On the compactness of isometry groups in complex analysis

We prove that the group of continuous isometries for the Kobayashi or Caratheodory metrics of a strongly convex domain in C-n is compact unless the domain is biholomorphic to the ball. A key ingredient, proved using differential geometric ideas, is that a continuous isometry between a strongly convex domain and the ball has to be biholomorphic or anti-biholomorphic. Combining this with a metric version of Pinchuk's rescaling technique gives the main result.

Genetic Heterogeneity in Wild Isolates of Cellular Slime Mold Social Groups

This study addresses the issues of spatial distribution, dispersal, and genetic heterogeneity in social groups of the cellular slime molds (CSMs). The CSMs are soil amoebae with an unusual life cycle that consists of alternating solitary and social phases. Because the social phase involves division of labor with what appears to be an extreme form of "altruism", the CSMs raise interesting evolutionary questions regarding the origin and maintenance of sociality. Knowledge of the genetic structure of social groups in the wild is necessary for answering these questions. We confirm that CSMs are widespread in undisturbed forest soil from South India. They are dispersed over long distances via the dung of a variety of large mammals. Consistent with this mode of dispersal, most social groups in the two species examined for detailed study, Dictyostelium giganteum and Dictyostelium purpureum, are multi-clonal.

Complexes of lanthanide nitrates with N,N-diethylantipyrine-4-carboxamide

New complexes of lanthanide nitrates with N, N-diethylantipyrine-4-carboxamide (DEAP), with the general formulae [Ln2(DEAP)3] [NO3]6 (where Ln = La, Pr, Nd, Sm, Tb, Ho, Er, Yb and Y) have been isolated and characterized by chemical analysis and various physical methods such as electrolytic conductance, IR and13C NMR spectral data. Electrolytic conductance values and infrared spectral studies indicate that the nitrate groups are coordinated. Infrared and13C NMR spectral analysis show that the ligand DEAP is coordinated to the tripositive metal ion through the diethylcarboxamide carbonyl and antipyrine carbonyl oxygens in a bidentate fashion.

Splittings of free groups, normal forms and partitions of ends

Splittings of a free group correspond to embedded spheres in the 3-manifold M = # (k) S (2) x S (1). These can be represented in a normal form due to Hatcher. In this paper, we determine the normal form in terms of crossings of partitions of ends corresponding to normal spheres, using a graph of trees representation for normal forms. In particular, we give a constructive proof of a criterion determining when a conjugacy class in pi (2)(M) can be represented by an embedded sphere.

Successive refinement of structures with data of increasing resolution: a theoretical study for triclinic space groups

The method of least squares could be used to refine an imperfectly related trial structure by adoption of one of the following two procedures: (i) using all the observed at one time or (ii) successive refinement in stages with data of increasing resolution. While the former procedure is successful in the case of trial structures which are sufficiently accurate, only the latter has been found to be successful when the mean positional error (i.e.<|[Delta]r|>) for the atoms in the trial structure is large. This paper makes a theoretical study of the variation of the R index, mean phase-angle error, etc. as a function of <|[Delta]r|> for data corresponding to different esolutions in order to find the best refinement procedure [i.e. (i) or (ii)] which could be successfully employed for refining trial structures in which <|[Delta]r|> has large, medium and low values. It is found that a trial structure for which the mean positional error is large could be refined only by the method of successive refinement with data of increasing resolution.

Intermolecular Chelate Linkage Isomerism of the Hydroxyimino Group in the Nickel(II), Copper(II), and Palladium(II) Complexes of Quadridentate Schiff-base Ligands

The C-nitrosation of bivalent quadridentate β-imino ketone complexes of nickel(II), copper(II), and palladium(II), with nitrosating reagents has been investigated. The chemical analysis and spectroscopic results reveal that one of the α-CH groups of the coordinated lignad undergoes selective nitrosation forming mono(hydroxyimino) derivative. The hydroxyimino group introduced coordinates through either N- or O- atom to metal(II) by dislodging the carbonyl group already coordinated. This gives rise to two linkage isomers, one with N-bonded and the other with O-bonded hydroxyimino group in the case of nickel(II) (except for 1d) and palladium(II), and a single isomer with O-bonded hydroxyimino group in copper(II) complexes. The isomers obtained from 1b and 1i have been separated by column chromatography. In chloroform each of the isomers of nickel(II) isomerizes to give an equilibrium mixture of two isomers, but not those of copper(II) and palladium(II).

Structure-Reactivity Correlations of Benzoin Alkyl Ethers. Structures of 2-Methoxy-1,2-diphenylethanone (I) and 2-Isopropoxy-1,2-diphenylethanone (II)

(I): C15H1402, Mr---226.27, triclinic, Pi,a=8.441 (2), b= 10.276 (1), c= 15.342 (2)A, a=91.02 (2), ~ t= 79.26 (2), y= 105.88 (2) °, V=1256.8 (4)A 3, Z=4, D,,= 1.209 (flotation in KI),D x - 1.195 g cm -3, #(Mo, 2 = 0.7107/~) = 0.44 cm -~,F(000) = 480, T= 293 K, R -- 0.060 for 1793 significant reflections. (II): C~THlsO2, Mr= 254.83, orthorhombic, Pca21, a=8.476 (1); b= 16.098 (3), c=10.802(3)A, V=1473.9 (5) A s, Z=4, Dm=1.161 (flotation in KI), Dx= 1.148gem -3, /~(Mo, 2=0.7107 A) =0.41 cm -~, F(000) = 544, T= 293 K, R = 0.071 for 867 significant reflections. Both (I) and (II) crystallize in a cisoid conformation for the carbonyl group and alkoxy groups. Compounds (I) and (II) are photostable on irradiation in the solid state in spite of the favourable conformation of the functional groups for intramolecular H abstraction. Absence of photoreaction of (I)and (II) in the solid state is rationalized in the light of unfavourable intramolecular geometry.

