently transformed to tricyclic furanosesquiterpenoids related to metabolites of some marine organisms.Deceased.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 156–163, January, 1994.The authors are grateful to the representative of the Bruker company in Moscow, Uve Eichhof, who allowed us to use an AMX-400 spectrometer.