Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2): an application to the attitude control of a spacecraft

This paper considers left-invariant control systems defined on the Lie groups SU(2) and SO(3). Such systems have a number of applications in both classical and quantum control problems. The purpose of this paper is two-fold. Firstly, the optimal control problem for a system varying on these Lie Groups, with cost that is quadratic in control is lifted to their Hamiltonian vector fields through the Maximum principle of optimal control and explicitly solved. Secondly, the control systems are integrated down to the level of the group to give the solutions for the optimal paths corresponding to the optimal controls. In addition it is shown here that integrating these equations on the Lie algebra su(2) gives simpler solutions than when these are integrated on the Lie algebra so(3).

Reaction of (±)-1,1′-binaphthyl-2,2′-diyl hydrogen phosphate {(±)-phosH} with copper(II), cobalt(II) and iron(II) compounds; Identification by x-ray diffraction of [Co(CH3OH)4(H2O)2][(+)-phos][(−)-phos]. 2CH3OH·H2O

[Cu2(μO2CCH3)4(H2O)2], [CuCO3·Cu(OH)2], [CoSO4·7H2O], [Co((+)-tartrate)], and [FeSO4·7H2O] react with excess racemic (±)- 1,1′-binaphthyl-2,2′-diyl hydrogen phosphate {(±)-PhosH} to give mononuclear CuII, CoII and FeII products. The cobalt product, [Co(CH3OH)4(H2O)2]((+)-Phos)((−)-Phos) ·2CH3OH·H2O (7), has been identified by X-ray diffraction. The high-spin, octahedral CoII atom is ligated by four equatorial methanol molecules and two axial water molecules. A (+)- and a (−)-Phos− ion are associated with each molecule of the complex but are not coordinated to the metal centre. For the other CoII, CuII and FeII samples of similar formulation to (7) it is also thought that the Phos− ions are not bonded directly to the metal. When some of the CuII and CoII samples are heated under high vacuum there is evidence that the Phos− ions are coordinated directly to the metals in the products.

Square planar mononuclear Pd(II) complexes of substituted 2-(pyrazole-1-yl)phenylamines with a helical twist

X-ray crystal structure shows that 3,5-dimethyl-1-(2-nitrophenyl)-1H-pyrazole (DNP) belongs to the rare class of helically twisted synthetic organic molecules. Hydrogenation of DNP gives 2-(3,5-dimethylpyrazole-1-yl)phenylamine (L) which on methylation yields [2-(3,5-dimethylpyrazole-1-yl)phenyl]dimethylamine (L'). Two Pd(II) complexes, PdLCl2 (1) and PdL'Cl-2 (2), are synthesized and characterized by NMR. X-ray crystallography reveals that 1 and 2 are unprecedented square planar complexes which possess well discernible helical twists. (C) 2007 Elsevier B.V. All rights reserved.

Synthesis and structure of Ir4Sn3(CO)6{CH(SiMe3)2}5O3; a heterometallic ‘raft’ with sail hoisted!

Heterometallic raft clusters have been obtained previously for a variety of metals but none for tin and iridium, and more significantly none to date have had metal groups bonded above the raft plane. We report a hexametallic Ir4Sn2 raft to which a third tin group is attached by a single short IrSn bond and three IrOSn bridges.

Anticancer activity of organotin compounds. 2. Interaction of diorganotin dihalides with nucleic acid bases and nucleosides; the synthesis of adenine, adenosine and 9-methyladenine adducts

The syntheses of the complexes formulated as SnMe2Cl2(Ad)2 (I), SnMe2Cl2(Ado)2 (II), SnMe2Cl2- (9-MeAd)2 (III) [Ad = adenine, Ado = adenosine, 9-MeAd = 9-methyladenine] as well as the more unexpected SnPhCl2(OH)(Ad)2·3H2O (IV) and SnPhCl3(Ado)2 (V) by reaction of SnMe2Cl2 or SnPh2Cl2 with the appropriate bases in methanol is described. 1H NMR studies suggest that coordination is through the N-7 position of the adenine base.

