A simple method of calculating eigenvalues and resonances in domains with infinite regular ends

A new approach is presented for the solution of spectral problems on infinite domains with regular ends, which avoids the need to solve boundary-value problems for many trial values of the spectral parameter. We present numerical results both for eigenvalues and for resonances, comparing with results reported by Aslanyan, Parnovski and Vassiliev.

The influence of carbon surface oxygen groups on Dubinin–Astakhov equation parameters calculated from CO2 adsorption isotherm

We present the results of a systematic study of the influence of carbon surface oxidation on Dubinin–Astakhov isotherm parameters obtained from the fitting of CO2 adsorption data. Using GCMC simulations of adsorption on realistic VPC models differing in porosity and containing the most frequently occurring carbon surface functionalities (carboxyls, hydroxyls and carbonyls) and their mixtures, it is concluded that the maximum adsorption calculated from the DA model is not strongly affected by the presence of oxygen groups. Unfortunately, the same cannot be said of the remaining two parameters of this model i.e. the heterogeneity parameter (n) and the characteristic energy of adsorption (E0). Since from the latter the pore diameters of carbons are usually calculated, by inverse-type relationships, it is concluded that they are questionable for carbons containing surface oxides, especially carboxyls.

Self-assembled molecular complexes and coordination polymers of CdII, hexamine, and monocarboxylates: structural analysis and theoretical studies of supramolecular interactions

Four new cadmium(II) complexes [Cd-2(bz)(4)(H2O)(4)(mu 2-hmt)]center dot Hbz center dot H2O (1), [Cd-3(bz)(6)(H2O)(6)(mu 2-hmt)(2)]center dot 6H(2)O (2), [Cd(pa)(2)(H2O)(mu(2)-hmt)](n) (3), and {[Cd-3(ac)(6)(H2O)(3)(mu(3)-hmt)(2)]center dot 6H(2)O}(n) (4) with hexamine (hmt) and monocarboxylate ions, benzoate (bz), phenylacetate (pa), or acetate (ac) have been synthesized and characterized structurally. Structure determinations reveal that 1 is dinuclear, 2 is trinuclear, 3 is a one-dimensional (1D) infinite chain, and 4 is a two-dimensional (2D) polymer with fused hexagonal rings consisting of Cd-II and hmt. All the Cd-II atoms in the four complexes (except one CdII in 2) possess seven-coordinate pentagonal bipyramidal geometry with the various chelating bidentate carboxylate groups in equatorial sites. One of the CdII ions in 2, a complex that contains two monodentate carboxylates is in a distorted octahedral environment. The bridging mode of hmt is mu 2- in complexes 1-3 but is mu 3- in complex 4. In all complexes, there are significant numbers of H-bonds, C-H/pi, and pi-pi interactions which play crucial roles in forming the supramolecular networks. The importance of the noncovalent interactions in terms of energies and geometries has been analyzed using high level ab initio calculations. The effect of the cadmium coordinated to hmt on the energetic features of the C-H/pi interaction is analyzed. Finally, the interplay between C-H/pi and pi-pi interactions observed in the crystal structure of 3 is also studied.

Nickel(II) and copper(II) complexes of Schiff base ligands containing N4O2 and N4S2 donors with pyrrole terminal binding groups: synthesis, characterization, X-ray structures, DFT and electrochemical studies

A series of hexadentate ligands, H2Lm (m = 1−4), [1H-pyrrol-2-ylmethylene]{2-[2-(2-{[1H-pyrrol-2-ylmethylene]amino}phenoxy)ethoxy]phenyl}amine (H2L1), [1H-pyrrol-2-ylmethylene]{2-[4-(2-{[1H-pyrrol-2-ylmethylene]amino}phenoxy)butoxy]phenyl}amine (H2L2), [1H-pyrrol-2-ylmethylene][2-({2-[(2-{[1H-pyrrol-2-ylmethylene]amino}phenyl)thio]ethyl}thio)phenyl]amine (H2L3) and [1H-pyrrol-2-ylmethylene][2-({4-[(2-{[1H-pyrrol-2-lmethylene]amino}phenyl)thio]butyl}thio) phenyl]amine (H2L4) were prepared by condensation reaction of pyrrol-2-carboxaldehyde with {2-[2-(2-aminophenoxy)ethoxy]phenyl}amine, {2-[4-(2-aminophenoxy)butoxy]phenyl}amine, [2-({2-[(2-aminophenyl)thio]ethyl}thio)phenyl]amine and [2-({4-[(2-aminophenyl)thio]butyl}thio)phenyl]amine respectively. Reaction of these ligands with nickel(II) and copper(II) acetate gave complexes of the form MLm (m = 1−4), and the synthesized ligands and their complexes have been characterized by a variety of physico-chemical techniques. The solid and solution states investigations show that the complexes are neutral. The molecular structures of NiL3 and CuL2, which have been determined by single crystal X-ray diffraction, indicate that the NiL3 complex has a distorted octahedral coordination environment around the metal while the CuL2 complex has a seesaw coordination geometry. DFT calculations were used to analyse the electronic structure and simulation of the electronic absorption spectrum of the CuL2 complex using TDDFT gives results that are consistent with the measured spectroscopic behavior of the complex. Cyclic voltammetry indicates that all copper complexes are electrochemically inactive but the nickel complexes with softer thioethers are more easily oxidized than their oxygen analogs.

