The Schwarzian derivative for harmonic mappings

Journal d'Analyse Mathématique -     

Chiral (Diphosphonite)platinum Complexes in Asymmetric Hydroformylation

The chiral diphosphonite ligand (11bR,11′bR)‐4,4′‐(9,9‐dimethyl‐9H‐xanthene‐4,5‐diyl)bis[dinaphtho[2,1‐d:1′,2′‐f][1,3,2]dioxaphosphepin] ((R,R)‐XantBino; (R)‐ 1 ), based on a rigid xanthene backbone, was applied in the Pt/Sn‐catalyzed hydroformylation of styrene ( 4a ), 4‐methylstyrene ( 4b ), vinyl acetate ( 4c ), and allyl acetate ( 4d ), by using a Pt/Sn ratio of 1 : 1. High ee of up to 80% were observed, along with good regioselectivities towards the desired branched aldehydes. For styrene, an interesting inversion in the stereoselection process was observed at elevated temperatures, and a mechanism is proposed considering the temperature dependence of the regioselectivity. The complex [PtCl₂{(S,S)‐XantBino}] ((S)‐ 2 ) was characterized by X‐ray crystal‐structure analysis, revealing an unusual out‐of‐plane ligand coordination of the metal fragment. The complex [PtCl(SnCl₃){(R,R)‐XantBino}] ((R)‐ 3 ) was characterized by means of ³¹P‐NMR spectroscopy.     

The effect of arsenic exposure on the biochemical and mineral contents of Labeo rohita bones: An FT-IR study

Arsenic compounds are ubiquitous and widespread in the environment as a result of natural or anthropogenic occurrence. Fish are the major source of protein for human consumption. They are also a source of contamination, because of the amounts of heavy elements they can contain, some of which are highly toxic. Fish bones are high in calcium, which is an essential mineral for normal body function. It consists of water, organic material, and mineral matter. Chelating agents have been used clinically as antidotes for acute and chronic metal intoxications. In the present study, an attempt is made to investigate the bio-accumulation of arsenic and its effect on the biochemical and mineral contents of Labeo rohita bones using, Fourier transform infrared (FT-IR) spectroscopy. The results of the present study indicate that arsenic exposure induces significant reduction on the biochemical and mineral contents of the L. rohita bones. Further, the DMSA treatment significantly improves these levels. This shows that DMSA is an effective chelator for arsenic toxicity. Quantitative curve-fitting analyses of amide I band have proved useful in studying the nature and the extent of protein conformational changes. A decrease in α-helical and random coil structures and an increase in β-sheet structures have been observed due to arsenic exposure. In conclusion, the present study shows that the FT-IR spectroscopy coupled with second derivative and curve-fitting analysis gives useful information about the biochemical and mineral contents of the L. rohita bones.     

FTIR study of zinc-induced biochemical changes in the liver of Indian carp <Emphasis Type="Italic">Labeo rohita</Emphasis>

Zinc is an essential metal for different physiological functions and becomes toxic when elevated concentrations are introduced into the environment. In the present study, an attempt is made to analyze zinc-induced biochemical changes in the liver tissues of freshwater fingerlings of Labeo rohita using Fourier Transformation Infrared Spectroscopy. Several important features have been observed in the FTIR spectra of zinc-intoxicated liver tissues, namely, altered membrane lipid, altered protein profile, and increased glycogen content, indicating an alteration in the lipid and protein profiles leading to modification in membrane composition. Further, it is observed that acute exposure to zinc causes some alteration in protein profile with a decrease in α-helix and an increase in random coil structure. Treatment with the chelating agent D-penicillamine reduces the biochemical contents in the liver tissues. This shows that D-penicillamine is a good antidote for zinc toxicity. Published in Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 5, pp. 746–752, September–October, 2008.     

Trajectories of the zeros of hypergeometric polynomials F(−n, b; 2b; z) for b < − 1/2

In a previous paper [2] we studied the zeros of hypergeometric polynomials F(−n, b; 2b; z), where b is a real parameter. Making connections with ultraspherical polynomials, we showed that for b > − 1/2 all zeros of F(−n, b; 2b; z) lie on the circle |z − 1| = 1, while for b < 1 − n all zeros are real and greater than 1. Our purpose now is to describe the trajectories of the zeros as b descends below the critical value − 1/2 to 1 − n. The results have counterparts for ultraspherical polynomials and may be said to “explain” the classical formulas of Hilbert and Klein for the number of zeros of Jacobi polynomials in various intervals of the real axis. These applications and others are discussed in a further paper [3].     

Generalized support points of the set of univalent functions

The solutions to linear extremal problems, or the support points of the classS, have been extensively studied. Every support point is known to be a monotone slit mapping whose omitted arc is analytic. Our purpose here is to consider a more general class of continuous linear functionals onS and to investigate the geometric properties of their associated extremal functions. Under appropriate hypotheses we show that the generalized support points so produced are monotone slit mappings. We then give an example where the omitted set is not an analytic arc, thus proving the existence of an extreme point which is not a support point in the usual sense. Here we follow an idea of Hamilton [4], which he used for the same purpose, but our construction is simpler.     

Smirnov domains

This is an expository article which briefly surveys some of V. I. Smirnov's early contributions to the theory of H^p spaces, with emphasis on Smirnov domains and related developments.Published in Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 170, pp. 95–101, 1989.     

Bioconcentration of zinc and its effect on the biochemical constituents of the gill tissues of Labeo rohita: An FT-IR study

In the present work, an attempt has been made to assess the bioconcentration and distribution of zinc on the selected organs of Labeo rohita and to study the effect of zinc exposure on the biochemical constitutions of gill tissues of L. rohita by using FT-IR Spectroscopy. The concentration pattern in the organs reveals that the liver is the prime site of metal binding and muscle accumulates least metal concentration. The accumulation profile is in the order: liver > gill > kidney > brain > bone > muscle. It has also been observed that the administration of chelating agent d-Penicillamine (DPA) reduces the zinc concentration in all tissues more effectively than the administration of the chelating agent Ethylene Diamine Tetra Acetic acid. The FT-IR spectra reveal that zinc exposure causes significant changes in the biochemical constitutions of the gill tissues. It causes an alteration in the protein secondary structures by decreasing the α-helix and increasing the β-sheet contents. Further, it has been observed that the administration of chelating agent DPA improves the protein and lipid contents in the gill tissues compared to zinc exposed tissues. This result shows that DPA is the effective chelator of zinc in reducing the body burden of L. rohita fingerlings. In conclusion, the findings of the current study suggest that zinc exposure causes significant changes in both lipids and proteins of the gill tissues, and changes the protein profile in favour of β-sheet structure.