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.

Geometrical interpretation of Inönü-Wigner contractions

The Inönü-Wigner contractions which interrelate the Lie algebras of the isometry groups of metric spaces are discussed with reference to deformations of the absolutes of the spaces. A general formula is derived for the Lie algebra commutation relations of the isometry group for anyN-dimensional metric space. These ideas are illustrated by a discussion of important particular cases, which interrelate the four-dimensional de Sitter, Poincaré, and Galilean groups.

3-MANIFOLD GROUPS, KÄHLER GROUPS AND COMPLEX SURFACES

Let G be a Kahler group admitting a short exact sequence 1 -> N -> G -> Q -> 1 where N is finitely generated. (i) Then Q cannot be non-nilpotent solvable. (ii) Suppose in addition that Q satisfies one of the following: (a) Q admits a discrete faithful non-elementary action on H-n for some n >= 2. (b) Q admits a discrete faithful non-elementary minimal action on a simplicial tree with more than two ends. (c) Q admits a (strong-stable) cut R such that the intersection of all conjugates of R is trivial. Then G is virtually a surface group. It follows that if Q is infinite, not virtually cyclic, and is the fundamental group of some closed 3-manifold, then Q contains as a finite index subgroup either a finite index subgroup of the three-dimensional Heisenberg group or the fundamental group of the Cartesian product of a closed oriented surface of positive genus and the circle. As a corollary, we obtain a new proof of a theorem of Dimca and Suciu in Which 3-manifold groups are Kahler groups? J. Eur. Math. Soc. 11 (2009) 521-528] by taking N to be the trivial group. If instead, G is the fundamental group of a compact complex surface, and N is finitely presented, then we show that Q must contain the fundamental group of a Seifert-fibered 3-manifold as a finite index subgroup, and G contains as a finite index subgroup the fundamental group of an elliptic fibration. We also give an example showing that the relation of quasi-isometry does not preserve Kahler groups. This gives a negative answer to a question of Gromov which asks whether Kahler groups can be characterized by their asymptotic geometry.

Synthesis of novel poly[(2,5-dimethoxy-p-phenylene)vinylene] precursors having two eliminatable groups: An approach for the control of conjugation length

Poly[(2,5-dimethoxy-p-phenylene)vinylene] (DMPPV) of varying conjugation length was synthesized by selective elimination of organic soluble precursor polymers that contained two eliminatable groups, namely, methoxy and acetate groups. These precursor copolymers were in turn synthesized by competitive nucleophilic substitution of the sulfonium polyelectrolyte precursor (generated by the standard Wessling route) using methanol and sodium acetate in acetic acid. The composition of the precursor copolymer, in terms of the relative amounts of methoxy and acetate groups, was controlled by varying the composition of the reaction mixture during nucleophilic substitution. Thermal elimination of these precursor copolymers at 250 degrees C, yielded partially conjugated polymers, whose color varied from light yellow to deep red. FT-IR studies confirmed that, while essentially all the acetate groups were eliminated, the methoxy groups were intact and caused the interruption in conjugation. Preliminary photoluminescence studies of the partially eliminated DMPPV samples showed a gradual shift in the emission maximum from 498 to 598 nm with increasing conjugation lengths, suggesting that the color of LED devices fabricated from such polymers can, in principle, be fine-tuned.

Identification of amino groups in the carbohydrate binding activity of winged bean acidic agglutinin

Chemical modification studies reveal that the modification of amino groups in WBA II leads to a complete loss in the hemagglutinating and saccharide binding activities. Since WBA II is a dimeric molecule and contains two binding sites, one amino group in each of the binding sites is inferred to be essential for its activity. The presence of amino group which has a potential to form hydrogen bonded interactions with the ligand, substantiates our observation regarding the forces involved in WBA II-receptor and WBA II-simple sugar interactions.

