On a notion of unilateral slope for the Mumford-Shah functional

In this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed functional.     

Cost allocation protocols for supply contract design in network situations

The class of Construct and Charge (CC-) rules for minimum cost spanning tree (mcst) situations is considered. CC-rules are defined starting from the notion of charge systems, which specify particular allocation protocols rooted on the Kruskal algorithm for computing an mcst. These protocols can be easily implemented in practical network situations (for instance, in supply transportation networks), are flexible to changes in the network situation and meet the requirement of continuous monitoring by the agents involved. Special charge systems, that we call conservative, lead to a subclass of CC-rules that coincides with the class of obligation rules for mcst situations. The authors thank two anonymous referees both for detailed remarks and for interesting general comments on a previous version of the paper. Stef Tijs and Rodica Branzei are indebted to Daniel Granot for useful discussions on the topics treated in this paper and his hospitality during our research visit at British Columbia University at Vancouver in July–August 2003.     

Studies of high-repetition-rate laser plasma EUV sources from droplet targets

The water droplet laser plasma source has been shown to have many attractive features as a continuous, almost debris-free source for extreme ultraviolet (EUV) and X-ray applications. Through a dual experimental and theoretical study, we analyze the interaction physics between the laser light and the target. The hydrodynamic laser plasma simulation code, Medusa103 is used to model the electron density distribution for comparison to electron density distributions obtained through Abel inversion of plasma interferograms. In addition, flat field EUV spectra are compared to synthetic spectra calculated with the atomic physics code RATION. Received: 31 October 2002 / Accepted: 8 February 2003 / Published online: 28 May 2003 RID="*" ID="*"Present address: Naval Reseach Laboratory, Washington D.C. RID="**" ID="**"Present address: Xtreme Technologies, G?ttingen, Germany. RID="***" ID="***"Corresponding author. Fax: +1-407/823-3570, E-mail: mrichard@mail.ucf.edu     

Scanning electrochemical microscopy (SECM) of nanolitre droplets using an integrated working/reference electrode assembly

Scanning electrochemical microscopy (SECM) has been performed in the restricted space of nanolitre droplets with a robust and easy-to-handle coaxial electrode assembly centring a Pt microdisk in a circular Ag electrode. Straightforward and reproducible fabrication of the specially designed probe tips was achieved by using Tollens reaction to chemically deposit a uniform and well-adhering layer of silver on the body of a glass-insulated Pt microdisk electrode. The suitability of the novel dual-electrode SECM tip for measurement in small volumes was evaluated by imaging an array of four Pt band microelectrodes in 500 nL electrolyte.     

1,5-dihydroxyanthraquinones and an anthrone from roots of Rumex crispus

From the roots of Rumex crispus, two known anthraquinones and a new one together with a new anthrone were isolated and the structures of compounds 1-4 were elucidated by spectroscopic means. The singlet oxygen generation capacity was tested with 1,3-diphenylisobenzofuran (DPBF) for compounds 1-4.     

Mechanisms for oscillations in a biological competition model

A four-dimensional dynamical system that models perceptual bistability in the brain is analyzed. Two variables represent the activity of two competing neural populations and they evolve in fast time; other two variables are slow and they are associated with an intrinsic negative feedback to each population. The external stimulus strength I is the bifurcation parameter. We construct the normal form and prove that oscillations occur in the system through supercritical Hopf bifurcations: as I decreases from large to moderate values a limit cycle is born; then it disappears for lower values of I. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis,physico-chemical characterization and bioevaluation of Ni(II), Pd(II), and Pt(II) complexes with 1-(o-tolyl)biguanide: Antimicrobial and antitumor studies

New complexes of type [M(tbg)₂]Cl₂ [tbg = 1-(o-tolyl)biguanide; M = Ni(II), Pd(II), and Pt(II)] were synthesized and characterized to develop new biologically active compounds. The features of the complexes were assigned from microanalytical and thermal data. The NMR, FT-IR, and UV-Vis spectra were established by comparison with HtbgCl. All complexes exhibit a square-planar geometry resulting from the chelating behavior of tbg. The HtbgCl and [Ni(tbg)₂]Cl₂ complexes were fully characterized by single-crystal X-ray diffraction. The HtbgCl species crystallize in the monoclinic C2/c spatial group, while the Ni(II) complex adopts an orthorhombic Pna2₁ spatial group. The structure is stabilized by a complex hydrogen bonds network. The in vitro antimicrobial assays revealed improved antimicrobial activity for complexes in comparison with the ligand against both planktonic and biofilm embedded microbial cells. The most efficient compound, showing the largest spectrum of antimicrobial activity, including Gram-positive and Gram-negative bacteria, as well as fungal strains, in both planktonic and biofilm growth states was the Pd(II) complex, followed by the Pt(II) complex. The Pt(II) compound exhibited the most significant antiproliferative activity on the human cervical cancer SiHa cell line, inducing a cell cycle arrest in the G2/M phase.     

Lipase-catalyzed asymmetric acylation in the chemoenzymatic synthesis of furan-based alcohols

Eight racemic 1-(furan-2-yl)ethanols were prepared from the corresponding carbonyl compounds for enantioselective acylation studies, and seven of them were used in preparative-scale kinetic resolutions with Candida antarctica lipase B (Novozym 435) and vinyl acetate in dried diisopropyl ether. Mechanism-based competition between the (R)-acetate (enzymatic acylation product), vinyl acetate (added acylating reagent), and acetic acid (enzymatic hydrolysis product) toward CAL-B, together with the residual water of the lipase were shown to be potential reasons for side reactions, which affected the course of the kinetic resolution of 1-[5-(2-chlorophenyl) and (4-bromophenyl)furan-2-yl]ethanols. Clear effects were not observed with the other alcoholic substrates. Alcoholysis of the enantiomerically enriched (R)-acetates with methanol and CAL-B in diisopropyl ether was shown to be a potential method for the deprotection of the (R)-acetates and the formation of (R)-alcohols.