Remarks on a simple optimal control problem with monotone control functions

We consider the minimization of the mean-square deviation of a prescribed function from the class of monotone functions. Two problems are considered. The first problem places no restriction on the initial value of the controls, while the second problem assumes that all the control functions must start at a fixed initial value. Optimal controls are exhibited in both problems. Finally, we consider the situation with general payoff and dynamics and give the heuristic characterization of the value function for such problems.     

Poly(vinylpyrrolidone)‐stabilized silver nanoparticles for strained‐silicon surface enhanced Raman spectroscopy

Poly(vinylpyrrolidone)‐stabilized silver nanoparticles deposited onto strained‐silicon layers grown on graded Si_1−xGe_x virtual substrates are utilized for selective amplification of the Si–Si vibration mode of strained silicon via surface‐enhanced Raman scattering spectroscopy. This solution‐based technique allows rapid, highly sensitive and accurate characterization of strained silicon whose Raman signal would usually be overshadowed by the underlying bulk SiGe Raman spectra. The analysis was performed on strained silicon samples of thickness 9, 17.5 and 42 nm using a 488 nm Ar⁺ micro‐Raman excitation source. The quantitative determination of strained‐silicon enhancement factors was also made. Copyright © 2011 John Wiley & Sons, Ltd.     

Molecular structure of (tBu)3Al[O=C(OPh)2]

The molecular structure of (^tBu)₃Al[O=C(OPh)₂] has been determined. The increase in the C=O bond distance [1.258(4) Å] when compared to free O=C(OPh)₂ [1.191(3) Å], is presented in respect to the activating ability of aluminum Lewis acids. Crystal data: monoclinic, P2₁/n, a = 10.653(2), b = 18.486(4), c = 14.551(3) Å, = 108.07(3)°, and V = 2724.3(9) ų for Z = 4.     

Post‐Synthetic Ligand Exchange in Zirconium‐Based Metal–Organic Frameworks: Beware of The Defects!

Post‐synthetic ligand exchange in the prototypical zirconium‐based metal–organic framework (MOF) UiO‐66 was investigated by in situ solution ¹H NMR spectroscopy. Samples of UiO‐66 having different degrees of defectivity were exchanged using solutions of several terephthalic acid analogues in a range of conditions. Linker exchange only occurred in defect‐free UiO‐66, whereas monocarboxylates grafted at defect sites were found to be preferentially exchanged with respect to terephthalic acid over the whole range of conditions investigated. A 1:1 exchange ratio between the terephthalic acid analogue and modulator was observed, providing evidence that the defects had missing‐cluster nature. Ex situ characterisation of the MOF powders after exchange corroborated these findings and showed that the physical‐chemical properties of the MOF depend on whether the functionalisation occurs at defective sites or on the framework.     

Three‐Dimensional Branched and Faceted Gold–Ruthenium Nanoparticles: Using Nanostructure to Improve Stability in Oxygen Evolution Electrocatalysis

Achieving stability with highly active Ru nanoparticles for electrocatalysis is a major challenge for the oxygen evolution reaction. As improved stability of Ru catalysts has been shown for bulk surfaces with low‐index facets, there is an opportunity to incorporate these stable facets into Ru nanoparticles. Now, a new solution synthesis is presented in which hexagonal close‐packed structured Ru is grown on Au to form nanoparticles with 3D branches. Exposing low‐index facets on these 3D branches creates stable reaction kinetics to achieve high activity and the highest stability observed for Ru nanoparticle oxygen evolution reaction catalysts. These design principles provide a synthetic strategy to achieve stable and active electrocatalysts.     

Molecular structure of [(tBu)2Al(3,5-Me2py)]2(μ-O): Preferential hydrolysis of an aluminum-aryl over an aluminum-alkyl

The structure of [(^tBu)₂Al(3,5-Me₂py)]₂(μ-O) has been determined as a consequence of the preferential hydrolytic cleavage of an Al–O versus an Al–C bond from the hydrolysis of the quinone bridged compound, [(^tBu)₂Al(3,5-Me₂py)]₂(μ-OC₆H₄O). The Al–O distance is 1.710(1) Å and the Al–O–Al angle is 180° because of crystallographic symmetry. Crystal data: triclinic, P $\overline 1$ , a = 9.334(2) Å, b = 10.639(2) Å, c = 10.661(2) Å, α = 112.65(3)°, β = 93.84(3)°, γ = 115.84(3)°, V = 843.4(3) ų, Z = 1, R = 0.0581, R _w = 0.1674.     

Molecular structure of AlH3[N(CH2CH2)3CH]2

Reaction of AlH₃[N(CH₂CH₂)₃CH] with hexamethyltrisiloxane, (OSiMe₂)₃, gives rise to the bis-quinuclidine complex AlH₃[N(CH₂CH₂)₃CH]₂, which has been characterized by ¹H and ¹³C NMR spectroscopy and X-ray crystallography. The molecular structure of AlH₃[N(CH₂CH₂)₃CH]₂ consists of a trigonal bipyramidal aluminum with axial coordination of the quinuclidine ligands. Crystal data: orthorhombic, space group Pbcn, a = 10.6895(9), b = 12.266(1), c = 12.3794(9) Å, V = 1623.2(2) ų, and Z = 4.     

Molecular structures of M(tfac)3 (M=Al, Co) and Cu(H2O)(fod)2: Examples of unusual supramolecular architecture

The molecular structures of Al(tfac)₃ (1), Co(tfac)₃ (2) (H-tfac = 1,1,1-trifluoroacetylacetone) and Cu(H₂O)(fod)₂ (3) (H-fod = 1,1,1,2,2,3,3-hepta-fluoro-7,7-dimethyloctane-4,6-dione) have been determined. The metal coordination spheres in compounds 1 and 2 are essentially the same as the respective M(acac)₃ derivatives. Despite the isomorphous nature of the structures of compounds 1 and 2, the identity of the nearest intermolecular van der Waals contacts are altered by minor changes in the metal coordination sphere. The geometry about copper in compound 3 is close to that of an ideal square bipyramid with the -diketonate ligands occupying the basal plane. The water ligand in each molecule of compound 3 is hydrogen bonded to an oxygen of a -diketonate ligand on an adjacent molecule resulting in the formation of dimers, which form rods along the y-axis due to weak C–F···Cu interactions. Crystal data: (1) orthorhombic, Pca2₁, a = 14.949(3), b = 19.806(4), c = 13.624(3) Å, V = 4033(1) ų, and Z = 8, and (2) orthorhombic, Pca2₁, a = 14.930(3), b = 19.620(4), c = 13.540(3) Å, V = 3966(1) ų, and Z = 8,; (3) monoclinic, P2₁/c, a = 12.447(3), b = 10.486(2) c = 21.980(4) Å, = 102.65(3)°, V = 2799(1) ų, and Z = 4.