An Euler-type formula for β(2n)\beta(2n) and closed-form expressions for a class of zeta series

In a recent work, Dancs and He found an Euler-type formula for $\,\zeta{(2\,n+1)}$, $\,n\,$ being a positive integer, which contains a series they could not reduce to a finite closed-form. This open problem reveals a greater complexity in comparison to $\zeta(2n)$, which is a rational multiple of $\pi^{2n}$. For the Dirichlet beta function, the things are `inverse': $\beta(2n+1)$ is a rational multiple of $\pi^{2n+1}$ and no closed-form expression is known for $\beta(2n)$. Here in this work, I modify the Dancs-He approach in order to derive an Euler-type formula for $\,\beta{(2n)}$, including $\,\beta{(2)} = G$, the Catalan's constant. I also convert the resulting series into zeta series, which yields new exact closed-form expressions for a class of zeta series involving $\,\beta{(2n)}$ and a finite number of odd zeta values. A closed-form expression for a certain zeta series is also conjectured.Comment: 11 pages, no figures. A few small corrections. ACCEPTED for publication in: Integral Transf. Special Functions (09/11/2011

Efficient Pattern Matching in Python

Pattern matching is a powerful tool for symbolic computations. Applications include term rewriting systems, as well as the manipulation of symbolic expressions, abstract syntax trees, and XML and JSON data. It also allows for an intuitive description of algorithms in the form of rewrite rules. We present the open source Python module MatchPy, which offers functionality and expressiveness similar to the pattern matching in Mathematica. In particular, it includes syntactic pattern matching, as well as matching for commutative and/or associative functions, sequence variables, and matching with constraints. MatchPy uses new and improved algorithms to efficiently find matches for large pattern sets by exploiting similarities between patterns. The performance of MatchPy is investigated on several real-world problems

Constraints on the Cosmic Infra-Red Background based on BeppoSAX and CAT spectra of Mkn 501

The TeV and X-ray data obtained by the imaging Cherenkov telescope CAT and X-ray satellite BeppoSAX during the remarkable flare of Mkn 501 in April 16, 1997 are used to constrain the flux of the Cosmic Infrared Background (CIB) using different CIB models. We show that a non-negligible absorption of gamma-rays due to the CIB could take place already in the low-energy (sub-TeV) domain of the spectrum of Mkn 501. This implies that the data of the low-energy threshold CAT telescope contain very important information about the CIB at short wavelengths, 0.4 mum <= lambda <= 3. mum. The analysis of almost simultaneous spectroscopic measurements of Mkn 501 in a high state by CAT and BeppoSAX in the framework of the standard homogeneous Synchrotron-Self-Compton (SSC) framework model leads to the conclusion that the density of the near-infrared background with typical ``starlight spectrum'' around 1 mum should be between 5 and 35 nW m^-2 sr^-1 (99 % CL), with most likely value around 20 nW m^-2 sr^-1. Also we argue that the CAT gamma-ray data alone allow rather robust upper limits on the CIB, lambda F_lambda <= 60 nW m^-2 sr^-1 at 1 mum, taking into account that for any reasonable scenario of gamma-ray production the differential intrinsic spectrum of gamma-ray hardly could be flatter than dN/dE == E^-1. This estimate agrees, within statistical and systematic uncertainties, with recent reports about tentative detections of the CIB at 2.2 and 3.5 mum by the Diffuse Infrared Background Experiment (DIRBE), as well as with the measurements of the background radiation at optical wavelengths from absolute photometry. We also discuss the impact of the intergalactic absorption effect in derivation of the SSC parameters for the jet in Mkn 501

Genetic comparison of Campylobacter coli resulting from pigs and poultry with isolates resulting from human campylobacteriosis

133 isolates of Campylobacter coli isolated from Brittany in France and collected in 2003 were analysed by RFLP/PFGE. They came from pig (65), poultry (56) and human campylobacteriosis (12). No pulsotype common to the 3 origins could be detected but the analysis of the genetic similarity at 80% of the isolates made it possible to build 19 groups of similarity in 3 cases. Poultry isolates were found in groups containing human isolates. Neverthless, the pig isolates were always in groups different from the poultry isolates and the human ones. These results tend to indicate that the two animal productions would have their own genotype and that the campylobacters from pigs are rarely responsible of human campylobacteriosis

Genetic transfer of resistance to powdery mildew and of an associated molecular marker from Aegilops ventricosa to hexaploid wheat.

