On transformation formulas for theta hypergeometric functions

Using an identity and certain summation formulas for truncated theta hypergeometric series, we establish transformation formulas for finite bilateral theta hypergeometric series.За допомогою однiєї тотожностi та формул пiдсумовування скорочених гiпергеометричних тета-рядiв встановлено формули перетворення для скiнченних двостороннiх гiпергеометричних тета-рядiв

Multilateral inversion of A_r, C_r and D_r basic hypergeometric series

In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic hypergeometric matrix inverse with applications to bilateral basic hypergeometric series. This matrix inversion result was directly extracted from an instance of Bailey's very-well-poised 6-psi-6 summation theorem, and involves two infinite matrices which are not lower-triangular. The present paper features three different multivariable generalizations of the above result. These are extracted from Gustafson's A_r and C_r extensions and of the author's recent A_r extension of Bailey's 6-psi-6 summation formula. By combining these new multidimensional matrix inverses with A_r and D_r extensions of Jackson's 8-phi-7 summation theorem three balanced very-well-poised 8-psi-8 summation theorems associated with the root systems A_r and C_r are derived.Comment: 24 page

Risk profiles and one-year outcomes of patients with newly diagnosed atrial fibrillation in India: Insights from the GARFIELD-AF Registry.

BACKGROUND: The Global Anticoagulant Registry in the FIELD-Atrial Fibrillation (GARFIELD-AF) is an ongoing prospective noninterventional registry, which is providing important information on the baseline characteristics, treatment patterns, and 1-year outcomes in patients with newly diagnosed non-valvular atrial fibrillation (NVAF). This report describes data from Indian patients recruited in this registry. METHODS AND RESULTS: A total of 52,014 patients with newly diagnosed AF were enrolled globally; of these, 1388 patients were recruited from 26 sites within India (2012-2016). In India, the mean age was 65.8 years at diagnosis of NVAF. Hypertension was the most prevalent risk factor for AF, present in 68.5% of patients from India and in 76.3% of patients globally (P < 0.001). Diabetes and coronary artery disease (CAD) were prevalent in 36.2% and 28.1% of patients as compared with global prevalence of 22.2% and 21.6%, respectively (P < 0.001 for both). Antiplatelet therapy was the most common antithrombotic treatment in India. With increasing stroke risk, however, patients were more likely to receive oral anticoagulant therapy [mainly vitamin K antagonist (VKA)], but average international normalized ratio (INR) was lower among Indian patients [median INR value 1.6 (interquartile range {IQR}: 1.3-2.3) versus 2.3 (IQR 1.8-2.8) (P < 0.001)]. Compared with other countries, patients from India had markedly higher rates of all-cause mortality [7.68 per 100 person-years (95% confidence interval 6.32-9.35) vs 4.34 (4.16-4.53), P < 0.0001], while rates of stroke/systemic embolism and major bleeding were lower after 1 year of follow-up. CONCLUSION: Compared to previously published registries from India, the GARFIELD-AF registry describes clinical profiles and outcomes in Indian patients with AF of a different etiology. The registry data show that compared to the rest of the world, Indian AF patients are younger in age and have more diabetes and CAD. Patients with a higher stroke risk are more likely to receive anticoagulation therapy with VKA but are underdosed compared with the global average in the GARFIELD-AF. CLINICAL TRIAL REGISTRATION-URL: http://www.clinicaltrials.gov. Unique identifier: NCT01090362

On some Ramanujan-Selberg continued fraction.

On page 55 of his `lost' notebook, Ramanujan has recorded several P-Q eta-function identities with two moduli. In this paper, we establish several P-Q modular equations of degree 4. We also establish modular relations and explicit evaluations of Ramanujan-Selberg continued fraction

Wind profiles within a cassava field as affected by plant height and leaf area index

La vitesse et la direction du vent sont deux facteurs qui affectent la dispersion de la mosaïque africaine du manioc. Une étude a été conduite au champ de 1986 à 1988 pour déterminer l'importance de la hauteur des plantes et l'architecture du feuillage sur la réduction de la vitesse du vent au dessus et dans le couvert du manioc. Les profils verticaux ont une forme logarithmique au-dessus de la canopée alors qu'à l'intérieur du couvert, la forme dépend de la hauteur (H) des plantes, de l'indice foliaire (LAI) et de la distribution de la surface foliaire. La réduction de la vitesse du vent par le couvert de manioc augmente avec la force du vent et peut atteindre 50% à 0,2 H au-dessus de la canopée. Les profils horizontaux montrent que la réduction de la vitesse du vent commence avant le bord d'attaque. La réduction maximale est obtenue 2 à 4 m après le bord d'attaque et varie de 50 à 100% en fonction de l'indice foliaire, de la hauteur de mesure et de la vitesse maximale du vent en amont. (Résumé d'auteur