Explicit multipeakon solutions of Novikov's cubically nonlinear integrable Camassa-Holm type equation

Recently Vladimir Novikov found a new integrable analogue of the Camassa-Holm equation, admitting peaked soliton (peakon) solutions, which has nonlinear terms that are cubic, rather than quadratic. In this paper, the explicit formulas for multipeakon solutions of Novikov's cubically nonlinear equation are calculated, using the matrix Lax pair found by Hone and Wang. By a transformation of Liouville type, the associated spectral problem is related to a cubic string equation, which is dual to the cubic string that was previously found in the work of Lundmark and Szmigielski on the multipeakons of the Degasperis-Procesi equation.Comment: 41 pages, LaTeX + AMS packages + pstrick

Nucleotide-Binding Sites of the Heterodimeric LmrCD ABC-Multidrug Transporter of Lactococcus lactis Are Asymmetric

LmrCD is a lactococcal, heterodimeric multidrug transporter, which belongs to the ABC superfamily. It consists of two half-transporters, LmrC and LmrD, that are necessary and sufficient for drug extrusion and ATP hydrolysis. LmrCD is asymmetric in terms of the conservation of the functional motifs of the nucleotide-binding domains (NBDs). Important residues of the nucleotide-binding site of LmrC and the C loop of LmrD are not conserved. To investigate the functional importance of the LmrC and LmrD subunits, the putative catalytic base residue adjacent to the Walker B motif of both NBDs were substituted for the respective carboxamides. Our data demonstrate that Glu587 of LmrD is essential for both drug transport and ATPase activity of the LmrCD heterodimer, whereas mutation of Asp495 of LmrC has a less severe effect on the activity of the complex. Structural and/or functional asymmetry is further demonstrated by differential labeling of both subunits by 8-azido-[α-32P]ATP, which, at 4 °C, occurs predominantly at LmrC, while aluminiumfluoride (AlFx)-induced trapping of the hydrolyzed nucleotide at 30 °C results in an almost exclusive labeling of LmrD. It is concluded that the LmrCD heterodimer contains two structurally and functionally distinct NBDs.

Tests of Gravity from Imaging and Spectroscopic Surveys

Tests of gravity on large-scales in the universe can be made using both imaging and spectroscopic surveys. The former allow for measurements of weak lensing, galaxy clustering and cross-correlations such as the ISW effect. The latter probe galaxy dynamics through redshift space distortions. We use a set of basic observables, namely lensing power spectra, galaxy-lensing and galaxy-velocity cross-spectra in multiple redshift bins (including their covariances), to estimate the ability of upcoming surveys to test gravity theories. We use a two-parameter description of gravity that allows for the Poisson equation and the ratio of metric potentials to depart from general relativity. We find that the combination of imaging and spectroscopic observables is essential in making robust tests of gravity theories. The range of scales and redshifts best probed by upcoming surveys is discussed. We also compare our parametrization to others used in the literature, in particular the gamma parameter modification of the growth factor.Comment: 18 pages, 10 figures, to be submitte

Quantum mechanical calculations of state-to-state cross sections and rate constants for the F + DCl → Cl + DF reaction

9 págs.; 10 figs.; 3 tabs.© 2015 AIP Publishing LLC. We present accurate state-to-state quantum wave packet calculations of integral cross sections and rate constants for the title reaction. Calculations are carried out on the best available ground 12A′ global adiabatic potential energy surface of Deskevich et al. [J. Chem. Phys. 124, 224303 (2006)]. Converged state-to-state reaction cross sections have been calculated for collision energies up to 0.5 eV and different initial rotational and vibrational excitations, DCl(v = 0, j = 0 − 1; v = 1, j = 0). Also, initial-state resolved rate constants of the title reaction have been calculated in a temperature range of 100-400 K. It is found that the initial rotational excitation of the DCl molecule does not enhance reactivity, in contract to the reaction with the isotopologue HCl in which initial rotational excitation produces an important enhancement. These differences between the isotopologue reactions are analyzed in detail and attributed to the presence of resonances for HCl(v = 0, j), absent in the case of DCl(v = 0, j). For vibrational excited DCl(v = 1, j), however, the reaction cross section increases noticeably, what is also explained by another resonance.Financial support from the Scientific and Technological Research Council of TURKEY (TUBITAK) (Project No. TBAG- 112T827) is gratefully acknowledged. Computations have been done on the High Performance and Grid Computing Center (TR-Grid) machine at ULAKBIM/TURKEY. O.R. has been supported by the Ministerio de Economía e Innovación under Grant Nos. CSD2009-00038 and FIS2011-29596-C02 and used the CESGA computing centre under computing ICTS grants and also acknowledge the Chemistry and Molecular Sciences and Technologies COST Action CM1401. J.K. is grateful for the financial support from the U.S. National Science Foundation (Grant No. CHE-1213332 to M. H. Alexander). O.R. and N.B. also acknowledge CSIC for a travelling Grant No. I-LINK0775.Peer Reviewe

Polarized Spectroscopy Studies of Single Molecules of Porphycenes

Using ambient atmosphere instead of pure nitrogen environment enabled efficient recording of room temperature fluorescence from single molecules of porphycenes, chromophores with a high triplet formation efficiency. Double hydrogen transfer between two chemically identical trans tautomers has been demonstrated for parent porphycene and three alkyl derivatives by the analysis of spatial patterns of the emission obtained after raster scanning the sample excited with an appropriately polarized laser beam. Because of tautomerization, fluorescence in porphycenes is due to two nearly orthogonal transition dipole moments. This property allows the spatial orientation of the single molecule chromophores to be determined using radially and azimuthally polarized laser beams as excitation sources

Ammonia and hydrogen sulphide flux and dry deposition velocity estimates using vertical gradient method at a commercial beef cattle feedlot

Ammonia and hydrogen sulphide flux and dry deposition velocity were estimated using micrometeorological vertical gradient flux method at a commercial cattle feedyard of approximately 50,000 head of beef cattle and average 14.4 m²/head (150 ft²/head) stocking density. Ammonia-N and H2S-S loss had general diurnal patterns with the highest fluxes in daytime and lowest fluxes in nighttime that correlated to temperature changes and active evaporation process during daytime. The highest average deposition velocities also occurred during daytime with unstable atmospheric conditions and the lowest during nighttime with very stable conditions. There are exponential relationship between NH3-N flux and ambient temperature with R² = 0.57 for NH3 (NH3-N flux = – 1.46 + 7.96e0.077*Temperature) and R² = 0.22 for H2S-S (H2S-S flux = – 0.75 + 0.8e-0.013*Temperature)

Polynomial worst-case iteration complexity of quasi-Newton primal-dual interior point algorithms for linear programming

Quasi-Newton methods are well known techniques for large-scale numerical optimization. They use an approximation of the Hessian in optimization problems or the Jacobian in system of nonlinear equations. In the Interior Point context, quasi-Newton algorithms compute low-rank updates of the matrix associated with the Newton systems, instead of computing it from scratch at every iteration. In this work, we show that a simplified quasi-Newton primal-dual interior point algorithm for linear programming enjoys polynomial worst-case iteration complexity. Feasible and infeasible cases of the algorithm are considered and the most common neighborhoods of the central path are analyzed. To the best of our knowledge, this is the first attempt to deliver polynomial worst-case iteration complexity bounds for these methods. Unsurprisingly, the worst-case complexity results obtained when quasi-Newton directions are used are worse than their counterparts when Newton directions are employed. However, quasi-Newton updates are very attractive for large-scale optimization problems where the cost of factorizing the matrices is much higher than the cost of solving linear systems