Iterated hard-thresholding for linear inverse problems with sparsity constraints

We describe an iterative algorithm for the minimization of Tikhonov type functionals which involve sparsity constraints in form of ℓ^p -penalties which have been proposed recently for the regularization of ill-posed problems. In contrast to the well-known algorithm considered by Daubechies, Defrise and De Mol, it uses hard instead of soft thresholding. This hard thresholding algorithm is based on the generalized conditional gradient method. General results on the convergence of the generalized conditional gradient method enable us to prove strong convergence of the iterates. Furthermore we are able to establish convergence rates of O (n^–1/2) and O (λⁿ) for p = 1 and 1 < p ≤ 2 respectively. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Catalytic Oxidative Quinone Heterofunctionalization Method: Synthesis of Strongylophorine‐26

The preparation of heteroatom‐substituted p‐quinones is ideally performed by direct addition of a nucleophile followed by in situ reoxidation. Albeit an appealing strategy, the reactivity of the p‐quinone moiety is not easily tamed and no broadly applicable method for heteroatom functionalization exists. Shown herein is that Co(OAc)₂ and Mn(OAc)₃?2 H₂O act as powerful catalysts for oxidative p‐quinone functionalization with a collection of O, N, and S nucleophiles, using oxygen as the terminal oxidant. Preliminary mechanistic observations and the first synthesis of the cytotoxic natural product strongylophorine‐26 is presented.     

Some stability results for explicit Runge-Kutta methods

The theory of positive real functions is used to provide bounds for the largest possible disk to be inscribed in the stability region of an explicit Runge-Kutta method. In particular, we show that the closed disk |+r| r can be contained in the stability region of an explicitm-stage Runge-Kutta method of order two if and only ifr m – 1.     

Synthesis,solution dynamics and chemical vapour deposition of heteroleptic zinc complexes via ethyl and amide zinc thioureides

Ethyl and amide zinc thioureides [L¹ZnEt]₂ (1), [L¹*ZnEt]₂ (2) and [L¹Zn(N(SiMe₃)₂)]₂ (3) have been synthesised from the equimolar reaction of thiourea ligands (HL¹ = ⁱPrN(H)CSNMe₂ and HL¹* = PhN(H)CSNMe₂) with diethyl zinc and zinc bis[bis(trimethylsilyl)amide] respectively. New routes towards heteroleptic complexes have been investigated through reactions of 1, 2 and 3 with β-ketoiminates (HL² = [(Me)CN(H){ⁱPr}–CHC(Me) O]), bulky aryl substituted β-diiminates (HL³ = [(Me)CN(H){Dipp}–CHC(Me) N{Dipp}] (Dipp = diisopropylphenyl) and HL³* = [(Me)CN(H){Dep}–CHC(Me) N{Dep}] (Dep = diethylphenyl)) and donor-functionalised alcohols (HL⁴ = Et₂N(CH₂)₃OH and HL⁴* = Me₂N(CH₂)₃OH) and have led to the formation of the heteroleptic complexes [L¹*ZnL³*] (5), [L¹ZnL⁴]₂ (6), [L¹ZnL⁴*]₂ (7), [L¹*ZnL⁴] (8) and [L¹*ZnL⁴*] (9). All complexes have been characterised by ¹H and ¹³C NMR, elemental analysis, and the X-ray structures of HL¹*, 1, 2, 6 and 7 have been determined via single crystal X-ray diffraction. Variable temperature ¹H, COSY and NOESY NMR experiments investigating the dynamic behaviour of 5, 6 and 7 have shown these molecules to be fluxional. On the basis of solution state fluxionality and thermogravimetric analysis (TGA), alkoxyzinc thioureides 6 and 7 were investigated as single-source precursors for the deposition of the ternary material zinc oxysulfide, Zn(O,S), a buffer layer used in thin film photovoltaic devices. The aerosol-assisted chemical vapour deposition (AACVD) reaction of 7 at 400 °C led to the deposition of the heterodichalcogenide material Zn(O,S), which was confirmed by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS) and energy dispersive X-ray analysis (EDX), with optical properties investigated using UV/vis spectroscopy, and surface morphology and film thickness examined using scanning electron microscopy (SEM).

