Singularities of optimal control problems on some 6-D lie groups

This paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices.

Case studies to demonstrate the range of applications of the Southampton Hand Assessment Procedure

The Southampton Hand Assessment Procedure (SHAP) was devised to assess quantitatively the functional range of injured and healthy adult hands. It was designed to be a practical tool for use in a busy clinical setting; thus, it was made simple to use and easy to interpret. This paper describes four examples of its use: before and after a surgical procedure, to observe the impact of an injury, use with prostheses, and during recovery following a fracture. The cases show that the SHAP is capable of monitoring progress and recovery, identifying functional abilities in prosthetic hands and comparing the capabilities of different groups of injuries.

The influence of pomegranate by-product and punicalagins on selected groups of human intestinal microbiota.

We have examined the gut bacterial metabolism of pomegranate by-product (POMx) and major pomegranate polyphenols, punicalagins, using pH-controlled, stirred, batch culture fermentation systems reflective of the distal region of the human large intestine. Incubation of POMx or punicalagins with faecal bacteria resulted in formation of the dibenzopyranone-type urolithins. The time course profile confirmed the tetrahydroxylated urolithin D as the first product of microbial transformation, followed by compounds with decreasing number of phenolic hydroxy groups: the trihydroxy analogue urolithin C and dihydroxylated urolithin A. POMx exposure enhanced the growth of total bacteria, Bifidobacterium spp. and Lactobacillus spp., without influencing the Clostridium coccoides–Eubacterium rectale group and the C. histolyticum group. In addition, POMx increased concentrations of short chain fatty acids (SCFA) viz. acetate, propionate and butyrate in the fermentation medium. Punicalagins did not affect the growth of bacteria or production of SCFA. The results suggest that POMx oligomers, composed of gallic acid, ellagic acid and glucose units, may account for the enhanced growth of probiotic bacteria.

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.

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.

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.

The potential for community groups to promote sustainable living

In recent times there has been a growing recognition amongst policy-makers of the role for community-based action in contributing to the broader aims of energy policy and climate change. In this paper, we will examine the potential for existing community groups to use their influence and elements of internal cohesion to encourage more widespread understanding and adoption of sustainable lifestyle habits; both amongst their members and within the broader communities of which they are a part. Findings are presented from recent empirical work with a range of well-established community groups for whom environmental issues are not their main priority. A central aspect of the research was to explore both the current status and potential role of groups that may have the capacity to reach and influence a broader sphere of the public than energy/environment specific initiatives of recent times have been able to achieve. Representing a diversity of interests, age groups and functionality, the results suggest that the potential for more effective ‘bottom-up’ engagement on climate change and sustainable living might be given fresh impetus by these types of established community groups and their networks. An assessment of what motivates participation and membership in the groups highlights a series of factors common to all groups and a smaller number that are significant for particular groups individually. It is argued that an appreciation of motivating factors can be useful in understanding more clearly how such groups are able to survive and maintain cohesion over time. The findings also suggest that climate change action means different things for different groups, with the diversity of the groups bringing with it the challenge of making sustainable living relevant to a range of interests and different shared values.