Askey-Wilson Type Functions, With Bound States

The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22], are slightly modified so as to make it transparent that these functions satisfy a beautiful symmetry property. It essentially means that the geometric and the spectral parameters are interchangeable in these functions. We call the resulting functions the Askey-Wilson functions. Then, we show that by adding bound states (with arbitrary weights) at specific points outside of the continuous spectrum of some instances of the Askey-Wilson difference operator, we can generate functions that satisfy a doubly infinite three-term recursion relation and are also eigenfunctions of $q$-difference operators of arbitrary orders. Our result provides a discrete analogue of the solutions of the purely differential version of the bispectral problem that were discovered in the pioneering work [8] of Duistermaat and Gr\"unbaum.Comment: 42 pages, Section 3 moved to the end, minor correction

The nomenclature and application of the names Euphorbia candelabrum Welw. and Euphorbia ingens in tropical Africa

During the last 40 years, one of the most widespread and conspicuous succulent trees in East and north‐east Africa has been referred to as Euphorbia candelabrum Kotschy or as E. candelabrum Trémaux ex Kotschy. This name is a later homonym of E. candelabrum Welw., and consequently it is illegitimate. The species to which the name E. candelabrum Kotschy has been widely applied is shown to be conspecific with E. ingens, which occurs from southern Ethiopia to subtropical South Africa.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152821/1/tax12091_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/152821/2/tax12091.pd

Effects of N, P and K on Striga asiatica (L.) Kuntze seed germination and infestation of sorghum

Sorghum (Sorghum bicolor (L.) Moench) plants were grown in pots with 12.5 and 50 mg applied N kg−1 soil. With an increase of soil N, the Striga asiatica (L.) Kuntze infestation, as well as the sorghum shoot dry matter losses due to infestation, decreased. The relative differences in stimulant capacity to induce Striga seed germination among the four sorghum genotypes were not consistent over the 0 to 150 mg N 1−1 range. The sorghum root exudate was considerably more active at 0 mg N 1−1, than at 30 mg N 1−1, and the stimulant produced at 150 mg N 1−1 failed to induce Striga seed germination. Presence of N in the growth medium considerably reduced the effectiveness of the stimulating substance produced by sorghum roots, whereas K promoted stimulant activity only in the absence of N. The presence or absence of P in the growth medium did not affect Striga seed germinability, probably due to the inability of this element to interfere with the production or activity of the stimulating substance from the host plants. It can be concluded, therefore, that sorghum plants seem to produce active root exudate only in conditions of N deficienc

Use of SMS texts for facilitating access to online alcohol interventions: a feasibility study

A41 Use of SMS texts for facilitating access to online alcohol interventions: a feasibility study In: Addiction Science & Clinical Practice 2017, 12(Suppl 1): A4

Scattering of lower-hybrid waves by density fluctuations

The investigation of the scattering of lower-hybrid waves by density fluctuations in tokamaks is distinguished by the presence in the wave equation of a large, random, derivative-coupling term. Assuming the fluctuations to be of long wavelength compared to the incident wave the similarity of the wave equation to the Schroedinger equation for a particle in a random magnetic field is used to derive a two-way diffusion equation for the wave energy density. The diffusion constant found disagrees with earlier findings and the source of the discrepancy is pointed out. When the correct boundary conditions are imposed this equation can be solved by separation of variables. However most of the important features of the solution are apparent without detailed algebra