Directing role of functional groups in selective generation of C-H center dot center dot center dot pi interactions: In situ cryo-crystallographic studies on benzyl derivatives

The in situ cryo-crystallization study of benzyl derivatives reveals that the molecular packing in these compounds is either through methylene (sp(3)) C-H center dot center dot center dot pi or aromatic (sp(2)) C-H center dot center dot center dot pi interactions depending on the level of acidity of the benzyl proton. These studies of low melting compounds bring out the subtle features of such weak interactions and point to the directional preferences depending on the nature (electron withdrawing, polarizability) of the neighbouring functional group.

A helical peptide containing a majority of valyl residues. The crystal structure of t-butyloxy- carbonyl-(L-valyl-_-aminoisobutyryl)3-L-valyl methyl ester onohydrate

The monohydrate of the heptapeptide t-butyloxycarbonyl-(L-valyl-α-aminoiso-butyryl)3-L-valyl methyl ester crystallizes in the orthorhombic space group P212121 with four molecules in a unit cell with the dimensions α= 9.375, b = 19.413 and c = 25.878 ÅA. The structure has been solved by direct methods and refined to an R value of 0.059 for 3633 observed reflections. The molecule in the structure exists as a slightly distorted 310-helix stabilized by five 4 -> 1 intramolecular hydrogen bonds, indicating the overwhelming influence of α-aminoisobutyryl (Aib) residues in dictating helical fold even when a majority of residues in the peptide have a low intrinsic propensity to be in helices. Contrary to what is expected in helical structures, the valyl side chains, two of which are disordered, exhibit all three possible conformations. The molecules arrange themselves in a head-to-tail fashion along the c-axis. The columns thus generated pack nearly hexagonally in the crystal.

Aspects of tautomerism. 7. Study of keto participation in alkaline hydrolysis of normal esters of .gamma.-keto acids

Study of the alkaline hydrolysis of a number of variously substituted normal o-benzoylbenzoic esters has been reported. Although carbonyl-assisted hydrolysis is the general rule, in compounds containing strongly electron-donating groups, the ester function is directly attacked. The cause of rate enhancement in carbonyl-assisted hydrolysis and in greater detail the case of 6-substituted derivatives are discussed. It is shown that the carbonyl-assisted hydrolyses are characterized by decreased sensitivity to leaving-group structure. The implications of this result are pointed out.

Segal-Bargmann Transform and Paley-Wiener Theorems on Motion Groups

We study the Segal-Bargmann transform on a motion group R-n v K, where K is a compact subgroup of SO(n) A characterization of the Poisson integrals associated to the Laplacian on R-n x K is given We also establish a Paley-Wiener type theorem using complexified representations

Debenzylation by Ni-A1 alloy

Nickel-aluminum alloy in aqueous sodium hydroxide-ethanol medium brings about facile hydro-enolrsis of benzyl ether function in substrates carrying a vicinal methoxy group. Simplicity of the reaction conditions and cheapness of the reagent are some of the advanrages of the procedure. Additionally, carbonyl functions when present are untouched and alkaline medium of the reaction makes it compatible with the presence of acid-sensitite groups.

Geometric Characterizations for Patterson-Sullivan Measures of Geometrically Finite Kleinian Groups

The main results of this thesis show that a Patterson-Sullivan measure of a non-elementary geometrically finite Kleinian group can always be characterized using geometric covering and packing constructions. This means that if the standard covering and packing constructions are modified in a suitable way, one can use either one of them to construct a geometric measure which is identical to the Patterson-Sullivan measure. The main results generalize and modify results of D. Sullivan which show that one can sometimes use the standard covering construction to construct a suitable geometric measure and sometimes the standard packing construction. Sullivan has shown also that neither or both of the standard constructions can be used to construct the geometric measure in some situations. The main modifications of the standard constructions are based on certain geometric properties of limit sets of Kleinian groups studied first by P. Tukia. These geometric properties describe how closely the limit set of a given Kleinian group resembles euclidean planes or spheres of varying dimension on small scales. The main idea is to express these geometric properties in a quantitative form which can be incorporated into the gauge functions used in the modified covering and packing constructions. Certain estimation results for general conformal measures of Kleinian groups play a crucial role in the proofs of the main results. These estimation results are generalizations and modifications of similar results considered, among others, by B. Stratmann, D. Sullivan, P. Tukia and S. Velani. The modified constructions are in general defined without reference to Kleinian groups, so they or their variants may prove useful in some other contexts in addition to that of Kleinian groups.

Donor properties of some flexidentate hydroxyimino-β-diketones in their rhodium(III) complexes

A series of rhodium(III) complexes of certain hydroxyimino-beta-diketones were synthesised and their structures assigned on the basis of elemental analyses and i.r. and1H n.m.r. spectral studies, The complexes exhibit coordination through carbonyl oxygen and nitrogen of the hydroxy-imino groups in the ligands.1H and13C n.m.r. studies show that the ligands exist in the isonitroso form in CDCl3.