Twisted conjugacy classes in nilpotent groups

A group is said to have the R(infinity) property if every automorphism has an infinite number of twisted conjugacy classes. We study the question whether G has the R(infinity) property when G is a finitely generated torsion-free nilpotent group. As a consequence, we show that for every positive integer n >= 5, there is a compact nilmanifold of dimension n on which every homeomorphism is isotopic to a fixed point free homeomorphism. As a by-product, we give a purely group theoretic proof that the free group on two generators has the R(infinity) property. The R(infinity) property for virtually abelian and for C-nilpotent groups are also discussed.

EQUIVARIANT PATH FIELDS ON TOPOLOGICAL MANIFOLDS

A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf`s result to topological manifolds, replacing vector fields with path fields. In this note, we give an equivariant analog of Brown`s theorem for locally smooth G-manifolds where G is a finite group.

The 3-colored Ramsey number of even cycles

Denote by R(L, L, L) the minimum integer N such that any 3-coloring of the edges of the complete graph on N vertices contains a monochromatic copy of a graph L. Bondy and Erdos conjectured that when L is the cycle C(n) on n vertices, R(C(n), C(n), C(n)) = 4n - 3 for every odd n > 3. Luczak proved that if n is odd, then R(C(n), C(n), C(n)) = 4n + o(n), as n -> infinity, and Kohayakawa, Simonovits and Skokan confirmed the Bondy-Erdos conjecture for all sufficiently large values of n. Figaj and Luczak determined an asymptotic result for the `complementary` case where the cycles are even: they showed that for even n, we have R(C(n), C(n), C(n)) = 2n + o(n), as n -> infinity. In this paper, we prove that there exists n I such that for every even n >= n(1), R(C(n), C(n), C(n)) = 2n. (C) 2009 Elsevier Inc. All rights reserved.

Total phenolic content and free radical scavenging activities of methanolic extract powders of tropical fruit residues

Methanolic extract powders of acerola, passion fruit and pineapple industrial residues, including pulp, seeds and peel, altogether (except for acerola) devoid of seeds, were screened for antioxidant capacity. The total phenolic contents (TPCs) of the extract powders were compared with their radical-scavenging activities (RSA) against both DPPH(center dot) and superoxide anion (O(2)(center dot-)) radicals, and their protective effect against liposome peroxidation, triggered by peroxyl radical. Lipid peroxidation was followed by the fluorescence decay of the probe, 4,4-difluoro-5-(4-phenyl-1,3-butadienyl)-4-bora-3a,4a-diaza-s-indacene-3-undecanoic acid (C(11)-BODIPY(581/591)). The TPCs of acerola, passion fruit and pineapple extract powders were (94.6 +/- 7.4); (41.2 +/- 4.2) and (9.1 +/- 1.3) mg of gallic acid equivalents g(-1) of dry extract, respectively. Acerola showed the best RSA-DPPH(center dot) scores, whereas passion fruit was more protective on the RSA-O(2)(center dot-) system. Together with the protective effects against lipid peroxidation (rate of BODIPY decay) which, were similar for acerola and passion fruit extracts, these data suggest that the methanolic extracts of acerola and passion fruit residues may be useful as antioxidant supplements, particularly the acerola extract, due to its high phenolic content. (C) 2008 Elsevier Ltd. All rights reserved

GRASSIUS: A Platform for Comparative Regulatory Genomics across the Grasses

Transcription factors (TFs) are major players in gene regulatory networks and interactions between TFs and their target genes furnish spatiotemporal patterns of gene expression. Establishing the architecture of regulatory networks requires gathering information on TFs, their targets in the genome, and the corresponding binding sites. We have developed GRASSIUS (Grass Regulatory Information Services) as a knowledge-based Web resource that integrates information on TFs and gene promoters across the grasses. In its initial implementation, GRASSIUS consists of two separate, yet linked, databases. GrassTFDB holds information on TFs from maize (Zea mays), sorghum (Sorghum bicolor), sugarcane (Saccharum spp.), and rice (Oryza sativa). TFs are classified into families and phylogenetic relationships begin to uncover orthologous relationships among the participating species. This database also provides a centralized clearinghouse for TF synonyms in the grasses. GrassTFDB is linked to the grass TFome collection, which provides clones in recombination-based vectors corresponding to full-length open reading frames for a growing number of grass TFs. GrassPROMDB contains promoter and cis-regulatory element information for those grass species and genes for which enough data are available. The integration of GrassTFDB and GrassPROMDB will be accomplished through GrassRegNet as a first step in representing the architecture of grass regulatory networks. GRASSIUS can be accessed from www.grassius.org.

