A sharp condition for existence of an inertial manifold

It is shown that a perturbation argument that guarantees persistence of inertial (invariant and exponentially attracting) manifolds for linear perturbations of linear evolution equations applies also when the perturbation is nonlinear. This gives a simple but sharp condition for existence of inertial manifolds for semi-linear parabolic as well as for some nonlinear hyperbolic equations. Fourier transform of the explicitly given equation for the tracking solution together with the Plancherel's theorem for Banach valued functions are used.     

Rheological behaviour of two-phase flow of solid particles in a gas

The present investigation was concerned with the rheological behaviour of dilute suspensions of solid particles in a gas in a vertical cocurrent flow moving upwards. Starting from the experimentally determined dependence of the pressure drop on the concentration of solid particles and the Reynolds number of the carrier medium in the steady flow region, the rheological parameters were estimated using pseudo-shear diagrams. Air was the carrier medium and the dispersed phase was one of six fractions of polypropylene powder and five fractions of glass ballotini. The results show that the investigated two-phase systems have pseudoplastic character which becomes more pronounced with increases in concentration, equivalent diameter and density of solid particles in the flowing suspension. C _d coefficient of particle resistance - d _e equivalent diameter of particles - D column diameter - Fr Froude number - g gravitational acceleration - K rheological parameter - L length - n rheological parameter - p _t pressure drop due to friction - p _m total pressure drop - p _ag pressure drop due to acceleration of the gas phase - p _as pressure drop due to acceleration of the solid phase - p _g hydrostatic pressure of the gas phase - p _s specific effective weight of the dispersed phase - r radius - Re Reynolds number - Re _p Reynolds number of a particle - Re _G generalized Reynolds number - Re _G1 generalized Reynolds number relating to the end of the laminar flow region - Re _G2 generalized Reynolds number relating to the beginning of the turbulent flow region - w _z axial component of velocity - u _t steady free-fall velocity of a single particle - w average velocity - w _g average velocity of the gas phase - w _s average velocity of the dispersed phase of solid particles - relative mass fraction of solid particles - x _s volume fraction of solid particles - _g coefficient of pressure drop due to friction - µ dynamic viscosity - _g density of the gas phase - _m density of the suspension - _s density of solid particles - _ds density of the dispersed phase - _w shear stress at the wall     

Down-regulation of Bcl-2 and Akt induced by combination of photoactivated hypericin and genistein in human breast cancer cells

Presented experiment considers combination of genistein and photodynamic therapy with hypericin with a view to achieve higher therapeutic outcome in human breast adenocarcinoma cell lines MCF-7 and MDA-MB-231, both identified in our conditions as photodynamic therapy resistant. Since genistein is known to suppress Bcl-2 expression, we predicted that photodynamic therapy with hypericin might benefit from mutual therapeutic combination. In line with our expectations, combined treatment led to down-regulation of Bcl-2 and up-regulation of Bax in both cell lines as well as to suppression of Akt and Erk1/2 phosphorylation induced by photoactivated hypericin in MCF-7 cells. Although Akt and Erk1/2 phosphorylation was not stimulated by photodynamic therapy with hypericin in MDA-MB-231 cells, it was effectively suppressed in combination. Variations in cell death signaling favoring apoptosis were indeed accompanied by cell cycle arrest in G₂/M-phase, activation of caspase-7, PARP cleavage and increased occurrence of cells with apoptotic morphology of nucleus. All these events corresponded with suppression of proliferation and significantly lowered clonogenic ability of treated cells. In conclusion, our results indicate that pre-treatment with tyrosine kinase inhibitor genistein may significantly improve the effectiveness of photodynamic therapy with hypericin in MCF-7 and MDA-MB-231 breast cancer cells.     

Communication: Experimental proof of symmetry breaking in tilted smectics composed of molecules with axial chirality

For the first time, domains with twisted structures have been established in planar samples of achiral compounds in tilted smectic C phase. This evidences separation of molecular conformers differing in the sense of axial chirality and confirms polar C(2) symmetry of these domains. A simple model considering polar surface anchoring energy and bulk energy of the twist can account for this finding. Conditions for coexistence of twisted and homogeneous domains are discussed.     

Non-adiabatic dynamics of pyrrole: Dependence of deactivation mechanisms on the excitation energy

Non-adiabatic dynamics simulations were performed for pyrrole at time-dependent density functional theory level using the trajectory surface hopping approach. Initial conditions were prepared based on the UV-absorption spectrum so as to simulate monochromatic absorption in three distinct spectral regions. The results showed predominance of the NH-stretch mechanism for excited-state relaxation. With increasing initial energy, however, other mechanisms are activated as well, even though they still occurred for a minor fraction of the trajectories. Dynamics starting at the origin of the absorption spectrum exhibited internal conversion to the ground state with a time constant of 20 fs. In contrast, dynamics starting at higher energies gave rise to much longer time constants for internal conversion near 200 fs.     

