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.

Geometry changes induced by negative hyperconjugative interactions involving carbonyl and thiocarbonyl groups

MNDO geometry optimizations have been carried out on a series of acyclic and cyclic unsymmetrically disubstituted carbonyl and thiocarbonyl compounds. The C=X unit shows a consistent and often sizeable tilt towards one of the substituents, following the order O > Snot, vert, similarN > C > B. Reference ab initio calculations and available experimental results support the MNDO results. The effect, which is particularly dramatic in small rings, is attributed primarily to favorable negative hyperconjugative interaction between the lone pair on X and a low lying adjacent σ* orbital. Such an interaction can lead to highly distorted structures, including perhaps to a planar molecule with an inverted sp2 carbon center.

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.

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.

Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations

Stability results are given for a class of feedback systems arising from the regulation of time-varying discrete-time systems using optimal infinite-horizon and moving-horizon feedback laws. The class is characterized by joint constraints on the state and the control, a general nonlinear cost function and nonlinear equations of motion possessing two special properties. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee uniform asymptotic stability of both the optimal infinite-horizon and movinghorizon feedback systems. The infinite-horizon cost associated with the moving-horizon feedback law approaches the optimal infinite-horizon cost as the moving horizon is extended.

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.

Flow And Heat-Transfer Over An Upstream Moving Wall With A Magnetic-Field And A Parallel Free Stream

The flow and heat transfer over an upstream moving non-isothermal wall with a parallel free stream have been considered. The magnetic field has been applied in the free stream parallel to the wall and the effect of induced magnetic field has been included in the analysis. The boundary layer equations governing the steady incompressible electrically conducting fluid flow have been solved numerically using a shooting method. This problem is interesting because a solution exists only when the ratio of the wall velocity does not exceed a certain critical value and this critical value depends on the magnetic field and magnetic Prandtl number. Also dual solutions exist for a certain range of wall velocity.

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

Non-Newtonian boundary layers on a moving cylinder

The analysis of steady laminar forced convection boundary layer of power-law non-Newtonian fluids on a continuously moving cylinder with the surface maintained at a uniform temperature or uniform heat flux is presented. Of interest were the effects of power-law viscosity index, transverse curvature, generalized Prandtl number and streamwise coordinate on the local Nusselt number as well as on the velocity and temperature profiles. The two thermal boundary conditions yield quite similar results. Comparison of the calculated results with available series expansion solutions for a Newtonian fluid shows a very good performance of the present numerical procedure.

Dynamic response of a beam on elastic foundation of finite depth under a moving force

In this paper, dynamic response of an infinitely long beam resting on a foundation of finite depth, under a moving force is studied. The effect of foundation inertia is included in the analysis by modelling the foundation as a series of closely spaced axially vibrating rods of finite depth, fixed at the bottom and connected to the beam at the top. Viscous damping in the beam and foundation is included in the analysis. Steady state response of the beam-foundation system is obtained. Detailed numerical results are presented to study the effect of various parameters such as foundation mass, velocity of the moving load, damping and axial force on the beam. It is shown that foundation inertia can considerably reduce the critical velocity and can also amplify the beam response.

Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups

We define lacunary Fourier series on a compact connected semisimple Lie group G. If f is an element of L-1 (G) has lacunary Fourier series and f vanishes on a non empty open subset of G, then we prove that f vanishes identically. This result can be viewed as a qualitative uncertainty principle.

Thiol-ene Clickable Hyperscaffolds Bearing Peripheral Allyl Groups

Radical catalyzed thiol-ene reaction has become a useful alternative to the Huisgen-type click reaction as it helps to expand the variability in reaction conditions as well as the range of clickable entities. Thus, direct generation of hyper-branched polymers bearing peripheral allyl groups that could be clicked using a variety of functional thiols would be of immense value. A specifically designed AB(2) type monomer, that carries two allyl benzyl ethers groups and one alcohol functionality, was shown to undergo self-condensation under acid-catalyzed melt-transetherification to yield a hyperbranched polyether that carries numerous allyl end-groups. Importantly, it was shown that the kinetics of polymerization is not dramatically affected by the change of the ether unit from previously studied methyl benzyl ether to an allyl benzyl ether. The peripheral allyl groups were readily clicked quantitatively, using a variety of thiols, to generate an hydrocarbon-soluble octadecyl-derivative, amphiphilic systems using 2-mercaptoethanol and chiral amino acid (N-benzoyl cystine) derivatized hyperbranched structures; thus demonstrating the versatility of this novel class of clickable hyperscaffolds. (C) 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 49:1735-1744, 2011

Coalition Formation With Communication Ranges and Moving Targets

A team of unmanned aerial vehicles (UAVs) with limited communication ranges and limited resources are deployed in a region to search and destroy stationary and moving targets. When a UAV detects a target, depending on the target resource requirement, it is tasked to form a coalition over the dynamic network formed by the UAVs. In this paper, we develop a mechanism to find potential coalition members over the network using principles from internet protocol and introduce an algorithm using Particle Swarm Optimization to generate a coalition that destroys the target is minimum time. Monte-Carlo simulations are carried out to study how coalition are formed and the effects of coalition process delays.