Pennisetum section Brevivalvula in West Africa : morphological and genetic variation in an agamic species complex

Section Brevivalvula is one of five sections in the large tropical grass genus Pennisetum . It belongs to the tertiary genepool of P. glaucum (L.) R. Br., pearl millet, and consists of six morphological species: P. atrichum Stapf & Hubb., P. hordeoides (Lam.) Steud., P. pedicellatum Trin., P. polystachion (L.) Schult., P. setosum (Swartz) L. Rich. and P. subangustum (Schum.) Stapf & Hubb. P. setosum and P. atrichum are perennials, the other species are annual.Four euploid (2x, 4x, 5x, and 6x with x = 9) chromosome levels are known in the section. Tetraploid cytotypes are dominant in all taxa, except P. setosum , which is predominantly hexaploid. Diploids and pentaploids are rare.Some of the polyploid cytotypes of P. pedicellatum , P. hordeoides , and P. polystachion are at least partly facultative apomicts, while diploid P. polystachion and P. subangustum are reproducing sexually.A morphological analysis showed that all taxa intergrade with at least one other taxon. P. pedicellatum , with one - or more - pedicelled spikelets in large, fluffy involucres, has differentiated from the group with a single sessile spikelet per involucrum, but intermediate plants with one almost sessile spikelet exist as well. The group with a single sessile spikelet shows a gradient from slender plants with scabrous involucral bristles on narrow inflorescences ( P . hordeoides ), to slender plants with hairy involucral bristles on narrow inflorescences ( P.subangustum ), to large plants with hairy involucral bristles on large inflorescences ( P.polystachion ), to large perennial plants with hairy involucral bristles, on large yellowish inflorescences ( P. setosum ). P. atrichum is grouped near P. hordeoides , because of its scabrous involucral bristles, but it is also perennial and rather large.Isozyme electrophoresis of 635 plants resulted in 146 different 5-locus genotypes from combinations of 26 alleles. More than 85% of the samples of different species are connected by patterns of identical genotypes. When the proportions of 20 alleles are compared between species, ploidy levels or geographical areas, significant differences are found everywhere. The results also indicate that the samples share the same gene pool.These results indicate that the complex is in an active state of evolution. Speciation occurs at a low rate because of sexuality in the diploids as well as facultative apomixis in part of the polyploids, which cause hybridization events among the taxa, obscuring species boundaries. Speciation can become successful when a morphotype finds a specific niche for itself. This is clearly the case for P. pedicellatum , which is better adapted to drier climats than the other taxa. Because of the hybridizations, a fully unambiguous description of the other species of Pennisetum section Brevivalvula is impossible.</p

Basic Methods for Computing Special Functions

This paper gives an overview of methods for the numerical evaluation of special functions, that is, the functions that arise in many problems from mathematical physics, engineering, probability theory, and other applied sciences. We consider in detail a selection of basic methods which are frequently used in the numerical evaluation of special functions: converging and asymptotic series, including Chebyshev expansions, linear recurrence relations, and numerical quadrature. Several other methods are available and some of these will be discussed in less detail. We give examples of recent software for special functions where these methods are used. We mention a list of new publications on computational aspects of special functions available on our website

Study of the lineshape of the chi(c1) (3872) state

A study of the lineshape of the chi(c1) (3872) state is made using a data sample corresponding to an integrated luminosity of 3 fb(-1) collected in pp collisions at center-of-mass energies of 7 and 8 TeV with the LHCb detector. Candidate chi(c1)(3872) and psi(2S) mesons from b-hadron decays are selected in the J/psi pi(+)pi(-) decay mode. Describing the lineshape with a Breit-Wigner function, the mass splitting between the chi(c1 )(3872) and psi(2S) states, Delta m, and the width of the chi(c1 )(3872) state, Gamma(Bw), are determined to be (Delta m=185.598 +/- 0.067 +/- 0.068 Mev,)(Gamma BW=1.39 +/- 0.24 +/- 0.10 Mev,) where the first uncertainty is statistical and the second systematic. Using a Flatte-inspired model, the mode and full width at half maximum of the lineshape are determined to be (mode=3871.69+0.00+0.05 MeV.)(FWHM=0.22-0.04+0.13+0.07+0.11-0.06-0.13 MeV, ) An investigation of the analytic structure of the Flatte amplitude reveals a pole structure, which is compatible with a quasibound D-0(D) over bar*(0) state but a quasivirtual state is still allowed at the level of 2 standard deviations

Measurement of the CKM angle γγ in B±→DK±B^\pm\to D K^\pm and B±→Dπ±B^\pm \to D π^\pm decays with D→KS0h+h−D \to K_\mathrm S^0 h^+ h^-

A measurement of $CP$-violating observables is performed using the decays $B^\pm\to D K^\pm$ and $B^\pm\to D \pi^\pm$, where the $D$ meson is reconstructed in one of the self-conjugate three-body final states $K_{\mathrm S}\pi^+\pi^-$ and $K_{\mathrm S}K^+K^-$ (commonly denoted $K_{\mathrm S} h^+h^-$). The decays are analysed in bins of the $D$-decay phase space, leading to a measurement that is independent of the modelling of the $D$-decay amplitude. The observables are interpreted in terms of the CKM angle $\gamma$. Using a data sample corresponding to an integrated luminosity of $9\,\text{fb}^{-1}$ collected in proton-proton collisions at centre-of-mass energies of $7$, $8$, and $13\,\text{TeV}$ with the LHCb experiment, $\gamma$ is measured to be $\left(68.7^{+5.2}_{-5.1}\right)^\circ$. The hadronic parameters $r_B^{DK}$, $r_B^{D\pi}$, $\delta_B^{DK}$, and $\delta_B^{D\pi}$, which are the ratios and strong-phase differences of the suppressed and favoured $B^\pm$ decays, are also reported