The fekete-szegö problem for close-to-convex functions with respect to the koebe function

An analytic function f   in the unit disk D :={z ∈ ? : |z| < 1}$\mathbb{D}\hspace{0.17em}:=\left\{z\hspace{0.17em}\in \hspace{0.17em}?\hspace{0.17em}:\hspace{0.17em}\left|z\right|\hspace{0.17em}<\hspace{0.17em}1\right\}$, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/(1−z)², z ∈ D$k\left(z\right)\hspace{0.17em}:=\hspace{0.17em}z/{\left(1-z\right)}^2,\hspace{0.17em}z\hspace{0.17em}\in \hspace{0.17em}\mathbb{D}$ if there exists δ∈(-π/2,π/2) such that Re{eiδ(1−z)²f^′(z)} > 0, ∈ D$\text{Re}\left\{{\text{e}}^{\text{i}\delta }{\left(1-z\right)}^2{f}^{\prime }\left(z\right)\right\}\hspace{0.17em}>\hspace{0.17em}0,\hspace{0.17em}\in \hspace{0.17em}\mathbb{D}$. For the class C(k) of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szegö problem is studied.     

Bioelectrochemical application of some PQQ-dependent enzymes.

This paper focuses on the use of PQQ-dependent enzymes (PQQ enzymes) in amperometrical biosensors and gives emphasis on their innovative designs and applications. The study covers some aspects in the evolution of biosensors based on PQQ enzymes. Main attention is focused on the electrochemical properties of PQQ enzymes as very promising materials for the formation of electrochemical biosensors. Immobilization approaches and redox mediators recently used in PQQ enzymes based biosensors are reviewed. The acceptance of polypyrrole as a very promising immobilization matrix for some PQQ enzymes is discussed.     

Influence of velocity distribution in the multiphase flow on the building of aerobic granules in a Sequencing Batch Reactor (SBR)

In present contribution a study is presented, where fluid dynamic measurements are used to observe multiphase flow pattern in a bioreactor. It can be shown that hydrodynamic effects have a major influence on the formation, shape and size of Granular Activated Sludge (GAS) in a Sequencing Batch Reactor (SBR) under aerobic condition. In order to analyse multiphase flow pattern (water, air, granules) in the bioreactor in-situ techniques with optical measurements are applied. LASER IIIB and video lamp are used as a light source. Due to a transient spatial velocity distribution in the bioreactor our experiments are carried out in different levels of SBR. Tracer particles are employed to visualise the fluid flow pattern. Velocity field of the liquid phase in the bioreactor is determined by use of PIV method (Particle Image Velocimetry). PTV (Particle Tracking Velocimetry) is implemented to observe velocity field of individual granules (solid phase). (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences

This paper is devoted to various considerations on a family of sharp interpolation inequalities on the sphere, which in dimension greater than 1 interpolate between Poincaré, logarithmic Sobolev and critical Sobolev (Onofri in dimension two) inequalities. The connection between optimal constants and spectral properties of the Laplace-Beltrami operator on the sphere is emphasized. The authors address a series of related observations and give proofs based on symmetrization and the ultraspherical setting.     

Kinetics,catalysis, and mechanism of isomerization of N-[(benzotriazol-1-yl)methyl]anilines into the benzotriazol-2-yl derivatives

The ¹H NMR technique was applied for the measurement of the isomerization rates of N-ethyl-N-[(benzotriazol-1-yl)methyl]aniline ( 4 ) and 4-butyl-N-[(benzotriazol-1-yl)methyl]aniline ( 7 ) to the corresponding benzotriazol-2-yl isomers in dioxane-d₈ at 35°C. The rate constants obtained for pure dioxane-d₈ were 1.62 and 0.28 h^?1 for 4 and 7 , respectively. For both compounds, addition to acetic acid to the dioxane solutions accelerated the isomerizations whereas addition of triethylamine retarded it strongly. Addition of water slowed the isomerization of 4 but accelerated that of 7 : the different effects operating in the two cases are discussed and rationalized. © 1995 John Wiley & Sons, Inc.     

Label-free molecular imaging of immunological synapses between dendritic and T cells by Raman micro-spectroscopy

Confocal Raman micro-spectroscopy (CRMS) was used to measure spectral images of immunological synapse formation between dendritic and T cells without using molecular labels or other invasive procedures. The purpose-built inverted CRMS instrument integrated an environmental enclosure and a near-infrared laser to allow measurements on live cells maintained under physiological conditions. The integration of the wide-field fluorescence also enabled viability assays and direct comparison between Raman spectral images and gold-standard immuno-fluorescence images for specific molecules. Raman spectral images of nucleus and proteins were built by fuzzy c-mean clustering method. The Raman images were found to be in good correspondence with the immuno-fluorescence images of DNA and actin. These results indicate that actin is a main contributor to the Raman spectrum of the cytoplasm of dendritic and T cells. While for control cells the Raman spectral images of proteins indicated a more homogeneous distribution of proteins in the cytoplasm of dendritic cells, they indicated a higher accumulation of proteins at the immunological synapses when dendritic cells were pre-treated with laminin. These conclusions were also supported by confocal immuno-fluorescence imaging after cell fixation and labelling. This study demonstrates the potential of CRMS for label-free non-invasive imaging of junctions between live cells. Therefore, this technique may become a useful tool for studying cellular processes in live cells and where non-invasive molecular specific imaging is desirable, such as cell-cell interactions.     

Convenient Synthesis of Julolidines Using Benzotriazole Methodology

Reaction of N,N-bis[(benzotriazol-1-yl)methyl]aniline (2) with 1-vinylpyrrolidin-2-one gives a mixture of diastereomeric 1,7-bis(2-oxopyrrolidin-1-yl)julolidines 3. After reduction of 3 with LAH, the predominant trans diastereomer of 1,7-di(pyrrolidin-1-yl)julolidine (4) is separated. Reaction of 2 with ethyl vinyl ether yields predominantly trans-1,7-di(benzotriazol-1-yl)julolidine (11). Stepwise synthesis from tetrahydroquinoline 15 gives access to julolidines with two different substituents on C-1 and C-7. Reaction of 1-[(benzotriazol-1-yl)methyl]-1,2,3,4-tetrahydroquinoline (25) with enolizable aldehydes gives a mixture of tetrahydroquinolines 26-29 which are converted into single julolidine products upon treatment with sodium hydride, LAH, or phenylmagnesium bromide. Reactions of 1,2,3,4-tetrahydroquinolines with benzotriazole and 2 molar equiv of enolizable aldehydes gives 1,2,3-trisubstituted julolidines 38-41, which with lithium aluminum hydride, sodium hydride, or a Grignard reagent produce single diastereomers of products 42, 43, and 45, respectively.