Discrepancy and Signed Domination in Graphs and Hypergraphs

For a graph G, a signed domination function of G is a two-colouring of the vertices of G with colours +1 and -1 such that the closed neighbourhood of every vertex contains more +1's than -1's. This concept is closely related to combinatorial discrepancy theory as shown by Fueredi and Mubayi [J. Combin. Theory, Ser. B 76 (1999) 223-239]. The signed domination number of G is the minimum of the sum of colours for all vertices, taken over all signed domination functions of G. In this paper, we present new upper and lower bounds for the signed domination number. These new bounds improve a number of known results.Comment: 12 page

Role of gluons in soft and semi-hard multiple hadron production in pp collisions at LHC

Hadron inclusive spectra in pp collisions are analyzed within the modified quark-gluon string model including both the longitudinal and transverse motion of quarks in the proton in the wide region of initial energies. The self-consistent analysis shows that the experimental data on the inclusive spectra of light hadrons like pions and kaons at ISR energies can be satisfactorily described at transverse momenta not larger than 1-2 GeV/c. We discuss some difficulties to apply this model at energies above the ISR and suggest to include the distribution of gluons in the proton unintegrated over the internal transverse momentum. It leads to an increase in the inclusive spectra of hadrons and allows us to extend the satisfactory description of the data in the central rapidity region at energies higher than ISR.Comment: 19 pages, 20 figure

Towards the NNLL precision in Bˉ→Xsγ\bar B \to X_s \gamma

The present NLL prediction for the decay rate of the rare inclusive process $\bar B \to X_s \gamma$ has a large uncertainty due to the charm mass renormalization scheme ambiguity. We estimate that this uncertainty will be reduced by a factor of 2 at the NNLL level. This is a strong motivation for the on-going NNLL calculation, which will thus significantly increase the sensitivity of the observable $\bar B \to X_s \gamma$ to possible new degrees of freedom beyond the SM. We also give a brief status report of the NNLL calculation.Comment: 5 pages, 2 figures, contribution to the proceedings of EPS-HEP 200

Reduction of Charm Quark Mass Scheme Dependence in Bˉ→Xsγ\bar B \to X_s \gamma at the NNLL Level

The uncertainty of the theoretical prediction of the $\bar B \to X_s \gamma$ branching ratio at NLL level is dominated by the charm mass renormalization scheme ambiguity. In this paper we calculate those NNLL terms which are related to the renormalization of $m_c$, in order to get an estimate of the corresponding uncertainty at the NNLL level. We find that these terms significantly reduce (by typically a factor of two) the error on ${BR}(\bar B \to X_s \gamma)$ induced by the definition of $m_c$. Taking into account the experimental accuracy of around 10% and the future prospects of the $B$ factories, we conclude that a NNLL calculation would increase the sensitivity of the observable $\bar B \to X_s \gamma$ to possible new degrees of freedom beyond the SM significantly.Comment: 13 pages including 3 figure

The totally asymmetric exclusion process with generalized update

We consider the totally asymmetric exclusion process in discrete time with generalized updating rules. We introduce a control parameter into the interaction between particles. Two particular values of the parameter correspond to known parallel and sequential updates. In the whole range of its values the interaction varies from repulsive to attractive. In the latter case the particle flow demonstrates an apparent jamming tendency not typical for the known updates. We solve the master equation for $N$ particles on the infinite lattice by the Bethe ansatz. The non-stationary solution for arbitrary initial conditions is obtained in a closed determinant form.Comment: 11 pages, 3 figure

Application of scanning electron microscopy for diagnosing phytoplasmas in single and mixed (virus-phytoplasma ) infection in Papaya

Phytoplasma and some viruses, papaya ring spot (PRSV) and papaya mosaic (PapMV) have been reported in papaya, from different Mexican states. Some symptoms of yellow type diseases, such as mosaics, stunting, bunchy top and leaf chlorosis, necrosis and malformations are somewhat similar in appearance, but caused by distinct pathogens. Using a scanning electron microscopy (SEM) technique phytoplasmas were detected in the phloem tissues of field and greenhouse-indexed papaya plants from Baja California Sur (BCS). Samples from 32 local varieties, as well as cv. Maradol, showing numerous symptoms of dieback, mosaics, bunchy top, and yellow crinkle were analyzed. The pathogen was detected in stems, leafstalks, roots, axillary leaflets, leaf veins and flowers. Phytoplasma was also detected in dry and in germinated seeds within the fruit, suggesting seed transmission of the pathogen. Some ultrastructural peculiarities of phytoplasma in infected tissues were also observed. No viral infection with PRSV and PapMV was revealed neither in test-plants nor by molecular techniques. Application of SEM technique for analysis of papaya samples from Veracruz and Irapuato, both from field-grown and mechanically inoculated plants with PRSV and PapMV in various combinations also revealed phytoplasmas in the phloem of most of tested samples. In some cases, along with phytoplasmas, rod-shaped bacteria were distinguished.Keywords: Papaya, phytoplasma, papaya ringspot virus, papaya mosaic virus, scanning electron microscopy, Mexic

Optical Transition and Momentum Transfer in Atomic Wave Packets

It is shown that the population Rabi-floppings in a lossless two-level atom, interacting with a monochromatic electromagnetic field, in general are convergent in time. The well-known continuous floppings take place because the restricted choosing of initial conditions, that is when the atom initially is chosen on ground or excited level before the interaction, simultaneously having a definite value of momentum there. The convergence of Rabi-floppings in atomic wave-packet-states is a direct consequence of Doppler effect on optical transition rates (Rabi-frequencies): it gradually leads to ''irregular'' chaotic-type distributions of momentum in ground and excited energy levels, smearing the amplitudes of Rabi-floppings. Conjointly with Rabi-floppings, the coherent accumulation of momentum on each internal energy level monotonically diminishes too.Comment: 6 pages, 10 Figure

Three-leg correlations in the two component spanning tree on the upper half-plane

We present a detailed asymptotic analysis of correlation functions for the two component spanning tree on the two-dimensional lattice when one component contains three paths connecting vicinities of two fixed lattice sites at large distance $s$ apart. We extend the known result for correlations on the plane to the case of the upper half-plane with closed and open boundary conditions. We found asymptotics of correlations for distance $r$ from the boundary to one of the fixed lattice sites for the cases $r\gg s \gg 1$ and $s \gg r \gg 1$.Comment: 16 pages, 5 figure