Dirichletsche Reihen auf arithmetischen Progressionen

A characterisation of all real Δ≠0 is given, such that $$\overline {f(\sigma + i\Delta \mathbb{N})} = \overline {f(\sigma + i\mathbb{R})} $$ holds for all Dirichlet seriesf(s)=Σa _n n ^?s and all σ greater than the abscissa of absolute convergence off. For only countably many Δ relation (*) is not valid. By using transcendental results it is shown, that (*) holds in the special case, Δ=1.     

Synthesis and structural characterization of functionalized dimeric aluminophosphonates and a monomeric gallophosphonate anion

Reaction of t-BuP(O)(OSiMe(3))(OH) with Me(3)Al leads to the formation of [Me(2)Al(mu-O)(2)P(OSiMe(3))(t-Bu)](2) (1) whereas Me(2)AlCl reacts with Ph(2)P(O)(OH) to yield [(Cl)(Me)Al(mu-O)(2)PPh(2)](2) (2). These compounds represent the first examples of functionalized dimeric four-ring type aluminophosphonate systems. The double four-ring type gallophosphonate, namely, [t-BuPO(3)GaMe](4), reacts with n-Bu(4)NHF(2) under ambient conditions, resulting in the formation of a monomeric gallophosphonate [n-Bu(4)N][MeGa[t-BuPO(2)(OH)](3)] (3). These derivatives have been adequately characterized using various spectroscopic techniques and X-ray diffraction studies.     

Tri- and pentanuclear tungsten-(mu-S)-M clusters (M = W, Cu, Ag)

The thiotungstate [Et4N]2[OW(WS4)2], [Et4N]2.1, containing the linear [[S2W(VI)(mu-S)2]2W(IV)=O] core, was prepared from [Et4N]2[WS4] in the presence of the sulfide scavenger Cd2+. Addition of 1,2-bis(o-diphenylphosphinophenyl)ethane (diphosphine) and Cu+ or Ag+ to solutions of 1 in MeCN/DMF led to coordination of the (diphosphine)Cu/Ag fragments to the terminal sulfido ligands of 1, yielding novel linear pentanuclear, heterometallic clusters [mu-[OW(IV)(DMF)(W(VI)S4)2][M(diphosphine)]2], 2 (M = Cu) and 3 (M = Ag). Along with 2, the trinuclear cluster [[mu-(W(VI)S4)[Cu(diphosphine)(2)]], 4, was also obtained. The molecular and crystal structures of [Et4N]2.1, 2.MeCN, 3.MeCN, and 4.2MeCN.CH2Cl2 have been determined.     

A note on debye potentials for spherically gyrotropic media

The Debye potentials are generalized to the case of electromagnetic fields in spherically gyrotropic media. A medium is called spherically gyrotropic if it is locally gyrotropic with the distinguished axis having a radial direction determined by a central point. Expressions for electromagnetic fields in terms of the generalized potentials are presented and the system of differential equations for the potentials is derived. The results are summarized in the form of a theorem. Basic facts about the Debye potentials in isotropic media are recalled.     

Dynamics of protein and mixed protein/surfactant adsorption layers at the water/fluid interface

The adsorption behaviour of proteins and systems mixed with surfactants of different nature is described. In the absence of surfactants the proteins mainly adsorb in a diffusion controlled manner. Due to lack of quantitative models the experimental results are discussed partly qualitatively. There are different types of interaction between proteins and surfactant molecules. These interactions lead to protein/surfactant complexes the surface activity and conformation of which are different from those of the pure protein. Complexes formed with ionic surfactants via electrostatic interaction have usually a higher surface activity, which becomes evident from the more than additive surface pressure increase. The presence of only small amounts of ionic surfactants can significantly modify the structure of adsorbed proteins. With increasing amounts of ionic surfactants, however, an opposite effect is reached as due to hydrophobic interaction and the complexes become less surface active and can be displaced from the interface due to competitive adsorption. In the presence of non-ionic surfactants the adsorption layer is mainly formed by competitive adsorption between the compounds and the only interaction is of hydrophobic nature. Such complexes are typically less surface active than the pure protein. From a certain surfactant concentration of the interface is covered almost exclusively by the non-ionic surfactant. Mixed layers of proteins and lipids formed by penetration at the water/air or by competitive adsorption at the water/chloroform interface are formed such that at a certain pressure the components start to separate. Using Brewster angle microscopy in penetration experiments of proteins into lipid monolayers this interfacial separation can be visualised. A brief comparison of the protein adsorption at the water/air and water/n-tetradecane shows that the adsorbed amount at the water/oil interface is much stronger and the change in interfacial tension much larger than at the water/air interface. Also some experimental data on the dilational elasticity of proteins at both interfaces measured by a transient relaxation technique are discussed on the basis of the derived thermodynamic model. As a fast developing field of application the use of surface tensiometry and rheometry of mixed protein/surfactant mixed layers is demonstrated as a new tool in the diagnostics of various diseases and for monitoring the progress of therapies.     