Insulin receptor substrate-2 gene variants in subjects with metabolic syndrome: association with plasma fatty acid levels and insulin resistance

Several insulin receptor substrate-2 (IRS-2) polymorphisms have been studied in relation to insulin resistance and type 2 diabetes. To examine whether the genetic variability at the IRS-2 gene locus was associated with the degree of insulin resistance and plasma fatty acid levels in metabolic syndrome (MetS) subjects. Methods and results: Insulin sensitivity, insulin secretion, glucose effectiveness, plasma fatty acid composition and three IRS-2 tag-single nucleotide polymorphisms (SNPs) were determined in 452 MetS subjects. Among subjects with the lowest level of monounsaturated (MUFA) (below the median), the rs2289046 A/A genotype was associated with lower glucose effectiveness (p<0.038), higher fasting insulin concentrations (p<0.028) and higher HOMA IR (p<0.038) as compared to subjects carrying the minor G-allele (A/G and G/G). In contrast, among subjects with the highest level of MUFA (above the median), the A/A genotype was associated with lower fasting insulin concentrations and HOMA-IR, whereas individuals carrying the G allele and with the highest level of ω-3 polyunsaturated fatty acids (above the median) showed lower fasting insulin (p<0.01) and HOMA-IR (p<0.02) as compared with A/A subjects. Conclusion: The rs2289046 polymorphism at the IRS2 gene locus may influence insulin sensitivity by interacting with certain plasma fatty acids in MetS subjects.

Co3(SO4)3(OH)2[enH2]: a newS= 3/2 Kagome-type layered sulfate with a unique connectivity

The Kagome lattice, comprising a two-dimensional array of corner-sharing equilateral triangles, is central to the exploration of magnetic frustration. In such a lattice, antiferromagnetic coupling between ions in triangular plaquettes prevents all of the exchange interactions being simultaneously satisfied and a variety of novel magnetic ground states may result at low temperature. Experimental realization of a Kagome lattice remains difficult. The jarosite family of materials of nominal composition AM3(SO4)2(OH)6 (A = monovalent cation; M= Fe3+, Cr3+), offers perhaps one of the most promising manifestations of the phenomenon of magnetic frustration in two dimensions. The magnetic properties of jarosites are however extremely sensitive to the degree of coverage of magnetic sites. Consequently, there is considerable interest in the use of soft chemical techniques for the design and synthesis of novel materials in which to explore the effects of spin, degree of site coverage and connectivity on magnetic frustration.

The central European floods of August 2002: Part 2 - Synoptic causes and considerations with respect to climatic change

In the first part of this paper (Ulbrich et al. 2003), we gave a description of the August 2002 rainfall events and the resultant floods, in particular of the flood wave of the River Elbe. The extreme precipitation sums observed in the first half of the month were primarily associated with two rainfall episodes. The first episode occurred on 6/7 August 2002. The main rainfall area was situated over Lower Austria, the south-western part of the Czech Republic and south-eastern Germany. A severe flash flood was produced in the Lower Austrian Waldviertel (`forest quarter’ ). The second episode on 11± 13 August 2002 most severely affected the Erz Mountains and western parts of the Czech Republic. During this second episode 312mm of rain was recorded between 0600GMT on 12 August and 0600GMT on 13 August at the Zinnwald weather station in the ErzMountains, which is a new 24-hour record for Germany. The flash floods resulting from this rainfall episode and the subsequent Elbe flood produced the most expensive weatherrelated catastrophe in Europe in recent decades. In this part of the paper we discuss the meteorological conditions and physical mechanisms leading to the two main events. Similarities to the conditions that led to the recent summer floods of the River Oder in 1997 and the River Vistula in 2001 will be shown. This will lead us to a consideration of trends in extreme rainfall over Europe which are found in numerical simulations of anthropogenic climate change.

