Reactions of the carbonyl complexes M(CO)3(L)3 (L = py,M = Mo,W; L = NH3, M = Mo) and M(CO)4(2-Mepy)2 (M = Mo,W) with HgX2 (X = Cl,CN, SCN)

The reactions of the substituted Group VI metal carbonyls of the type M(CO)₄(2-Mepy)₂ (M = Mo, w) and M(CO)₃(L)₃ (L = py, M = Mo, W; L = NH₃, M = Mo) with mercuric derivatives HgX₂ (X = Cl, CN, SCN) have given rise to three series of tricarbonyl complexes: M(CO)₃(py)HgCl₂ · 1/2HgCl₂ (M = Mo, W); 2[M(CO)₃(L)]Hg(CN)·nHg(CN)_x (L = py, M = Mo, W, n = $\text{1}\text{2}$, × = 2; L = 2- Mepy, × = 1; M = Mo, n = 3; M = W, n = 1); and [M(CO)₃(L)Hg(SCN)₂ · nHg(SCN)₂] (L = py, M = Mo,W, n = 0; L = 2-Mepy, M = Mo, W, n = $\text{1}\text{2}$; L = NH₃, M = Mo, n = 0) depending on which mercuric compound is employed. All the reactions with Hg(SCN)₂ give isolable products whereas those with Hg(CN)₂ and HgCl₂ did so far only the reactions with [M(CO)₄(2-Mepy)₂] and M(CO)₃(py)₃. The greater reactivity of Hg(SCN)₂ than of Hg(CN)₂ and HgCl₂ is consistent with the various acceptor capacities of the groups bonded to the mercury atom.The reactions studied always involve displacement of the N-donor ligand of the original complex and partial or total displacement of the halide or pseudohalide groups of the mercury compound to give in all cases compounds containing MHg bonds. In addition, elimination of a CO group in the tetracarbonyl complexes M(CO)₄(2-Mepy)₂occurs.     

An Overview of the Antimicrobial Properties of Lignocellulosic Materials

Pathogenic microbes are a major source of health and environmental problems, mostly due to their easy proliferation on most surfaces. Currently, new classes of antimicrobial agents are under development to prevent microbial adhesion and biofilm formation. However, they are mostly from synthetic origin and present several disadvantages. The use of natural biopolymers such as cellulose, hemicellulose, and lignin, derived from lignocellulosic materials as antimicrobial agents has a promising potential. Lignocellulosic materials are one of the most abundant natural materials from renewable sources, and they present attractive characteristics, such as low density and biodegradability, are low-cost, high availability, and environmentally friendly. This review aims to provide new insights into the current usage and potential of lignocellulosic materials (biopolymer and fibers) as antimicrobial materials, highlighting their future application as a novel drug-free antimicrobial polymer.     

Interior of a Schwarzschild Black Hole Revisited

The Schwarzschild solution has played a fundamental conceptual role in general relativity, and beyond, for instance, regarding event horizons, spacetime singularities and aspects of quantum field theory in curved spacetimes. However, one still encounters the existence of misconceptions and a certain ambiguity inherent in the Schwarzschild solution in the literature. By taking into account the point of view of an observer in the interior of the event horizon, one verifies that new conceptual difficulties arise. In this work, besides providing a very brief pedagogical review, we further analyze the interior Schwarzschild black hole solution. Firstly, by deducing the interior metric by considering time-dependent metric coefficients, the interior region is analyzed without the prejudices inherited from the exterior geometry. We also pay close attention to several respective cosmological interpretations, and briefly address some of the difficulties associated to spacetime singularities. Secondly, we deduce the conserved quantities of null and timelike geodesics, and discuss several particular cases in some detail. Thirdly, we examine the Eddington–Finkelstein and Kruskal coordinates directly from the interior solution. In concluding, it is important to emphasize that the interior structure of realistic black holes has not been satisfactorily determined, and is still open to considerable debate.     

Electrodynamics and Spacetime Geometry: Foundations

We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.     