Identification of putative regulatory motifs in the upstream regions of co-expressed functional groups of genes in Plasmodium falciparum

Background: Regulation of gene expression in Plasmodium falciparum (Pf) remains poorly understood. While over half the genes are estimated to be regulated at the transcriptional level, few regulatory motifs and transcription regulators have been found. Results: The study seeks to identify putative regulatory motifs in the upstream regions of 13 functional groups of genes expressed in the intraerythrocytic developmental cycle of Pf. Three motif-discovery programs were used for the purpose, and motifs were searched for only on the gene coding strand. Four motifs – the 'G-rich', the 'C-rich', the 'TGTG' and the 'CACA' motifs – were identified, and zero to all four of these occur in the 13 sets of upstream regions. The 'CACA motif' was absent in functional groups expressed during the ring to early trophozoite transition. For functional groups expressed in each transition, the motifs tended to be similar. Upstream motifs in some functional groups showed 'positional conservation' by occurring at similar positions relative to the translational start site (TLS); this increases their significance as regulatory motifs. In the ribonucleotide synthesis, mitochondrial, proteasome and organellar translation machinery genes, G-rich, C-rich, CACA and TGTG motifs, respectively, occur with striking positional conservation. In the organellar translation machinery group, G-rich motifs occur close to the TLS. The same motifs were sometimes identified for multiple functional groups; differences in location and abundance of the motifs appear to ensure different modes of action. Conclusion: The identification of positionally conserved over-represented upstream motifs throws light on putative regulatory elements for transcription in Pf.

Gauge theory of a group of diffeomorphisms. II. The conformal and de Sitter groups

The extension of Hehl's Poincaré gauge theory to more general groups that include space-time diffeomorphisms is worked out for two particular examples, one corresponding to the action of the conformal group on Minkowski space, and the other to the action of the de Sitter group on de Sitter space, and the effect of these groups on physical fields.

Algebraic and geometric intersection numbers for free groups

We show that the algebraic intersection number of Scott and Swarup for splittings of free groups Coincides With the geometric intersection number for the sphere complex of the connected sum of copies of S-2 x S-1. (C) 2009 Elsevier B.V. All rights reserved.

Choice of the End Functional Groups in Tri(p-phenylenevinylene) Derivatives Controls Its Physical Gelation Abilities

New supramolecular organogels based on all-trans-tri(p-phenylenevinylene) (TPV) systems possessing different terminal groups, e.g., oxime, hydrazone, phenylhydrazone, and semicarbazone have been synthesized. The self-assembly properties of the compounds that gelate in specific organic solvents and the aggregation motifs of these molecules in the organogels were investigated using UV−vis, fluorescence, FT-IR, and 1H NMR spectroscopy, electron microscopy, differential scanning calorimetry (DSC), and rheology. The temperature variable UV−vis and fluorescence spectroscopy in different solvents clearly show the aggregation pattern of the self-assemblies promoted by hydrogen bonding, aromatic π-stacking, and van der Waals interactions among the individual TPV units. Gelation could be controlled by variation in the number of hydrogen-bonding donors and acceptors in the terminal functional groups of this class of gelators. Also wherever gelation is observed, the individual fibers in gels change to other types of networks in their aggregates depending on the number of hydrogen-bonding sites in the terminal functions. Comparison of the thermal stability of the gels obtained from DSC data of different gelators demonstrates higher phase transition temperature and enthalpy for the hydrazone-based gelator. Rheological studies indicate that the presence of more hydrogen-bonding donors in the periphery of the gelator molecules makes the gel more viscoelastic solidlike. However, in the presence of more numbers of hydrogen-bonding donor/acceptors at the periphery of TPVs such as with semicarbazone a precipitation as opposed to gelation was observed. Clearly, the choice of the end functional groups and the number of hydrogen-bonding groups in the TPV backbone holds the key and modulates the effective length of the chromophore, resulting in interesting optical properties.

Embedding Of Non-Simple Lie-Groups, Coupling-Constant Relations And Non-Uniqueness Of Models Of Unification

A general derivation of the coupling constant relations which result on embedding a non-simple group like SU L (2) @ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin~0=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons like E 6, while addition of extra charged fermion singlets can reduce the value of sin ~ 0 to 1/4. We point out that at the present time the models of grand unification are far from unique.

