Optimal control of a class of discrete–continuous non-linear systems — decomposition and hierarchical structure

A technique is derived for solving a non-linear optimal control problem by iterating on a sequence of simplified problems in linear quadratic form. The technique is designed to achieve the correct solution of the original non-linear optimal control problem in spite of these simplifications. A mixed approach with a discrete performance index and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local sub-system problems and a co-ordinator within a hierarchical framework. An analysis of the optimality and convergence properties of the algorithm is presented and the effectiveness of the technique is demonstrated using a simulation example with a non-separable performance index.

Synthesis, characterization and molecular structure of 1,1′ bis(diphenylphosphino ferrocene)dioxide complex of uranyl nitrate

A 1,1' bis(diphenylphosphino ferrocene) dioxide complex of uranyl nitrate was synthesized and characterized by IR, H-1 and P-31{H-1} NMR spectroscopic and X-ray diffraction methods. The structure of the compound shows that the uranium atom is surrounded by eight oxygen atoms in a hexagonal bi-pyramidal geometry. Two oxygen atoms from 1,1' bis(diphenylphosphino ferrocene) dioxide ligand and four oxygen atoms from the nitrate groups form a planar hexagon. The two uranyl oxygen atoms occupy the axial position. The 1,1' bis(diphenylphosphino ferrocene) dioxide ligand acts as a bidentate chelating ligand with a bite angle of 71.56(8)degrees around the uranium(VI) atom, which is much smaller in value compare to any of the previously reported values (90.1 degrees-154.0 degrees) for this ligand.

Appraiser behaviour and appraisal smoothing: some qualitative and quantitative evidence

There is a substantial literature which suggests that appraisals are smoothed and lag the true level of prices. This study combines a qualitative interview survey of the leading fund manager/owners in the UK and their appraisers with a empirical study of the number of appraisals which change each month within the IPD Monthly Index. The paper concentrates on how the appraisal process operates for commercial property performance measurement purposes. The survey interviews suggest that periodic appraisal services are consolidating in fewer firms and, within these major firms, appraisers adopt different approaches to changing appraisals on a period by period basis, with some wanting hard transaction evidence while others act on "softer' signals. The survey also indicates a seasonal effect with greater effort and information being applied to annual and quarterly appraisals than monthly. The analysis of the appraisals within the Investment Property Databank Monthly Index confirms this effect with around 5% more appraisals being moved at each quarter day than the other months. January and August have significantly less appraisal changes than other months.

Conformational studies of mixed-ligand copper(II) chelates. Crystal and molecular structure of (N,N-dimethyl-N′-ethyl-1,2-diaminoethane-(1-phenyl-1,3,-butanedionato)copper(II) perchlorate

The IR and ligand field spectra and the structure of the mixed-ligand compound [N,N-dimethyl-N′-ethyl-1,2-diaminoethane(1-phenyl-1,3-butanedionato)(perchlorato)copper(II)]), [Cu(dmeen)bzac(OClO3)], are reported. The structure was determined by single crystal X-ray diffraction analysis (triclinic, space group ). The structure is square pyramidal with the apical position occupied by one oxygen of the tetrahedral perchlorato group (distance from copper 2.452(5) Å). The plane of the phenyl ring is tilted forming an angle of 16.72(14)° with the plane of the β-dionato moiety. The nitrogenous base adopts the gauche conformation with torsional angle of 108.72(14)°. The ethyl group is cis oriented relative to the phenyl group, occupying the equatorial position with the vector of the carbon-nitrogen bond forming an angle of 143.9(3)° with the CuNN plane. The interactions of the adjacent axial hydrogen with an oxygen of the perchlorato group result in hydrogen bond formation. The IR spectra reveal that in the solid state the Br− or Cl− displace easily the ClO4− group. The shifts in the ligand field spectra indicate that polar solvents participate in donor-acceptor interactions with the metal centre along an axis perpendicular to the CuN2O2 plane.

The synthesis and properties of [Fe3(CO)11(RCN)] derivatives, and a high-yield general route to mono- and di-substituted derivatives of [Fe3(CO)12]; the crystal and molecular structure of [Fe3(CO)11(NCC6H4-2-Me)]

The clusters [Fe3(CO)11(RCN)] (1: R = Me, C3H5, C6H5, or C6H4-2-Me) have been prepared at low temperature from [Fe3(CO)12] and RCN in the presence of Me3NO. Compounds 1 react essentially quantitatively with a wide range of two-electron donors, L, (viz.: CO, PPh3, P(OMe)3, PPh2H, PPh2Me, PF3, CyNC (Cy = cyclohexyl), P(OEt)3, SbPh3, PBu3, AsPh3, or SnR2 (R = CH(SiMe3)2)) to give [Fe3(CO)11L] (2). In some cases (2), on treatment with Me3NO and then L′ (L′ = a second two-electron donor) yields [Fe3(CO)10LL′] in high yield. The crystal and molecular structures of 1 (L = NCC6H4Me-2) have been determined by a full single crystal structure analysis, and shown to have an axial nitrile coordinated at the unique iron atom, with two CO groups bridging the other two metal atoms.

