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.     

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.     

Energy release rate and stress intensity factor in antiplane elasticity

In the setting of antiplane linearized elasticity, we show the existence of the stress intensity factor and its relation with the energy release rate when the crack path is a C1,1 curve. Finally, we show that the energy release rate is continuous with respect to the Hausdorff convergence in a class of admissible cracks.     

Synthesis and characterization of water‐dispersible,superparamagnetic single‐wall carbon nanotubes decorated with iron oxide nanoparticles and well‐defined chelating diblock copolymers

A novel approach for the fabrication of magneto‐active carbon nanotubes (CNTs) stabilized in aqueous media, involving the combination of carboxylated single‐wall carbon nanotubes (SWCNTs) with a new class of methacrylate‐based chelating diblock copolymers, is described. More precisely, a well‐defined diblock copolymer consisting of hexa(ethylene glycol) methyl ether methacrylate (hydrophilic and thermo‐responsive) and 2‐(acetoacetoxy)ethyl methacrylate (hydrophobic and metal‐chelating) synthesized by reversible addition‐fragmentation chain transfer polymerization has been used to prepare polymer‐coated magneto‐active SWCNTs decorated with iron oxide nanoparticles. Further to the characterization of the compositional and thermal properties using transmission electron microscopy, Fourier transform infrared spectroscopy, X‐ray diffraction spectroscopy and thermal gravimetric analysis, assessment of the magnetic characteristics by vibrational sample magnetometry disclosed superparamagnetic behavior at room temperature. The latter, combined with the thermo‐responsive properties of the polymeric coating and the unique, inherent properties of the carbon nanotubes may allow for their future exploitation in the biomedical field. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1389–1396, 2011     

Positive solutions for systems of nonlinear second‐order multipoint boundary value problems

We study the existence of positive solutions for systems of second‐order nonlinear ordinary differential equations, subject to multipoint boundary conditions. Copyright © 2013 John Wiley & Sons, Ltd.