TAUT REPRESENTATIONS OF COMPACT SIMPLE LIE GROUPS

The concept of taut submanifold of Euclidean space is due to Carter and West, and can be traced back to the work of Chern and Lashof on immersions with minimal total absolute curvature and the subsequent reformulation of that work by Kuiper in terms of critical point theory. In this paper, we classify the reducible representations of compact simple Lie groups, all of whose orbits are tautly embedded in Euclidean space, with respect to Z(2)-coefficients.

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.

A group topology on the free abelian group of cardinality c that makes its square countably compact

Under p = c, we prove that it is possible to endow the free abelian group of cardinality c with a group topology that makes its square countably compact. This answers a question posed by Madariaga-Garcia and Tomita and by Tkachenko. We also prove that there exists a Wallace semigroup (i.e., a countably compact both-sided cancellative topological semigroup which is not a topological group) whose square is countably compact. This answers a question posed by Grant.

Star-group identities and groups of units

Analogous to *-identities in rings with involution we define *-identities in groups. Suppose that G is a torsion group with involution * and that F is an infinite field with char F not equal 2. Extend * linearly to FG. We prove that the unit group U of FG satisfies a *-identity if and only if the symmetric elements U(+) satisfy a group identity.

Spaces of compact operators on C(2(m) circle plus [0, alpha]) spaces

We classify up to isomorphism the spaces of compact operators K(E, F), where E and F are Banach spaces of all continuous functions defined on the compact spaces 2(m) circle plus [0, alpha], the topological sum of Cantor cubes 2(m) and the intervals of ordinal numbers [0, alpha]. More precisely, we prove that if 2(m) and aleph(gamma) are not real-valued measurable cardinals and n >= aleph(0) is not sequential cardinal, then for every ordinals xi, eta, lambda and mu with xi >= omega(1), eta >= omega(1), lambda = mu < omega or lambda, mu is an element of [omega(gamma), omega(gamma+1)[, the following statements are equivalent: (a) K(C(2(m) circle plus [0, lambda]), C(2(n) circle plus [0, xi])) and K(C(2(m) circle plus [0, mu]), C(2(n) circle plus [0, eta]) are isomorphic. (b) Either C([0, xi]) is isomorphic to C([0, eta] or C([0, xi]) is isomorphic to C([0, alpha p]) and C([0, eta]) is isomorphic to C([0,alpha q]) for some regular cardinal alpha and finite ordinals p not equal q. Thus, it is relatively consistent with ZFC that this result furnishes a complete isomorphic classification of these spaces of compact operators. (C) 2010 Elsevier Inc. All rights reserved.

SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

Abelian torsion groups with a countably compact group topology

Comfort and Remus [W.W. Comfort, D. Remus, Abelian torsion groups with a pseudo-compact group topology, Forum Math. 6 (3) (1994) 323-337] characterized algebraically the Abelian torsion groups that admit a pseudocompact group topology using the Ulm-Kaplansky invariants. We show, under a condition weaker than the Generalized Continuum Hypothesis, that an Abelian torsion group (of any cardinality) admits a pseudocompact group topology if and only if it admits a countably compact group topology. Dikranjan and Tkachenko [D. Dikranjan. M. Tkachenko, Algebraic structure of small countably compact Abelian groups, Forum Math. 15 (6) (2003) 811-837], and Dikranjan and Shakhmatov [D. Dikranjan. D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151 (1-3) (2005) 2-54] showed this equivalence for groups of cardinality not greater than 2(c). We also show, from the existence of a selective ultrafilter, that there are countably compact groups without non-trivial convergent sequences of cardinality kappa(omega), for any infinite cardinal kappa. In particular, it is consistent that for every cardinal kappa there are countably compact groups without non-trivial convergent sequences whose weight lambda has countable cofinality and lambda > kappa. (C) 2009 Elsevier B.V. All rights reserved.

