A remark on "Study of a Leslie-Gower-type tritrophic population model" [Chaos, Solitons and Fractals 14 (2002) 1275-1293]

In [Aziz-Alaoui, 2002] a three species ODE model, based on a modified Leslie-Gower scheme is investigated. It is shown that under certain restrictions on the parameter space, the model has bounded solutions for all positive initial conditions, which eventually enter an invariant attracting set. We show that this is not true. To the contrary, solutions to the model can blow up in finite time, even under the restrictions derived in [Aziz-Alaoui, 2002], if the initial data is large enough. We also prove similar results for the spatially extended system. We validate all of our results via numerical simulations.Comment: 10 pages, 4 figure

Estimation de l'humidité du sol à haute résolution spatio-temporelle : une nouvelle approche basée sur la synergie des observations micro-ondes actives/passives et optiques/thermiques

Les capteurs micro-ondes passifs SMOS et SMAP fournissent des données d'humidité du sol (SM) à une résolution d'environ 40 km avec un intervalle de 2 à 3 jours à l' échelle mondiale et une profondeur de détection de 0 à 5 cm. Ces données sont très pertinentes pour les applications cli- matiques et météorologiques. Cependant, pour les applications à échelle régionales (l'hydrologie) ou locales (l'agriculture), des données de SM à une haute résolution spatiale (typiquement 100 m ou plus fine) seraient nécessaires. Les données collectées par les capteurs optiques/thermiques et les radars peuvent fournir des indicateurs de SM à haute résolution spatiale, mais ces deux approches alternatives ont des limites. En particulier, les données optiques/thermiques ne sont pas disponibles sous les nuages et sous les couverts végétaux. Quant aux données radar, elles sont sensibles à la rugosité du sol et à la structure de la végétation, qui sont tous deux difficiles à caractériser depuis l'espace. De plus, la résolution temporelle de ces données est d'environ 6 jours. Dans ce contexte, la ligne directrice de la thèse est de proposer une nouvelle approche qui combine pour la première fois des capteurs passifs micro-ondes, optiques/thermiques et actifs micro-ondes (radar) pour estimer SM sur de grandes étendues à une résolution de 100 m chaque jour. Notre hypothèse est d'abord de nous appuyer sur une méthode de désagrégation existante (DISPATCH) des données SMOS/SMAP pour atteindre la résolution cible obtenue par les radars. A l'origine, DISPATCH est basé sur l'efficacité d' évaporation du sol (SEE) estimée sur des pixels partiellement végétalisés à partir de données optiques/thermiques (généralement MODIS) de température de surface et de couverture végétale à résolution de 1 km. Les données désagrégées de SM sont ensuite combinées avec une méthode d'inversion de SM basée sur les données radar afin d'exploiter les capacités de détection des radars Sentinel-1. Enfin, les capacités de l'assimilation des donnés satellitaires de SM dans un modèle de bilan hydrique du sol sont évaluées en termes de prédiction de SM à une résolution de 100 m et à une échelle temporelle quotidienne.Dans une première étape, l'algorithme DISPATCH est amélioré par rapport à sa version actuelle, principalement 1) en étendant son applicabilité aux pixels optiques entièrement végétalisés en utilisant l'indice de sécheresse de la végétation basé sur la température et un produit de couverture végétale amélioré, et 2) en augmentant la résolution de désagrégation de 1 km à 100 m en utilisant les données optiques/thermiques de Landsat (en plus de MODIS). Le produit de SM désagrégé à la résolution de 100 m est validé avec des mesures in situ collectées sur des zones irriguées au Maroc, indiquant une corrélation spatiale quotidienne variant de 0,5 à 0,9. Dans un deuxième étape, un nouvel algorithme est construit en développant une synergie entre les données DISPATCH et radar à 100 m de résolution. En pratique, le produit SM issu de DISPATCH les jours de ciel clair est d'abord utilisé pour calibrer un modèle de transfert radiatif radar en mode direct. Ensuite, le modèle de transfert radiatif radar