Limit Groups are Cat(0)

We prove that every limit group acts geometrically on a CAT(0)space with the isolated flats property.     

A Combination Theorem for Relatively Hyperbolic Groups

Given a graph of -hyperbolic spaces, this paper gives sufficientconditions that ensure that the graph itself is -hyperbolic.As an application, a simple proof is given to show that limitgroups are relatively hyperbolic. 2000 Mathematics Subject Classification57M07, 20F65.     

Remark on inequalities for the Laplacian spread of graphs

Two inequalities for the Laplacian spread of graphs are proved in this note. These inequalities are reverse to those obtained by Z.You, B. Liu: The Laplacian spread of graphs, Czech. Math. J. 62 (2012), 155–168.     

Plasma electrochemistry: electroreduction in a flame

The manipulation of electron transfer reactions at surfaces forms the cornerstone of electrodeposition and processing of materials on substrates with precise control of stoichiometry and oxidation state. However, the utility of this technique, which is mainly carried out in liquid electrolytes, is ultimately limited by the electrolysis of the solvent which limits a potential window to at best 4.8 V in nonaqueous solutions (A. J. Bard and L. R. Faulkner, Electrochemical Methods: Fundamentals and Applications, Wiley, New York, NY, 2nd edn, 2001; ref. 1) and can be up to 6 V in ionic liquids (A. P. Abbott, K. J. McKenzie, Phys. Chem. Chem. Phys., 2006, 8, 4265-4279; ref. 2). A long-sought-after goal has been to develop a corresponding technique at the solid/gas interface in the absence of a solvent which will allow in principle a potential window in excess of 100 V (J. M. Goodings, J. Guo, A. N. Hayhurst and S. G. Taylor, Int. J. Mass Spectrom., 2001, 206, 137-151; ref. 3). This extended potential window will enable chemistry at the solid/gas interface that is not possible at the solid/liquid interface. Here we describe a new approach to gas-phase electrochemistry using a flame plasma as the electrolyte medium. We demonstrate the controlled electrochemical reduction of Cu(+) to Cu(0) at an electrode surface in a flame environment with resulting deposition of either Cu(2)O or Cu species on conducting diamond electrodes. This approach is novel in that it involves the application of an electrochemical potential difference to change the redox state of surface confined species, not the measurement of flame bore ions (as in flame ionisation detectors). This new technique will permit deposition of films and particles on surfaces with control over the oxidation state of the species. This will provide a valuable enhancement to the capabilities of materials preparation methods such as flame spray deposition.     

Structural and electrical characterisation of Li(2)O : TiO(2) : SnO(2) : P(2)O(5) electrolyte glass

Glasses of general formula 50Li(2)O : xSnO(2) : (10 -x)TiO(2) : 40P(2)O(5)(0.0 < or = x < or = 10) were investigated by differential scanning calorimetry, X-ray diffraction and ac impedance, (31)P solid-state NMR and IR spectroscopies. Three isotropic resonances can be identified in the (31)P NMR spectra, which have been assigned to various phosphate species. Analysis of the ratios of integrated intensities in the (31)P spectra leads to models for the Ti and Sn coordination environments. Both TiO(2) and SnO(2) are found to be predominantly network forming with Ti and Sn proposed to be in five- and four-coordinate environments respectively. Analysis of ac impedance spectra collected at low temperatures reveals two forms of permittivity dispersion, viz: high frequency conductivity dispersion and Cole-Cole type relaxation of permittivity. The activation energy of the relaxation frequency of the permittivity dispersion is equal to that of the dc conductivity, which is consistent with cooperative motion of lithium ions. The results also suggest that the observed increase in conductivity with temperature appears to be mainly due to an increase in mobility rather than increase in carrier concentration.     

Inequalities for real number sequences with applications in spectral graph theory

Czechoslovak Mathematical Journal - Let a = (a1,a2, …, an) be a nonincreasing sequence of positive real numbers. Denote by S = {1, 2, …, n} the index set and by Jk = {I = {r1, r2,...     

