Electric-field-induced steering in soliton direction of propagation in chiral nematic liquid crystals

In this work we demonstrate the properties of spatial solitary waves in chiral nematic liquid crystals with an external electric field. Such self-trapped beams, called nematicons, were created due to the optical reorientation nonlinearity for a light power of a few tens of milliwatts. We show that the direction of propagation of such nematicons can be changed by applying an external electric field. Additionally, this effect can be modified by changing the input polarization of the light beam. The experimental results were obtained in four independent guiding layers created by a chiral nematic structure.     

Multi‐dimensional Lotka–Volterra systems for carcinogenesis mutations

In the paper we consider three classes of models describing carcinogenesis mutations. Every considered model is described by the system of (n+1) equations, and in each class three models are studied: the first is expressed as a system of ordinary differential equations (ODEs), the second—as a system of reaction–diffusion equations (RDEs) with the same kinetics as the first one and with the Neumann boundary conditions, while the third is also described by the system of RDEs but with the Dirichlet boundary conditions. The models are formulated on the basis of the Lotka–Volterra systems (food chains and competition systems) and in the case of RDEs the linear diffusion is considered. The differences between studied classes of models are expressed by the kinetic functions, namely by the form of kinetic function for the last variable, which reflects the dynamics of malignant cells (that is the last stage of mutations). In the first class the models are described by the typical food chain with favourable unbounded environment for the last stage, in the second one—the last equation expresses competition between the pre‐malignant and malignant cells and the environment is also unbounded, while for the third one—it is expressed by predation term but the environment is unfavourable. The properties of the systems in each class are studied and compared. It occurs that the behaviour of solutions to the systems of ODEs and RDEs with the Neumann boundary conditions is similar in each class; i.e. it does not depend on diffusion coefficients, but strongly depends on the class of models. On the other hand, in the case of the Dirichlet boundary conditions this behaviour is related to the magnitude of diffusion coefficients. For sufficiently large diffusion coefficients it is similar independently of the class of models, i.e. the trivial solution that is unstable for zero diffusion gains stability. Copyright © 2009 John Wiley & Sons, Ltd.     

Reversed-phase high-performance liquid chromatography determination of selected phenolic acids in propolis concentrates in terms of standardization for drug manufacturing purposes

A reversed-phase high-performance liquid chromatography method with gradient elution was developed for the determination of the caffeic, p-coumaric, and ferulic acids in propolis concentrates. Solid-phase extraction on an RP18 column was applied for preliminary purification, and chromatographic separation was performed on 100 RP18e Lichrospher column of particle size 5 microm. The mobile phase was obtained by mixing in appropriate ratios 0.03 mM NaH2PO4, acidified with H3PO4 up to pH = 3.0, with acetonitrile to obtain a gradient in the elution process. Spectrophotometric detection was conducted at 320 nm. Under the established conditions, the method featured high sensitivity, good precision, and comparability of results, as proven by method validation and statistical analysis of the obtained results. The limits of detection were 0.315, 0.325, and 0.695 microg/mL for caffeic, p-coumaric, and ferulic acids, respectively. The corresponding recovery values were 98.14, 101.05, and 99.42% and the linearity ranges from 1.31 to 99.18 microg/mL, 1.52 to 119.16 microg/mL, and 2.42 to 184.14 microg/mL. The precision of the method was expresed by relative standard deviation values that did not exceed 3%. It was also shown that the propolis concentrates under examination had similar antibacterial activity against Staphylococcus aureus ranging from 119.8 to 124.3 microg/mL, contrary to model mixtures that showed no antibacterial activity.     

Legendre–Fenchel transform of the spectral exponent of polynomials of weighted composition operators

For the spectral radius of weighted composition operators with positive weight e ^φ T _α , \({\varphi\in C(X)}\) , acting in the spaces L ^p (X, μ) the following variational principle holds

$\ln r(e^\varphi T_\alpha)=\max_{\nu\in M^1_\alpha} \left\{\int\limits_X\varphi d\nu-\frac{\tau_\alpha(\nu)}{p}\right\},$

where X is a Hausdorff compact space, \({\alpha:X\mapsto X}\) is a continuous mapping and τ _α some convex and lower semicontinuous functional defined on the set \({M^1_\alpha}\) of all Borel probability and α-invariant measures on X. In other words \({\frac{\tau_\alpha}{p}}\) is the Legendre– Fenchel conjugate of ln r(e ^φ T _α ). In this paper we consider the polynomials with positive coefficients of weighted composition operator of the form \({A_{\varphi, {\bf c}}= \sum_{k=0}^n e^{c_k} (e^{\varphi} T_{\alpha})^k}\) , \({{\bf c}=(c_k)\in {\Bbb R}^{n+1}}\) . We derive two formulas on the Legendre–Fenchel transform of the spectral exponent ln r(A _φ,c) considering it firstly depending on the function φ and the variable c and secondly depending only on the function φ, by fixing c.