On the reactivity of carboxyl groups of ribonuclease-A in anhydrous methanol

The esterification of Ribonuclease-A in methanol/0.1 M hydrochloric acid has been studied by measuring the decrease in the number of titratable groups of the protein and estimating the amount of methanol incorporated. Esterification of nearly five of the 11 free carboxyl groups of the protein resulted in almost complete inactivation of the enzyme. The initial products of esterification have been chromatographed on Amberlite columns, and five partially active methyl ester derivatives of Ribonuclease-A have been isolated. The dimethyl ester, the initial product of esterification with reduced catalytic activity, has the carboxyl groups of Glu-49 and Asp-53 modified. Even in the non-aqueous solvent, as in the native structure of the protein in aqueous solution, these carboxyl groups are the fast reacting ones. Subsquently, the esterification reaction appears to proceed preferentially at the C-terminal region of the molecule. Comparison of the reactivities of carboxyl groups of Ribonuclease-A in acidic methanol to that known in aqueous solutions (with carbodiimides) suggests that the structure of Ribonuclease-A in the non-aqueous solvent resembles, at least in part, the structure in aqueous environment.

Synthesis of a one-dimensional coordination polymer containing pendant hydrosulfide groups

In view of the recent interest in compounds containing M-SH units, an organotin hydrosulfide compound, Me2Sn(SH)(O2CMe) (1) was prepared by controlled hydrolysis of the diorganotin thioacetate. Under similar mild hydrolytic conditions the corresponding benzoate could not be isolated. Instead, the thiobenzoate complex, Me2Sn(SOCPh)(2) (3) was obtained in excellent yields indicating that there was no hydrolysis. Both 1 and 3 were characterized by X-ray crystallography. Some properties of the polymeric compound 1, such as spectral, electrical conductivity and NLO response were also studied. The reactivity and properties were explained using density functional calculations.

Preparation of Palladium(II) Complexes of Isonitrosoacetylacetoneimines Having O- and N-Coordinated Isonitroso Groups

Methods for the preparation of palladium(II) complexes of the type Pd(R-IAI)(IAI'), where IAI' is the anion of isonitrosoacetylacetoneimine and R-IAI, its N-alkyl or N-aryl derivative, are given.

The influence of esterification of carboxyl groups of ribonuclease-a on its structure and immunological activity

The effect of modification of carboxyl groups of Ribonuclease-Aa on the enzymatic activity and the antigenic structure of the protein has been studied. Modification of four of the eleven free carboxyl groups of the protein by esterification in anhydrous methanol/0.1 M hydrochloric acid resulted in nearly 80% loss in enzymatic activity but had very little influence on the antigenic structure of the protein. Further increases in the modification of the carboxyl groups caused a progressive loss in immunological activity, and the fully methylated RNase-A exhibited nearly 30% immunological activity. Concomitant with this change in the antigenic structure of the protein, the ability of the molecule to complement with RNase-S-protein increased, clearly indicating the unfolding of the peptide "tail" from the remainder of the molecule. The susceptibility to proteolysis, accessibility of methionine residues for orthobenzoquinone reaction and the loss in immunological activity of the more extensively esterified derivatives of RNase-A are suggestive of the more flexible conformation of these derivatives as compared with the compact native conformation. The fact that even the fully methylated RNase-A retains nearly 30% of its immunological activity suggested that the modified protein contained antibody recognizable residual native structure, which presumably accommodates some antigenic determinants.

Aggregation of apolar peptides in organic solvents. Concentration dependence of 1H-nmr parameters for peptide NH groups in 310 helical decapeptide fragment of suzukacillin

Peptide NH chemical shifts and their temperature dependences have been monitored as a function of concentration for the decapeptide, Boc-Aib-Pro-Val-Aib-Val-Ala-Aib-Ala-Aib-Aib-OMe in CDCl3 (0.001-0.06M) and (CD3)2SO (0.001-0.03M). The chemical shifts and temperature coefficients for all nine NH groups show no significant concentration dependence in (CD3)2SO. Seven NH groups yield low values of temperature coefficients over the entire range, while one yields an intermediate value. In CDCl3, the Aib(1) NH group shows a large concentration dependence of both chemical shift and temperature coefficient, in contrast to the other eight NH groups. The data suggest that in (CD3)2SO, the peptide adopts a 310 helical conformation and is monomeric over the entire concentration range. In CDCl3, the 310 helical peptide associates at a concentration of 0.01M, with the Aib(1) NH involved in an intermolecular hydrogen bond. Association does not disrupt the intramolecular hydrogen-bonding pattern in the decapeptide.