A hydrogen-1 nuclear magnetic resonance, mass spectral and extended Hückel study of some olefin complexes of rhodium(I) and iridium(I) and the crystal and molecular structure of η4-2,4-dimethylpenta-1,4-diene(η5-formylcyclopentadienyl)rhodium(I)

A 1H NMR study of monosubstituted η-cyclopentadienyl-rhodium(I) complexes of type LLRh(C5H4X) and -iridium(I) complexes of type L2Ir(C5H4X) (L = ethene, LL = 1,3- or 1,5-diolefin; X = C(C6H5)3, CHO, or COOCH3) has been carried out. For complexes of both metals in which the neutral ligand is ethene or a non-conjugated diolefin the NMR spectra of the cyclopentadienyl protons are unusual in that H(2), H(5) resonate to high field either at room temperature or below. The corresponding NMR spectra for the cyclopentadienyl ring protons of complexes where the neutral ligand is a conjugated diene are, with one exception, normal. A single crystal X-ray structural analysis of (η4-2,4-dimethylpenta-1,4-diene)(η5-formylcyclopentadienyl)rhodium(I) (which exhibits an abnormal 1H NMR spectrum) reveals substantial localisation of electron density in the C(3)C(4) Cp ring bond (1.283(33) Å) which may be consistent with a contribution from an ‘allyl-ene’ rotamer to the ring—metal bonding scheme. An extended Hückel calculation with self consistent charge iteration was performed on this complex. The results predict a greater Mulliken overlap population for the C(3)C(4) bond in the cyclopentadienyl ring and show that the localisation is dependent on both the Cp ring substituent and the nature of the diolefin. The mass spectral fragmentation patterns of some representative diene complexes of iridium(I) and rhodium(I) are presented.

Metal cluster expansion by addition of low-valent group 4B reagents: crystal and molecular structure of [Os3SnH2(CO)10{CH(SiMe3)2}2]; a compound with hydrogen bridging osmium and tin

Cluster expansion of [Os3H2(CO)10] with [SnR2][R = CH(SiMe3)2] take place in high yield to give [Os3SnH2(CO)10R2], the first closed triosmium–main-group metal cluster to be structurally characterized; a novel feature is the presence of a hydrogen atom bridging the tin atom and one of the osmium atoms.

Alkenyl derivatives of the metals. Oxidative addition to intermediate tin(II) alkenyls; isolation, and crystal and molecular structure of n-butyltris(triphenylethenyl)tin(IV)

Reaction of tin(II) chloride with Li(CPhCPh2) at –78 °C in diethyl ether–hexane–tetrahydrofuran affords a deep red solution whose colour fades on warming, and which we believe contains the (unstable) first dialkenyltin(II) species. The latter survives long enough at low temperatures to undergo intermolecular oxidative addition, and one such adduct leads ultimately to the formation of Sn(CPhCPh2)3Bun, which has been fully characterised including a crystal and molecular structure study. The mechanism of formation of the final product has been examined and results are reported.

Spectroscopic properties of alkenylferrocenes; crystal and molecular structure of (Z)-(1,2-diphenylethenyl)ferrocene

Studies of the 1H n.m.r. and electronic spectra of a series of alkenylferrocenes including (E) and (Z) stereoisomers of various styrylferrocenes, have provided methods of structure elucidation. Crystals of the title compound are monoclinic, space group P21/c with Z= 4 in a unit cell of dimensions a= 17.603(2), b= 10.218(2), c= 10.072 Å, β= 103.27(2)°. The structure has been determined by the heavy-atom method from diffractometer data and refind by full-matrix least-squares techniques to R= 0.043 for 2 219 unique reflections.

Synthesis and X-ray crystal and molecular structure of tetrakis(2,2-dimethyl-1-phenylethenyl)chromium(IV), the first structurally-characterised homoleptic alkenyl compound of a transition metal

The title compound, the first homoleptic Group 6A metal alkenyl, has been prepared from CrCl3·3(thf), and its properties, including X-ray crystal structure determination, are reported.