     

Optimal control problems of hyperbolic systems with operator and nonoperator equality constraints

In the paper two kinds of optimal control problems of hyperbolic systems with additional equality constraints are considered: a problem with the operator equality constraint in the form of terminal condition and a problem with nonoperator equality constraint in the u(.)ε U where - some set. The extremum principles are proved: for the first problem - by using some specification of the Dubovitskii-Milyutin method in the case of n equality constraints in the operator form and for the second one - by using some generalization of the Dubovitskii-Milyutin theory     

Chromatographic analysis of penstemide and serrulatoloside by high-performance liquid chromatography and gradient thin-layer chromatography

Summary A sensitive capillary gas chromatographic method is described for the simultaneous determination of lidocaine, tetracaine, procaine and dibucaine. The method was applied to the determination of anesthetics in tissue homogenates incubated at 38°C at doses between 10 and 400 mg/kg. In the liver tissue thein vitro metabolization of the studied anesthetics is most rapid for tetracaine, also fast for procaine, while for lidocaine and dibucaine the metabolization is very slow. In brain tissue thein vitro metabolization of anesthetics is very slow.The method shows good analytical parameters: linearity between 5 and 40 g/ml; day-to-day reproducibility ca. 8% for a concentration of 20 g/ml, precision ca. 7% for a concentration of 20g/ml. Accuracy is also very good.     

Die Löslichkeit der Übergangsphasen von Cadmiumferrit in Salpetersäure

Zusammenfassung Es wurde die Löslichkeit in 2n-HNO₃ von durch Sinterung eines Gemisches von CdO mit Fe₂O₃ bei 500°C bis 1100°C erhaltenen Präparaten untersucht. Es wurde eine gänzliche Auflösung des Cadmiums nach kurzen Lösezeiten für 700°C Glühtemperatur festgestellt. Oberhalb dieser Temperature fällt der Cd²⁺-Gehalt der Lösung langsam ab. Das Fe³⁺ geht in Lösung aus bei 700 bis 900°C geglühten Präparaten. Oberhalb 900°C fällt sein Gehalt in der Lösung merklich ab. Röntgenographisch wurde ein fortschreitender Ferritisierungsprozeß, von 700°C beginnend, festgestellt. Oberhalb 950°C tritt eine Ferritphase auf.

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Solubility of the transition phases of cadmium ferrite in nitric acid

Preparations, which where obtained by baking mixtures of CdO and Fe₂O₃ between 500 and 1100°C, where investigated in regard to their solubilities in 2n-HNO₃. Complete dissolution of Cd within short periods of time was observed for baking temperatures of 700°C. Above this temperature, the Cd²⁺-content of the solutions decreases slowly. Fe³⁺ dissolves out of preparations between 700 and 900°C. When heated above 900°, the Fe³⁺ content in solutions decreases. X-ray powder investigations showed a progressive process of ferrite formation, starting at 700°. Above 950°, a ferrite phase is formed.

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Mit 3 Abbildungen     

Über die ferromagnetischen Produkte erwärmter Mischungen von Cu(OH)2/Fe(OH)3

Zusammenfassung Die Kochprodukte der Mischungen von gemeinsam gefällten Eisen- und Kupferhydroxiden wurden durch Röntgenaufnahmen und magnetische Messungen identifiziert.Der Ferromagnetismus des Präparates nach dem Kochen wird durch das Eisen(III)--oxid hervorgerufen.

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The products of boiling mixtures of simultaneously precipitated iron and copper hydroxides were identified by means of X-ray diffraction and magnetic measurements. The ferro-magnetism of the preparation after boiling is caused by iron(III)--oxid.

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Mit 5 Abbildungen     

Surface and micellar properties of new nonionic gemini aldonamide-type surfactants

A new group of gemini aldonamide-type surfactants-N,N'-bisalkyl-N,N'-bis[(3-gluconylamide)propyl]ethylenediamines, N,N'-bisdodecyl-N,N'-bis[(3-glucoheptonylamide)propyl]ethylenediamine, and N,N'-bisalkyl-N,N'-bis[(3-lactobionylamide)propyl]ethylenediamines, (alkyl: n-C(8)H(17), n-C(12)H(25)), were synthesized and characterized. The surface properties, such as surface excess concentration, Gamma(cmc), surface area demand per molecule, A(min), efficiency in surface tension reduction, pC(20), the effectiveness of surface tension reduction, gamma(cmc), critical micelle concentration, cmc, and a measure of the tendency of the surfactant to adsorb at the aqueous/air interface relative to its tendency to form micelles in the bulk surfactant solution, cmc/C(20), and standard free energy of micellization, DeltaG(mic)(0), have been obtained by means of surface tension measurements. The standard fluorescence shift technique using PRODAN as a probe provide confirmation of the cmc values by an alternative method. Additionally, the micellar properties for the concentration near above the cmc have been characterized by the aggregation number, N(agg). The presence of the dimeric segments with the aldonamide hydrophilic units in the surfactant molecule is found to be the source of their unusual physicochemical behavior. They are very efficient at adsorbing at the free surface and at forming micelles in water. Their critical micelle concentration values are remarkably low. They reveal remarkably low A(min) values in relation to conventional nonionic surfactants, which is unexpected from the molecular dimensions for the molecule but which is possible if one assumes some type of multilayer structure or a coherent interfacial film.