A Molecular Analogue of the C−H Activation Intermediate of the Silica-Supported Ga(III) Single-Site Propane Dehydrogenation Catalyst: Structure and XANES Signature

Propane dehydrogenation is an important field of research due to an increasing world-wide demand of propene while classical production routes through naphtha cracking are in decline. In that context, silica-supported Ga(III) sites, synthesized from surface organometallic chemistry principles, show high selectivity and stability in the propane dehydrogenation reaction. This performance is in significant contrast to the reported fast deactivation and lower selectivity of most Ga₂O₃ and CrO₃ based materials. The Ga-catalyzed propane dehydrogenation reaction is proposed to proceed through the formation of Ga alkyl intermediates for which it would be desirable to have detailed structural and spectroscopic information. Here, we prepare a consistent series of Ga(III) molecular complexes with varying numbers of alkyl and siloxide ligands; they are characterized by single crystal X-Ray diffraction and X-Ray Absorption Near Edge Structure analysis, which is known to be highly sensitive to the Ga coordination environment. We report in particular the structure and the spectroscopic signatures of [Ga(ⁱPr)(OSi(O^tBu)₃)₂(HOSi(O^tBu)₃)], a molecular mimic of the key proposed reaction intermediates in the Ga-catalyzed PDH reaction.     

New Trends in Asymmetric Phase Transfer Catalysis

Phase Transfer Catalysis (PTC) is a powerful tool to perform reactions in a practical fashion, both in laboratory and industrial scale. Significant cost savings and major process improvements can be achieved in reactions performed under PTC conditions. In the last few years remarkable results in stereoselective reactions were achieved using chiral, non-racemic quaternary ammonium salts. Moreover, the use of bulky, chiral phosphate anions paired with achiral cations to generate lipophilic ion pairs allowed to design new avenues for the stereoselective construction of important building blocks. Hydrogen bond interactions were also shown to provide new pathways for asymmetric nucleophilic substitutions using insoluble reagents under PTC conditions. This Review will focus on recent advances in developing practical synthetic routes to construct molecules in a stereoselective fashion under PTC conditions.     

Spectral stability results for higher-order operators under perturbations of the domain

We analyze the spectral behavior of higher-order elliptic operators when the domain is perturbed. We provide general spectral stability results for Dirichlet and Neumann boundary conditions. Moreover, we study the bi-harmonic operator with the so-called intermediate boundary conditions. We give special attention to this last case and analyze its behavior when the boundary of the domain has some oscillatory behavior. We will show that there is a critical oscillatory behavior and that the limit problem depends on whether we are above, below or just sitting on this critical value.     

Chaos and reproduction in sea level

Prediction of sea-level is an important task for navigation, coastal engineering and geodetic applications, as well as recreational activities. This study presents a comparison of Chaos theory and Auto-Regressive Integrated Moving Average (ARIMA) techniques for sea level modelling for daily, weekly, 10-day and monthly time scale at the Cocos (Keeling) islands from 1992 to 2001. The state space reconstruction of the unknown underlying process is directly employed from time series data, through Takens delay embedding method: optimal embedding dimension and delay time are obtained from false nearest neighbours and average mutual information techniques, respectively. Optimal values are then used for the estimation of the correlation dimension and the largest Lyapunov exponent, for inspecting possible signatures of chaotic dynamics. We find a positive Lyapunov exponent an evident feature of chaos. Indeed, the nonlinear prediction of sea level, in the period ranging from January 2001 to December 2001, is in an excellent agreement with the data for the same period, evidencing the nonlinear nature of the process. ARIMA method is also used for sea level modelling, for the same time scales; the performances of the two models are compared using such statistical indices as the root mean square error (RMSE) and correlation coefficient (CC). The comparative analyses show that the chaos theory model has a slight edge over ARIMA while both models are in principal acceptable.     

An Extension of the Birkhoff Integrability for Multifunctions

A comparison between a set-valued Gould type and simple Birkhoff integrals of bf(X)-valued multifunctions with respect to a non-negative set function is given. Relationships among them and Mc Shane multivalued integrability is given under suitable assumptions.     

Existence of proper semihypergroups of type U on the right

We generalize the classical definition of hypergroups of type U on the right to semihypergroups, and we prove some properties of their subsemihypergroups and subhypergroups. In particular, we obtain that a finite proper semihypergroup of type U on the right can exist only if its order is at least 6. We prove that one such semihypergroup of order 6 actually exists. Moreover, we show that there exists a hypergroup of type U on the right of cardinality 9 containing a proper non-trivial subsemihypergroup. In this way, we solve a problem left open in [D. Freni, Sur les hypergroupes de type U et sous-hypergroupes engendrés par un sous-ensemble, Riv. Mat. Univ. Parma 13 (1987) 29-41].     

A note on almost kähler manifolds

For anyn ≥ 2, we give examples of almost Kähler conformally flat manifoldsM ²ⁿ which are not Kähler. We discuss the meaning of these examples in the context of the Goldberg conjecture on almost Kahler manifolds.     

Mixture models for ordinal responses to account for uncertainty of choice

In CUB models the uncertainty of choice is explicitly modelled as a Combination of discrete Uniform and shifted Binomial random variables. The basic concept to model the response as a mixture of a deliberate choice of a response category and an uncertainty component that is represented by a uniform distribution on the response categories is extended to a much wider class of models. The deliberate choice can in particular be determined by classical ordinal response models as the cumulative and adjacent categories model. Then one obtains the traditional and flexible models as special cases when the uncertainty component is irrelevant. It is shown that the effect of explanatory variables is underestimated if the uncertainty component is neglected in a cumulative type mixture model. Visualization tools for the effects of variables are proposed and the modelling strategies are evaluated by use of real data sets. It is demonstrated that the extended class of models frequently yields better fit than classical ordinal response models without an uncertainty component.