Global exponential periodicity of a class of bidirectional associative memory networks with finite distributed delays

In this paper, we study the periodic oscillatory behavior of a class of bidirectional associative memory (BAM) networks with finite distributed delays. A set of criteria are proposed for determining global exponential periodicity of the proposed BAM networks, which assume neither differentiability nor monotonicity of the activation function of each neuron. In addition, our criteria are easily checkable. (c) 2005 Elsevier Inc. All rights reserved.

Rossby wave propagation on potential vorticity fronts with finite width

The horizontal gradient of potential vorticity (PV) across the tropopause typically declines with lead time in global numerical weather forecasts and tends towards a steady value dependent on model resolution. This paper examines how spreading the tropopause PV contrast over a broader frontal zone affects the propagation of Rossby waves. The approach taken is to analyse Rossby waves on a PV front of finite width in a simple single-layer model. The dispersion relation for linear Rossby waves on a PV front of infinitesimal width is well known; here an approximate correction is derived for the case of a finite width front, valid in the limit that the front is narrow compared to the zonal wavelength. Broadening the front causes a decrease in both the jet speed and the ability of waves to propagate upstream. The contribution of these changes to Rossby wave phase speeds cancel at leading order. At second order the decrease in jet speed dominates, meaning phase speeds are slower on broader PV fronts. This asymptotic phase speed result is shown to hold for a wide class of single-layer dynamics with a varying range of PV inversion operators. The phase speed dependence on frontal width is verified by numerical simulations and also shown to be robust at finite wave amplitude, and estimates are made for the error in Rossby wave propagation speeds due to the PV gradient error present in numerical weather forecast models.

Synthesis, structure, and electrochemical properties of a family of 2-(arylazo)phenolate complexes of ruthenium with unusual C-C coupling and N=Ncleavage

Reaction of 2-(4'-R-phenylazo)-4-methylphenols (R = OCH3, CH3, H, Cl, and NO2) with [Ru(dmso)(4)Cl-2] affords a family of five ruthenium(III) complexes, containing a 2-(arylazo)phenolate ligand forming a six-membered chelate ring and a tetradentate ligand formed from two 2-(arylazo) phenols via an unusual C-C coupling linki.ng the two ortho carbons of the phenyl rings in the arylazo fragment. A similar reaction with 2-(2'-methylphenylazo)-4-methylphenol with [Ru(dmso)(4)Cl-2] has afforded a similar complex, in which one 2-(2'-methylphenylazo)-4-methylphenolate ligand is coordinated forming a six-membered chelate ring, and the other two ligands have undergone the C-C coupling reaction, and the coupled species is coordinated as a tetradentate ligand forming a five-membered N,O-chelate ring, a nine-membered N,N-chelate ring, and another five-membered chelate ring. Reaction of 2-(2',6'-dimethylphenylazo)-4-methylphenol with [Ru(dmso)(4)Cl-2] has afforded a complex in which two 2-(2',6'-dimethylphenylazo)-4-methylphenols are coordinated as bidentate N,O-donors forming five- and six-membered chelate rings, while the third one has undergone cleavage across the N=N bond, and the phenolate fragment, thus generated, remains coordinated to the metal center in the iminosemiquinonate form. Structures of four selected complexes have been determined by X-ray crystallography. The first six complexes are one-electron paramagnetic and show rhombic ESR spectra. The last complex is diamagnetic and shows characteristic H-1 NMR signals. All the complexes show intense charge-transfer transitions in the visible region and a Ru(III)-Ru(IV) oxidation on the positive side of SCE and a Ru(III)-Ru(II) reduction on the negative side.