Room Temperature Ionic Liquid-Lithium Salt Mixtures: Optical Kerr Effect Dynamical Measurements

The addition of lithium salts to ionic liquids causes an increase in viscosity and a decrease in ionic mobility that hinders their possible application as an alternative solvent in lithium ion batteries. Optically heterodyne-detected optical Kerr effect spectroscopy was used to study the change in dynamics, principally orientational relaxation, caused by the addition of lithium bis(trifluoromethylsulfonyl)imide to the ionic liquid 1-buty1-3-methylimidazolium bis(trifluoromethylsulfonyl)imide. Over the time scales studied (1 ps-16 ns) for the pure ionic liquid, two temperature-independent power laws were observed: the intermediate power law (1 ps to similar to 1 ns), followed by the von Schweidler power law. The von Schweidler power law is followed by the final complete exponential relaxation, which is highly sensitive to temperature. The lithium salt concentration, however, was found to affect both power laws, and a discontinuity could be found in the trend observed for the intermediate power law when the concentration (mole fraction) of lithium salt is close to chi(LiTf(2)N) = 0.2. A mode coupling theory (MCT) schematic model was also used to fit the data for both the pure ionic liquid and the different salt concentration mixtures. It was found that dynamics in both types of liquids are described very well by MCT.

(+)- and (-)-Mutisianthol: First Total Synthesis, Absolute Configuration, and Antitumor Activity

The first synthesis of the natural product (+)-mutisianthol was accomplished in 11 steps and in 21% overall yield from 2-methylanisole. The synthesis of its enantiomer was also performed in a similar overall yield. The absolute configuration of the sesquiterpene (+)-mutisianthol was assigned as (1S,3R). Key steps in the route are the asymmetric hydrogenation of a nonfunctionalized olefin using chiral iridium catalysts and the ring contraction of 1,2-dihydronaphthalenes using thallium(III) or iodine(III). The target molecules show moderate activity against the human tumor cell lines SF-295, HCT-8, and MDA-MB-435.

Entropy Drives an Attached Water Molecule from the C- to N-Terminus on Protonated Proline

Results from infrared photodissociation (IRPD) spectroscopy and kinetics of singly hydrated, protonated proline indicate that the water molecule hydrogen bonds preferentially to the formally neutral carboxylic acid at low temperatures and at higher temperatures to the protonated N-terminus, which bears the formal charge. Hydration isomer populations obtained from IRPD kinetic data as a function of temperature are used to generate a van`t Hoff plot that reveals that C-terminal binding is enthalpically favored by 4.2-6.4 kJ/mol, whereas N-terminal binding is entropically favored by 31-43 J/(mol K), consistent with a higher calculated barrier for water molecule rotation at the C-terminus.

Identification of an Operon, Pil-Chp, That Controls Twitching Motility and Virulence in Xylella fastidiosa

Xylella fastidiosa is an important phytopathogenic bacterium that causes many serious plant diseases, including Pierce`s disease of grapevines. Disease manifestation by X. fastidiosa is associated with the expression of several factors, including the type IV pili that are required for twitching motility. We provide evidence that an operon, named Pil-Chp, with genes homologous to those found in chemotaxis systems, regulates twitching motility. Transposon insertion into the pilL gene of the operon resulted in loss of twitching motility (pilL is homologous to cheA genes encoding kinases). The X. fastidiosa mutant maintained the type IV pili, indicating that the disrupted pilL or downstream operon genes are involved in pili function, and not biogenesis. The mutated X. fastidiosa produced less biofilm than wild-type cells, indicating that the operon contributes to biofilm formation. Finally, in planta the mutant produced delayed and less severe disease, indicating that the Pil-Chp operon contributes to the virulence of X. fastidiosa, presumably through its role in twitching motility.

Spatiotemporal Pattern Formation in the Oscillatory Electro-Oxidation of Sulfide on a Platinum Disk

Spatiotemporal pattern formation in the electrocatalytic oxidation of sulfide on a platinum disk is investigated using electrochemical methods and a charge-coupled device (CCD) camera simultaneously. The system is characterized by different oscillatory regions spread over a wide potential range. An additional series resistor and a large electrode area facilitate observation of multiple regions of kinetic instabilities along the current/potential curve. Spatiotemporal patterns on the working electrode, such as fronts, pulses, spirals, twinkling eyes, labyrinthine stripes, and alternating synchronized deposition and dissolution, are observed at different operating conditions of series resistance and sweep rate.