On the Fekete-Szego problem for concave univalent functions

We consider the Fekete-Szego problem with real parameter lambda for the class Co(alpha) of concave univalent functions. (C) 2010 Elsevier Inc. All rights reserved.

On some results of A. E. Livingston and coefficient problems for concave univalent functions

We consider functions that map the open unit disc conformally onto the complement of a bounded convex set. We call these functions concave univalent functions. In 1994, Livingston presented a characterization for these functions. In this paper, we observe that there is a minor flaw with this characterization. We obtain certain sharp estimates and the exact set of variability involving Laurent and Taylor coefficients for concave functions. We also present the exact set of variability of the linear combination of certain successive Taylor coefficients of concave functions.

Substitution of chromium for univalent copper in superconducting Pb2Sr2(Ca,Y)Cu3O8+delta

Following considerations of geometry and the similarity between chromate and carbonate groups in terms of size and charge, we have investigated the possibility of replacing the two-coordinate Cu-I in superconducting lead cuprates of the general formula Pb2Sr2(Ca, Y)CU3O8 by Cr. A high-resolution electron microscopy study coupled with energy dispersive X-ray analysis on small crystals of the title phases suggests that between 10 and 15% of the Cu-I can be replaced by Cr. While from the present structural study using HRTEM and Rietveld refinement of X-ray powder data we are unable to precisely obtain the oxidation state and oxygen coordination of Cr, we suggest in analogy with Cr substitution in other similar cuprates that in the title phases (CuO2)-O-I rods are partially replaced by tetrahedral CrO42- groups. Infrared spectroscopy supports the presence of CrO42- groups. The phases Pb1.75Sr2Ca0.2Y0.8O8+delta and Pb1.75Sr2Ca0.2Y0.8CCu2.85Cr0.15O8+delta are superconducting as-prepared, but the substitution of Cr for Cu-I results in a decrease of the Te as well as the superconducting volume fraction. (C) 1996 Academic Press, lnc.

On concave univalent functions

We consider functions that map the open unit disc conformally onto the complement of an unbounded convex set with opening angle pa, a ? (1, 2], at infinity. In this paper, we show that every such function is close-to-convex of order (a - 1) and is included in the set of univalent functions of bounded boundary rotation. Many interesting consequences of this result are obtained. We also determine the extreme points of the set of concave functions with respect to the linear structure of the Hornich space.

Mechanism of aromatic hydroxylation *1, , *2, , *3: Properties of a model for pyridine nucleotide-dependent flavoprotein hydroxylases

A model (NADH-phenazine methosulfate-O2) formally similar to pyridine nucleotide-dependent flavoprotein hydroxylases catalyzed the hydroxylation of several aromatic compounds. The hydroxylation was maximal at acid pH and was inhibited by ovine Superoxide dismutase, suggesting that perhydroxyl radicals might be intermediates in this process. The stoichiometry of the reaction indicated that a univalent reduction of oxygen was occurring. The correlation between the concentration of semiquinone and hydroxylation, and the inhibition of hydroxylation by ethanol which inhibited semiquinone oxidation, suggested the involvement of phenazine methosulfate-semiquinone. Activation of hydroxylation by Fe3+ and Cu2+ supported the contention that univalently reduced species of oxygen was involved in hydroxylation. Catalase was without effect on the hydroxylation by the model, ruling out H2O2 as an intermediate. A reaction sequence, involving a two-electron reduction of phenazine methosulfate to reduced phenazine methosulfate followed by disproportionation with phenazine methosulfate to generate the semiquinone, was proposed. The semiquinone could donate an electron to O2 to generate O2 which could be subsequently protonated to form the perhydroxyl radical.

An immunochemical study of ovine pituitary follicle-stimulating hormone (FSH)

An immunochemical study of ovine follicle-stimulating hormone and its antibody carried out by using precipitin, agglutinating and complement-fixation systems, has suggested that the follicle-stimulating hormone, possibly by virtue of it being a univalent antigen, forms a soluble complex with its specific antibody. This antiserum is species nonspecific in that it is able to neutralize the follicle-stimulating activity of rat, mouse, hamster, guinea pig pituitary extracts, and pregnant mare serum gonadotropin. Human chorionic gonadotropin, however, has been shown not to form a complex with the follicle-stimulating hormone specific antibody.