Why are large cities faster? Universal scaling and self-similarity in urban organization and dynamics

Cities have existed since the beginning of civilization and have always been intimately connected with humanity's cultural and technological development. Much about the human and social dynamics that takes place is cities is intuitively recognizable across time, space and culture; yet we still do not have a clear cut answer as to why cities exist or to what factors are critical to make them thrive or collapse. Here, we construct an extensive quantitative characterization of the variation of many urban indicators with city size, using large data sets for American, European and Chinese cities. We show that social and economic quantities, characterizing the creation of wealth and new ideas, show increasing returns to population scale, which appear quantitatively as a power law of city size with an exponent β≃ 1.15 > 1. Concurrently, quantities characterizing material infrastructure typically show economies of scale, namely β≃ 0.8 < 1. The existence of pervasive scaling relations across city size suggests a universal social dynamics common to all cities within an urban system. We sketch some of their general ingredients, which include the acceleration of social life and a restructuring of individual social networks as cities grow larger. We also build simple dynamical models to show that increasing returns in wealth and innovation can fuel faster than exponential growth, which inexorably lead to crises of urban organization. To avoid them we show that growth may proceed in cycles, separated by major urban adaptations, with the unintended consequence that the duration of such cycles decreases with larger urban population size and is now estimated to be shorter than a human lifetime.     

Synthesis and Characterization of Surface-Active Ionic Liquids Used in the Disruption of Escherichia Coli Cells

Twelve surface-active ionic liquids (SAILs) and surface-active derivatives, based on imidazolium, ammonium, and phosphonium cations and containing one, or more, long alkyl chains in the cation and/or the anion, were synthetized and characterized. The aggregation behavior of these SAILs in water, as well as their adsorption at solution/air interface, were studied by assessing surface tension and conductivity. The CMC values obtained (0.03–6.0 mM) show a high propensity of these compounds to self-aggregate in aqueous media. Their thermal properties were also characterized, namely the melting point and decomposition temperature by using DSC and TGA, respectively. Furthermore, the toxicity of these SAILs was evaluated using the marine bacteria Aliivibrio fischeri (Gram-negative). According to the EC₅₀ values obtained (0.3–2.7 mg L⁻¹), the surface-active compounds tested should be considered “toxic” or “highly toxic”. Their ability to induce cell disruption of Escherichia coli cells (also Gram-negative), releasing the intracellular green fluorescent protein (GFP) produced, was investigated. The results clearly evidence the capability of these SAILs to act as cell disruption agents.     

The skin effect in vibrating systems with many concentrated masses

We address the asymptotic behaviour of the vibrations of a body occupying a domain $\Omega\subset\mathbb{R}^n, n=2,3$. The density, which depends on a small parameter $\varepsilon$\nopagenumbers\end , is of the order $O(1)$\nopagenumbers\end out of certain regions where it is $O(\varepsilon^{‐m})$\nopagenumbers\end with $m>2$\nopagenumbers\end . These regions, the concentrated masses with diameter $O(\varepsilon)$\nopagenumbers\end , are located near the boundary, at mutual distances $O(\eta)$\nopagenumbers\end , with $\eta=\eta(\varepsilon)\rightarrow 0$\nopagenumbers\end . We impose Dirichlet (resp. Neumann) conditions at the points of $\partial\Omega$\nopagenumbers\end in contact with (resp. out of) the masses. We look at the asymptotic behaviour, as $\varepsilon\rightarrow 0$\nopagenumbers\end , of the eigenvalues of order $O(1)$\nopagenumbers\end , the high frequencies, of the corresponding eigenvalue problem. We show that they accumulate on the whole positive real axis and characterize those giving rise to global vibrations of the whole system. We use the fact that the corresponding eigenfunctions, microscopically, present a skin effect in the concentrated masses. Copyright © 2001 John Wiley & Sons, Ltd.     

Asymptotics for the eigenelements of vibrating membranes with very heavy thin inclusionsComportement asymptotique des éléments propres pour des membranes vibrantes avec des couches très minces et très lourdes

We consider the vibrations of a membrane that contains a very thin and heavy inclusion around a curve γ. We assume that the membrane occupies a domain $\text{Ω}$ of $\text{R}{}^2$. The inclusion occupies a layer-like domain $\text{ω}{}_{\mathrm{\epsilon }}\text{?Ω}$ of width 2ε and it has a density of order O(ε^?3). The density is of order O(1) outside this inclusion, the concentrated mass around the curve γ. ε is a positive parameter, ε∈(0,1). By means of asymptotic expansions, we describe the behaviour, as ε→0, of the eigenelements (λ^ε,u^ε) of the associated spectral problem. We provide complete asymptotic series for the low frequencies λ^ε=O(ε²), the medium frequencies λ^ε=O(ε) and the corresponding eigenfunctions u^ε. To cite this article: Y. Golovaty et al., C. R. Mecanique 330 (2002) 777–782.