Approximation durch Polynomfunktionen auf universellen Algebren

LetA be a topological universal algebra,F(A)=A ^A the full function algebra endowed with the producttopology andP(A) the algebra of polynomial functions onA, i. e. the subalgebra ofF(A) generated by the constant mappings and the identity.A has the local approximation property ifP(A) is dense inF(A)., TopologicalT ₂-groupsG (resp.T ₂-ringsR) of order >2 have the local approximation property if an only if all proper normal subgroups (resp. ideals) are dense inG (resp.R) andG is non-abelian (R is not a zeroring). In particular all subringsR of satisfying R ( resp. denoting the field of rational resp. real numbers) yield examples of rings having this property thus showing that the local approximation property is a far-reaching generalization of the well-known interpolation property.

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Meinem verehten Lehrer, Herrn Professor Dr. E. Hlawka, zum 65. Geburtstag gewidmet     

Zur Synthese von Human-Big-Gastrin I

The synthesis of the tetratriacontapeptide amide corresponding to the revised primary structure of human big gastrin I is described. For this purpose the fragments were designed in view of the maximum use of those utilized in our previous synthesis of human big gastrin I according to the first sequence proposal. Consequently the key tripeptide-Pro-Pro-His- (sequence 7–9) was prepared in suitably protected form to be used as amino or carboxyl component for assembly of the segments 1–9 and 1–14, respectively. Final condensation of the latter nona- and tetradecapeptide derivatives with the C-terminal segments 10–34 and 15–34 via the azide and the dicyclohexylcarbodiimide/N-hydroxysuccinimide procedure, respectively, leads to crude fully protected human big gastrin I. Upon deprotection by exposure to trifluoroacetic acid in presence of ethanedithiol-(1,2) as scavanger, ion exchange chromatography and partition chromatography, the desired tetratriacontapeptide amide was isolated in satisfactory yield with a high degree of purity. The identical immunological behaviour of the synthetic material, if compared with that of natural human big gastrin I, represents ulterior strong evidence for the correctness of the newly proposed structure for this putative prohormonal form of the gastrins.

Kurzmitteilung:Wünsch E., Wendlberger G., Mladenova-Orlinova L., Göhring W., Jaeger E., Scharf R., Gregory R. A., Dockray G. J., Hoppe-Seyler's Z. Physiol. Chem.362, 179 (1981).     

Die photometrische Bestimmung des Wismuts mit Thioharnstoff

Zusammenfassung Es wird gezeigt, daß die Bestimmung des Wismuts mit Thioharnstoff in bromwasserstoffsaurer Lösung auf photometrischem Wege mit dem Gerät ELKO II durchgeführt werden kann. Hierbei benutzt man zweckmäßig das Gerät mit der Glühlampe und Filter S 47 E oder den Quecksilberbrenner in Verbindung mit Filter Hg 436. Damit die Extinktion des gelbgefärbten Komplexes von der Thioharnstoffkonzentration unabhängig wird, muß die Lösung bei Benutzung des Filters S 45 E mindestens 10% Thiohamstoff, bei Benutzung des Filters Hg 436 mindestens 5% Thioharnstoff enthalten. Auch die Bromwasserstoffsäure übt einen Einfluß auf die Ausbildung der Extinktion aus. Wenn man die Messung mit dem Filter S 45 E durchführt und den Thioharnstoffgehalt mit 12% konstant hält, so darf die Bromwasserstoffkonzentration zwischen 1,2–9,2% betragen, um gleichbleibende Extinktionswerte zu erhalten. Benutzt man das Filter Hg 436 bei der gleichen Thioharnstoffkonzentration, so muß der Bromwasserstoffgehalt zwischen 3,0–7,5% liegen. Die Temperatur übt nur einen geringen Einfluß auf die Ausbildung des ThioharnstoffWismutkomplexes aus. Die Extinktion ist zeitunabhängig. Die Extinktionswerte ändern sich innerhalb 3 Std nach Zusammengeben der Reagenslösungen nicht. Das BEERsche Gesetz ist erfüllt. Das Verfahren besitzt erhebliche praktische Bedeutung, da sich sehr viele Metalllegierungen in denen Wismut zu bestimmen ist, mit Hilfe von Bromwasserstoffsäure und Brom sehr schnell lösen lassen.     

