Variants Of Miyachi’S Theorem For Nilpotent Lie Groups

We formulate and prove two versions of Miyachi’s theorem for connected, simply connected nilpotent Lie groups. This allows us to prove the sharpness of the constant 1/4 in the theorems of Hardy and of Cowling and Price for any nilpotent Lie group. These theorems are proved using a variant of Miyachi’s theorem for the group Fourier transform.

Growth of rutile TiO2 nanorods on TiO2 seed layer deposited by electron beam evaporation

Dense rutile TiO2 nanorods were grown on anatase TiO2 seed layer coated glass substrate by solution technique. The crystalline nature of nanorods has confirmed by transmission electron microscopy. The band gap of the TiO2 seed layer and nanorods were calculated using the UV-vis absorption spectrum and the band gap value of the anatase seed layer and rutile nanorods were 3.39 eV and 3.09 eV respectively. Water contact angle measurements were also made and showed that the contact angle of rutile nanorods was (134 degrees) larger than the seed layer contact angle (93 degrees). The RMS surface roughness of the TiO2 seed layer (0.384 nm) and nanorods film (18.5 nm) were measured by an atomic force microscope and correlated with their contact angle values. (C) 2011 Elsevier B.V. All rights reserved.

Thermal instability and the feedback regulation of hot haloes in clusters, groups and galaxies

We present global multidimensional numerical simulations of the plasma that pervades the dark matter haloes of clusters, groups and massive galaxies (the intracluster medium; ICM). Observations of clusters and groups imply that such haloes are roughly in global thermal equilibrium, with heating balancing cooling when averaged over sufficiently long time- and length-scales; the ICM is, however, very likely to be locally thermally unstable. Using simple observationally motivated heating prescriptions, we show that local thermal instability (TI) can produce a multiphase medium with similar to 104 K cold filaments condensing out of the hot ICM only when the ratio of the TI time-scale in the hot plasma (tTI) to the free-fall time-scale (tff) satisfies tTI/tff? 10. This criterion quantitatively explains why cold gas and star formation are preferentially observed in low-entropy clusters and groups. In addition, the interplay among heating, cooling and TI reduces the net cooling rate and the mass accretion rate at small radii by factors of similar to 100 relative to cooling-flow models. This dramatic reduction is in line with observations. The feedback efficiency required to prevent a cooling flow is similar to 10-3 for clusters and decreases for lower mass haloes; supernova heating may be energetically sufficient to balance cooling in galactic haloes. We further argue that the ICM self-adjusts so that tTI/tff? 10 at all radii. When this criterion is not satisfied, cold filaments condense out of the hot phase and reduce the density of the ICM. These cold filaments can power the black hole and/or stellar feedback required for global thermal balance, which drives tTI/tff? 10. In comparison to clusters, groups have central cores with lower densities and larger radii. This can account for the deviations from self-similarity in the X-ray luminositytemperature () relation. The high-velocity clouds observed in the Galactic halo can be due to local TI producing multiphase gas close to the virial radius if the density of the hot plasma in the Galactic halo is >rsim 10-5 cm-3 at large radii.

Seed dispersal in changing landscapes

A growing understanding of the ecology of seed dispersal has so far had little influence on conservation practice, while the needs of conservation practice have had little influence on seed dispersal research. Yet seed dispersal interacts decisively with the major drivers of biodiversity change in the 21st century: habitat fragmentation, overharvesting, biological invasions, and climate change. We synthesize current knowledge of the effects these drivers have on seed dispersal to identify research gaps and to show how this information can be used to improve conservation management. The drivers, either individually, or in combination, have changed the quantity, species composition, and spatial pattern of dispersed seeds in the majority of ecosystems worldwide, with inevitable consequences for species survival in a rapidly changing world. The natural history of seed dispersal is now well-understood in a range of landscapes worldwide. Only a few generalizations that have emerged are directly applicable to conservation management, however, because they are frequently confounded by site-specific and species-specific variation. Potentially synergistic interactions between disturbances are likely to exacerbate the negative impacts, but these are rarely investigated. We recommend that the conservation status of functionally unique dispersers be revised and that the conservation target for key seed dispersers should be a population size that maintains their ecological function, rather than merely the minimum viable population. Based on our analysis of conservation needs, seed dispersal research should be carried out at larger spatial scales in heterogenous landscapes, examining the simultaneous impacts of multiple drivers on community-wide seed dispersal networks. (C) 2011 Elsevier Ltd. All rights reserved.

