On theK-property of some planar hyperbolic billiards

TheK-property is demonstrated for a class of planar billiards satisfying Wojtkowski's principles. Their boundary may consist of convex-scattering, concave and linear pieces. Earlier Wojtkowski showed that these billards had non-zero Lyapunov exponents.     

Synchronization Analysis of Coupled Noncoherent Oscillators

We present two different approaches to detect and quantify phase synchronization in the case of coupled non-phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the R?ssler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators.     

Maximal triangle-free graphs with restrictions on the degrees

We investigate the problem that at least how many edges must a maximal triangle-free graph on n vertices have if the maximal valency is ≤D. Denote this minimum value by F(n, D). For large enough n, we determine the exact value of F(n, D) if D ≥ (n ? 2)/2 and we prove that lim F(n, cn)/n = K(c) exists for all 0 < c with the possible exception of a sequence c_k → 0. The determination of K(c) is a finite problem on all intervals [γ, ∞). For D = cn^?, 1/2 < ? < 1, we give upper and lower bounds for F(n, D) differing only in a constant factor. (Clearly, D < (n - 1)^1/2 is impossible in a maximal triangle-free graph.)     

On the resolving power of high-contrast saturated absorption spectroscopy

Recently Svanberg et al. [Optics Lett. 11 (1986) 138; J. Opt. Soc. Am. B 4 (1987) 462] obtained saturated absorption resonances with subnatural linewidth by working in the regime of high pumping intensities and optically thick atomic samples. We analyze here this new spectroscopic regime, within the formalism of Maxwell-Bloch-type equations, in the case of a Doppler broadened medium having two nearly degenerate but uncoupled resonances. We show that even in this most favourable case it is not possible to resolve spectral features that lie within the natural linewidth.     

Click chemistry in materials synthesis. III. Metal‐adhesive polymers from Cu(I)‐catalyzed azide–alkyne cycloaddition

1,2,3‐Triazole‐based polymers generated from the Cu(I)‐catalyzed cycloaddition between multivalent azides and acetylenes are effective adhesive materials for metal surfaces. The adhesive capacities of candidate mixtures of azide and alkyne components were measured by a modified peel test, using a customized adhesive tester. A particularly effective tetravalent alkyne and trivalent azide combination was identified, giving exceptional strength that matches or exceeds the best commercial formulations. The addition of Cu catalyst was found to be important for the synthesis of stronger adhesive polymers when cured at room temperature. Heating also accelerated curing rates, but the maximum adhesive strengths achieved at both room temperature and high temperature were the same, suggesting that crosslinking reaches the same advanced point in all cases. Polytriazoles also form adhesives to aluminum, but copper is bound more effectively, presumably because active Cu(I) ions may be leached from the surface to promote crosslinking and adhesion. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5182–5189, 2007     

Highly edge‐connected detachments of graphs and digraphs

Let G = (V,E) be a graph or digraph and r : V → Z₊. An r‐detachment of G is a graph H obtained by ‘splitting’ each vertex ν ∈ V into r(ν) vertices. The vertices ν₁,…,ν_r(ν) obtained by splitting ν are called the pieces of ν in H. Every edge uν ∈ E corresponds to an edge of H connecting some piece of u to some piece of ν. Crispin Nash‐Williams 9 gave necessary and sufficient conditions for a graph to have a k‐edge‐connected r‐detachment. He also solved the version where the degrees of all the pieces are specified. In this paper, we solve the same problems for directed graphs. We also give a simple and self‐contained new proof for the undirected result. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 67–77, 2003     

Accuracy of the chemical data evaluated from one-atom-at-a-time experiments

Studies of chemistry of the transactinoid elements, which are available only as single atoms, by gas (thermo)chromatographic techniques can provide the adsorption enthalpies of the atoms or molecules. These values serve the ultimate goal—to characterize bulk volatility of the species in terms like sublimation enthalpies. The paper attempts an in-depth discussion of the statistical significance of the adsorption enthalpies derived in such experiments. Usually, the counting statistics are very poor and one faces nonstandard problems in evaluating the confidence intervals for the values of parameters. Here, a most efficient way seems to be the Bayesian approach, realized, when necessary, by Monte Carlo simulations of the counting results. Necessarily, the adsorption enthalpy is not evaluated based on the second law of thermodynamics but through accepting an a priori value of the adsorption entropy. More additional assumptions about the mechanisms and parameters involved are needed. This may produce systematic errors in the quantitative conclusions; the analysis of some recent works with elements 106 and 108 corroborates this concern. Despite such problems, it is possible to reveal qualitative differences in the adsorption behavior of a transactinoid and its expected known congeners as well as to use chemistry for an independent assignment of the atomic numbers of transactinoid nuclides.     

Medicinal Organometallic Chemistry: Designing Metal Arene Complexes as Anticancer Agents

The field of medicinal inorganic chemistry is rapidly advancing. In particular organometallic complexes have much potential as therapeutic and diagnostic agents. The carbon‐bound and other ligands allow the thermodynamic and kinetic reactivity of the metal ion to be controlled and also provide a scaffold for functionalization. The establishment of structure–activity relationships and elucidation of the speciation of complexes under conditions relevant to drug testing and formulation are crucial for the further development of promising medicinal applications of organometallic complexes. Specific examples involving the design of ruthenium and osmium arene complexes as anticancer agents are discussed.     

Influence of the loading path on the strength of fiber-reinforced composites subjected to transverse compression and shear

The influence of the loading path on the failure locus of a composite lamina subjected to transverse compression and out-of-plane shear is analyzed through computational micromechanics. This is carried out using the finite element simulation of a representative volume element of the microstructure, which takes into account explicitly fiber and matrix spatial distribution within the lamina. In addition, the actual failure mechanisms (plastic deformation of the matrix and interface decohesion) are included in the simulations through the corresponding constitutive models. Two different interface strength values were chosen to explore the limiting cases of composites with strong or weak interfaces. It was found that failure locus was independent of the loading path for the three cases analyzed (pseudo-radial, compression followed by shear and shear followed by compression) in the composites with strong and weak interfaces. This result was attributed to the fact that the dominant failure mechanism in each material was the same in transverse compression and in shear. Failure is also controlled by the same mechanisms under a combination of both stresses and the failure locus depended mainly on the magnitude of the stresses that trigger fracture rather than in the loading path to reach the critical condition.     

Genetically Encoded Bioluminescent Indicator for ERK2 Dimer in Living Cells

In this study, a genetically encoded bioluminescent indicator for ERK2 dimer was developed with the split Renilla luciferase complementation method, in which the formation of ERK2 dimer induces a spontaneous emission of bioluminescence in living cells. In response to extracellular stimuli, such as epidermal growth factor (EGF) or 17β‐estradiol (E2), extracellular signal‐regulated kinase 2 (ERK2) is phosphorylated by its upstream kinase MEK, and also phosphorylates its substrates in various regions of the cell, including the nucleus. Phosphorylated ERK2 is led to form its dimer, thereby transporting itself into the nucleus. We demonstrated with the indicator that stimulation with EGF or E2 induces the formation of ERK2 dimer in living MCF‐7 cells. The dynamics of this dimer formation was examined and discussed.