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ARITHMETIC PROPERTIES OF PARTITIONS WITH 5-CORES
B. HEMANTHKUMAR,H. S. SUMANTH BHARADWAJ,M. S. MAHADEVA NAIKA 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.2
Let a5(n) denote the number of partitions of n that are 5-cores. By using theta function identities, we find several infinite families of congruences modulo 3, 4 and 8 for a5(n).
ON SOME NEW MODULAR RELATIONS FOR RAMANUJAN'S REMARKABLE PRODUCT OF THETA FUNCTIONS
M. S. MAHADEVA NAIKA,S. Chandankumar,B. HEMANTHKUMAR 장전수학회 2013 Advanced Studies in Contemporary Mathematics Vol.23 No.3
In this paper, we establish several new P{Q mixed modular equations involving theta{ functions which are similar to those recorded by Ramanujan in his notebooks. As an application, we establish several new general formulas for explicit evaluations of Ramanujan's remarkable product of theta{functions and a remarkable product of theta{functions.
Use of human patient simulator for apnea studies: a preliminary in vitro trial
Tripathy Debendra K,Dhar Mridul,Bhardwaj Bharat B,Hemanthkumar K,Talawar Praveen,Rao Shalinee 대한마취통증의학회 2022 Korean Journal of Anesthesiology Vol.75 No.5
Background: Modern human patient simulators (HPSs) could be used for researching critical scenarios such as apnea oxygenation. We aimed to study the use of a high-fidelity HPS to assess prolonged apnea using various oxygenation strategies with a simple high-flow nasal cannula (15 L/min). Methods: An experimental simulation study using an HPS (CAE Healthcare™) was conducted after obtaining approval from the Institutional Review Board. The HPS responded according to real-time physiologically modeled responses to external gases, such as oxygen (O2). Apnea experiments were performed with different physiological settings, such as shunt fraction (5%) and O2 consumption (250, 500, and 750 ml/min). The following four apnea experiments were conducted: no oxygenation (NO), apnea oxygenation alone (AO), preoxygenation alone (PO), and para-oxygenation (PAO). The time to 92%, 75%, and 50% saturation was recorded. Alveolar and arterial gas levels were recorded till 50% saturation. Results: At 250 ml/min, PO (1121 s) and PAO (1274.5 s) had a significantly longer time to 50% saturation (400% increase) compared to NO (222.5 s) and AO (239 s). A similar trend was observed for the time to 92% and 75% saturation. At higher O2 consumption rates, a shorter time to desaturation was observed. Conclusions: Apnea trends in the HPS correlated with similar prior human experiments. AO without preoxygenation was found to provide no additional benefit. Preoxygenation with high-flow O2 via nasal cannula prolonged the time to desaturation in the PAO more than PO scenario. Therefore, HPSs can be used in future studies where patient safety is a concern.