Bonding in Barium Boryloxides,Siloxides, Phenoxides and Silazides: A Comparison with the Lighter Alkaline Earths

Barium complexes ligated by bulky boryloxides [OBR₂]⁻ (where R=CH(SiMe₃)₂, 2,4,6-ⁱPr₃-C₆H₂ or 2,4,6-(CF₃)₃-C₆H₂), siloxide [OSi(SiMe₃)₃]⁻, and/or phenoxide [O-2,6-Ph₂-C₆H₃]⁻, have been prepared. A diversity of coordination patterns is observed in the solid state for both homoleptic and heteroleptic complexes, with coordination numbers ranging between 2 and 4. The identity of the bridging ligand in heteroleptic dimers [Ba(μ₂-X₁)(X₂)]₂ depends largely on the given pair of ligands X₁ and X₂. Experimentally, the propensity to fill the bridging position increases according to [OB{CH(SiMe₃)₂}₂)]⁻<[N(SiMe₃)₂]⁻<[OSi(SiMe₃)₃]⁻<[O(2,6-Ph₂-C₆H₃)]⁻<[OB(2,4,6-ⁱPr₃-C₆H₂)₂]⁻. This trend is the overall expression of 3 properties: steric constraints, electronic density and σ- and π-donating capability of the negatively charged atom, and ability to generate Ba ⋅ ⋅ ⋅ F, Ba ⋅ ⋅ ⋅ C(π) or Ba ⋅ ⋅ ⋅ H−C secondary interactions. The comparison of the structural motifs in the complexes [Ae{μ₂-N(SiMe₃)₂}(OB{CH(SiMe₃)₂}₂)]₂ (Ae = Mg, Ca, Sr and Ba) suggest that these observations may be extended to all alkaline earths. DFT calculations highlight the largely prevailing ionic character of ligand-Ae bonding in all compounds. The ionic character of the Ae-ligand bond encourages bridging coordination, whereas the number of bridging ligands is controlled by steric factors. DFT computations also indicate that in [Ba(μ₂-X₁)(X₂)]₂ heteroleptic dimers, ligand predilection for bridging vs. terminal positions is dictated by the ability to establish secondary interactions between the metals and the ligands.     

Exploring the latent segmentation space for the assessment of multiple change-point models

This paper addresses the retrospective or off-line multiple change-point detection problem. Multiple change-point models are here viewed as latent structure models and the focus is on inference concerning the latent segmentation space. Methods for exploring the space of possible segmentations of a sequence for a fixed number of change points may be divided into two categories: (i) enumeration of segmentations, (ii) summary of the possible segmentations in change-point or segment profiles. Concerning the first category, a dynamic programming algorithm for computing the top $N$ most probable segmentations is derived. Concerning the second category, a forward-backward dynamic programming algorithm and a smoothing-type forward-backward algorithm for computing two types of change-point and segment profiles are derived. The proposed methods are mainly useful for exploring the segmentation space for successive numbers of change points and provide a set of assessment tools for multiple change-point models that can be applied both in a non-Bayesian and a Bayesian framework. We show using examples that the proposed methods may help to compare alternative multiple change-point models (e.g. Gaussian model with piecewise constant variances or global variance), predict supplementary change points, highlight overestimation of the number of change points and summarize the uncertainty concerning the position of change points.     

Effondrement de quotients aléatoires de groupes hyperboliques avec torsion

We show that random quotients of hyperbolic groups with ‘harmful’ torsion collapse at densities smaller than expected. To cite this article: Y. Ollivier, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

The Relationship Between Stock Markets Of Major Developed Countries And Asian Emerging Markets

With the emergence of new capital markets and liberalization of stock markets in recent years, there has been an increase in investors' interest in international diversification. This is so because international diversification allows investors to have a larger basket of foreign securities to choose from as part of their portfolio assets, so as to enhance the reward-to-volatility ratio. This benefit would be limited if national equity markets tend to move together in the long run. This paper thus studies the issue of co-movement between stock markets in major developed countries and those in Asian emerging markets using the concept of cointegration. We find that there is co-movement between some of the developed and emerging markets, but some emerging markets do differ from the developed markets with which they share a long-run equilibrium relationship. Furthermore, it has been observed that there has been increasing interdependence between most of the developed and emerging markets since the 1987 Stock Market Crash. This interdependence intensified after the 1997 Asian Financial Crisis. With this phenomenon of increasing co-movement between developed and emerging stock markets, the benefits of international diversification become limited.     