Missing-link macrocycles: hybrid heterocalixarene analogues formed from several different building blocks

The synthesis and structural characterization of hybrid heterocalix[4]arene analogues containing pyrrole, benzene, methoxy-substituted benzene, and pyridine subunits is described. Macrocycles 1 and 2, examples of calix[2]benzene[2]pyrrole and calix[1]benzene[3]pyrrole systems, respectively, are synthesized by the condensation of pyrrole and an appropriate phenylbis(carbinol). Macrocycles 3 and 7, examples of calix[2]benzene[1]pyridine[1]pyrrole and calix[1]pyridine[3]pyrrole, respectively, are synthesized by the use of a carbene-based pyrrole-to-pyridine ring-expansion procedure. Single-crystal X-ray analysis reveals that compounds 1a, 1b, and 2b adopt 1,3-alternate conformations in the solid state, whereas compounds 3 and 7 display structures that are best described as "flattened partial cones" in terms of their conformation. (Series a refers to pure benzene-derived systems, whereas series b indicates macrocycles containing 5-methoxyphenyl subunits). In the solid state, the methoxy-functionalized macrocycles 1b and 2b, and the chloropyridine-containing macrocycle 7 exist as dimers. In the case of 1a and 7, these compounds interact with neutral solvent in the solid state. The conformations of the macrocycles in solution were explored by temperature-dependent proton NMR and NOESY spectral analysis. At 188 K, macrocycles 1a and 2a adopt flattened 1,3-alternate conformations, whereas macrocycles 3 and 7 exist in the form of flattened partial-cone conformations. Standard proton NMR titration analyses were carried out in the case of macrocycles 1a and 2a, and reveal that at least the second of these systems is capable of binding fluoride and chloride anions in CD(2)Cl(2) solution at room temperature (K(a)=571 and 17M(-1) in the case of 2a and F(-) and Cl(-), respectively).     

Das Reaktionsverhalten von Cp2NbCl2 gegenüber WF6—Struktur von [Cp2NbCl2]4[WF6]2[WCl6]

The oxidation of Cp₂NbCl₂ with pure WF₆ in SO₂ solution yielded the cationic metallocene species [Cp₂NbCl₂]⁺[WF₆]⁻ essentially in quantitative yield. The same reaction carried out in the presence of either equimolar amounts or a two-fold excess of HCN led to the preparation of the new niobocenium salt [Cp₂NbCl₂]₄⁺[WF₆]²⁻ which was studied by single crystal X-ray diffraction. This compound represents the first example of a structurally characterized metallocene-WF₆⁻ complex, and crystallizes in the tetragonal system: space group, P4₁2₁2(No. 92), a = 11.083(8) Å, c = 48.285 (9) Å; Z = 8; R = 0.0759, R_W = 0.0841. ab]Die Oxidation von Cp₂NbCl₂ mit reinem WF₆ führt in SO₂-Lösung zur Synthese von [Cp₂NbCl₂ ]⁺[WF₆]⁻ in nahezu quantitativer Ausbeute. Die analoge Reaktion führt unter Anwesenheit der äquimolaren Menge oder eines zweifachen Überschusses an HCN zur Ausbildung des Niobocenium-Komplexsalzes [Cp₂NbCl₂]₄⁺ [WF₆]₂⁻[WCl₆]²⁻, von dem eine Röntgenstrukturanalyse angefertigt wurde. Diese Verbindung repräsentiert den ersten structurell charakterisierten Vertreter eines Metallocen-WF₆⁻-Komplexes und kristallisiert im tetragonalen System: Raumgruppe P4₁2₁2 (Nr. 92), a = 11.083(8) Å, c = 48.285(9) Å; Z = 8; R = 0.0759, R_W = 0.0841. kw]Niobium; X-ray diffraction; Oxidation; Metallocenes     

Effect of non-planarity on the spin distribution in the radical anions containing the stilbene or the azobenzene π-system: An ESR and ENDOR Study

The radical anions of 5H-dibenzo[a,d]cycloheptene ( 9 ), 5 H-dibenzo[c,f][1,2]diazepine ( 10 ), 5,6-dihydrodibenzo[a,e]cyclooctene ( 11 ), 5,6-dihydrodibenzo[c,g][1,2]diazocine ( 12 ), and (E)-2,2,5,5-tetramethyl-3,4-diphenylhex-3-ene ( 13 ) were characterized by ESR and ENDOR spectroscopy. Their hyperfine data were compared with those previously reported for radical anions also containing the stilbene or the azobenzene π-system. Whereas the π-spin distribution in the radical anions of the stilbene series is only moderately sensitive to deviations of the π-system from planarity, the radical anions of the azobenzene series respond to steric strain by shifting the π-spin population from the benzene rings to the azo group. This finding is impressively demonstrated by the similar hyperfine data for 9 ^{· ?} and 11 ^{· ?} which contrast with the strongly highly hindered 13 ^{· ?}. A. plausible interpretation is readily provided by the electron affinities of the constituent π-moieties in stilbene and azobenzene. While those of benzene and ethene are both comparatively low, the azo group has a considerably higher electron affinity.     

Some remarks on the approximation in the strong sense

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On the 70th birthday of Professor S. M. Nikol'skii     

Strengthening the Connection between Science,Society and Environment to Develop Future French and European Bioeconomies: Cutting-Edge Research of VAALBIO Team at UCCS

The development of the future French and European bioeconomies will involve developing new green chemical processes in which catalytic transformations are key. The VAALBIO team (valorization of alkanes and biomass) of the UCCS laboratory (Unité de Catalyse et Chimie du Solide) are working on various catalytic processes, either developing new catalysts and/or designing the whole catalytic processes. Our research is focused on both the fundamental and applied aspects of the processes. Through this review paper, we demonstrate the main topics developed by our team focusing mostly on oxygen- and hydrogen-related processes as well as on green hydrogen production and hybrid catalysis. The social impacts of the bioeconomy are also discussed applying the concept of the institutional compass.