This work investigates the synthesis and solution dynamics of heteroleptic alkoxyzinc thioureides for the chemical vapour deposition of the heterochalcogenide material Zn(O,S).     

Refractive index of liquid water in different solvent models

We present a combined molecular dynamics/quantum chemical perturbation method for calculating the refractive index of liquid water at different temperatures. We compare results of this method with the refractive index obtained from other solvent models. The best agreement with the experimental refractive index of liquid water and its temperature dependence is obtained using correlated gas-phase polarizabilities in the classical Lorentz-Lorenz expression. Also, the iterative self-consistent reaction field approach in the semicontinuum implementation matches the experimental refractive index reasonably well.     

Powder diffraction study of a coordination polymer comprised of rigid building blocks: [Rh2(O2CCH3)4.mu2-Se2C5H8-Se,Se']infinity

The crystal structure of a new hybrid product comprised of two rigid building blocks, namely dirhodium(II) tetraacetate, [Rh(2)(O(2)CCH(3))(4)] (1), and 2,6-diselenaspiro[3.3]heptane, Se(2)C(5)H(8) (2), has been solved ab initio using laboratory source X-ray powder diffraction (XRPD) data. The rigid body refinement approach has been applied to assist in finding an adequate model and to reduce the number of the refined parameters. Complex [Rh(2)(O(2)CCH(3))(4).mu(2)-Se(2)C(5)H(8)-Se,Se'] (3) conforms to the triclinic unit cell with lattice parameters of a = 8.1357(4), b = 8.7736(4), and c = 15.2183(8) A, alpha = 77.417(3), beta = 88.837(3), and gamma = 69.276(4) degrees, V = 989.66(8) A(3), and Z = 2. The centrosymmetric P space group was selected for calculations. The final values of the reduced wR(p), R(p), and chi(2) were calculated at 0.0579, 0.0433, and 5.95, respectively. The structure of 3 is a one-dimensional zigzag polymer built on axial Rh...Se interactions at 2.632(6) A. The 2,6-diselenaspiro[3.3]heptane ligand acts as a bidentate linker bridging dirhodium units via both selenium atoms. The geometrical parameters of individual groups for rigid body refinement have been obtained from X-ray powder data for dirhodium(II) tetraacetate (1) and from single-crystal X-ray diffraction for diselenium molecule 2. The crystal structures of 1 and 2 are reported here for the first time. For 1 indexing based on XRPD data has resulted in the triclinic unit cell P with lattice parameters of a = 8.3392(7), b = 5.2216(5), and c = 7.5264(6) A, alpha = 95.547(10), beta = 78.101(6), and gamma = 104.714(13) degrees, V = 309.51(5) A(3), and Z = 1. The final values were wR(p) = 0.0452, R(p) = 0.0340, and chi(2) = 1.99. The 1D polymeric motif built on axial Rh.O interactions of the centrosymmetric dirhodium units has been confirmed for the solid-state structure of 1. Compound 2,6-diselenaspiro[3.3]heptane (2) conforms to the monoclinic space group P2(1)/c with the unit cell parameters of a = 5.9123(4), b = 19.6400(13), and c = 5.8877(4) A, beta = 108.5500(10) degrees, V = 648.15(8) A(3), and Z = 4.     

Catalytic enantioselective transamination of alpha-keto esters: an organic approach to enzymatic reactions

The half-transamination reaction of alpha-keto esters with pyridoxamine or 4-picolylamine was found to be catalysed by different metal catalysts in organic solvents giving moderate yields and enantioselectivities of up to 37% ee for methyl-3-indole pyruvate.