On the Cowen-Douglas Class for Banach Space Operators

In [3], M. J. Cowen and R. G. Douglas prove that the adjoint of a Hilbert space operator T is in the class if and only if T is unitarily equivalent with the operator M _z on a Hilbert space -valued analytic functions, where M _z denotes the operator of multiplication by the independent variable. The proof involves holomorphic vector bundles and Grauert’s theorem. In this paper we use a theorem by I. Gohberg and L. Rodman [4] to give a more elementary proof of this fact, which also works for Banach space operators.      

Shaper-assisted full-phase characterization of UV pulses without a spectrometer

A full-phase measurement of low-energy femtosecond UV pulses is presented. The method relies on phase retrieval of measured sonogram traces and is greatly simplified by a two-dimensional shaper-assisted cross correlation setup. As all required pulses are generated by the pulse shaper, the method is free of external references and additional tunable filter setups.     

An efficient and robust numerical algorithm for estimating parameters in Turing systems

We present a new algorithm for estimating parameters in reaction–diffusion systems that display pattern formation via the mechanism of diffusion-driven instability. A Modified Discrete Optimal Control Algorithm (MDOCA) is illustrated with the Schnakenberg and Gierer–Meinhardt reaction–diffusion systems using PDE constrained optimization techniques. The MDOCA algorithm is a modification of a standard variable step gradient algorithm that yields a huge saving in computational cost. The results of numerical experiments demonstrate that the algorithm accurately estimated key parameters associated with stationary target functions generated from the models themselves. Furthermore, the robustness of the algorithm was verified by performing experiments with target functions perturbed with various levels of additive noise. The MDOCA algorithm could have important applications in the mathematical modeling of realistic Turing systems when experimental data are available.     

The NiII,HgII and CuII complexes of 12‐membered‐ring mixed‐donor macrocycles

The structures of di­aqua(1,7‐dioxa‐4‐thia‐10‐aza­cyclo­do­decane)­nickel dinitrate, [Ni(C₈H₁₇NO₂S)(H₂O)₂](NO₃)₂, (I), bis­(nitrato‐O,O′)(1,4,7‐trioxa‐10‐aza­cyclo­do­decane)­mercury, [Hg(NO₃)₂(C₈H₁₇NO₃)], (II), and aqua­(nitrato‐O)(1‐oxa‐4,7,10‐tri­aza­cyclo­do­decane)copper nitrate, [Cu(NO₃)(C₈H₁₉N₃O)(H₂O)]NO₃, (III), reveal each macrocycle binding in a tetradentate manner. The conformations of the ligands in (I) and (III) are the same and distinct from that identified for (II). These differences are in agreement with molecular‐mechanics predictions of ligand conformation as a function of metal‐ion size.     

Crystal structure,dimensionality, and 4d electron distribution in K0.30MoO3 and Rb0.30MoO3

Single crystals of K_0.30MoO₃ and Rb_0.30MoO₃ were synthesized by electrolytic reduction of MoO₃/ A₂MoO₄ melts. The crystal structures were refined from X-ray diffraction data (3265 and 1280 independent reflections, respectively). The finalR andwR factors were 0.037 and 0.047 for the K bronze and 0.031 and 0.033 for the Rb bronze. The lattice parameters of the body-centered cells used in the present refinements were: K_0.30Mo0₃,a = 16.2311(7),b = 7.5502(4),c = 9.8614(4)A?,β = 94.895(4)^o; Rb_0.30MoO₃,a = 16.361(3),b = 7.555(1),c = 10.094(2)A?,β = 93.87(5)^o. The 4d electron distribution over the 20 Mo sites [4Mo(1), 8Mo(2), 8Mo(3)] of the unit cell are 10, 45, and 45% for K_0.30Mo0₃ and 14, 43, and 43% for Rb_0.30MoO₃, respectively. In both cases about 90% of the 4d electrons are situated on those sites which contribute to the electrical conductivity. The variations of the lattice parameters versus temperature are reported. The thermal linear-expansion coefficient is highly anisotropic. The structural dimensionality depends upon the sublattice under consideration. The K, Mo, and O sublattices are mono-, two-, and three-dimensional, respectively. The relationship between the structural dimensionality of K_0.30MoO₃ and the physical properties is discussed.     

Ring Enlargement of Three-Membered Heterocycles by Treatment with In Situ Formed Tricyanomethane

Although the chemistry of elusive tricyanomethane (cyanoform) has been studied during a period of more than 150 years, this compound has very rarely been utilized in the synthesis or modification of heterocycles. Three-membered heterocycles, such as epoxides, thiirane, aziridines, or 2H-azirines, are now treated with tricyanomethane, which is generated in situ by heating azidomethylidene-malonodinitrile in tetrahydrofuran at 45 °C or by adding sulfuric acid to potassium tricyanomethanide. This leads to ring expansion with formation of 2-(dicyanomethylidene)oxazolidine derivatives or creation of the corresponding thiazolidine, imidazolidine, or imidazoline compounds and opens up a new access to these push–pull-substituted olefinic products. The regio- and stereochemistry of the ring-enlargement processes are discussed, and the proposed reaction mechanisms were confirmed by using ¹⁵N-labeled substrates. It turns out that different mechanisms are operating; however, tricyanomethanide is always acting as a nitrogen-centered nucleophile, which is quite unusual if compared to other reactions of this species.     

Effect of nitrogen adsorption on the mid-infrared spectrum of water clusters

Experimental Fourier-transform infrared spectra and DFT calculated infrared spectra are compared to investigate the effect of adsorbed nitrogen on the OH-stretch band complex of water clusters. Using a collisional cooling experiment, pure as well as partially and completely N(2)-covered water clusters consisting of 20-200 water molecules have been generated in thermal equilibrium in the aerosol phase within the temperature range of 5-80 K. Computational IR-spectra simulations have been performed for discrete pure and N(2)-covered water clusters including 10, 15, 20, and 30 water molecules. The adsorbed N(2) molecules especially affect the three-coordinated water molecules at the cluster surface which could be observed as a blue shift of the companion O-H band at 2900 cm(-1) and a red shift of the dangling O-H band at 3700 cm(-1) by about 20 cm(-1) in both cases. The most striking effect of the N(2) adsorbate is an intensity increase of the dangling O-H band by a factor of 3-5. Furthermore, the onset temperature of nitrogen adsorption at the water cluster surface was experimentally found to be roughly 30 K for cluster sizes of about 100 water molecules. Experimental and computational results are in good agreement. The presented results are based on and support the work of V. Buch, J. P. Devlin, and co-workers (e.g., J. Phys. Chem. B, 1997; J. Phys. Chem. A, 2003; Int. Rev. Phys. Chem., 2004).     

Solvent release upon ion association from entropy data

The translational entropy loss on the association of two ions to form an ion pair or 11 complex is overcompensated by a rotational entropy gain, an electrostatic entropy gain, and an entropy gain due to solvent release from translational immobilization. The first three effects can be calculated, leaving the fourth as a difference from the experimental entropy change on association. The ratio of the solvent release entropy gain to the entropy change on melting of the solvent indicates the number of solvent molecules released on the association. A similar value is obtained from data for the volume change on association.Presented as a poster at the 10th International Conference on Non-Aqueous Solvents (ICNAS) at Leuven, Belgium, August 1986, and at the 24th International Congress on Coordination Chemistry (ICCC) at Athens, Greece, August 1986.