The transcriptional response to cadmium, organic hydroperoxide, singlet oxygen and UV-A mediated by the sigma(E)-ChrR system in Caulobacter crescentus

Caulobacter crescentus sigma(E) belongs to the ECF (extracytoplasmic function) subfamily of RNA polymerase sigma factors, whose members regulate gene expression in response to distinct environmental stresses. During physiological growth conditions, data indicate that sigma(E) is maintained in reduced levels due to the action of ChrR, a negative regulator of rpoE gene expression and function. However, once bacterial cells are exposed to cadmium, organic hydroperoxide, singlet oxygen or UV-A irradiation, transcription of rpoE is induced in a sigma(E)-dependent manner. Site-directed mutagenesis indicated that residue C188 in ChrR is critical for the cadmium response while residues H140 and H142 are required for the bacterial response to organic hydroperoxide, singlet oxygen and UV-A. Global transcriptional analysis showed that sigma(E) regulates genes involved in protecting cells against oxidative damages. A combination of transcriptional start site identification and promoter prediction revealed that some of these genes contain a putative sigma(E)-dependent motif in their upstream regions. Furthermore, deletion of rpoE and two sigma(E)-dependent genes (cfaS and hsp20) impairs Caulobacter survival when singlet oxygen is constantly generated in the cells.

A two-component system, an anti-sigma factor and two paralogous ECF sigma factors are involved in the control of general stress response in Caulobacter crescentus

The extracytoplasmic function sigma factor sigma(T) is the master regulator of general stress response in Caulobacter crescentus and controls the expression of its paralogue sigma(U). In this work we showed that PhyR and NepR act, respectively, as positive and negative regulators of sigma(T) expression and function. Biochemical data also demonstrated that NepR directly binds sigma(T) and the phosphorylated form of PhyR. We also described the essential role of the histidine kinase gene CC3474, here denominated phyK, for expression of sigma(T)-dependent genes and for resistance to stress conditions. Additionally, in vivo evidence of PhyK-dependent phosphorylation of PhyR is presented. This study also identified a conserved cysteine residue (C95) located in the periplasmic portion of PhyK that is crucial for the function of the protein. Furthermore, we showed that PhyK, PhyR and sigma(T) regulate the same set of genes and that sigma(T) apparently directly controls most of its regulon. In contrast, sigma(U) seems to have a very modest contribution to the expression of a subset of sigma(T)-dependent genes. In conclusion, this report describes the molecular mechanism involved in the control of general stress response in C. crescentus.

Role of sigma(54) in the regulation of genes involved in type I and type IV pili biogenesis in Xylella fastidiosa

The phytopathogen Xylella fastidiosa produces long type IV pili and short type I pili involved in motility and adhesion. In this work, we have investigated the role of sigma factor sigma(54) (RpoN) in the regulation of fimbrial biogenesis in X. fastidiosa. An rpoN null mutant was constructed from the non-pathogenic citrus strain J1a12, and microarray analyses of global gene expression comparing the wild type and rpoN mutant strains showed few genes exhibiting differential expression. In particular, gene pilA1 (XF2542), which encodes the structural pilin protein of type IV pili, showed decreased expression in the rpoN mutant, whereas two-fold higher expression of an operon encoding proteins of type I pili was detected, as confirmed by quantitative RT-PCR (qRT-PCR) analysis. The transcriptional start site of pilA1 was determined by primer extension, downstream of a sigma(54)-dependent promoter. Microarray and qRT-PCR data demonstrated that expression of only one of the five pilA paralogues, pilA1, was significantly reduced in the rpoN mutant. The rpoN mutant made more biofilm than the wild type strain and presented a cell-cell aggregative phenotype. These results indicate that sigma(54) differentially regulates genes involved in type IV and type I fimbrial biogenesis, and is involved in biofilm formation in X. fastidiosa.

Role of Polyelectrolyte for Layer-by-Layer Compact TiO(2) Films in Efficiency Enhanced Dye-Sensitized Solar Cells

Efficient compact TiO(2) films using different polyeleetrolytes are prepared by the layer-by-layer technique (LbL) and applied as an effective contact and blocking film in dye-sensitized solar cells (DSCs). The polyanion thermal stability plays a major role on the compact layers, which decreases back electron transfer processes and current losses at the FTO/TiO(2) interface. FESEM images show that polyelectrolytes such is sodium sullonated polystyrene (PSS) and sulfonated lignin (SE), in comparison to poly(acrylic acid) (FAA), ensure an adequate morphology for the LbL TiO(2) layer deposited before the mesoporous film, even triter the sintering step at 450 degrees C. The so treated photoanode in DSCs leads to a 30% improvement On the overall conversion efficiency. Electrochemical impedance spectroscopy (EIS) is employed to ascertain the role of die compact films with such polyelectrolytes. The significant increase in V(oc) of the solar cells with adequate polyelectrolytes in the LbL TiO(2) films shows their pivotal role in decreasing the electron recombination at the FTO surface and enhancing the electrical contact of FTO with the mesoporous TiO(2) layer.