Primary reactions of bacteriophytochrome observed with ultrafast mid-infrared spectroscopy

Phytochromes are red-light photoreceptor proteins that regulate a variety of responses and cellular processes in plants, bacteria, and fungi. The phytochrome light activation mechanism involves isomerization around the C(15)═C(16) double bond of an open-chain tetrapyrrole chromophore, resulting in a flip of its D-ring. In an important recent development, bacteriophytochrome (Bph) has been engineered for use as a fluorescent marker in mammalian tissues. Bphs covalently bind a biliverdin (BV) chromophore, naturally abundant in mammalian cells. Here, we report an ultrafast time-resolved mid-infrared spectroscopic study on the Pr state of two highly related Bphs from Rps. palustris , RpBphP2 (P2) and RpBphP3 (P3) with distinct photoconversion and fluorescence properties. We observed that the BV excited state of P2 decays in 58 ps, while the BV excited state of P3 decays in 362 ps. By combining ultrafast mid-IR spectroscopy with FTIR spectroscopy on P2 and P3 wild type and mutant proteins, we demonstrate that the hydrogen bond strength at the ring D carbonyl of the BV chromophore is significantly stronger in P3 as compared to P2. This result is consistent with the X-ray structures of Bph, which indicate one hydrogen bond from a conserved histidine to the BV ring D carbonyl for classical bacteriophytochromes such as P2, and one or two additional hydrogen bonds from a serine and a lysine side chain to the BV ring D carbonyl for P3. We conclude that the hydrogen-bond strength at BV ring D is a key determinant of excited-state lifetime and fluorescence quantum yield. Excited-state decay is followed by the formation of a primary intermediate that does not decay on the nanosecond time scale of the experiment, which shows a narrow absorption band at ～1540 cm(-1). Possible origins of this product band are discussed. This work may aid in rational structure- and mechanism-based conversion of BPh into an efficient near-IR fluorescent marker.     

Fluorescence quantum yield and photochemistry of bacteriophytochrome constructs

Bacteriophytochromes (Bphs) are red-light photoreceptor proteins with a photosensory core that consists of three distinct domains, PAS, GAF and PHY, and covalently binds biliverdin (BV) to a conserved cysteine in the PAS domain. In a recent development, PAS-GAF variants were engineered for use as a near-infrared fluorescent marker in mammalian tissues (Tsien and co-workers, Science, 2009, 324, 804-807). Here, we report the fluorescence quantum yield and photochemistry of two highly-related Bphs from Rps. palustris, RpBphP2 (P2) and RpBphP3 (P3) with distinct photoconversion and fluorescence properties. We applied ultrafast spectroscopy to wild type P3 and P2 PAS-GAF proteins and their P3 D216A, Y272F and P2 D202A PAS-GAF-PHY mutant proteins. In these mutants hydrogen-bond interactions between a conserved aspartate (Asp) which connects the BV chromophore with the PHY domains are disrupted. The excited-state lifetime of the truncated P3 and P2 PAS-GAF proteins was significantly longer than in their PAS-GAF-PHY counterparts that constitute the full photosensory core. Mutation of the conserved Asp to Ala in the PAS-GAF-PHY protein had a similar but larger effect. The fluorescence quantum yields of the P3 D216A and Y272F mutants were 0.066, higher than that of wild type P3 (0.043) and similar to the engineered Bph of Tsien and co-workers. We conclude that elimination of a key hydrogen-bond interaction between Asp and a conserved Arg in the PHY domain is responsible for the excited-state lifetime increase in all Bph variants studied here. H/D exchange resulted in a 1.4-1.7 fold increase of excited-state lifetime. The results support a reaction model in which deactivation of the BV chromophore proceeds via excited-state proton transfer from the BV pyrrole nitrogens to the backbone of the conserved Asp or to a bound water. This work may aid in rational structure- and mechanism-based conversion of constructs based on P3 and other BPhs into efficient near-IR, deep tissue, fluorescent markers.