Stress–strain state of flexible ring plates of variable stiffness in a magnetic field

A nonlinear two-dimensional model of a magnetoelastic flexible current-carrying ring plate is developed.Asystem of nonlinear equations describing the stress–strain state of flexible current-carrying plates in nonstationary mechanical and electromagnetic fields is derived. The stress state of a flexible plate of variable stiffness in a magnetic field is determined     

Sufficient conditions for the existence of bound states in a potential without spherical symmetry

We give in this paper several suffieient conditions for the existence of negative energy bound states in a purely attractive potential without spherical symmetry. These conditions generalize the condition obtained recently by K. Chadan and A. Martin (C. R. Acad. Sci. Paris290 (1980), 151), and can ensure the existence of n bound states. For the spherically symmetric case, one gets simple formulae which are also new.     

Synthesis and structure of <Emphasis Type="Italic">N</Emphasis>-substituted (1-ferrocenylethyl)amine derivatives

N-Acetyl-(1-ferrocenylethyl)amine (8) was synthesized by N-acylation of (1-ferrocenylethyl)amine (7) in 84% yield. Reaction of N-acetyl-[1-(1′-bromo-ferrocenyl)ethyl]amine (4) (which was prepared by multistep sequence starting from bromoferrocene) with n-BuLi/ClCOOEt gave 77% of N-acetyl-N-ethoxycarbonyl-(1-ferrocenylethyl)amine (6) instead of the expected ethyl 1′-[1-(acetamido)ethyl]ferrocene-1-carboxylate (5). Both structures were undoubtedly confirmed by (HR)MS spectroscopy and single crystal X-ray structure analysis.     

On the roots of Wiener polynomials of graphs

The Wiener polynomial of a connected graph $G$ is defined as $W(G;x)=\sum x^{d(u,v)}$, where $d(u,v)$ denotes the distance between $u$ and $v$, and the sum is taken over all unordered pairs of distinct vertices of $G$. We examine the nature and location of the roots of Wiener polynomials of graphs, and in particular trees. We show that while the maximum modulus among all roots of Wiener polynomials of graphs of order $n$ is $\left(\genfrac{}{}{0ex}{}{n}{2}\right)?1$, the maximum modulus among all roots of Wiener polynomials of trees of order $n$ grows linearly in $n$. We prove that the closure of the collection of real roots of Wiener polynomials of all graphs is precisely $(?\infty ,0]$, while in the case of trees, it contains $(?\infty ,?1]$. Finally, we demonstrate that the imaginary parts and (positive) real parts of roots of Wiener polynomials can be arbitrarily large.     

Solid-state tubular assemblies of thiolactones: synthesis and structural characterization

The synthesis of cyclic thiolactones, 2,5,8-trithiacyclododecane-1,9-dione (4), 2,5,8,14,17,20-hexathiacyclotetracosane-1,9,13,21-tetraone (5), 2,5,8-trithiacyclotetradecane-1,9-dione (6) and 2,5,8,16,19,22-hexathiacyclooctacosane-1,9,15,23-tetraone (7) was achieved by tin-template reaction of 2,2-dibutyl-2-stanna-1,3,6-trithiacyclooctane (1) with corresponding diacyl chlorides. The structures of 12-, 14-, 24- and 28-membered ring systems of 4, 6, 5, and 7, respectively, were investigated by X-ray structure analysis. These investigations revealed that, in the solid-state, thiolactones 4 and 7 form tubular assemblies. However, the crystal structure of 5 forms layered packing dominated by CH?O hydrogen bonds whereas 6 forms three-dimensional network via CH?O hydrogen bonds and van der Waals interactions.     

γH2AX,an Accurate Marker That Analyzes UV Genotoxic Effects on Human Keratinocytes and on Human Skin

The phosphorylated form of histone H2AX, γH2AX, is a component of the DNA repair system. Most studies have focused on the role of γH2AX during cell transformation and human cancer, but little is known about its role in keratinocytes and the skin during UV irradiation. We analyzed the response to UV irradiation focusing on the phosphorylation of histone H2AX both in vitro, in keratinocyte cultures and in artificial epidermis, and then in vivo, in human skin. Acute UVB irradiation of human keratinocytes increased the phosphorylation of H2AX in a dose-dependent manner; two types of γH2AX response were observed either in vitro or in vivo. After a low nonapoptotic UVB irradiation, cells contained phosphorylated H2AX and arrested their cell cycle to repair the DNA damages. For a stronger and proapoptotic UVB irradiation, keratinocytes dramatically increased the phosphorylation of H2AX and committed apoptosis. Our results indicate that γH2AX constitutes a highly sensitive marker relevant for studying subapoptotic doses as well as proapoptotic doses of UVB in human skin.