SATgene dietary model to implement diets of differing fat composition in prospectively genotyped groups (apoE) using commercially available foods

esponse to dietary fat manipulation is highly heterogeneous, yet generic population-based recommendations aimed at reducing the burden of CVD are given. The APOE epsilon genotype has been proposed to be an important determinant of this response. The present study reports on the dietary strategy employed in the SATgenɛ (SATurated fat and gene APOE) study, to assess the impact of altered fat content and composition on the blood lipid profile according to the APOE genotype. A flexible dietary exchange model was developed to implement three isoenergetic diets: a low-fat (LF) diet (target composition: 24 % of energy (%E) as fat, 8 %E SFA and 59 %E carbohydrate), a high-saturated fat (HSF) diet (38 %E fat, 18 %E SFA and 45 %E carbohydrate) and a HSF-DHA diet (HSF diet with 3 g DHA/d). Free-living participants (n 88; n 44 E3/E3 and n 44 E3/E4) followed the diets in a sequential design for 8 weeks, each using commercially available spreads, oils and snacks with specific fatty acid profiles. Dietary compositional targets were broadly met with significantly higher total fat (42·8 %E and 41·0 %E v. 25·1 %E, P ≤ 0·0011) and SFA (19·3 %E and 18·6 %E v. 8·33 %E, P ≤ 0·0011) intakes during the HSF and HSF-DHA diets compared with the LF diet, in addition to significantly higher DHA intake during the HSF-DHA diet (P ≤ 0·0011). Plasma phospholipid fatty acid analysis revealed a 2-fold increase in the proportion of DHA after consumption of the HSF-DHA diet for 8 weeks, which was independent of the APOE genotype. In summary, the dietary strategy was successfully implemented in a free-living population resulting in well-tolerated diets which broadly met the dietary targets set.

Crystallization of random aromatic copolyesters containing flexible spacer chains and side-groups

The crystallization behaviour of a series of random copolymers of varying chemical composition is reported. For polymers containing a high proportion of alternating rigid aromatic units and flexible spacers, conventional liquid crystalline and crystalline phase behaviour is observed. The introduction of a substantial fraction of a second shorter rigid unit containing side-chains leads to a broad endotherm in the d.s.c. scan covering some 150°C. Subsequent isothermal crystallization at any point within the broad endotherm leads to the generation of sharp endotherms at temperatures just above the recrystallization temperature. We attribute this behaviour to the crystallization of clusters of molecules containing similar random sequences. Such crystals are non-periodic along the chain direction.

Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .

In vitro fermentation of a red wine extract by human gut microbiota: changes in microbial groups and formation of phenolic metabolites

An in vitro batch culture fermentation experiment was conducted with fecal inocula from three healthy volunteers in the presence and absence of a red wine extract. Changes in main bacterial groups were determined by FISH during a 48 h fermentation period. The catabolism of main flavonoids (i.e., flavan-3-ols and anthocyanins) and the formation of a wide a range of phenolic microbial metabolites were determined by a targeted UPLC-PAD-ESI-TQ MS method. Statistical analysis revealed that catechol/pyrocatechol, as well as 4-hydroxy-5-(phenyl)-valeric, 3- and 4-hydroxyphenylacetic, phenylacetic, phenylpropionic, and benzoic acids, showed the greatest increases in concentration during fermentation, whereas 5-(3′-hydroxyphenyl)-γ-valerolactone, its open form 4-hydroxy-5-(3′-hydroxyphenyl)-valeric acid, and 3,4-dihydroxyphenylacetic acid represented the largest interindividual variations in the catabolism of red wine polyphenols. Despite these changes, microbial catabolism did not produce significant changes in the main bacterial groups detected, although a slight inhibition of the Clostridium histolyticum group was observed.