Nevanlinna functions as quotients

Let be a holomorphic function in the unit ball. Then is a Nevanlinna function if and only if there exist Smirnov functions , such that and has no zeros in the ball.

     

Nanosized Au4Pd32(CO)28(PMe3)14 Containing a Highly Distorted Encapsulated Au4 Tetrahedron: Proposed Multi-Twinned Growth-Pattern from Two Deformed Au-Centered Double Icosahedral-Based Fragments*

As part of an extensive effort to synthesize a variety of nanosized gold–palladium carbonyl phosphine clusters, the neutral Au₄Pd₃₂(CO)₂₈(PMe₃)₁₄ (1) was isolated and unambiguously characterized by low-temperature CCD X-ray diffraction and IR measurements. This nanosized Au₄Pd₃₂ cluster was prepared in low yields (<5%) from the room-temperature reaction of Pd₁₀(CO)₁₂(PMe₃)₆ (2) with Au(SMe₂)Cl in THF/acetone. The heretofore unknown molecular geometry of 1 of pseudo-D₂ (222) symmetry (without methyl substituents) may be viewed to arise from a relatively strong (Au–Au)-bonded linkage (2.64 Å (av)) of two pentagonal-bipyramidal (μ₅-Au)(μ₅-Pd)Pd₅ polyhedra; this generated 14-atom Au₂Pd₁₂ unit may be considered as a markedly deformed part of a 19-atom Au-centered double icosahedron without the inner pentagon (corresponding to five missing inner atoms). In turn, two Au₂Pd₁₂ units form a central composite-twinned Au₄Pd₂₂ kernel via vertex-fusion of two common Pd atoms along with additional formation of four Pd–Pd bonding, four Au–Pd bonding, and two weaker secondary Au–Au bonding interactions at 2.90 Å (av) (versus the other two diagonal Au–Au nonbonding ones at 3.51 Å (av)); this resulting Au₄Pd₂₂P₈ kernel is augmented by the addition of two triangular Pd₃P core-fragments and four exopolyhedral PdP groups to give the Au₄Pd₃₂P₁₄ framework of 1. This cluster is stabilized by 28 bridging COs, of which 20 are doubly bridging and 8 triply bridging. The largest metal-core diameter of 1 along one pseudo C₂ axis is 1.1 nm. This new type of multi-twinned metal cluster has direct relevance to both ligated and non-ligated (naked) non-crystalline metal nanoparticles, many of which possess multiple twinning and/or disorder.^*Dedicated to Professor F. A. Cotton on the occasion of his 75th birthday in recognition of numerous seminal contributions to modern Inorganic Chemistry. Professor Cotton has a truly unparalleled scientific career in Inorganic Chemistry in terms of the overall composite effects of his highly prolific research productivity, his tremendous impact on former graduate students, postdoctoral associates, and collaborators, and his matchless textbooks/monographs.     

The mechanism of tin-promoted electrochemical oxidation of organic substances on platinum

The promoting action of tin in the binary system platinum tin has been studied. A direct correlation of polarization and adsorption measurements has been carried out using an adsorption method of applying the promoter. The method of fast potentiodynamic pulses has been used to control the amount of tin and organic species on the surface. Studies have been made with smooth and platinized electrodes on the adsorption and oxidation of formic acid and methanol. A comparison of electro-oxidation rates at constant organic species coverage has made it possible to reveal the true catalytic effect as a result of introduction of tin. This effect has been found to be independent of both the nature of the substance under oxidation and the state of the electrode surface (smooth or rough). The promoting effect of tin is observed in the reactions where the limiting stage is represented by R+OH_ads; in the reactions where the limiting stage is represented by electron transfer or else the interaction R+H_ads, the promoting effect of tin does not show up, which fact points to the selectivity of its catalytic action.     

Generalized scheme of chemisorption,electrooxidation and electroreduction of simple organic compounds on platinum group metals

A generalized scheme of successive stages for chemisorption, electrooxidation and electroreduction of simple organic compounds from methane to CO₂ on platinum group metals has been developed on the basis of experimental data. The actual pathway of electrooxidation or electroreduction of an organic compound and the yield of the reaction products depend on the ratio between the rates of individual steps which, in their turn, are determined by various factors (potential, temperature, coverage of the surface with H_ads and OH_ads, with reacting and intermediate organic particles, as well as with foreign particles). The accumulation of chemisorbed compounds on the electrode surface depends on the relationship between the rates of their formation and subsequent transformation.     

Inner Mappings, Hyperbolic Gradients and Composition Operators

Let φ be a holomorphic mapping between complex unit balls. We obtain quantitative versions of the following heuristic principle: if the hyperbolic gradient of φ does not grow sufficiently rapidly, then φ is far from being inner.     

Speciation in strongly acidic metastable solutions of oxotungstate(vi) compounds

The ionic composition of long-lived metastable aqueous solutions of oxo compounds of tungsten(IV) with pH ≤ 1 was studied by spectrophotometry. The nature of some isopolytung-states formed in these solutions in the presence of various inorganic acids (HCl, HClO₄, HNO₃, H₂SO₄, and H₂SeO₄) was established.     

Approximation of average cost optimal policies for general Markov decision processes with unbounded costs

The aim of the paper is to show that Lyapunov-like ergodicity conditions on Markov decision processes with Borel state space and possibly unbounded cost provide the approximation of an average cost optimal policy by solvingn-stage optimization problems (n = 1, 2, ...). The used approach ensures the exponential rate of convergence. The approximation of this type would be useful to find adaptive procedures of control and to estimate stability of an optimal control under disturbances of the transition probability.Research supported in part by Consejo Nacional de Ciencia y Tecnologia (CONACYT) under grant 0635P-E9506.Research supported by Fondo del Sistema de Investigatión del Mar de Cortés under Grant SIMAC/94/CT-005.     

Certaines méthodes de sommation de séries de Fourier donnant le meilleur ordre d'approximation

Sans résumé     

Unexpected bond activation of small organic molecules on a metal oxide-butane/CaO(100)

We present the first example of bond activation of small alkanes (n-/iso-butane) on a metal oxide surface-CaO(100)-at ultra-high vacuum (UHV) conditions and at low surface temperatures studied by molecular beam scattering and thermal desorption spectroscopy.