Understanding the Solvent Effect on the Catalytic Oxidation of 1,4‐Butanediol in Methanol over Au/TiO2 Catalyst: NMR Diffusion and Relaxation Studies

The effect of water on the catalytic oxidation of 1,4‐butanediol in methanol over Au/TiO₂ has been investigated by catalytic reaction studies and NMR diffusion and relaxation studies. The addition of water to the dry catalytic system led to a decrease of both conversion and selectivity towards dimethyl succinate. Pulsed‐field gradient (PFG)‐NMR spectroscopy was used to assess the effect of water addition on the effective self‐diffusivity of the reactant within the catalyst. NMR relaxation studies were also carried out to probe the strength of surface interaction of the reactant in the absence and presence of water. PFG‐NMR studies revealed that the addition of water to the initial system, although increasing the dilution of the system, leads to a significant decrease of effective diffusion rate of the reactant within the catalyst. From T₁ and T₂ relaxation measurements it was possible to infer the strength of surface interaction of the reactant with the catalyst surface. The addition of water was found to inhibit the adsorption of the reactant over the catalyst surface, with the T₁/T₂ ratio of 1,4‐butanediol decreasing significantly when water was added. The results overall suggest that both the decrease of diffusion rate and adsorption strength of the reactant within the catalyst, due to water addition, limits the access of reactant molecules to the catalytic sites, which results in a decrease of reaction rate and conversion.     

Conformational features and recognition properties of a conformationally blocked calix[7]arene derivative

The shaping of a calix[7]arene macrocycle into cone-like structure 3, through exhaustive alkylation of doubly bridged calix[7]arene derivative 2 with bulky groups, has been investigated. Conformational details about the structure adopted by calix[7]arene derivative 3 in solution have been obtained by using chemical shift surface maps, as previously reported by our group. Thus, chemical shift contour plots indicated that 3 adopted a cone-shaped structure in solution analogous to that adopted by the known p-tert-butylcalix[7]arene heptacarboxylic acid derivative 4. Interestingly, the X-ray structure of derivative 3 showed a high degree of similarity to the theoretical structure, which confirmed the validity of the contour plots method. The preorganized calix[7]arene host 3 showed interesting recognition abilities toward both organic and alkali cations. In fact, an unprecedented endo-cavity complexation of linear and branched alkyl ammonium cations with a larger calix[7]arene host was evidenced. A comparable affinity for branched tBuNH(3)(+) and linear nBuNH(3)(+) guests was observed.     

Acetylene and argon adsorption in a supramolecular organic zeolite

The adsorption properties of a new nanoporous organic zeolite with respect to acetylene and Ar were studied by volumetric adsorption analysis, microcalorimetric experiments, and synchrotron high-resolution X-ray powder diffraction. This allowed us to locate the guest molecules inside the host channels and characterize the host-guest interactions.     

Regioselective O-substitution of C-undecylresorcin[4]arene

Selectively functionalized resorcinarenes were obtained by weak-base-promoted O-alkylation of C-undecylresorcin[4]arene 1. Tetrasubstituted derivatives with C(4)-1,3,5,7, C(2v)-1,2,5,6, C(s)-1,2,4,7, and C(i)-1,2,4,6 pattern were obtained in workable yields by using K(2)CO(3) as the base in acetone at reflux. The good regioselectivity with respect to the statistical distribution was explained in terms of preferential formation of H-bonded monoanions. Heptaaroylated resorcin[4]arenes were also easily obtained by reaction of 1 with aroyl chlorides in pyridine.     

Portfolio insurance under a risk-measure constraint

We study the problem of portfolio insurance from the point of view of a fund manager, who guarantees to the investor that the portfolio value at maturity will be above a fixed threshold. If, at maturity, the portfolio value is below the guaranteed level, a third party will refund the investor up to the guarantee. In exchange for this protection, the third party imposes a limit on the risk exposure of the fund manager, in the form of a convex monetary risk measure. The fund manager therefore tries to maximize the investor’s utility function subject to the risk-measure constraint. We give a full solution to this non-convex optimization problem in the complete market setting and show in particular that the choice of the risk measure is crucial for the optimal portfolio to exist. Explicit results are provided for the entropic risk measure (for which the optimal portfolio always exists) and for the class of spectral risk measures (for which the optimal portfolio may fail to exist in some cases).     

Forward and inverse dynamics of nonholonomic mechanical systems

This paper deals with the forward and the inverse dynamic problems of mechanical systems subjected to nonholonomic constraints. The intrinsically dual nature of these two problems is identified and utilised to develop a systematic approach to formulate and solve them according to an unified framework. The proposed methodology is based on the fundamental equations of constrained motion which derive from Gauss’s principle of least constraint. The main advantage arising from using the fundamental equations of constrained motion is that they represent an effective method capable to derive the generalised acceleration of a mechanical system, constrained in general by a set of nonholonomic constraints, together with the generalized constraint forces (forward dynamics). When the constraint equations are used to represent the desired behaviour of the mechanical system under study, the generalised constraint forces deriving from the fundamental equations of constrained motion provide the control actions which reproduce the specified motion for the system (inverse dynamics). This approach is systematically extended to underactuated mechanical systems introducing a new method named underactuation equivalence principle. The underactuation equivalence principle is founded on the key idea that the underactuation property of a mechanical system can be mathematically represented using a particular set of nonholonomic constraint equations. Two simple case-studies are reported to exemplify the proposed methodology. In the first case-study the computation of the generalised constraint forces relative to the revolute joint constraints of a physical pendulum is illustrated. In the second case-study the calculation of the control action which solves the swing-up problem for an inverted pendulum is described.     

Copolymerization of ethylene with isoprene promoted by titanium complexes containing a tetradentate [OSSO]‐type bis(phenolato) ligand

Copolymerization of ethylene with isoprene (IP) catalyzed by 1,4‐dithabutanediyl‐linked bis(phenolato) titanium complexes 1 and 2 and methylaluminoxane (MAO) produced exclusively ethylene‐IP copolymers with good activity. The copolymer microstructure can be varied by changing the ratio between the monomers in the copolymerization feed, affording copolymers with IP content ～60%. The copolymer microstructure was fully elucidated by ¹³C‐NMR spectroscopy of the copolymers with various IP content revealing a strong tendency to the alternating microstructure. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 4200–4206, 2010