Resistance to powdery mildew, caused by the fungus Erysiphe graminis f.sp. tritici, has been transferred from Aegilops ventricosa (genomes DvMv) to hexaploid wheat (Triticum aestivum, ABD). In two transfer lines, H-93-8 and H-93-35, the resistance gene was linked to a gene encoding protein U-1, whereas one line, H-93-33, was resistant but lacked the molecular marker, and another line, H-93-1, was susceptible but carried the gene for U-1, indicating that the original Mv chromosome from Ae. ventricosa, carrying the two genes, had undergone recombination with a wheat chromosome in the last two lines

Resistance to the cereal cyst nematode (Heterodera avenae) transferred from the wild grass Aegilops ventricosa to hexaploid wheat by a "stepping-stone" procedure

Transfer of resistance toHeterodera avenae, the cereal cyst nematode (CCN), by a stepping-stoneprocedure from the wild grassAegilops ventricosa to hexaploid wheat has been demonstrated. The number of nematodes per plant was lower, and reached a plateau much earlier, in the resistant introgression line H93-8 (1–2 nematodes per plant) than in the recipient H10-15 wheat (14–16 nematodes per plant). Necrosis (hypersensitive reaction) near the nematode, little cell fusion, and few, often degraded syncytia were observed in infested H93-8 roots, while abundant, well-formed syncytia were present in the susceptible H10-15 wheat. Line H93-8 was highly resistant to the two Spanish populations tested, as well as the four French races (Fr1-Fr4), and the British pathotype Hall, but was susceptible to the Swedish pathotypes HgI and HgIII. Resistance was inherited as though determined by a single quasi-dominant factor in the F2 generations resulting from crosses of H93-8 with H10-15 and with Loros, a resistant wheat carrying the geneCre1 (syn.Ccn1). The resistance gene in H93-8 (Cre2 orCcn2) is not allelic with respect to that in Loros. RFLPs and other markers, together with the cytogenetical evidence, indicate that theCre2 gene has been integrated into a wheat chromosome without affecting its meiotic pairing ability. Introduction ofCre2 by backcrossing into a commercial wheat backgroud increases grain yield when under challenge by the nematode and is not detrimental in the absence of infestation

Very High Energy Gamma-ray spectral properties of Mrk 501 from CAT Cerenkov telescope observations in 1997

The BL Lac object Mrk 501 went into a very high state of activity during 1997, both in VHE gamma-rays and X-rays. We present here results from observations at energies above 250 GeV carried out between March and October 1997 with the CAT Cerenkov imaging Telescope. The average differential spectrum between 30 GeV and 13 TeV shows significant curvature and is well represented by phi_0 * E_TeV^{-(alpha + beta*log10(E_TeV))}, with: phi_0 = 5.19 +/- 0.13 {stat} +/- 0.12 {sys-MC} +1.66/-1.04 {sys-atm} * 10^-11 /cm^2/s/TeV alpha = 2.24 +/- 0.04 {stat} +/- 0.05 {sys} beta = 0.50 +/- 0.07 {stat} (negligible systematics). The TeV spectral energy distribution of Mrk 501 clearly peaks in the range 500 GeV-1 TeV. Investigation of spectral variations shows a significant hardness-intensity correlation with no measurable effect on the curvature. This can be described as an increase of the peak TeV emission energy with intensity. Simultaneous and quasi-simultaneous CAT VHE gamma-ray and BeppoSAX hard X-ray detections for the highest recorded flare on 16th April and for lower-activity states of the same period show correlated variability with a higher luminosity in X-rays than in gamma-rays. The observed spectral energy distribution and the correlated variability between X-rays and gamma-rays, both in amplitude and in hardening of spectra, favour a two-component emission scheme where the low and high energy components are attributed to synchrotron and inverse Compton (IC) radiation, respectively.Comment: Submitted to Astronomy and Astrophysics, 8 pages including 6 figures. Published with minor change

Observation of the Crab Nebula Gamma-Ray Emission Above 220 Gev by the Cat Cherenkov Imaging Telescope

The CAT imaging telescope, recently built on the site of the former solar plant Themis (French Pyrenees), observed gamma-rays from the Crab nebula from October 1996 to March 1997. This steady source, often considered as the standard candle of very-high-energy gamma-ray astronomy, is used as a test-beam to probe the performances of the new telescope, particularly its energy threshold (220 GeV at 20 degrees zenith angle) and the stability of its response. Due to the fine-grain camera, an accurate analysis of the longitudinal profiles of shower images is performed, yielding the source position in two dimensions for each individual shower.Comment: 5 pages, 3 figures, Tex, contribution to 25th ICRC Durba

Detection of Vhe Gamma-Rays from MRK 501 with the Cat Imaging Telescope

The CAT imaging telescope on the site on the former solar plant Themis has been observing gamma-rays from Mrk501 above 220 GeV in March and April 1997. This source is shown to be highly variable and the light curve is presented. The detected gamma-ray rate for the most intense flare is in excess of 10 per minute.Comment: 5 pages, 4 figures, Tex, contribution to 25th ICRC Durba