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.     

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]).     

Free Radicals, Salicylic Acid and Mycotoxins in Asparagus After Inoculation with Fusarium proliferatum and F. oxysporum

Electron paramagnetic resonance was used to monitor free radicals and paramagnetic species like Fe, Mn, Cu generation, stability and status in Asparagus officinalis infected by common pathogens Fusarium proliferatum and F. oxysporum. Occurrence of F. proliferatum and F. oxysporum, level of free radicals and other paramagnetic species, as well as salicylic acid and mycotoxins content in roots and stems of seedlings were estimated on the second and fourth week after inoculation. In the first term free and total salicylic acid contents were related to free radicals level in stem (P?=?0.010 and P?=?0.033, respectively). Concentration of Fe(3+) ions in porphyrin complexes (g?=?2.3, g?=?2.9) was related to the species of pathogen. There was no significant difference between Mn(2+) concentrations in stem samples; however, the level of free radicals in samples inoculated with F. proliferatum was significantly higher when compared to F. oxysporum.     

Investigation of turbulent flow field in a Kenics static mixer by Laser Doppler Anemometry

The main purpose of the present paper was to apply the Laser Doppler Anemometry (LDA) technique to measure turbulent liquid flow in a Kenics static mixer. The LDA set-up was a one-channel backscatter system with argon-ion laser. Measurements in the static mixer were carried out for three values of the Reynolds number: 5000, 10000, and 18000. Water was used as the process liquid. Values of the axial and tangential components of the local, mean, and root mean square velocities were measured inside the static mixer. It was observed that the shape of the velocity profile depends strongly on the Reynolds number, Re, as well as on the axial, h, and radial, α, position of the measurement point. Strong dependence of the velocity fluctuations on the Reynolds number was found in the investigated range of Re and the measurement point position. Furthermore, one-dimensional energy spectra of the velocity fluctuations were also obtained by means of the Fast Fourier Transform. Fluctuation spectra of the axial and tangential velocities provided information about the energy density of velocity fluctuations in the observed range of Reynolds numbers. A study of the energy spectra led to the conclusion that the energy density increases with the increasing radial distance from the mixer walls at constant values of h, _Re, and α. Minor variations in the mean value of the energy density, E, were observed together with variations of the measurement point angular position, α. In addition, it was observed that an increase of the Reynolds number causes significant increase of the power spectral density.