Raman spectroscopic study of the uranyl sulphate mineral zippeite: low wavenumber and U–O stretching regions

The uranyl sulphate mineral zippeite was studied by Raman spectroscopy. The phase purity of the sample was initially checked by X-ray powder diffraction and its chemical composition was defined by electron microprobe (wavelength dispersive spectroscopy, WDS) analysis. The Raman spectroscopy research focused on the low wavenumber and uranyl stretching vibration regions. Vibration bands down to 50 cm^–1 were tentatively assigned. The U–O bond lengths were calculated based on empirical relations. Inferred values are consistent with those obtained from the crystal structure analysis of synthetic zippeite. Number of bands was interpreted on the basis of factor group analysis.     

Measurement of growth and survival curves of microorganisms influenced by radiation

Growth curves in liquid peptone-glucose medium and survival curves of the Saccharomyces cerevisiae culture from variously irradiated inoculum were evaluated. Irradiation of yeast cells in solution physiological (salt) was performed with γ-rays of ⁶⁰Co in Gammacell 220 or with UV-irradiation using ultraviolet lamps UVH 1016-6 and Photochemical reactors, Ltd, Sylvania for various time periods. Various dose rates of both types of radiation were used. The absorbed doses reached some hundreds Gy for both γ and UV radiation. The growth curves were measured using the nephelometric data of yeast suspension in various time periods of growth. The results of repeated measurements showed that the slope of growth curves express relatively exactly the negative influence of irradiation when the standard and uniform method of evaluation was used. When the curves were fitted to the data points by the least-squares method, the average standard errors were found to be in the range from 0.6 to 0.8% and from 0.2 to 0.5% for γ- and UV-irradiation, respectively. The negative effect of irradiation depended monotonously and non-linearly on the applied dose of irradiation. Quantitatively different effects were found in the case of γ and UV irradiation.     

Role of the shape of various bacteria in their separation by Microthermal Field-Flow Fractionation

The steady-state movement of the spherical and non-spherical particles, such as prolate or oblate rotational ellipsoids, cylinders, or parallelepipeds, suspended in a liquid and exposed to a unidirectional temperature gradient, is analyzed theoretically. The differences in the ratios of the rotational to translational diffusion coefficients of the non-spherical to spherical particles, the heterogeneity of thermal conductivity of the particle body, and the heterogeneity in surface chemical nature make possible to separate the particles according to differences in shape. Preliminary experimental separations of Gram-positive and Gram-negative, nearly spherical and rod-shaped bacteria performed by Microthermal Field-Flow Fractionation confirmed that the fractionation of the cells according to differences in shape is possible.     

Regioisomeric analysis of triacylglycerols using silver-ion liquid chromatography-atmospheric pressure chemical ionization mass spectrometry: comparison of five different mass analyzers

Silver-ion high-performance liquid chromatography (HPLC) coupled to atmospheric pressure chemical ionization mass spectrometry (APCI-MS) is used for the regioisomeric analysis of triacylglycerols (TGs). Standard mixtures of TG regioisomers are prepared by the randomization reaction from 8 mono-acid TG standards (tripalmitin, tristearin, triarachidin, triolein, trielaidin, trilinolein, trilinolenin and tri-gamma-linolenin). In total, 32 different regioisomeric doublets and 11 triplets are synthesized, separated by silver-ion HPLC using three serial coupled chromatographic columns giving a total length of 75cm. The retention of TGs increases strongly with the double bond (DB) number and slightly for regioisomers having more DBs in sn-1/3 positions. DB positional isomers (linolenic vs. γ-linolenic acids) are also separated and their reverse retention order in two different mobile phases is demonstrated. APCI mass spectra of all separated regioisomers are measured on five different mass spectrometers: single quadrupole LC/MSD (Agilent Technologies), triple quadrupole API 3000 (AB SCIEX), ion trap Esquire 3000 (Bruker Daltonics), quadrupole time-of-flight micrOTOF-Q (Bruker Daltonics) and LTQ Orbitrap XL (Thermo Fisher Scientific). The effect of different types of mass analyzer on the ratio of [M+H-R(i)COOH](+) fragment ions in APCI mass spectra is lower compared to the effect of the number of DBs, their position on the acyl chain and the regiospecific distribution of acyl chains on the glycerol skeleton. Presented data on [M+H-R(i)COOH](+) ratios measured on five different mass analyzers can be used for the direct regioisomeric determination in natural and biological samples.     

Grüss-type bounds for covariances and the notion of quadrant dependence in expectation

We show that Grüss-type probabilistic inequalities for covariances can be considerably sharpened when the underlying random variables are quadrant dependent in expectation (QDE). The herein established covariance bounds not only sharpen the classical Grüss inequality but also improve upon recently derived Grüss-type bounds under the assumption of quadrant dependency (QD), which is stronger than QDE. We illustrate our general results with examples based on specially devised bivariate distributions that are QDE but not QD. Such results play important roles in decision making under uncertainty, and particularly in areas such as economics, finance, and insurance.