Weighted Radon transforms for which the Chang approximate inversion formula is precise

We describe all weighted Radon transforms on the plane for which the Chang approximate inversion formula is precise. Some subsequent results, including the Cormack type inversion for these transforms, are also given

On problem of polarization tomography, I

The polarization tomography problem consists of recovering a matrix function f from the fundamental matrix of the equation $D\eta/dt=\pi_{\dot\gamma}f\eta$ known for every geodesic $\gamma$ of a given Riemannian metric. Here $\pi_{\dot\gamma}$ is the orthogonal projection onto the hyperplan $\dot\gamma^{\perp}$. The problem arises in optical tomography of slightly anisotropic media. The local uniqueness theorem is proved: a $C^1$- small function f can be recovered from the data uniquely up to a natural obstruction. A partial global result is obtained in the case of the Euclidean metric on $R^3$

A role for 3′-O-β-D-ribofuranosyladenosine in altering plant immunity

Our understanding of how, and the extent to which, phytopathogens reconfigure host metabolic pathways to enhance virulence is remarkably limited. Here we investigate the dynamics of the natural disaccharide nucleoside, 3′-O-β-D-ribofuranosyladenosine, in leaves of Arabidopsis thaliana infected with virulent Pseudomonas syringae pv. tomato strain DC3000. 3′-O-β-D-ribofuranosyladenosine is a plant derived molecule that rapidly accumulates following delivery of P. syringae type III effectors to represent a major component of the infected leaf metabolome. We report the first synthesis of 3′-O-β-D-ribofuranosyladenosine using a method involving the condensation of a small excess of 1-O-acetyl-2,3,5-three-O-benzoyl-β-ribofuranose activated with tin tetrachloride with 2′,5′-di-O-tert-butyldimethylsilyladenosine in 1,2-dichloroethane with further removal of silyl and benzoyl protecting groups. Interestingly, application of synthetic 3′-O-β-D-ribofuranosyladenosine did not affect either bacterial multiplication or infection dynamics suggesting a major reconfiguration of metabolism during pathogenesis and a heavy metabolic burden on the infected plant

Evolving Lorentzian Wormholes

Evolving Lorentzian wormholes with the required matter satisfying the Energy conditions are discussed. Several different scale factors are used and the corresponding consequences derived. The effect of extra, decaying (in time) compact dimensions present in the wormhole metric is also explored and certain interesting conclusions are derived for the cases of exponential and Kaluza--Klein inflation.Comment: 10 pages( RevTex, Twocolumn format), Two figures available on request from the first author. transmission errors corrected

Raise the anchor! Synthesis, X-ray and NMR characterization of 1,3,5-triazinanes with an axial tert-butyl group

N-t-Bu-N’,N’’-disulfonamide-1,3,5-triazinanes were synthesized and characterized by X-ray single crystal structure analysis. In the course of the X-ray structure elucidation, the first solid experimental evidence of the axial position of the tert-butyl group in unconstrained hexahydro-1,3,5-triazacyclohexanes was obtained. Dynamic low-temperature NMR analysis allowed to fully investigate a rare case of crystallization-driven unanchoring of the tert-butyl group in the chair conformation of saturated sixmembered cycles. DFT calculations show that the use of explicit solvent molecules is necessary to explain the equatorial position of the t-Bu group in solution. Otherwise, the axial conformer is the thermodynamically stable isomer.Fil: Kletskov, Alexey V.. University of Russia; RusiaFil: Zatykina, Anastasya D.. University of Russia; RusiaFil: Grudova, Mariya V.. University of Russia; RusiaFil: Sinelshchikova, Anna A.. Academy of Sciences; RusiaFil: Grigoriev, Mikhail. Academy of Sciences; RusiaFil: Zaytsev, Vladimir P.. University of Russia; RusiaFil: Gil, Diego Mauricio. Universidad Nacional de Tucumán. Instituto de Biotecnología Farmacéutica y Alimentaria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán. Instituto de Biotecnología Farmacéutica y Alimentaria; Argentina. Universidad Nacional de Tucumán. Facultad de Bioquímica, Química y Farmacia. Instituto de Química Orgánica; ArgentinaFil: Novikov, Roman A.. Academy of Sciences; RusiaFil: Zubkov, Fedor Ivanovich. University of Russia; RusiaFil: Frontera, Antonio. Universidad de las Islas Baleares; Españ

