Cyclodextrins containing an acetone bridge. Synthesis and study as epoxidation catalysts

Three cyclodextrine derivatives (6A,6D-di-O-(prop-2-one-1,3-dienyl)-alpha-cyclodextrin (1), 6-O-(prop-2-one-1-yl)-alpha-cyclodextrin (2) and 6A,6D-di-O-(prop-2-one-1,3-dienyl)-beta-cyclodextrin (3)) were synthesised and investigated as epoxidation catalysts. The three compounds were synthesised from the corresponding perbenzylated cyclodextrins which were mono- or didebenzylated in the 6-position using Sina?'s method. Reaction with NaH and methallyl chloride in the case of 2, or methallyl dichloride in the case of 1 and 3, followed by dihydroxylation, periodate cleavage and protection group removal gave the target compounds. All three compounds catalysed, in the presence of oxone, the epoxidation of a series of alkenes. Epoxidation was compared to the reaction catalysed by simple ketones and inhibition was studied.     

A generalization of imaginary parts of eigenvalues for matrices: Chain rotation numbers

Rotation numbers and chain rotation numbers may be interpreted as a generalization of the imaginary parts for matrices. In dimension two they measure how the solutions of a linear autonomous differential equation rotate in the phase space, and they reduce to the imaginary parts of the eigenvalues of the system’s matrix. In higher dimensions they measure how a two-frame of vectors rotate under the induced flow in the plane which is spanned by the frame. For their calculation, only special sets in the oriented Grassmann manifold of planes are relevant, and to each of these sets corresponds a compact interval of chain rotation numbers. In this paper we will determine these relevant sets and calculate the corresponding sets of chain rotation numbers.     

On Fictitious Domain Formulations for Maxwell''s Equations

We consider fictitious domain-Lagrange multiplier formulations for variational problems in the space H(curl: Ω{\bf)} derived from Maxwell's equations. Boundary conditions and the divergence constraint are imposed weakly by using Lagrange multipliers. Both the time dependent and time harmonic formulations of the Maxwell's equations are considered, and we derive well-posed formulations for both cases. The variational problem that arises can be discretized by functions that do not satisfy an a-priori divergence constraint.     

Creating composite indicators with DEA and robustness analysis: the case of the Technology Achievement Index

Composite indicators (CIs) are often used for benchmarking countries' performance, but they frequently stir controversies about the unavoidable subjectivity in their construction. Data Envelopment Analysis helps to overcome some key limitations, as it does not need any prior information on either the normalization of sub-indicators or on an agreed unique set of weights. Still, subjective decisions remain, and such modelling uncertainty propagates onto countries' CI scores and rankings. Uncertainty and sensitivity analysis are therefore needed to assess the robustness of the final outcome and to analyse how much each source of uncertainty contributes to the output variance. The current paper reports on these issues, using the Technology Achievement Index as an illustration.     

Compactness and domination

It is well known that each dominated family of probability measures is compact in the sense of Pitcher. In this paper the converse direction is investigated. It is shown that a family of probability measures on a-field is dominated if it is compact with respect to each sub- -field. If is only compact with respect to the basic-field settheoretical assumptions are needed to obtain domination.     

Optical model analysis of proton-carbon elastic scattering in the range 20 to 50 MeV

The differential cross-sections for the elastic scattering of protons from¹²C with incident energies ranging in approximately 2 MeV steps between 20 and 50 MeV, are analyzed using a standard optical model.     

Experimental and theoretical study of the elastic break-up of the alpha particle on58Ni nuclei atE α=172.5 MeV

The triton-proton angular correlation function has been measured for the⁵⁸Ni(α, t p)⁵⁸Ni reaction leading to the ground state of the target nucleus. The obtained experimental data have been interpreted in terms of the direct break-up (fragmentation) of the alpha particle on the target nucleus potential. It is shown that the main features of the measured double differential cross section are well predicted by the DWBA theory of the break-up. The dependence of the elastic and inclusive break-up cross sections upon the fragment-target interaction potentials is discussed.     

Nonstandard characterization of convergence in law for -valued random variables

We prove for random variables with values in the space of cadlag functions - endowed with the supremum metric - that convergence in law is equivalent to nonstandard constructions of internal -cadlag processes, which represent up to an infinitesimal error the limit process. It is not required that the limit process is concentrated on the space , so that the theory is applicable to a wider class of limit processes as e.g. to Poisson processes or Gaussian processes. If we consider in the Skorokhod metric - instead of the supremum metric - we obtain a corresponding equivalence to constructions of internal processes with -separated jumps. We apply these results to functional central limit theorems.

     

Controlling Through-Space and Through-Bond Exchange Pathways in Bis-Cobaltocenes for Molecular Spintronics

Pinching molecules via chemical strain suggests intuitive consequences, such as compression at the pinched site and clothespin-like opening of other parts of the structure. If this opening affects two spin centers, it should result in reduced communication between them. We show that for naphthalene-bridged biscobaltocenes with competing through-space and through-bond pathways, the consequences of pinching are far less intuitive: despite the known dominance of through-space interactions, the bridge plays a much larger role for exchange spin coupling than previously assumed. Based on a combination of chemical synthesis, structural, magnetic, and redox characterization, and a newly developed theoretical pathway analysis, we can suggest a comprehensive explanation for this non-intuitive behavior. These results are of interest for molecular spintronics, as naphthalene-linked cobaltocenes can form wires on surfaces for potential spin-only information transfer.     

Coverage-Controlled Superstructures of C3-Symmetric Molecules: Honeycomb versus Hexagonal Tiling

The competition between honeycomb and hexagonal tiling of molecular units can lead to large honeycomb superstructures on surfaces. Such superstructures exhibit pores that may be used as 2D templates for functional guest molecules. Honeycomb superstructures of molecules that comprise a C₃ symmetric platform on Au(111) and Ag(111) surfaces are presented. The superstructures cover nearly mesoscopic areas with unit cells containing up to 3000 molecules, more than an order of magnitude larger than previously reported. The unit cell size may be controlled by the coverage. A fairly general model was developed to describe the energetics of honeycomb superstructures built from C₃ symmetric units. Based on three parameters that characterize two competing bonding arrangements, the model is consistent with the present experimental data and also reproduces various published results. The model identifies the relevant driving force, mostly related to geometric aspects, of the pattern formation.