EXPLICIT FORMULAS AND MEROMORPHIC EXTENSION OF BESSEL FUNCTIONS ON TANGENT SPACES TO NONCOMPACTLY CAUSAL SYMMETRIC SPACES

Assume that $G/H$ is a noncompactly causal symmetric space with restricted root system of the non-exceptional type and the multiplicity of the short roots is even. Using shift operators we obtain explicit formulas for the Bessel function on the tangent space to $G/H$ at the origin. This enable us to investigate the nature and order of the singularities of the Bessel function, and to formulate a conjecture on this matter

The source operator method: an overview

This is an overview on the {source operator method} which leads to the construction of symmetry breaking differential operators (SBDO) in the context of tensor product of two principals series representations for the conformal group of a simple real Jordan algebra. This method can be applied to other geometric contexts: in the construction of SBDO for differential forms and for spinors, and also for the construction of Juhl's operators corresponding to the restriction from the sphere $S^n$ to $S^{n-1}$

Ouarsenis : Langue et sociolinguistique

L’étymologie berbère de l’oronyme Ouarsenis est transparente : il s’agit d’un syntagme composé de war, morphème privatif “sans” + (s-)nnig, préposition locative « au-dessus » + -s « lui » (aff. pers. 3e pers. sing.), avec affaiblissement de la vélaire [g] en semi-voyelle palatale [y] (API [j]), caractéristiques des parlers de la région, puis vocalisation en [ī] long, selon un processus d’ailleurs largement attesté dans divers parlers berbères contemporains : war sənnig-s war sənniy-s Warsən..

Laguerre semigroup and Dunkl operators

We construct a two-parameter family of actions \omega_{k,a} of the Lie algebra sl(2,R) by differential-difference operators on R^N \setminus {0}. Here, k is a multiplicity-function for the Dunkl operators, and a>0 arises from the interpolation of the Weil representation of Mp(N,R) and the minimal unitary representation of O(N+1,2) keeping smaller symmetries. We prove that this action \omega_{k,a} lifts to a unitary representation of the universal covering of SL(2,R), and can even be extended to a holomorphic semigroup \Omega_{k,a}. In the k\equiv 0 case, our semigroup generalizes the Hermite semigroup studied by R. Howe (a=2) and the Laguerre semigroup by the second author with G. Mano (a=1). One boundary value of our semigroup \Omega_{k,a} provides us with (k,a)-generalized Fourier transforms F_{k,a}, which includes the Dunkl transform D_k (a=2) and a new unitary operator H_k (a=1), namely a Dunkl-Hankel transform. We establish the inversion formula, and a generalization of the Plancherel theorem, the Hecke identity, the Bochner identity, and a Heisenberg uncertainty inequality for F_{k,a}. We also find kernel functions for \Omega_{k,a} and F_{k,a} for a=1,2 in terms of Bessel functions and the Dunkl intertwining operator.Comment: final version (some few typos, updated references

Effects of temperature, water activity and incubation time on fungal growth and aflatoxin B1 production by toxinogenic Aspergillus flavus isolates on sorghum seeds

Sorghum, which is consumed in Tunisia as human food, suffers from severe colonization by several toxigenic fungi and contamination by mycotoxins. The Tunisian climate is characterized by high temperature and humidity that stimulates mold proliferation and mycotoxin accumulation in foodstuffs. This study investigated the effects of temperature (15, 25 and 37 ◦C), water activity (aw, between 0.85 and 0.99) and incubation time (7, 14, 21 and 28 d) on fungal growth and aflatoxin B1 (AFB1) production by three Aspergillus flavus isolates (8, 10 and 14) inoculated on sorghum grains. The Baranyi model was applied to identify the limits of growth and mycotoxin production. Maximum diameter growth rates were observed at 0.99 aw at 37 ◦C for two of the isolates. The minimum aw needed for mycelial growth was 0.91 at 25 and 37 ◦C. At 15 ◦C, only isolate 8 grew at 0.99 aw. Aflatoxin B1 accumulation could be avoided by storing sorghum at low water activity levels (≤0.91 aw). Aflatoxin production was not observed at 15 ◦C. This is the first work on the effects of water activity and temperature on A. flavus growth and AFB1 production by A. flavus isolates on sorghum grains.We thank M. Prim for her encouragement and technicalassistance. The authors are grateful to the European Union(MYCORED KBBE-2007-2-5-05 project) and Tunisian Govern-ment for financial support

SMOS based high resolution soil moisture estimates for Desert locust preventive management

This paper presents the first attempt to include soil moisture information from remote sensing in the tools available to desert locust managers. The soil moisture requirements were first assessed with the users. The main objectives of this paper are: i) to describe and validate the algorithms used to produce a soil moisture dataset at 1 km resolution relevant to desert locust management based on DisPATCh methodology applied to SMOS and ii) the development of an innovative approach to derive high-resolution (100 m) soil moisture products from Sentinel-1 in synergy with SMOS data. For the purpose of soil moisture validation, 4 soil moisture stations where installed in desert areas (one in each user country). The soil moisture 1 km product was thoroughly validated and its accuracy is amongst the best available soil moisture products. Current comparison with in-situ soil moisture stations shows good values of correlation (R>0.7R>0.7) and low RMSE (below 0.04 m3 m−3). The low number of acquisitions on wet dates has limited the development of the soil moisture 100 m product over the Users Areas. The Soil Moisture product at 1 km will be integrated into the national and global Desert Locust early warning systems in national locust centres and at DLIS-FAO, respectively

Association between metformin use and below-the-knee arterial calcification score in type 2 diabetic patients.

BACKGROUND Vascular calcification (VC) is common in type 2 diabetes, and is associated with cardiovascular complications. Recent preclinical data suggest that metformin inhibits VC both in vitro and in animal models. However, metformin's effects in patients with diabetic VC have not previously been characterized. The present study investigated the association between metformin use and lower-limb arterial calcification in patients with type 2 diabetes and high cardiovascular risk. METHODS The DIACART cross-sectional cohort study included 198 patients with type 2 diabetes but without severe chronic kidney disease. Below-the-knee calcification scores were assessed by computed tomography and supplemented by colour duplex ultrasonography. Data on anti-diabetic drugs were carefully collected from the patients' medical records and during patient interviews. Biochemical and clinical data were studied as potential confounding factors. RESULTS Metformin-treated patients had a significantly lower calcification score than metformin-free patients (mean ± standard deviation: 2033 ± 4514 and 4684 ± 9291, respectively; p = 0.01). A univariate analysis showed that metformin was associated with a significantly lower prevalence of severe below-the-knee arterial calcification (p = 0.02). VC was not significantly associated with the use of other antidiabetic drugs, including sulfonylureas, insulin, gliptin, and glucagon like peptide-1 analogues. A multivariate logistic regression analysis indicated that the association between metformin use and calcification score (odds ratio [95% confidence interval] = 0.33 [0.11-0.98]; p = 0.045) was independent of age, gender, tobacco use, renal function, previous cardiovascular disease, diabetes duration, neuropathy, retinopathy, HbA1c levels, and inflammation. CONCLUSIONS In patients with type 2 diabetes, metformin use was independently associated with a lower below-the-knee arterial calcification score. This association may contribute to metformin's well-known vascular protective effect. Further prospective investigations of metformin's potential ability to inhibit VC in patients with and without type 2 diabetes are now needed to confirm these results