Binary systems of neutral mesons in Quantum Field Theory

Quasi-degenerate binary systems of neutral mesons of the kaon type are investigated in Quantum Field Theory (QFT). General constraints cast by analyticity and discrete symmetries P, C, CP, TCP on the propagator (and on its spectral function) are deduced. Its poles are the physical masses; this unambiguously defines the propagating eigenstates. It is diagonalized and its spectrum thoroughly investigated. The role of ``spurious'' states, of zero norm at the poles, is emphasized, in particular for unitarity and for the realization of TCP symmetry. The K_L-K_S mass splitting triggers a tiny difference between their CP violating parameters \epsilon_L and \epsilon_S, without any violation of TCP. A constant mass matrix like used in Quantum Mechanics (QM) can only be introduced in a linear approximation to the inverse propagator, which respects its analyticity and positivity properties; it is however unable to faithfully describe all features of neutral mesons as we determine them in QFT, nor to provide any sensible parameterization of eventual effects of TCP violation. The suitable way to diagonalize the propagator makes use of a bi-orthogonal basis; it is inequivalent to a bi-unitary transformation (unless the propagator is normal, which cannot occur here). Problems linked with the existence of different ``in'' and ``out'' eigenstates are smoothed out. We study phenomenological consequences of the differences between the QFT and QM treatments. The non-vanishing of semi-leptonic asymmetry \delta_S - \delta_L does not signal, unlike usually claimed, TCP violation, while A_TCP keeps vanishing when TCP is realized. We provide expressions invariant by the rephasing of K0 and K0bar.Comment: 44 pages, 2 figures. Version to appear in Int. J. Mod. Phys.

Planck intermediate results. VIII. Filaments between interacting clusters

About half of the baryons of the Universe are expected to be in the form of filaments of hot and low density intergalactic medium. Most of these baryons remain undetected even by the most advanced X-ray observatories which are limited in sensitivity to the diffuse low density medium. The Planck satellite has provided hundreds of detections of the hot gas in clusters of galaxies via the thermal Sunyaev-Zel'dovich (tSZ) effect and is an ideal instrument for studying extended low density media through the tSZ effect. In this paper we use the Planck data to search for signatures of a fraction of these missing baryons between pairs of galaxy clusters. Cluster pairs are good candidates for searching for the hotter and denser phase of the intergalactic medium (which is more easily observed through the SZ effect). Using an X-ray catalogue of clusters and the Planck data, we select physical pairs of clusters as candidates. Using the Planck data we construct a local map of the tSZ effect centered on each pair of galaxy clusters. ROSAT data is used to construct X-ray maps of these pairs. After having modelled and subtracted the tSZ effect and X-ray emission for each cluster in the pair we study the residuals on both the SZ and X-ray maps. For the merging cluster pair A399-A401 we observe a significant tSZ effect signal in the intercluster region beyond the virial radii of the clusters. A joint X-ray SZ analysis allows us to constrain the temperature and density of this intercluster medium. We obtain a temperature of kT = 7.1 +- 0.9, keV (consistent with previous estimates) and a baryon density of (3.7 +- 0.2)x10^-4, cm^-3. The Planck satellite mission has provided the first SZ detection of the hot and diffuse intercluster gas.Comment: Accepted by A&

Continuous Symmetries of Difference Equations

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalized symmetries acting on solutions of difference equations, but leaving the lattice invariant. The other is to restrict to point symmetries, but to allow them to also transform the lattice.Comment: Review articl

Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts

We present cluster counts and corresponding cosmological constraints from the Planck full mission data set. Our catalogue consists of 439 clusters detected via their Sunyaev-Zeldovich (SZ) signal down to a signal-to-noise ratio of 6, and is more than a factor of 2 larger than the 2013 Planck cluster cosmology sample. The counts are consistent with those from 2013 and yield compatible constraints under the same modelling assumptions. Taking advantage of the larger catalogue, we extend our analysis to the two-dimensional distribution in redshift and signal-to-noise. We use mass estimates from two recent studies of gravitational lensing of background galaxies by Planck clusters to provide priors on the hydrostatic bias parameter, (1−b). In addition, we use lensing of cosmic microwave background (CMB) temperature fluctuations by Planck clusters as an independent constraint on this parameter. These various calibrations imply constraints on the present-day amplitude of matter fluctuations in varying degrees of tension with those from the Planck analysis of primary fluctuations in the CMB; for the lowest estimated values of (1−b) the tension is mild, only a little over one standard deviation, while it remains substantial (3.7σ) for the largest estimated value. We also examine constraints on extensions to the base flat ΛCDM model by combining the cluster and CMB constraints. The combination appears to favour non-minimal neutrino masses, but this possibility does little to relieve the overall tension because it simultaneously lowers the implied value of the Hubble parameter, thereby exacerbating the discrepancy with most current astrophysical estimates. Improving the precision of cluster mass calibrations from the current 10%-level to 1% would significantly strengthen these combined analyses and provide a stringent test of the base ΛCDM model