Log-convexity and log-concavity of hypergeometric-like functions

We find sufficient conditions for log-convexity and log-concavity for the functions of the forms $a\mapsto\sum{f_k}(a)_kx^k$, $a\mapsto\sum{f_k}\Gamma(a+k)x^k$ and $a\mapsto\sum{f_k}x^k/(a)_k$. The most useful examples of such functions are generalized hypergeometric functions. In particular, we generalize the Tur\'{a}n inequality for the confluent hypergeometric function recently proved by Barnard, Gordy and Richards and log-convexity results for the same function recently proved by Baricz. Besides, we establish a reverse inequality which complements naturally the inequality of Barnard, Gordy and Richards. Similar results are established for the Gauss and the generalized hypergeometric functions. A conjecture about monotonicity of a quotient of products of confluent hypergeometric functions is made.Comment: 13 pages, no figure

Planck scale effects in neutrino physics

We study the phenomenology and cosmology of the Majoron (flavon) models of three active and one inert neutrino paying special attention to the possible (almost) conserved generalization of the Zeldovich-Konopinski-Mahmoud lepton charge. Using Planck scale physics effects which provide the breaking of the lepton charge, we show how in this picture one can incorporate the solutions to some of the central issues in neutrino physics such as the solar and atmospheric neutrino puzzles, dark matter and a 17 keV neutrino. These gravitational effects induce tiny Majorana mass terms for neutrinos and considerable masses for flavons. The cosmological demand for the sufficiently fast decay of flavons implies a lower limit on the electron neutrino mass in the range of 0.1-1 eV.Comment: 24 pages, 1 figure (not included but available upon request), LaTex, IC/92/196, SISSA-140/92/EP, LMU-09/9

sPlotOpen – An environmentally balanced, open‐access, global dataset of vegetation plots

Assessing biodiversity status and trends in plant communities is critical for understanding, quantifying and predicting the effects of global change on ecosystems. Vegetation plots record the occurrence or abundance of all plant species co-occurring within delimited local areas. This allows species absences to be inferred, information seldom provided by existing global plant datasets. Although many vegetation plots have been recorded, most are not available to the global research community. A recent initiative, called ‘sPlot’, compiled the first global vegetation plot database, and continues to grow and curate it. The sPlot database, however, is extremely unbalanced spatially and environmentally, and is not open-access. Here, we address both these issues by (a) resampling the vegetation plots using several environmental variables as sampling strata and (b) securing permission from data holders of 105 local-to-regional datasets to openly release data. We thus present sPlotOpen, the largest open-access dataset of vegetation plots ever released. sPlotOpen can be used to explore global diversity at the plant community level, as ground truth data in remote sensing applications, or as a baseline for biodiversity monitoring