ainsi calibré est utilisé en mode inverse pour estimer SM à la résolution spatio-temporelle de Sentinel-1. Sur les sites de validation, les résultats indiquent une corrélation entre les mesures satellitaires et in situ, de l'ordre de 0,66 à 0,81 pour un indice de végétation inférieur à 0,6. Dans une troisième et dernière étape, une méthode d'assimilation optimale est utilisée pour interpoler dans le temps les données de SM à la résolution de 100 m. La dynamique du produit SM dérivé de l'assimilation de SM DISPATCH à 100 m de résolution est cohérente avec les événements d'irrigation. Cette approche peut être facilement appliquée sur de grandes zones, en considérant que toutes les données (télédétection et météorologique) requises en entrée sont disponibles à l' échelle globale.SMOS and SMAP passive microwave sensors provide soil moisture (SM) data at 40 km resolution every 2-3 days globally, with a 0-5 cm sensing depth relevant for climatic and meteorological applications. However, SM data would be required at a higher (typically 100 m or finer) spatial resolution for many other regional (hydrology) or local (agriculture) applications. Optical/thermal and radar sensors can be used for retrieving SM proxies at such high spatial resolution, but both techniques have limitations. In particular, optical/thermal data are not available under clouds and under plant canopies. Moreover, radar data are sensitive to soil roughness and vegetation structure, which are challenging to characterize from outer space, and have a repeat cycle of at least six days, limiting the observations' temporal frequency. In this context, the leading principle of the thesis is to propose a new approach that combines passive microwave, optical/thermal, and active microwave (radar) sensors for the first time to retrieve SM data at 100 m resolution on a daily temporal scale. Our assumption is first to rely on an existing disaggregation method (DISPATCH) of SMOS/SMAP SM data to meet the target resolution achieved by radars. DISPATCH is originally based on the soil evaporative efficiency (SEE) retrieved over partially vegetated pixels from 1 km resolution optical/thermal (typically MODIS) surface temperature and vegetation cover data. The disaggregated SM data is then combined with a radar-based SM retrieval method to exploit the sensing capabilities of the Sentinel-1 radars. Finally, the efficacy of the assimilation of satellite-based SM data in a soil water balance model is assessed in terms of SM predictions at the 100 m resolution and daily temporal scale. As a first step, the DISPATCH algorithm is improved from its current version by mainly 1) extending its applicability to fully vegetated optical pixels using the temperature vegetation dryness index and an enhanced vegetation cover product, and 2) increasing the targeted downscaling resolution from 1 km to 100 m using Landsat (in addition to MODIS) optical/thermal data. The 100 m resolution disaggregated SM product is validated with in situ measurements collected over irrigated areas in Morocco, showing a daily spatial correlation in the range of 0.5-0.9. As a second step, a new algorithm is built on a synergy between DISPATCH and radar 100 m resolution data. In practice, the DISPATCH SM product available on clear sky days is first used to calibrate a radar radiative transfer model in the direct mode. Then the calibrated radar radia- tive transfer model is used in the inverse mode to estimate SM at the spatio-temporal resolution of Sentinel-1. Results indicate a positive correlation between satellite and in situ measurements in the range of 0.66 to 0.81 for a vegetation index lower than 0.6. As a third and final step, an optimal assimilation method is used to interpolate 100 m resolution SM data in time. The assimilation exercise is undertaken over irrigated crop fields in Spain. The analyzed SM product derived from the assimilation of 100 m resolution DISPATCH SM is consistent with irrigation events. This approach can be readily applied over large areas, given that all the required input (remote sensing and meteorological) data are available globally