Synthesis, X-ray crystal structures and properties of complex salts and sterically crowded heteroleptic complexes of group 10 metal ions with aromatic sulfonyl dithiocarbimates and triphenylphosphine ligand

Two new complex salts of the form (Bu4N)(2)[Ni(L)(2)] (1) and (Ph4P)(2)[Ni(L)(2)] (2) and four heteroleptic complexes cis-M(PPh3)(2)(L) [M = Ni(II) (3), Pd(II) (4), L = 4-CH3OC6H4SO2N=CS2] and cis-M(PPh3)(2)(L') [M = Pd(II) (5), Pt(II) (6), L' = C6H5SO2N=CS2] were prepared and characterized by elemental analyses, IR, H-1, C-13 and P-31 NMR and UV-Vis spectra, solution and solid phase conductivity measurements and X-ray crystallography. A minor product trans-Pd(PPh3)(2)(SH)(2), 4a was also obtained with the synthesis of 4. The NiS4 and MP2S2 core in the complex salts and heteroleptic complexes are in the distorted square-plane whereas in the trans complex, 4a the centrosymmetric PdS2P2 core is perforce square planar. X-ray crystallography revealed the proximity of the ortho phenyl proton of the PPh3 ligand to Pd(II) showing rare intramolecular C-H center dot center dot center dot Pd anagostic binding interactions in the palladium cis-5 and trans-4a complexes. The complex salts with sigma(rt) values similar to 10 (5) S cm (1) show semi-conductor behaviors. The palladium and platinum complexes show photoluminescence properties in solution at room temperature.

Metal complexes with atropisomeric sulfur ligands in asymmetric hydroformylation X-ray structure of [Rh2(μ-biphes)(cod)2] (H2biphes = 4,4′-biphenanthrene-3,3′-dithiol)

The addition of the atropisomeric racemic sulfur compound 4,4′-biphenanthrene-3,3′-dithiol (H2 biphes) to a dichloromethane solution of [{M(μ-OMe)(cod)}2] (M = Rh, Ir, cod = cycloocta-1,5-diene) afforded the dithiolate-bridged complexes [{Rh2(μ-biphes)(cod)2}n] (n = 2 5 or n = 1 6) and [{Ir2(μ-biphes)(cod)2}n]·nCH2Cl27. When 1,1′-binaphthalene-2,2′-dithiol (H2 binas) reacted with [{Ir(μ-OMe)(cod)}2], complex [Ir2(μ-binas)(cod)2] 8 was obtained. Complexes 5 and 6 reacted with carbon monoxide to give the dinuclear tetracarbonyl complex [Rh2(μ-biphes)(CO)4] 9. The reaction of 9 with PR3 provided the mixed-ligand complexes [{Rh2(μ-biphes)(CO)2(PR3)2}2] · xCH2Cl2 (R = Ph, x = 2 10, C6H11, x = 1 11) and [{Rh2(μ-biphes)(CO)3(PR3)}2] · CH2Cl212 (R = OC6H4But-o). The crystal structure of 6 was determined by X-ray diffraction. Reaction of the dithioether ligand Me2biphes with [Rh(cod)2]ClO4 in CH2Cl2 solution afforded the cationic complex [Rh(cod)(Me2biphes)]ClO4 · CH2Cl213. Asymmetric hydroformylation of styrene was performed using the complexes described. The extent of aldehyde conversion ranges from 53 to 100%, with selectivities towards branched aldehydes in the range 51 to 96%. The enantioselectivities were quite low and did not exceed 20%.

Synthesis, X-ray crystal structure and catalytic activity of the manganese(II) complex [Mn(bdoa)(H2O)3](bdoaH2 =benzene-1,2-dioxyacetic acid)

Benzene-1,2-dioxyacetic acid (bdoaH2) reacts with Mn(CH3CO2)2·4H2O in an ethanol-water mixture to give the manganese(II) complex [Mn(bdoa)(H2O)3]. The X-ray crystal structure of the complex shows the metal to be pseudo seven-coordinate. The quadridentate bdoa2− dicar☐ylate ligand forms an essentially planar girdle around the metal, being strongly bondedtransoid by a car☐ylate oxygen atom from each of the two car☐ylate moieties (mean MnO 2.199A˚) and also weakly chelated by the two internal ether oxygen atoms (mean MnO 2.413A˚). The coordination sphere about the manganese is completed by three water molecules (mean MnO 2.146A˚) lying in a meridional plane orthogonal to that of the bdoa2− ligand. Magnetic, conductivity and voltammetry data for the complex are given, and its use as a catalyst for the disproportionisation of H2O2 is described.