An integrable example of gradient flow based on optimal transport of differential forms

Optimal transport theory has been a powerful tool for the analysis of parabolic equations viewed as gradient flows of volume forms (or, in other words, 0-currents) according to suitable transportation metrics. In this paper, we present an example of gradient flow for closed \((d-1)\)-differential forms, or, more appropriately, to closed 1-currents, which can be identified to divergence-free vector fields, in the Euclidean space \(\mathbb {R}^d\). In spite of its apparent complexity, the resulting very degenerate parabolic system is fully integrable and can be viewed, in a suitable sense, as an Eulerian version of the heat equation for loops in the Euclidean space. We analyze this system in terms of “relative entropy” and “dissipative solutions” and provide global existence and weak–strong uniqueness results.     

Nombres de Liouville et nombres normauxLiouville numbers and normal numbers

We prove that there exist Liouville numbers which are normal, as well as Liouville numbers which are non-normal to any base. To cite this article: Y. Bugeaud, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 117–120.     

Insights into the oxidation of propylene oxide through the analysis of experiments and kinetic modeling

Cyclic ethers are important intermediates in the oxidation of hydrocarbons and biofuels. Studying the oxidation and pyrolysis of cyclic ethers will help in improving our understanding of this functional group and provide consistency to the base mechanism where they play an important role. In this aspect, propylene oxide has been investigated in this study by obtaining ignition delay time measurements in the rapid compression machine and shock tube. The experiments were performed in a range of pressures varying from 10 to 40 bar at different equivalence ratios (0.5–2.0) and dilution percentages. Additionally, speciation measurements in the shock tube at pyrolysis conditions have been performed at a pressure of 40 bar to explore the isomerization pathways. A detailed kinetic mechanism was developed to describe both the oxidation and pyrolysis chemistry of propylene oxide. The mechanism is not only able to predict the data obtained from this study but also reproduces the data from the literature in a consistent trend. For a better understanding of the oxidation and pyrolysis chemistry of propylene oxide, the kinetic analyses were performed using the developed mechanism to comprehend the important reaction pathways and sensitive reactions. At the investigated regime, the consumption of propylene oxide through its isomerization channels is the critical pathway that controls the reactivity of the fuel.     

An experimental and kinetic modeling study on the oxidation of 1,3-dioxolane

The modern catalytic or enzymatic advances allow the production of novel biofuel. Among them, 1,3-dioxolane can be produced from formaldehyde and ethylene glycol, both can be obtained from biomass. In this study, the oxidation of 1,3-dioxolane is studied at stoichiometric conditions. The ignition delay times of 1,3-dioxolane/O₂/inert mixtures were measured in a shock tube and in a rapid compression machine at pressures of 20 to 40 bar and temperatures ranging from 630 to 1300 K. The pressure profiles recorded in the rapid compression machine show a first stage of ignition enlightening the influence of the low temperature chemistry of combustion. Furthermore, mole fraction profiles of the stable intermediates produced during the oxidation of 1,3-dioxolane were measured in a jet-stirred reactor at 10 bar. Following these observations, a detailed kinetic model was developed with reaction rate coefficients and thermochemical data calculated by theoretical calculations or estimated by analogies to suitable molecules. In order to get an insight into the most important reaction pathways brute force sensitivity analysis and reaction pathway analysis were performed with the proposed model and discussed. It became clear that in the fuel-in-air case for the alkylhydroperoxide of 1,3-dioxolane the ring opening beta-scission pathway is favored against the further alkane-like second addition to molecular oxygen, which leads to a limited negative temperature coefficient.     

Approximation by Algebraic Integers and Hausdorff Dimension

The paper computes the Hausdorff dimension of sets of real numberswhich are close to infinitely many real algebraic integers ofbounded degree. It also investigates the distribution of realalgebraic integers of bounded degree, which are proved to beevenly spaced.     

Sharp phase transition theorems for hyperbolicity of random groups

We prove that in various natural models of a random quotient of a group, depending on a density parameter, for each hyperbolic group there is some critical density under which a random quotient is still hyperbolic with high probability, whereas above this critical value a random quotient is very probably trivial. We give explicit characterizations of these critical densities for the various models.