44 resultados para isometry groups

em CentAUR: Central Archive University of Reading - UK


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This paper considers left-invariant control systems defined on the orthonormal frame bundles of simply connected manifolds of constant sectional curvature, namely the space forms Euclidean space E-3, the sphere S-3 and Hyperboloid H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1, 3). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to left-invariant control systems defined on Lie groups. In this paper a method for integrating these systems is given where the controls are time-independent. In the Euclidean case the elements of the Lie algebra se(3) are often referred to as twists. For constant twist motions, the corresponding curves g(t) is an element of SE(3) are known as screw motions, given in closed form by using the well known Rodrigues' formula. However, this formula is only applicable to the Euclidean case. This paper gives a method for computing the non-Euclidean screw motions in closed form. This involves decoupling the system into two lower dimensional systems using the double cover properties of Lie groups, then the lower dimensional systems are solved explicitly in closed form.

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This paper tackles the path planning problem for oriented vehicles travelling in the non-Euclidean 3-Dimensional space; spherical space S3. For such problem, the orientation of the vehicle is naturally represented by orthonormal frame bundle; the rotation group SO(4). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to control systems defined on Lie groups. The oriented vehicles, in this case, are constrained to travel at constant speed in a forward direction and their angular velocities directly controlled. In this paper we identify controls that induce steady motions of these oriented vehicles and yield closed form parametric expressions for these motions. The paths these vehicles trace are defined explicitly in terms of the controls and therefore invariant with respect to the coordinate system used to describe the motion.

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Motivated by the motion planning problem for oriented vehicles travelling in a 3-Dimensional space; Euclidean space E3, the sphere S3 and Hyperboloid H3. For such problems the orientation of the vehicle is naturally represented by an orthonormal frame over a point in the underlying manifold. The orthonormal frame bundles of the space forms R3,S3 and H3 correspond with their isometry groups and are the Euclidean group of motion SE(3), the rotation group SO(4) and the Lorentzian group SO(1; 3) respectively. Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to left-invariant control systems defined on Lie groups. In this paper a method for integrating these systems is given where the controls are time-independent. For constant twist motions or helical motions, the corresponding curves g(t) 2 SE(3) are given in closed form by using the well known Rodrigues’ formula. However, this formula is only applicable to the Euclidean case. This paper gives a method for computing the non-Euclidean screw/helical motions in closed form. This involves decoupling the system into two lower dimensional systems using the double cover properties of Lie groups, then the lower dimensional systems are solved explicitly in closed form.

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In this paper, the issues that arise in multi-organisational collaborative groups (MOCGs) in the public sector are discussed and how a technology-based group support system (GSS) could assist individuals within these groups. MOCGs are commonly used in the public sector to find solutions to multifaceted social problems. Finding solutions for such problems is difficult because their scope is outside the boundary of a single government agency. The standard approach to solving such problems is collaborative involving a diverse range of stakeholders. Collaborative working can be advantageous but it also introduces its own pressures. Conflicts can arise due to the multiple contexts and goals of group members and the organisations that they represent. Trust, communication and a shared interface are crucial to making any significant progress. A GSS could support these elements.

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Direct numerical simulations of turbulent flow over regular arrays of urban-like, cubical obstacles are reported. Results are analysed in terms of a formal spatial averaging procedure to enable interpretation of the flow within the arrays as a canopy flow, and of the flow above as a rough wall boundary layer. Spatial averages of the mean velocity, turbulent stresses and pressure drag are computed. The statistics compare very well with data from wind-tunnel experiments. Within the arrays the time-averaged flow structure gives rise to significant 'dispersive stress' whereas above the Reynolds stress dominates. The mean flow structure and turbulence statistics depend significantly on the layout of the cubes. Unsteady effects are important, especially in the lower canopy layer where turbulent fluctuations dominate over the mean flow.

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A series of eight synthetic self-assembling terminally blocked tripeptides have been studied for gelation. Some of them form gels in various aromatic solvents including benzene, toluene, xylene, and chlorobenzene. It has been found that the protecting groups play an important role in the formation of organogels. It has been observed that, if the C-terminal has been changed from methyl ester to ethyl ester the gelation property does not change significantly (keeping the N-terminal protecting group same), while the change of the protecting group from ethyl ester to isopropyl ester completely abolishes the gelation property. Similarly, keeping the identical C-terminal protecting group (methyl ester) the results of the gelation study indicate that the substitution of N-terminal protection Boc-(tert-butyloxycarbonyl) to Cbz-(benzyloxycarbonyl) does change the gelation property insignificantly, while the change from Boc- to pivaloyl (Piv-) or acetyl (Ac-) group completely eliminates the gelation property. Morphological studies of the dried gels of two of the peptides indicate the presence of an entangled nano-fibrillar network that might be responsible for gelation. FTIR studies of the gels demonstrate that an intermolecular hydrogen bonding network is formed during gelation. Results of X-ray powder diffraction studies for these gelator peptides in different states (dried gels, gel, and bulk solids) reflected that the structure in the wet gel is distinctly different from the dried gel and solid state structures. Single crystal X-ray diffraction studies of a non-gelator peptide, which is structurally similar to the gelator molecules reveal that the peptide forms an antiparallel beta-sheet structure in crystals. (c) 2007 Elsevier Ltd. All rights reserved.

