Drainage and critical thickness of foam films from aqueous solutions of mixed nonionic surfactants

The thinning and the critical thickness (of rupture or “black spots” formation) of foam films from aqueous solutions of mixed nonionic surfactants are studied under varied experimental conditions, as a function of film radius (0.05–0.15 mm), surfactant concentration (0.01–1.0 CMC) and ionic strength (0.001–0.1 M NaCl). The experimental values of the drainage coefficient (), determined from the film thickness versus time dependences, were used to calculate the theoretical values of the film critical thickness.

The real velocity of film thinning is a major factor in the process of reaching the state of kinetic instability when approaching the critical thickness (Scheludko's criterion). The classical equation used to describe the film thinning rate, proposed and named by Scheludko (1955) “Reynolds Law”, is applicable for small film radii (r < 0.05 mm). At larger radii the velocity of thinning follows the equation of Manev et al. [E.D. Manev, R. Tsekov, B. Radoev, J. Colloid Interf. Sci. 18 (1997) 769], which takes into account the effect of the film thickness local non-homogeneity.

The studied stabilizing surfactants include n-dodecyl-β-d-maltoside (β-C12G2) and hexaethyleneglycol monododecyl ether (C12E6). Along with confirming the dependences following from the theories of the critical thickness [B. Radoev, A. Scheludko, E.D. Manev, J. Colloid Interf. Sci. 95 (1983) 254] and film thinning [E.D. Manev, R. Tsekov, B. Radoev, J. Colloid Interf. Sci. 18 (1997) 769], the results of the present investigation established also certain deviations for films stabilized with mixed surfactants (β-C12G2 + C12E6). The effectiveness of the empirical equation, employing the drainage coefficient () to describe the film thinning, is emphatically proven here.     

Thermoxidative degradation of poly(vinyl alcohol) under dynamic thermogravimetric conditions. II. Influence of the hydrolysis degree

The influence of the degree of hydrolysis on thermoxidative degradation of the poly(vinyl alcohol) was studied. The thermoxidative degradation was carried out under dynamic thermal conditions. Taking into account the dependence of the activation energy values on the heating rate, molecular weight, degree of conversion, and degree of hydrolysis, some conclusions were drawn about the decomposition mechanism and the variation of the thermal stability.     

Anion Recognition by Uranyl–Salophen Derivatives as Probed by Infrared Multiple Photon Dissociation Spectroscopy and Ab Initio Modeling

The vibrational features and molecular structures of complexes formed by a series of uranyl–salophen receptors with simple anions, such as Cl^?, H^?, and HCOO^?, have been investigated in the gas phase. Spectra of the anionic complexes were studied in the $\tilde \nu $ =800–1800 cm^?1 range by mass‐selective infrared multiple photon dissociation (IRMPD) spectroscopy with a continuously tunable free‐electron laser. The gas‐phase decarboxylation of the formate adducts produces uranyl–salophen monohydride anions, which have been characterized for the first time and reveal a strong U?H bond, the nature of which has been elucidated theoretically. The spectra are in excellent agreement with the results obtained from high‐quality ab initio calculations, which provided the structure and binding features of the anion–receptor complexes.     

The γ-attenuation problem for systems with state dependent noise

The general γ-attenuation problem is considered for systems with statedependent noise. It is shown that if a controller exists which stabilizes a system with disturbance attenuation then certain LMI's must have positive-definite solutions satisfying a complementary rank condition. If such solutions exist for the considered LMI's the controller is obtained also by solving an LMI. In the absence of the noise the LMI's involved reduce to the ones introduced by Gahinet and al in [7]     

Optimal stabilizing compensator for linear systems under white noise perturbations

For time varying linear stochastic systems it is proved that the best stabilizing compensator is the one constructed by using stabilizing solutions for the standard control and estimation Riccati equations     

Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces

In this paper, we extend the coupled fixed point theorems for mixed monotone operators F:X×X→X obtained in [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379–1393] by significantly weakening the contractive condition involved. Our technique of proof is essentially different and more natural. An example as well as an application to periodic BVP is also given in order to illustrate the effectiveness of our generalizations.     

Structural characterization and photoluminescence of nanocrystalline Ho-doped BaTiO<Subscript>3</Subscript> derived from sol–gel method

Nanocrystalline Ho-doped BaTiO₃, with average nanocrystals size of 20 nm, have been prepared using a sol–gel combustion technique. The structural and morphological properties of the powders have been investigated by X-ray powder diffraction and high resolution transmission electron microscopy. Chemical states of the holmium on the Ba_0.97Ho_0.03TiO₃ ceramic surface were analyzed using X-ray photoelectron spectroscopy. Furthermore, their photoluminescence properties were analyzed.     

Randers metrics on CP2

The complex projective space CP² is a classical example of Einstein metric in Riemannian geometry. Moreover, beside this property, it has other interesting geometrical properties: it is a symmetric space, and a C manifold. We would like to know whether there is an Einstein metric of Randers type on CP² with similar properties. Based on some the generalization of Zermelo navigation problem for Finsler manifolds we construct such Randers metric on CP² and study some of its geometrical properties.