The Essential Norm of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions

For a wide class of radial weights we calculate the essential norm of a weighted composition operator uC_j{uC_\varphi} on the weighted Banach spaces of analytic functions in terms of the analytic function u \colon \mathbb D ? \mathbb C{u \colon \mathbb D \to \mathbb C} and the nth power of the analytic selfmap j{\varphi} of the open unit disc \mathbb D{\mathbb D} . We also apply our result to calculate the essential norm of composition operators acting on Bloch type spaces with general radial weights.     

The Altshuler–Shklovskii Formulas for Random Band Matrices I: the Unimodular Case

Communications in Mathematical Physics - We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We show that the correlation function of the local eigenvalue...     

On Synge-type angle condition for <Emphasis Type="Italic">d</Emphasis>-simplices

The maximum angle condition of J. L. Synge was originally introduced in interpolation theory and further used in finite element analysis and applications for triangular and later also for tetrahedral finite element meshes. In this paper we present some of its generalizations to higher-dimensional simplicial elements. In particular, we prove optimal interpolation properties of linear simplicial elements in ? ^d that degenerate in some way.     

Fourier's law from closure equations

We sketch a rigorous derivation of Fourier's law from a system of closure equations for a nonequilibrium stationary state of a Hamiltonian system of coupled oscillators subjected to heat baths on the boundary. The local heat flux is proportional to the temperature gradient with a temperature dependent heat conductivity and the stationary temperature exhibits a nonlinear profile.     

F‐bridged Anions of Bromine and Gold: Predictions of Unexpected Behavior

The significant similarity between MF₃, MF₄^–, and M₂F₇^– (M = Au, Br) is studied using quantum chemical methods. It is expected that compounds containing Au₃F₁₀^– anions are likely to be stable. A theoretical background for the ongoing attempts of their synthesis is provided by calculations on the stabilities and molecular structures of various bromine and gold anions with the general composition of M_nF_3n+1^– (n = 1, 2, 3, 4). The anions show unexpected differences and peculiarities in their energetically preferable molecular structures. Different chain‐like structures are predicted as the global minima for the hypothetical Au₃F₁₀^– and Br₄F₁₃^– anions.     

Intensely luminescent homoleptic alkynyl decanuclear gold(I) clusters and their cationic octanuclear phosphine derivatives

Treatment of Au(SC(4)H(8))Cl with a stoichiometric amount of hydroxyaliphatic alkyne in the presence of NEt(3) results in high-yield self-assembly of homoleptic clusters (AuC(2)R)(10) (R = 9-fluorenol (1), diphenylmethanol (2), 2,6-dimethyl-4-heptanol (3), 3-methyl-2-butanol (4), 4-methyl-2-pentanol (4), 1-cyclohexanol (6), 2-borneol (7)). The molecular compounds contain an unprecedented catenane metal core with two interlocked 5-membered rings. Reactions of the decanuclear clusters 1-7 with gold-diphosphine complex [Au(2)(1,4-PPh(2)-C(6)H(4)-PPh(2))(2)](2+) lead to octanuclear cationic derivatives [Au(8)(C(2)R)(6)(PPh(2)-C(6)H(4)-PPh(2))(2)](2+) (8-14), which consist of planar tetranuclear units {Au(4)(C(2)R)(4)} coupled with two fragments [AuPPh(2)-C(6)H(4)-PPh(2)(AuC(2)R)](+). The titled complexes were characterized by NMR and ESI-MS spectroscopy, and the structures of 1, 13, and 14 were determined by single-crystal X-ray diffraction analysis. The luminescence behavior of both Au(I)(10) and Au(I)(8) families has been studied, revealing efficient room-temperature phosphorescence in solution and in the solid state, with the maximum quantum yield approaching 100% (2 in solution). DFT computational studies showed that in both Au(I)(10) and Au(I)(8) clusters metal-centered Au → Au charge transfer transitions mixed with some π-alkynyl MLCT character play a dominant role in the observed phosphorescence.     

Intercomparison exercise on difficult to measure radionuclides in activated concrete—statistical analysis and comparison with activation calculations

Journal of Radioanalytical and Nuclear Chemistry - This paper reports the results obtained in a Nordic Nuclear Safety Research project during the second intercomparison exercise for the...     

Photochemistry with Chlorine Trifluoride: Syntheses and Characterization of Difluorooxychloronium(V) Hexafluorido(non)metallates(V), [ClOF2][MF6] (M=V,Nb, Ta,Ru, Os,Ir, P,Sb)

A photochemical route to salts consisting of difluorooxychloronium(V) cations, [ClOF₂]⁺, and hexafluorido(non)metallate(V) anions, [MF₆]⁻ (M=V, Nb, Ta, Ru, Os, Ir, P, Sb) is presented. As starting materials, either metals, oxygen and ClF₃ or oxides and ClF₃ are used. The prepared compounds were characterized by single-crystal X-ray diffraction and Raman spectroscopy. The crystal structures of [ClOF₂][MF₆] (M=V, Ru, Os, Ir, P, Sb) are layer structures that are isotypic with the previously reported compound [ClOF₂][AsF₆], whereas for M=Nb and Ta, similar crystal structures with a different stacking variant of the layers are observed. Additionally, partial or full O/F disorder within the [ClOF₂]⁺ cations of the Nb and Ta compounds occurs. In all compounds reported here, a trigonal pyramidal [ClOF₂]⁺ cation with three additional Cl⋅⋅⋅F contacts to neighboring [MF₆]⁻ anions is observed, resulting in a pseudo-octahedral coordination sphere around the Cl atom. The Cl−F and Cl−O bond lengths of the [ClOF₂]⁺ cations seem to correlate with the effective ionic radii of the M^V ions. Quantum-chemical, solid-state calculations well reproduce the experimental Raman spectra and show, as do quantum-chemical gas phase calculations, that the secondary Cl⋅⋅⋅F interactions are ionic in nature. However, both solid-state and gas-phase quantum-chemical calculations fail to reproduce the increases in the Cl−O bond lengths with increasing effective ionic radius of M in [MF₆]⁻ and the Cl−O Raman shifts also do not generally follow this trend.     

A Facile Molecular Machine: Optically Triggered Counterion Migration by Charge Transfer of Linear Donor‐π‐Acceptor Phosphonium Fluorophores

The D‐π‐A type phosphonium salts in which electron acceptor (A=‐⁺PR₃) and donor (D=‐NPh₂) groups are linked by polarizable π‐conjugated spacers show intense fluorescence that is classically ascribed to excited‐state intramolecular charge transfer (ICT). Unexpectedly, salts with π=‐(C₆H₄)_n‐ and ‐(C₁₀H₆C₆H₄)‐ exhibit an unusual dual emission (F₁ and F₂ bands) in weakly polar or nonpolar solvents. Time‐resolved fluorescence studies show a successive temporal evolution from the F₁ to F₂ emission, which can be rationalized by an ICT‐driven counterion migration. Upon optically induced ICT, the counterions move from ‐⁺PR₃ to ‐NPh₂ and back in the ground state, thus achieving an ion‐transfer cycle. Increasing the solvent polarity makes the solvent stabilization dominant, and virtually stops the ion migration. Providing that either D or A has ionic character (by static ion‐pair stabilization), the ICT‐induced counterion migration should not be uncommon in weakly polar to nonpolar media, thereby providing a facile avenue for mimicking a photoinduced molecular machine‐like motion.