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The development of two novel protecting groups for amines is described. Thus, a range of amines have been converted to ureas, and the deprotection of these upon exposure to mushroom tyrosinase (E.C. 1.14.18.1) has been demonstrated.

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Reactions of [Mo(eta(3)-C3H5)Br(CO)(2)(NCMe)(2)] with the bidentate nitrogen ligands 2-(2'-pyridyl)imidazole (L1), 2-(2'-pyridyl)benzimidazole (L2), N,N'-bis(2'-pyridinecarboxamido)-1,2-ethane (L3), and 2,2'-bisimidazole (L4) led to the new complexes [Mo(eta(3)-C3H5)Br(CO)(2)(L)] (L = L1, 1; L2, 2; L4, 4) and [{Mo(eta(3)-C3H5) Br(CO)(2)}(2)(mu-L-3)] (3). The reaction of complexes 2 and 3 with Tl[CF3SO3] afforded [Mo(eta(3)-C3H5)(CF3SO3)(CO)(2)(L2)] (2T) and [{Mo(eta(3)-C3H5)(CF3SO3)(CO)(2)}(2)(mu-L-3)] (3T). Complexes 3 and 2T were structurally characterized by single crystal X-ray diffraction, showing the facial allyl/carbonyls arrangement and the formation of the axial isomer. In 2T, two molecules are assembled in a hydrogen bond dimer. The four complexes 1-4 were tested as precursors in the catalytic epoxidation of cyclooctene and styrene, in the presence of t-butylhydroperoxide (TBHP), with moderate conversions and turnover frequencies for complexes 1-3 and very low ones for 4. The increasing number of N-H groups in the complexes seems to be responsible for the loss of catalytic activity, compared with other related systems. The cytotoxic activities of all the complexes were evaluated against HeLa cells. The results showed that compounds 1,2,4, and 2T exhibited significant activity, complexes 2 and 2T being particularly promising. (C) 2008 Elsevier B.V. All rights reserved.

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The present paper details the synthesis, characterization, and preliminary physical analyses of a series of polyisobutylene derivatives featuring urethane and urea end-groups that enable supramolecular network formation to occur via hydrogen bonding. These polymers are readily accessible from relatively inexpensive and commercially available starting materials using a simple two-step synthetic approach. In the bulk, these supramolecular networks were found to possess thermoreversible and elastomeric characteristics as determined by temperature-dependent rheological analysis. These thermoreversible and elastomeric properties make these supramolecular materials potentially very useful in applications such as adhesives and healable surface coatings.

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Aromatic poly(ether-ketone)s having pendant carboxyl groups have been obtained by direct, one-pot, Friedel-Crafts copolycondensation of 4,4'-diphenoxybenzophenone with a mixture of terephthaloyl chloride (TC) and trimellitic anhydride acid chloride (TAAC), over a wide range of TAAC/TC molar ratios, in the presence of anhydrous aluminum chloride. The syntheses were performed as precipitation-polycondensations, and the polymers were obtained in particulate form. Besides globular particles of polymer, small quantities of elongated, needlelike particles were observed when the mole ratio TAAC/TC was less than 1. Use of X-ray microdiffraction with synchrotron radiation has revealed that the needlelike material consists of a cyclic compound containing 10 phenylene units, i.e., the crystals are of a [2 + 2] macrocyclic dimer. The polymers obtained are soluble in strong acids and in mixtures of methanesulfonic acid or trifluoroacetic acid with chlorinated hydrocarbons. The molecular structures of the polymers were confirmed by H-1 and C-13 NMR spectroscopy. Reaction of TAAC with 4,4'-diphenoxybenzophenone produced mainly meta-orientation of the resulting ketone linkages. The size of the polymer particles, their molecular weights, and the melting behavior of the products obtained depend on the TAAC/TC ratio used. Ortho-keto acid residues, formed during reaction of anhydride groups of TAAC with 4,4'-diphenoxybenzophenone, exhibit ring-chain tautomerism. A carboxyl-containing aromatic polyketone derived from p-terphenyl, and thus having with no ether linkages in the main chain, was prepared by analogous chemistry, and functional derivatives of carboxy-substituted polyketones were also obtained and characterized.

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The prevalence of the metabolic syndrome (MetS), CVD and type 2 diabetes (T2D) is known to be higher in populations from the Indian subcontinent compared with the general UK population. While identification of this increased risk is crucial to allow for effective treatment, there is controversy over the applicability of diagnostic criteria, and particularly measures of adiposity in ethnic minorities. Diagnostic cut-offs for BMI and waist circumference have been largely derived from predominantly white Caucasian populations and, therefore, have been inappropriate and not transferable to Asian groups. Many Asian populations, particularly South Asians, have a higher total and central adiposity for a similar body weight compared with matched Caucasians and greater CVD risk associated with a lower BMI. Although the causes of CVD and T2D are multi-factorial, diet is thought to make a substantial contribution to the development of these diseases. Low dietary intakes and tissue levels of long-chain (LC) n-3 PUFA in South Asian populations have been linked to high-risk abnormalities in the MetS. Conversely, increasing the dietary intake of LC n-3 PUFA in South Asians has proved an effective strategy for correcting such abnormalities as dyslipidaemia in the MetS. Appropriate diagnostic criteria that include a modified definition of adiposity must be in place to facilitate the early detection and thus targeted treatment of increased risk in ethnic minorities.