Geosphere laminations in free groups

We construct for free groups, which are codimension one analogues of geodesic laminations on surfaces. Other analogues that have been constructed by several authors are dimension-one instead of codimension-one. Our main result is that the space of such laminations is compact. This in turn is based on the result that crossing, in the sense of Scott-Swarup, is an open condition. Our construction is based on Hatcher's normal form for spheres in the model manifold.

Rodent seed predation: effects on seed survival, recruitment, abundance, and dispersion of bird-dispersed tropical trees

Tropical tree species vary widely in their pattern of spatial dispersion. We focus on how seed predation may modify seed deposition patterns and affect the abundance and dispersion of adult trees in a tropical forest in India. Using plots across a range of seed densities, we examined whether seed predation levels by terrestrial rodents varied across six large-seeded, bird-dispersed tree species. Since inter-specific variation in density-dependent seed mortality may have downstream effects on recruitment and adult tree stages, we determined recruitment patterns close to and away from parent trees, along with adult tree abundance and dispersion patterns. Four species (Canarium resiniferum, Dysoxylum binectariferum, Horsfieldia kingii, and Prunus ceylanica) showed high predation levels (78.5-98.7%) and increased mortality with increasing seed density, while two species, Chisocheton cumingianus and Polyalthia simiarum, showed significantly lower seed predation levels and weak density-dependent mortality. The latter two species also had the highest recruitment near parent trees, with most abundant and aggregated adults. The four species that had high seed mortality had low recruitment under parent trees, were rare, and had more spaced adult tree dispersion. Biotic dispersal may be vital for species that suffer density-dependent mortality factors under parent trees. In tropical forests where large vertebrate seed dispersers but not seed predators are hunted, differences in seed vulnerability to rodent seed predation and density-dependent mortality can affect forest structure and composition.

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.

Adsorption on Edge-Functionalized Bilayer Graphene Nanoribbons: Assessing the Role of Functional Groups in Methane Uptake

A combination of ab initio and classical Monte Carlo simulations is used to investigate the effects of functional groups on methane binding. Using Moller-Plesset (MP2) calculations, we obtain the binding energies for benzene functionalized with NH2, OH, CH3, COOH, and H2PO3 and identify the methane binding sites. In all cases, the preferred binding sites are located above the benzene plane in the vicinity of the benzene carbon atom attached to the functional group. Functional groups enhance methane binding relative to benzene (-6.39 kJ/mol), with the largest enhancement observed for H2PO3 (-8.37 kJ/mol) followed by COOH and CH3 (-7.77 kJ/mol). Adsorption isotherms are obtained for edge-functionalized bilayer graphene nanoribbons using grand canonical Monte Carlo simulations with a five-site methane model. Adsorbed excess and heats of adsorption for pressures up to 40 bar and 298 K are obtained with functional group concentrations ranging from 3.125 to 6.25 mol 96 for graphene edges functionalized with OH, NH2, and COOH. The functional groups are found to act as preferred adsorption sites, and in the case of COOH the local methane density in the vicinity of the functional group is found to exceed that of bare graphene. The largest enhancement of 44.5% in the methane excess adsorbed is observed for COOH-functionalized nanoribbons when compared to H terminated ribbons. The corresponding enhancements for OH- and NH2-functionalized ribbons are 10.5% and 3.7%, respectively. The excess adsorption across functional groups reflects the trends observed in the binding energies from MP2 calculations. Our study reveals that specific site functionalization can have a significant effect on the local adsorption characteristics and can be used as a design strategy to tailor materials with enhanced methane storage capacity.

Revisiting Riesz transforms on Heisenberg groups

We characterise higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. Using transference theorems, we deduce boundedness theorems for Riesz transforms on the reduced Heisenberg group and hence also for the Riesz transforms associated to multiple Hermite and Laguerre expansions.