A Glivenko-Cantelli lemma and weak convergence for empirical processes of associated sequences

Summary With the help of an extension of Hoeffding's equality, we develop a way for estimating the covariance structures for empirical functions of associated sequences in terms of covariances of the original random variables. Based on these estimations, a Glivenko-Cantelli lemma for associated sequences and weak convergence for empirical processes of stationary associated sequences are obtained, all under the conditions on covariances of the original random variables.This research has been supported partially by a scholarship from the Faculty of Graduate Studies and Research of Carleton University, Ottawa, and by an NSERC Canada grant of M. Csörg     

A metallo-capped polyrotaxane containing calix[4]arenes and cyclodextrins and its highly selective binding for Ca2+

A water-soluble nanometer-scale metallocapped polyrotaxane has been prepared by the inclusion complexation of azo-calixarenes with metallo-bridged bis(beta-CD)s, displaying highly selective binding for Ca(2+).     

Diastereoselective allylation of planar chiral substituted ferrocenecarboxaldehyde: an efficient entry to chiral ferrocenyl ligands

2,2′-Disubstituted ferrocenecarboxaldehydes are subjected to zinc-mediated allylation to form homoallylic ferrocenyl alcohols. The effects of ortho-substituted functional groups on facial selectivities of planar chiral aldehydes were studied and it was found that the corresponding homoallylic alcohols were obtained as single diastereomers in excellent yields.     

A new serratane-type triterpene from Lycopodium phlegmaria

A new serratane-type triterpene, lycophlegmarin (1), has been isolated from Lycopodium phlegmaria L. Four known related triterpenoids were also found from the title plant. The structure of the new compound was elucidated on the basis of detailed spectroscopic analysis and chemical method. Lycophlegmarin exhibited modest growth-inhibitory activity in vitro against human hepatoma cells BEL 7402.     

Luminescence in NaLn(SO4)2H2O: A host lattice with high-energy vibrations

The luminescence of Ce³⁺, Sm³⁺, Eu³⁺, Gd³⁺, Tb³⁺, and Dy³⁺ in NaLn(SO₄)₂H₂O (Ln = lanthanide) is reported. Only Ce³⁺, Gd³⁺, and Tb³⁺ show efficient emission. This is explained in terms of an energy-gap law. Energy transfer is studied in several codoped compositions. The mutual transfer between Gd³⁺ ions is the only one encountered with high probability. The several transfers are discussed and where possible their rates are calculated.     

Intermolecular potential energy surface and spectra of He-HCl with generalization to other rare gas-hydrogen halide complexes

A two-dimensional (rigid monomer) intermolecular potential energy surface (PES) of the He-HCl complex has been obtained from ab initio calculations utilizing the symmetry-adapted perturbation theory (SAPT) and an spdfg basis set including midbond functions. The bond length in HCl was chosen to be equal to the expectation value in the ground vibrational state of isolated HCl. The rigid-monomer potential should be a very good approximation to the complete (three-dimensional) potential for H-Cl distances corresponding to the lowest vibrational levels of the monomer since the He-HCl interaction energy was found to be only weakly dependent on the HCl bond length in this region, at least as compared to systems such as Ar-HF. The calculated points were fitted using an analytic function with ab initio computed asymptotic coefficients. As expected, the complex is loosely bound, with the dispersion energy providing the majority of the attraction. Our SAPT PES agrees with the semiempirical PES of Willey et al. [J. Chem. Phys. 96, 898 (1992)], in finding that, atypically for rare gas-hydrogen halide complexes including the lighter halide atoms, the global minimum is on the Cl side (with intermonomer separation 3.35 A and depth of 32.8 cm(-1)), rather than on the H side, where there is only a local minimum (3.85 A, 30.8 cm(-1)). The ordering of the minima was confirmed by single-point calculations in larger basis sets and complete basis set extrapolations, and also using higher levels of theory. We show that the opposite findings in the recent calculations of Zhang and Shi [J. Mol. Struct: THEOCHEM 589, 89 (2002)] are due to the lack of midbond functions in their basis set. Despite the closeness in depth of the two linear minima, the existence of a relatively high barrier between them invalidates the assumption of isotropy, a feature of some literature potentials. The trends concerning the locations of minima within the family of rare gas-hydrogen halide complexes are rationalized in terms of the physical components of the intermolecular forces and related to monomer properties. The accuracy of the SAPT PES was tested by performing calculations of rovibrational levels. The transition frequencies obtained were found to be in excellent agreement (to within 0.02 cm(-1)) with the measurements of Lovejoy and Nesbitt [J. Chem. Phys. 93, 5387 (1990)]. The SAPT PES predicts a dissociation energy for the complex of 7.74 cm(-1) which is probably more accurate than the experimental value of 10.1+/-1.2 cm(-1). Our analysis of the ground-state rovibrational wave function shows that the He-HCl configuration is favored over the He-ClH configuration despite the ordering of minima. This is due to the greater volume of the well in the former case. We have also determined positions and widths of three low-lying resonance states through scattering calculations. These predictions are expected to be more accurate than values derived from experiment.     

Porous nanocomposites of zirconium dioxide and silicate

Highly porous nanocomposites of zirconium dioxide and silicate are synthesised in an aqueous system from an inorganic salt of zirconium; the nanacomposites, with tailorable pore structures, exhibit superior performance as catalyst supports.     

Synthesis and characterization of chitosan-graft-polycaprolactone copolymers

The graft copolymers of chitosan with polycaprolactone (PCL) were prepared through a protection-graft-deprotection route using phthaloylchitosan as intermediate. PCL macromonomers terminated with isocyanate groups reacted with hydroxyl groups of phthaloyl-protected chitosan regioselectively, and then phthaloyl groups were deprotected to give the free amino groups. The graft reaction was carried out in homogeneous system and yielded copolymers with high grafting content due to solubilization. FTIR, NMR and XRD were detected to characterize the resultant chitosan-graft-PCL copolymers.     

Co-C bond dissociation energy and reaction volume change of 2',5'-dideoxyadenosylcobalamin studied by laser-induced time-resolved photoacoustic calorimetry

Time resolved photoacoustic calorimetry (PAC) was applied to a study of the photolysis of a coenzyme B(12) analog 2',5'-dideoxyadenosylcobalamin, which lacks an -OH group at the 2' position of ribofuranose ring. In aqueous solution, we report for the first time the quantum yield Phi(d) (0.25+/-0.02), Co-C bond dissociation energy (BDE; 31.8+/-2.5 kcal mol(-1)) and reaction volume change deltaV(R) (6.5+/-0.5 ml mol(-1)) due to conformation changes of the corrin ring and its side chains accompanying the cleavage of the Co-C bond. These values for the analog are very similar to those for the natural cofactor. Based our results and previous studies, a possible explanation for the similarity in their structure and properties versus the large difference in their enzymatic activity is discussed.