Organic acid induced olefination reaction of lactones

(Z)-Selective olefination of several lactones with ketene silyl acetals was achieved by the catalysis of carbon acids (C-H acids) having a bis(triflyl)methyl group as an acidic functionality; in particular, the triple carbon acid having three bis(triflyl)methyl groups in phloroglucinol shows an excellent catalytic performance.     

Inclusion and dielectric properties of a vinylidene fluoride oligomer in coordination nanochannels

The dynamics of oligo(vinylidene fluoride) (OVDF) confined in regular nanochannels of a porous coordination polymer (PCP) was studied by means of dielectric spectroscopy. The OVDF chains in the PCP nanopores showed two Arrhenius-type relaxation processes at lower temperatures than the relaxation temperature observed for the neat OVDF, showing the enhanced mobility of the confined OVDF.     

A long-range-corrected time-dependent density functional theory

We apply the long-range correction (LC) scheme for exchange functionals of density functional theory to time-dependent density functional theory (TDDFT) and examine its efficiency in dealing with the serious problems of TDDFT, i.e., the underestimations of Rydberg excitation energies, oscillator strengths, and charge-transfer excitation energies. By calculating vertical excitation energies of typical molecules, it was found that LC-TDDFT gives accurate excitation energies, within an error of 0.5 eV, and reasonable oscillator strengths, while TDDFT employing a pure functional provides 1.5 eV lower excitation energies and two orders of magnitude lower oscillator strengths for the Rydberg excitations. It was also found that LC-TDDFT clearly reproduces the correct asymptotic behavior of the charge-transfer excitation energy of ethylene-tetrafluoroethylene dimer for the long intramolecular distance, unlike a conventional far-nucleus asymptotic correction scheme. It is, therefore, presumed that poor TDDFT results for pure functionals may be due to their lack of a long-range orbital-orbital interaction.     

New implementation of molecular double point‐group symmetry in four‐component relativistic Gaussian‐type spinors

A new, practical implementation of double‐group symmetry to relativistic Gaussian spinors is presented for four‐component relativistic molecular calculations. We show that the systematic adaptability to irreducible representations under arbitrary point‐group symmetry, as well as Kramers (time‐reversal) symmetry, is inherent in the present basis spinors, which possess the analytic structure of Dirac atomic spinors. The implementation of double‐group symmetry entails significant computational efficiencies in the relativistic second‐order Møller–Plesset perturbation calculation on Au₂ and the density functional theory (DFT) calculation with the B3LYP functional on octahedral UF₆, in which the highest symmetries used are, respectively, C and D. The four‐component B3LYP equilibrium geometry of UF₆ is reported. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Moments of partitions and derivatives of higher order

Journal of Algebraic Combinatorics - We define moments of partitions of integers, and show that they appear in higher-order derivatives of certain combinations of functions.     

Completion by Derived Double Centralizer

Let A be a commutative ring, and let $\mathfrak{a}$ be a weakly proregular ideal in A. (If A is noetherian then any ideal in it is weakly proregular.) Suppose M is a compact generator of the category of cohomologically $\mathfrak{a}$ -torsion complexes. We prove that the derived double centralizer of M is isomorphic to the $\mathfrak{a}$ -adic completion of A. The proof relies on the MGM equivalence from Porta et al. (Algebr Represent Theor, 2013) and on derived Morita equivalence. Our result extends earlier work of Dwyer et al. (Adv Math 200:357–402, 2006) and Efimov (2010).     

3D differential game guidance

Three-dimensional guidance in the neighborhood of collision course, based on a terminal differential game, renders ellipsoidal control sets. As a result, a saddle-point contains singularities. This paper (a) generalizes previous results on linear dynamics with terminal cost and ellipsoidal control sets and (b) applies the results to the above guidance problem to include general missile and target transfer functions. We further demonstrate the construction of the isocost surfaces (tubes).