The complete grapht-packings andt-coverings

The aim of this paper is to introduce the notions of floor and ceiling functions related to graph edge-decompositions intot mutually isomorphic parts. It is shown that, given any natural numbert, uniform and extremal t-packing andt-covering exist for each complete graph and each complete bipartite graph. Extremal in this context means that both a remainder and a surplus are absolutely minimum. In proofs, decompositions of multigraphs into matchings are involved. Open problems and conjectures are stated.     

Zur elektrometrischen Bestimmung von QuecksilberI neben QuecksilberII

Ohne Zusammenfassung     

Austausch von Chlorisotopen am Phosphoratom, 1. Mitt.: Dialkylchlorthiophosphate

Zusammenfassung An den Modellverbindungen Dialkylchlorthiophosphat (RO)₂P(S)Cl (R=Me, Et, n-Pr) und Diphenylchlorthiophosphat (PhO)₂P(S)Cl wurde der Austausch Chlorid—Radiochlorid am Thiophosphorylzentrum untersucht. Die bimolekularen Geschwindigkeitskonstanten, die Aktivierungsenergien und Aktivierungsentropien wurden berechnet. Der Einfluß von Substituenten auf bimolekulare Substitutionsreaktionen am vierfach koordinierten Phosphoratom wurde diskutiert.

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Chlorine isotopic exchange at phosphorus atoms, I.: Chloridothiophosphates

The chloride—radiochloride ion exchange at the thiophosphoryl centre has been studied using dialkylchloridothiophosphates (RO)₂P(S)Cl (R=Me, Et, n-Pr) and diphenylphosphorochloridothionate, (PhO)₂P(S)Cl, as model compounds. The bimolecular rate constants, energies and entropies of activation have been calculated. Effects of the substituents in the bimolecular displacement reaction on four-coordinated phosphorus atom have been discussed.

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Mit 3 Abbildungen     

Rhodopsin reconstituted into a planar-supported lipid bilayer retains photoactivity after cross-linking polymerization of lipid monomers

Transmembrane proteins (TMPs), particularly ion channels and receptors, play key roles in transport and signal transduction. Many of these proteins are pharmacologically important and therefore targets for drug discovery. TMPs can be reconstituted in planar-supported lipid bilayers (PSLBs), which has led to development of TMP-based biosensors and biochips. However, PSLBs composed of natural lipids lack the high stability desired for many technological applications. One strategy is to use synthetic lipid monomers that can be polymerized to form robust bilayers. A key question is how lipid polymerization affects TMP structure and activity. In this study, we have examined the effects of UV polymerization of bis-Sorbylphosphatidylcholine (bis-SorbPC) on the photoactivation of reconstituted bovine rhodopsin (Rho), a model G-protein-coupled receptor. Plasmon-waveguide resonance spectroscopy (PWR) was used to compare the degree of Rho incorporation and activation in fluid and poly(lipid) PSLBs. The results show that reconstitution of Rho into a supported lipid bilayer composed only of bis-SorbPC, followed by photoinduced lipid cross-linking, does not measurably diminish protein function.     

Pathwise global attractors for stationary random dynamical systems

Summary The asymptotic behaviour of random dynamical systems in Polish spaces is considered. Under the assumption of existence of a random compact absorbing set, assumption supposed to hold path by path, a candidate pathwise attractorA() is defined. The goal of the paper is to show that, in the case of stationary dynamical systems,A() attracts bounded sets, is measurable with respect to the -algebra of invariant sets, and is independent of when the system is ergodic. An application to a general class of Navier-Stokes type equations perturbed by a multiplicative ergodic real noise is discussed in detail.     

Multicomponent analysis with a computerized flow injection system using LED photometric detection

An original computer-controlled solid-state photometer has been developed and its potential for simultaneous multicomponent flow-injection analysis of binary and ternary mixtures is demonstrated. The device is simple in construction. Its principle of operation is based on rapid sequential measurements of the absorbance of the complexes formed by the analytes with chromogenic reagents at the wavelengths corresponding to the emission maxima of three light emitting diodes (563, 580 and 638 nm).     

Diastereoface Selectivity During Pthalimidonitrene Additions to (E)-and (Z)-configurated α, β-unsaturated esters,induced by a chiral center in the γ-position

In-situ-generated phthalimidonitrene was added to five α, β-unsaturated esters containing a chiral secondary O-function at C(γ). The additions were fully suprafacial, inasmuch as the (E)-isomers 1 afforded only the trans-aziridines 2 and 3 (J(β, γ) = 4.8?5.1 Hz) and the (Z)-isomers 4 only the cis-aziridines 5 and 6 (8.2?8.5 Hz). The products 2 , 3 , 5 , and 6 where shown to possess the arabino-, xylo-, ribo-, and lyxo- configuration, respectively, by X-ray structure analysis of 2b , 2d , and 6a . The diastereoface selectivity of the nitrene additions, induced by the chiral substructure around C(γ), resulted in more 2 than 3 from 1 , but more 6 than 5 from 4 , which means that the preference of attack at the double bond switches from one side to the other depending on the C=C configuration. The preferences were higher at lower temperature. The aziridines 2a , 2d , and 3d exhibit ¹H-NMR-visible isomerism at the ring N-atom; the major (78?95 %)invertomer A is always the one with the phthalimido group in trans-position to the (larger) substructure around C(γ). The other aziridines only show ¹H-NMR signals of one invertomer, which – by steric reasoning - ought to be A ; this is confirmed by a ¹H-NMR argument for 3a , 5a , 6a , 5c , and 6c .     

Dynamics of theD-dimensional FRW-cosmological models within the superstring-generated gravity model

We study the dynamics of the generalizedD-dimensional (D = 1+3+d) Friedman-Robertson-Walker (FRW) cosmological models in the framework of an extended gravity theory obtained by adding the Gauss-Bonnet term to the standard Einstein-Hilbert action. In our discussion we extensively use methods of dynamical systems. We consider models filled in with a perfect fluid obeying the equation of statep=(–1) and vacuum but non-flat models. We present a detailed analysis of the ten dimensional model and in particular we study the vacuum case. Several phase portraits show how the evolution of this model depends on the parameter.     

Convergence of multistep methods for Volterra functional differential equations

Summary This paper deals with the convergence of nonstationary quasilinear multistep methods with varying step, used for the numerical integration of Volterra functional differential equations. A Perron type condition (appearing in the differential equations theory) is imposed on the increment function. This gives a generalization of some results of Tavernini ([19–21]).