Different thermal reactivity of a 1,2-thiaphospholo[a]phosphirane in free and metal carbonyl complexed form

The W(CO)5 and Fe(CO)4 complexes of the bicyclic phosphirane 3,5,6,6-tetraphenyl-1-phospha-2-thiabicyclo[3.1.0]hex-3-ene undergo a thermal 2-phenylphosphirane --> dihydrophosphaisoindole ring expansion, while the free phosphirane suffers both a [2 + 1] cycloreversion and a fragmentation yielding a butadienyl sulfide.     

Vergleich von Potentiometrischer Stripping-Analyse und Anodischer Stripping-Voltammetrie in der Flie?injektionsanalyse. St?rungen bei der Bleibestimmung

Summary The interferences caused by inorganic ions, organic anions and Triton X-100 in the determination of lead by flow injection potentiometric and voltammetric stripping analysis at a mercury film electrode were investigated. The experiments were performed in the concentration range of 1–10 mg/l Pb²⁺. For both methods linear calibration plots were obtained in the presence of an excess of nitrate, chloride, perchlorate and sulphate. Iodide strongly interferes due to mercury complexation.Metal ion interference caused by formation of irreversible amalgams (as in the case of codeposition of Ni, Co, Fe and Cr) is avoided by proper choice of deposition potential. No effect of water soluble reduced species, i.e. Fe(II) and Cr(II), on the stripping signals was observed. The presence of acetate, citrate and tartrate does not limit the determination of lead by potentiometric stripping analysis (PSA) but has a marked effect on anodic stripping voltammetric (ASV) signals. No influence of Triton X-100 on the determination of lead by PSA was found. In ASV 10^–3% Triton X-100 diminished the peak current by 15%.

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Herrn Prof. Dr. Rolf Neeb aus Anlaß seines 60. Geburtstags gewidmet     

Leitfähigkeitsmessungen an Tetraethylammoniumhexacyanoferrat(III) und Tetrabutylammoniumhexacyanoferrat(III) in verschiedenen Lösungsmitteln

Based on conductivity measurements, the dissociation of tetraalkylam-moniumhexacyanoferrates(III) in water, ethanol, formamide,N-methylformamide,N,N-dimethylformamide, propylenecarbonate and acetonitrile is discussed. Interactions of the solvent as donor and as acceptor, the latter interaction being dominant, with (et ₄N)₃Fe(CN)₆ and (bu ₄N)₃Fe(CN) were found to be important factors in the formation of solvated ions.

     

A general formalism of deriving the pair potential of polymer chains for arbitrary interaction potentials between isolated chain segments at and close to the theta-point

A formalism has been worked out which allows to transform any non-punctiform segment-segment potential of isolated polymer segments ε of fairly short-ranged character into the pair-potentialU operating between linear polymer chains with a certain reference to the arguments as they have been originally put forward byFlory andKrigbaum. Although no restrictions are made in the derivation as to the repulsive or attractive contribution of the segment-segment potential ε because of some known general deficiencies of theFlory-Krigbaum treatment for exclusively repulsive interaction, the resulting equations are primarily intended to describe the thermodynamic situation at and close to the θ-point where repulsion and attraction—though working at different ranges of segment separation—cancel. As the equation derived is somewhat complicated two different approximate forms have been developed: The first one is based on aTaylor series expansion retaining terms up to the fourth order which allows to characterizeU by the second and the fourth moment of the pair segment-segment distribution function, β and γ (β being the so-called binary cluster integral of segment-segment interaction, which is considered to be zero for θ-conditions). In this caseU may be represented by an expression of the general form $$U/kT = A(1 - BR^2 )\exp \{ - bR^2 \} .$$ The second method is based on a separate integration over the repulsive and attractive ranges of ε giving the repulsive (U ₊) and the attractive (U _?) part ofU finally after some approximations leading to an equation of the general form $$U/kT = (U_ + + U_ - )/kT = A_1 \exp \{ - b_1 R^2 \} - A_2 \exp \{ - b_2 R^2 \} .$$ In both cases the knowledge of the exact form of ε is dispensable, only β and γ—or for the second case their repulsive (β₊ and γ₊) and attractive (β_? and γ_?) parts have to be known. It is shown that the approximations are in excellent accordance with the exact form so that they may be conveniently used to describe pair potentials of polymer chains and to analyze pair potentials of segment-segment interactions under the limitations and conditions indicated.     

