A martingale approach to directed polymers in a random environment

The diffusive behavior for a system of directed polymers in a random environment was first rigorously discussed by Imbrie and Spencer, and then by Bolthausen. By means of some basic properties of martingales we extend some results due to Imbrie and Spencer concerning the asymptotic behaviour of the mean square displacement. We also obtain a Wiener process behaviour with probability one for this system. Bolthausen already used some martingale limit theorems to prove a central limit theorem for this system.Partly supported by AvH Foundation.     

Randomlyn-cyclic digraphs

A digraphD is randomlyn-cyclic (n≥3) if for each vertexv ofD, every (directed) path with initial vertexv and having length at mostn−1 can be extended to av−v (directed) cycle of lengthn. Several results related to and examples of randomlyn-cyclic digraphs are presented. Also, all randomlyn-cyclic digraphs forn=3, 4, and 5 are determined. Research supported by a Western Michigan University faculty research fellowship. Research supported in part by a College of Arts and Sciences and Graduate College research assistantship from Western Michigan University.     

Photochemical substitution reactions of 4-Pyridinecarbonitrile with aliphatic alcohols in neutral and acidified medium

Chemical evidence is given that the title photo-reactions proceed via hydrogen abstraction by the photo-excited base from the alcohol in neutral medium and via electron-transfer process between the photo-excited base and the alcohol in hydrochloric acid acidified medium.     

Rosigenin,an unusual metabolite from mycosphaerella rosigena1

A new metabolite, 3,6-dimethyl-4,10-dihydroxy-2-oxaspiro[4.5]dec-7-en-1,9-dione (1a), was isolated from a strain of Mycosphaerella rosigena grown on potato-agar medium. The structure was determined on the basis of chemical and spectroscopic evidence and confirmed by X-ray analysis.     

Infrared intensities of methane and ethane. A starting set of electrooptical parameters for n-hydrocarbons

Sets of electrooptical parameters (eop's), suitable for longer n-paraffins and less constrained than those already used to fit the IR intensities of CH₄ and C₂H₆ and their deuterated derivatives, are presented and discussed. The technique adopted in the least-squares refinement of eop's from experimental data is discussed in detail.     

Anodic chlorination of aromatic compounds in acetic acid part II

The anodic chlorination of aromatic compounds in anhydrous acetic acid has been further investigated. Evidence has been found for two different methods of electrochemical chlorination, in the systems Cl₂/aromatic compounds and Cl^?/aromatic compounds. These methods were also compared with the uncatalyzed chemical chlorination reaction. The yields of monochlorinated products and the related isometric distributions were taken into account. Since the isomeric distributions are equal with chemical and electrochemical chlorination methods, the formation of the same intermediate was proposed for both.     

3-methylthiophene self-assembled monolayers on planar and nanoparticle Au surfaces

In this article the adsorption of 3-methylthiophene on planar and nanoparticle Au surfaces is investigated. The resulting systems are compared with a benchmark system based on 1-decanethiol. The characterization data collected evidence the formation of a packed 3-methylthiophene SAM on the planar surface. In particular, spectroscopic investigations suggest that 3-methylthiophene aromatic system is not adsorbed on the surface through the pi-electron system but rather through the S atom alone. On the other hand, the behavior of 3-methylthiophene on nanoparticle surfaces is notably different from that of the alkanethiol. Only a limited fraction of the surface of Au nanoparticles results to be actually coated after purification; this notwithstanding, the nanoparticle growth seems to be strongly influenced by the presence of such a labile encapsulating agent.     

ArQiologist: an integrated decision support tool for lead optimization

This paper describes ArQiologist, a Web-based tool that integrates chemical, analytical, biological, and computational data to facilitate decision support for lead optimization at ArQule. It features an easy-to-use graphical query builder that allows queries to be saved, reused, and shared by researchers. Query results can be viewed with built-in data browsers or exported with structures to external applications such as Microsoft Excel or Spotfire for further analysis.     

Elliptic Problems with Singular Potential and Double-Power Nonlinearity

We prove the existence of positive symmetric solutions to the semilinear elliptic problem