What is India speaking: The "Hinglish" invasion

While language competition models of diachronic language shift are increasingly sophisticated, drawing on sociolinguistic components like variable language prestige, distance from language centers and intermediate bilingual transitionary populations, in one significant way they fall short. They fail to consider contact-based outcomes resulting in mixed language practices, e.g. outcome scenarios such as creoles or unmarked code switching as an emergent communicative norm. On these lines something very interesting is uncovered in India, where traditionally there have been monolingual Hindi speakers and Hindi/English bilinguals, but virtually no monolingual English speakers. While the Indian census data reports a sharp increase in the proportion of Hindi/English bilinguals, we argue that the number of Hindi/English bilinguals in India is inaccurate, given a new class of urban individuals speaking a mixed lect of Hindi and English, popularly known as "Hinglish". Based on predator-prey, sociolinguistic theories, salient local ecological factors and the rural-urban divide in India, we propose a new mathematical model of interacting monolingual Hindi speakers, Hindi/English bilinguals and Hinglish speakers. The model yields globally asymptotic stable states of coexistence, as well as bilingual extinction. To validate our model, sociolinguistic data from different Indian classes are contrasted with census reports: We see that purported urban Hindi/English bilinguals are unable to maintain fluent Hindi speech and instead produce Hinglish, whereas rural speakers evidence monolingual Hindi. Thus we present evidence for the first time where an unrecognized mixed lect involving English but not "English", has possibly taken over a sizeable faction of a large global population.Comment: This paper has been withdrawan as the model has now been modified and the existing model has some error

A CRITICAL ANALYSIS OF BAL CHATURBHADRA CHURNA IN MANAGEMENT OF CHILDHOOD DISORDERS- EVIDENCES FROM AYURVEDA

Bal chaturbhadra churna is a poly-herbal formulation used in pediatric practice in Ayurveda especially in the treatment of vomiting, diarrhea, fever and respiratory disorders. The human clinical dose of Bal chaturbhadra churna is 1000 mg per day. It is prepared by mixing equal proportions of rhizome of Cyperus rotundus Linn. (Cyperaceae), fruit of Piper longum Linn. (Piperaceae), root of Aconitum heterophyllum Wall. ex. Royale. (Ranunculaceae) and gall of Pistacia integerrima Stew. Ex. Brandis. (Anacardiaceae). Aims and objectives: Critical analysis of Bal chaturbhadra churna in management of childhood disorder. Material and Methods: Various Ayurveda classics and studies published in journals related to use of Bal chaturbhadra churna in management of childhood disorder are reviewed and analyzed. Discussion: Contents of Bal chaturbhdra churna are mostly katu rasa, laghu guna, usna veerya and also deepana, pachana, krimighna, visaghna, hridya, ruchya, vrisya, rasayana, rochana, sthoulyahara, trisnanigrahana, tvakadosahara, jwaraghna etc. properties. Therefore due to presence of these qualities, it is used in vomiting, diarrhea, fever and respiratory disorders. According to studies published in journals, it is beneficial as immuno-modulator, anti inflammatory, anti spasmodic, anti asthmatic activity, anti bacterial activity, antidiabetic activity, antioxidant activity, anti-fungal activity, hepatoprotective action, analgesic activity.  Conclusion: Present review reveals Bal chaturbhadra churna is quite safe for administration among Children and therefore can be used in various ailments in children which can limit the irrational use of antibiotics in them

Management of Recurrent respiratory disorders: A Case Study

Recurrent respiratory tract infections are especially common in young children; in developed countries, they affect up to 25% of children under one year of age and 18% of children one to four years of age. Immune deficiencies are considered as underlying conditions predisposing to this pathology. This work is about to determine when and how to explore the immune system when facing recurrent respiratory infections. A 01 year and 05 months old female child came with complaints of recurrent common cold and cough since birth. Swarnaprashan maintained general health of the body and works as an immunomodulatory which decreased recurrent common cold and cough in children. Duration of swarnaprashan can be determined depending upon the administered and its duration can be determined depending upon the desired effects like decrease morbidity rate and increase immunity level in children