Investigation of sulfur release in ETV-ICP-AES and its application for the determination of sulfates

Electrothermal vaporization inductively coupled plasma atomic emission spectrometry was applied to the determination of sulfur species in aqueous solutions. The sensitivity for sulfur as sulfate was found to be depending on the cations in the sample. For understanding this phenomenon the thermal behavior of sulfuric acid, ammonium sulfate and the sulfates of sodium, zinc, magnesium and silver was studied. There were significant differences in the thermal release of sulfur from these sulfates. To explain these phenomena different reaction mechanisms were calculated using thermodynamic data. Pd(NO₃)₂ and Ge in KOH were successfully applied as modifiers for the stabilization of the sulfates during the thermal pre-treatment step and to establish a uniform thermal behavior of different sulfates. The stabilization of sulfur using Ge and Pd as modifiers is based on the reduction of the sulfates in presence of carbon, resulting in the formation of GeS and PdS, respectively. This explanation has been supported by comparing the experimental results with thermodynamic calculations considering different reactions for the thermal decomposition of the sulfates. Applying Ge (in KOH) as modifier the absolute detection limit was 300 pg sulfur (e.g. LOD 30 ng mL^–1). The significant influence of phosphates on the determination of sulfur could be essentially reduced by Pd as modifier. Received: 11 November 1997 / Revised: 14 January 1998 / Accepted: 18 January 1998     

Formation of dinuclear titanium and zirconium complexes by olefin metathesis--catalytic preparation of organometallic catalyst systems

The titanium complex [(C(5)H(4)bond;allyl)TiCl(3)] (2) undergoes olefin metathesis coupling when treated with 3 mol % of [Cl(2)(L(1))(L(2))Ru=CHPh] (L(1)=L(2)=PCy(3), 4 a; L(1)=PCy(3), L(2)=(H(2)IMes), 4 b) to yield the dimetallic complex [Cl(3)Ti(C(5)H(4))-CH(2)CH=CHCH(2)-(C(5)H(4))TiCl(3)] (5). The allyl-substituted titanocene complex [Cp(C(5)H(4)bond;allyl)TiCl(2)] (3) analogously yields the dimetallic system 6 when treated with 4. The ansa-zirconocene complex [Me(2)Si(C(5)H(4))(C(5)H(3)bond;allyl)ZrCl(2)] (7) cleanly yields the analogous dimetallic coupling product 8 (>95 % isomerically pure), when treated with catalytic amounts of 4 b in toluene. Complex 8 gives an active homogeneous ethene or propene polymerization catalyst, especially at elevated temperatures, when treated with excess methylalumoxane.     

Cyclic Heptapeptides Axinastatin 2, 3, and 4: Conformational analysis and evaluation of the biological potential

The conformational analysis of naturally occurring cytostatic cyclic heptapeptides axinastatin 2, 3, and 4 was carried out by two-dimensional NMR spectroscopy in combination with distance-geometry (DG) and molecular-dynamics (MD) calculations in explicit solvents. The synthesized secondary metabolites were examined in (D₆)DMSO. Axinastatin 2 was also investigated in CD₃OH. In all structures, Pro² is in the i + 1 position of a βI turn and Pro⁶ occupies the i + 2 position of a βVIa turn about the cis amide bond between residue 5 and Pro^6. In all peptides, a bifurcated H-bond occurs between residue 4 CO and the amide protons of residue 1 and 7. For axinastatin 2 and 3, an Asn I_g turn was found about Asn¹ and Pro^2. We compared these structures with conformations of cyclic heptapeptides obtained by X-ray and NMR studies. A β-bulge motif with two β turns and one bifurcated H-bond is found as the dominating backbone conformation of cyclic all-L-heptapeptides. Axinastatin 2, 3, and 4 can be characterized by six trans and one cis amide bond resulting in a β/βVI(a)-turn motif, a conformation found for many cyclic heptapeptides. Detailed biological tests of the synthetic compounds in different human cancer cell lines indicates these axinastatins to be inactive or of low activity.