Influence of pH of the BSA solutions on velocity of the rising bubbles and stability of the thin liquid films and foams

Influence of pH of the BSA solutions on velocity of the rising bubbles, stability of foams, and properties of single foam and wetting films was studied. It was found that the solution pH affected significantly the BSA surface activity and properties of the protein adsorption layer under dynamic and static conditions. At pH close to the isoelectric point (pH_IEP=4.8) the BSA showed the highest surface activity. The equilibrium microscopic foam films of thicknesses of 64–80 nm, depending on the BSA concentration, were obtained at pH=5.8. Under dynamic conditions the bubble rising velocity was reduced in a highest degree and the foam formed were most stable at the solutions pH-5.8 and 4.8. Lowering the bubble velocity shows that the BSA adsorption layer was formed, which retarded fluidity of the bubble surface. When the solution pH was significantly lower (pH=3.9) or much higher (pH=10) than the pH_IEP then the BSA practically had no influence on the bubble velocity and the foam stability was drastically reduced. Moreover, the pH variations affected also the time of the three-phase contact (TPC) formation on mica surface covered by the BSA adsorption layers. These pH dependent changes in the BSA surface activity indicate that the BSA linear conformers, existing at pH far away from the pH_IEP, have much higher affinity to aqueous phase resulting from higher net electrical charge present over the extended BSA molecule conformers.     

Three New Iron(II) Thiocyanato Coordination Polymers Based on 4,4′‐Bipyridine as Ligand and the Influence of Methanol on Their Structures

Reaction of iron(II) thiocyanate with 4,4‐bipyridine (bipy) in methanol leads to the formation of three new solvates of different composition depending on the reaction conditions: At room temperature two new ligand‐rich 1:2 (1:2 = ratio between metal and N‐donor ligand) polymorphic forms [Fe(NCS)₂(bipy)₂ · 2MeOH]_n ( 1I ) and [Fe(NCS)₂(bipy)(MeOH)₂ · (bipy)]_n ( 1II ) are obtained, whereas solvothermal conditions leads to the formation of the new ligand‐deficient 1:1 compound [{Fe(NCS)₂(bipy)(MeOH)}₂]_n ( 2 ). All crystal structures were determined by X‐ray single crystal structure analysis. In the crystal structure of modification 1I the metal atoms are coordinated by four bridging bipy ligands, which connect them into layers. The methanol molecules occupy voids in the structure. Compared to 1I in modification 1II the crystal structure contains of linear Fe–bipy–Fe chains, which are further connected by hydrogen bonds between coordinating MeOH and noncoordinated bipy ligands into layers. The ligand‐deficient 1:1 compound 2 shows a completely different coordination topology with linear Fe–bipy–Fe chains, which are connected by coordinating methanol molecules into double‐chains. In all compounds the thiocyanato anions are terminal N‐bonded to the metal atoms. Investigation of the thermal behavior of compound 1I shows a two‐step decomposition, in which ligand‐deficient intermediates are formed. Magnetic measurements on 1I reveal Curie–Weiss paramagnetism with increasing antiferromagnetic interactions on cooling.     

Detection of multivariate outliers in business survey data with incomplete information

Many different methods for statistical data editing can be found in the literature but only few of them are based on robust estimates (for example such as BACON-EEM, epidemic algorithms (EA) and transformed rank correlation (TRC) methods of Béguin and Hulliger). However, we can show that outlier detection is only reasonable if robust methods are applied, because the classical estimates are themselves influenced by the outliers. Nevertheless, data editing is essential to check the multivariate data for possible data problems and it is not deterministic like the traditional micro editing where all records are extensively edited manually using certain rules/constraints. The presence of missing values is more a rule than an exception in business surveys and poses additional severe challenges to the outlier detection. First we review the available multivariate outlier detection methods which can cope with incomplete data. In a simulation study, where a subset of the Austrian Structural Business Statistics is simulated, we compare several approaches. Robust methods based on the Minimum Covariance Determinant (MCD) estimator, S-estimators and OGK-estimator as well as BACON-BEM provide the best results in finding the outliers and in providing a low false discovery rate. Many of the discussed methods are implemented in the R package ${\tt{rrcovNA}}$ which is available from the Comprehensive R Archive Network (CRAN) at http://www.CRAN.R-project.org under the GNU General Public License.     

γ-Active Constraints in Convex Semi-Infinite Programming

In this article, we extend the definition of γ-active constraints for linear semi-infinite programming to a definition applicable to convex semi-infinite programming, by two approaches. The first approach entails the use of the subdifferentials of the convex constraints at a point, while the second approach is based on the linearization of the convex inequality system by means of the convex conjugates of the defining functions. By both these methods, we manage to extend the results on γ-active constraints from the linear case to the convex case.     

Motzkin predecomposable sets

We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i.e., those for which the convex cone in the decomposition is requested to be closed), while others are specific of the new family.     

Solution of the Feedback Control Problem in the Mathematical Model of Leukaemia Therapy

A mathematical model of leukaemia therapy based on the Gompertzian law of cell growth is investigated. The effect of the medicine on the leukaemia and normal cells is described in terms of therapy functions. A feedback control problem with the purpose of minimizing the number of the leukaemia cells while retaining as much as possible the number of normal cells is considered. This problem is reduced to solving the nonlinear Hamilton–Jacobi–Bellman partial differential equation. The feedback control synthesis is obtained by constructing an exact analytical solution to the corresponding Hamilton–Jacobi–Bellman equation.     

Influence of the type of light polarization on photoinduced processes

We investigate the influence of the type of light polarization (linear or circular) on the efficiency of non-linear optical processes in photoanisotropic materials. A theoretical model of photoprocesses in materials in which optical non-linearity is related to absorbing centres with intrinsic linear anisotropy is constructed. Theoretical calculations show that the photostationary concentration of the photoproducts (and the mean values of the non-linear changes in optical constants) in these materials is higher if the exciting light is circularly polarized. Experimental results on non-linear processes in samples of fluorescein incorporated in orthoboric acid and in azodye/polymer layers are in good agreement with the theory. This revised version was published online in November 2006 with corrections to the Cover Date.