The PDE-preserving operators on nuclearly entire functions of bounded type

The PDE-preserving operators O on the space of nuclearly entire functions of bounded type H_Nb(E) on a Banach space E are characterized. An operator is PDE-preserving when it preserves homogenous solutions to homogeneous convolution equations. We establish a one to one correspondence between O and a set Σ of sequences of entire functionals, i.e. exponential type functions. In this way, algebraic structures on Σ, such as ring structures, can be carried over to O and vice versa. In particular, it follows that O is a non-commutative ring (algebra) with unity with respect to composition and the convolution operators form a commutative subring (subalgebra). We discuss range and kernel properties, for the operators in O, and characterize the projectors (onto polynomial spaces) in O by determining the corresponding elements in Σ. This revised version was published online in June 2006 with corrections to the Cover Date.     

Electrocatalytic oxidation of ascorbic acid and voltammetric determination with a ferrocene-modified platinum electrode

Ferrocene attached to the surface of a platinum electrode catalyses the electrochemical oxidation of ascorbic acid in acidic buffer solutions. The overpotential for ascorbic acid oxidation is decreased by 150 mV at pH 2.2 compared with reaction at bare platinum; and an increase in anodic current and decrease in cathodic current for the redox reaction of ferrocene occurs on addition of ascorbic acid to the solution. The ferrocene-modified electrode is useful for the voltammetric determination of ascorbic acid in natural fruit juices. The advantages result from the electrocatalytic effect and from the prevention of adsorption of inhibitory substances from solution.     

Copolymeric (lR-trans)-N,N'-1,2-cyclohexylene-bisbenzamide oligodimethylsiloxane chiral stationary phase for gas chromatography

A copolymeric stationary phase, consisting of a chiral selective part, i.e. (1R-trans)-N,N'-1,2-cyclohexylenebisbenzamide, and an efficient siloxane oligomeric part, was successfully applied to open tubular column GC analysis. The efficiency and the chiral selectivity of this stationary phase were studied in detail, and high capacity and efficiency at elevated GC temperatures were especially noted. Several drugs and other enantiomeric pairs were separated. The shown examples demonstrate a broad application range for this type of chiral stationary phase in GC analysis.     

Synthesis of pyrrolo[3,2-b]benzofurans and pyrrolo[3,2-b]naphthofurans via addition of a silyloxypyrrole to activated quinones

The uncatalyzed reaction of N-(tert-butoxycarbonyl)-2-tert-butyldimethylsilyloxypyrrole 3 with 1,4-quinones bearing an electron withdrawing group at C-2 has been studied. Use of 1,4-quinones 4, 5 bearing an ester group at C-2 provided an efficient synthesis of the respective pyrrolidinobenzofuran adduct 9 or pyrrolidinonaphthofuran adduct 10 whereas use of 1,4-quinones 6, 7 and 8 bearing an acetyl group at C-2 afforded silyloxypyrroles 11, 12 and 13 resulting from direct electrophilic substitution of the silyloxypyrrole by the electrophilic quinone. Addition of Eu(fod)₃ to the reaction of 2-acetyl-1,4-naphthoquinone 7 and 3-acetyl-5-methoxy-1,4-naphthoquinone 8 with N-(tert-butoxycarbonyl)-2-tert-butyldimethylsilyloxypyrrole 3 provided a method for obtaining the pyrrolidinonaphthofuran adducts 14 and 15 together with silyloxypyrroles 12 and 13. Oxidative rearrangement of pyrrolidinonaphthofuran adduct 15 to pyrrolidino pyranonaphthoquinone 16 using ceric ammonium nitrate in acetonitrile provided a novel approach for the synthesis of an aza-analogue of the pyranonaphthoquinone antibiotic kalafungin.     

Über die Lineare Zerlegung der den Ganzen Modul-Formen von Höherer Stufe Entsprechenden Dirichletreihen in Vollständige Eulersche Produkte

Ohne Zusammenfassung     

Ein Summationsverfahren für die Poincaréschen Reihen von der Dimension—2 zu den hyperbolischen Fixpunktepaaren

Ohne ZusammenfassungHerrnC. Carathéodory zum siebzigsten Geburtstag am 13. September 1943.     

Native chemical ligation of thioamide-containing peptides: development and application to the synthesis of labeled α-synuclein for misfolding studies

Thioamide modifications of the peptide backbone are used to perturb secondary structure, to inhibit proteolysis, as photoswitches, and as spectroscopic labels. Thus far, their incorporation has been confined to single peptides synthesized on solid phase. We have generated thioamides in C-terminal thioesters or N-terminal Cys fragments and examined their compatibility with native chemical ligation conditions. Most sequence variants can be coupled in good yields with either TCEP or DTT as the reductant, though some byproducts are observed with prolonged TCEP incubations. Furthermore, we find that thioamides are compatible with thiazolidine protection of an N-terminal Cys, so that multiple ligations can be used to construct larger proteins. Since the acid-lability of the thioamide prohibits on-resin thioester synthesis using Boc chemistry, we devised a method for the synthesis of thioamide peptides with a masked C-terminal thioester that is revealed in situ. Finally, we have shown that thioamidous peptides can be coupled to expressed protein fragments to generate large proteins with backbone thioamide labels by synthesizing labeled versions of the amyloid protein α-synuclein for protein folding studies. In a proof-of-principle experiment, we demonstrated that quenching of fluorescence by thioamides can be used to track conformational changes during aggregation of labeled α-synuclein.     

The beryllium dimer potential

The convergence of ab initio calculations of the beryllium dimer potential is examined with several basis sets orders of perturbation theory. When the atomic pair natural orbital basis set calculations are extrapolated to the complete basis set and full CI limits, the calculated parameters: R_e=2.447 Å, D_e=827 cm⁻¹, ν₀₁=212.7 cm⁻¹, ν₁₂=167.2 cm⁻¹, ν₂₃=121.5 cm⁻¹ and ν₃₄=77.7 cm⁻¹ are in good agreement with the experimental parameters: R_e=2.45 Å, D_e=839±10 cm⁻¹, ν₀₁=223.2 cm⁻¹, ν₁₂=169.7 cm⁻¹, ν₂₃=122.5 cm⁻¹, and ν₃₄=79 cm⁻¹.     

Semi-wet growth and characterization of multi-functional nano-engineered mixed metal oxides for industrial application

This review paper covers the low temperature wet growth of nano-engineered particles of ZnO-based mixed metal oxides, their growth mechanism, and characterization using X-ray diffraction, SEM, TEM and IR, UV–visible, and XPS spectral techniques. Main focus of this article is centered on low temperature semi-wet methods of synthesis that are suitable for large scale production of zinc oxide-based systems mixed with iron oxide, copper oxide, nickel oxide and cobalt oxide. These mixed metal oxides have broad industrial applications as catalyst, semiconductors, adsorbents, superconductors, electro-ceramics, and antifungal agents in addition to extensive applications in medicines. This paper discusses the low-cost and environment friendly synthesis of these mixed metal oxides, measurement of properties and applicability of these materials systems.