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

Social selection and the evolution of cooperative groups: The example of the cellular slime moulds

In social selection the phenotype of an individual depends on its own genotype as well as on the phenotypes, and so genotypes, of other individuals. This makes it impossible to associate an invariant phenotype with a genotype: the social context is crucial. Descriptions of metazoan development, which often is viewed as the acme of cooperative social behaviour, ignore or downplay this fact. The implicit justification for doing so is based on a group-selectionist point of view. Namely, embryos are clones, therefore all cells have the same evolutionary interest, and the visible differences between cells result from a common strategy. The reasoning is flawed, because phenotypic heterogeneity within groups can result from contingent choices made by cells from a flexible repertoire as in multicellular development. What makes that possible is phenotypic plasticity, namely the ability of a genotype to exhibit different phenotypes. However, co-operative social behaviour with division of labour requires that different phenotypes interact appropriately, not that they belong to the same genotype, or have overlapping genetic interests. We sketch a possible route to the evolution of social groups that involves many steps: (a) individuals that happen to be in spatial proximity benefit simply by virtue of their number; (b) traits that are already present act as preadaptations and improve the efficiency of the group; and (c) new adaptations evolve under selection in the social context-that is, via interactions between individuals-and further strengthen group behaviour. The Dictyostelid or cellular slime mould amoebae (CSMs) become multicellular in an unusual way, by the aggregation of free-living cells. In nature the resulting group can be genetically homogeneous (clonal) or heterogeneous (polyclonal); in either case its development, which displays strong cooperation between cells (to the extent of so-called altruism) is not affected. This makes the CSMs exemplars for the study of social behaviour.

Reaction of diisopropoxytitanium(III) tetrahydroborate with selected organic compounds containing representative functional groups

Diisopropoxytitanium(III) tetrahydroborate, ((PrO)-Pr-1)(2)TiBH4), generated in situ in dichloromethane from diisopropoxytitanium dichloride and benzyltriethylammonium borohydride in a 1:2 ratio selectively reduces aldehydes, ketones, acid chlorides, carboxylic acids, and N-Boc-protected amino acids to the corresponding alcohols in excellent yield under very mild reaction conditions (-78 to 25 degrees C).

Micellar structures of dimeric surfactants with phosphate head groups and wettable spacers: A small-angle neutron scattering study

Dimeric or gemini surfactants consist of two hydrophobic chains and two hydrophilic head groups covalently connected by a hydrophobic or hydrophilic spacer. This paper reports the small-angle neutron scattering (SANS) measurements from aqueous micellar solutions of two different recently developed types of dimeric surfactants: (i) bis-anionic C16H33PO4--(CH2)(m)-PO4-C16H33,2Na(+) dimeric surfactants composed of phosphate head groups and a hydrophobic polymethylene spacer, referred to as 16-m-16,2Na(+), for spacer lengths m = 2, 4, 6, and 10, (ii) bis-cationic C16H33N+(CH3)(2)-CH2-(CH2-O-CH2)(p)-CH2-N+ (CH3)(2)C16H33,2Br(-) dimeric surfactants composed of dimethylammonium head groups and a wettable polyethylene oxide spacer, referred to as 16-CH2-p-CH2-16,2Br(-), for spacer lengths p = 1 - 3. The micellar structures of these surfactants are compared with the earlier studied bis-cationic C16H33N+ (CH3)(2)-(CH2)(m)-N+ (CH3)(2)C16H33,2Br(-) dimeric surfactants composed of dimethylammonium head groups and a hydrophobic polymethylene spacer, referred to as 16-m-16,2Br(-). It is found that 16-m-16,2Na(+), similar to 16-m-16,2Br(-), form various micellar structures depending on the spacer length. Micelles an disklike for rn = 2, rodlike for m = 4, and prolate ellipsoidal fur m = 6 and 10. The micelles of 16-CH2-p-CH2-16,2Br(-) are prolate ellipsoidal for all the values of p = 1 - 3. It is also found that micelles of 16-m-16,2Na(+) and 16-CH2-p-CH2-16,2Br(-) are large in comparison to those of 16-in-16,2Br(-) for similar spacer lengths. This is connected with the fact that both in 16-m-16,2Na(+) and 16-CH2-p-CH2-16,2Br(-), the head group or the spacer is more hydrated as compared to that in the 16-m-16,2Br(-). An increase in the hydration of the spacer or the head group increases the screening of the Coulomb repulsion between the charged head groups. This effect has been found to be more pronounced in the dimeric surfactants having wettable spacers. [S1063-651X(99)00303-7].

Nanotubes of the disulfides of groups 4 and 5 metals

The layered chalcogenides, having structures analogous to graphite, are known to be unstable toward bending and show high propensity to form curved structures, thus eliminating dangling bonds at the edges. Since the discovery of fullerene and nanotube structures of WS2 and MoS2 by Tenne et al. [1-3], there have been attempts to prepare and characterize nanotubes of other layered dichalcogenides with structures analogous to MoS2. Nanotubes of MoS2 and WS2 were prepared by Tenne et al. by reducing the corresponding oxides to the suboxides followed by heating in an atmosphere of forming gas (5 % H-2 + 95 % N-2) and H2S at 700-900 degreesC [1-3]. Alternative methods of synthesis of MoS2 and WS2 nanotubes have since been proposed by employing the decomposition of the ammonium thiometallates or the corresponding trisulfide precursors. This alternative procedure was based on the observation that the trisulfide seems to be formed as an intermediate in the synthesis of the MoS2 and WS2 nanotubes [4]. Accordingly, the decomposition of the trisulfides of MoS2 and W in a reducing atmosphere directly yielded nanotubes of the disulfides MoS2 and WS2 [5]. In this article, we describe the synthesis, structure, and characterization of a few novel nanotubes of the disulfides of groups 4 and 5 metals. These include nanotubes of NbS2, TaS2, ZrS2, and HfS2. The study enlarges the scope of the inorganic nanotubes significantly and promises other interesting possibilities, including the synthesis of the diselenide nanotubes of these metals.

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.

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.

Autonomous and non-autonomous traits mediate social cooperation in Dictyostelium discoideum

In the trishanku (triA(-)) mutant of the social amoeba Dictyostelium discoideum, aggregates are smaller than usual and the spore mass is located mid-way up the stalk, not at the apex. We have monitored aggregate territory size, spore allocation and fruiting body morphology in chimaeric groups of (quasi-wild-type) Ax2 and triA(-) cells. Developmental canalisation breaks down in chimaeras and leads to an increase in phenotypic variation. A minority of triA(-) cells causes largely Ax2 aggregation streams to break up; the effect is not due to the counting factor. Most chimaeric fruiting bodies resemble those of Ax2 or triA(-). Others are double-deckers with a single stalk and two spore masses, one each at the terminus and midway along the stalk. The relative number of spores belonging to the two genotypes depends both on the mixing ratio and on the fruiting body morphology. In double-deckers formed from 1:1 chimaeras, the upper spore mass has more Ax2 spores, and the lower spore mass more triA(-) spores, than expected. Thus, the traits under study depend partly on the cells' own genotype and partly on the phenotypes, and so genotypes, of other cells: they are both autonomous and non-autonomous. These findings strengthen the parallels between multicellular development and behaviour in social groups. Besides that, they reinforce the point that a trait can be associated with a genotype only in a specified context.

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.

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.

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.