MAASS SPACE FOR LIFTING TO GL(2,B) OVER A DIVISION QUATERNION ALGEBRA

Muto, Narita and Pitale construct counterexamples to the Generalized Ramanujan Conjecture for GL(2,B) over the division quaternion algebra B with discriminant two via a lift from SL(2). In this dissertation, I characterize the image of this lift in terms of the Fourier coefficients. The previous methods of Maass, Kohnen or Kojima do not apply here, hence I approached this problem via a combination of classical and representation theory techniques to identify the image. Crucially, I used the Jacquet Langlands correspondence described by Badulescu and Renard to characterize the representations

An explicit lifting construction of CAP forms on O(1, 5) (Automorphic form, automorphic LL-functions and related topics)

This article is the write-up of what the fist named author presented on January 25th in 2022 during the RJMS workshop. We explicitly construct non-tempered cusp forms on the orthogonal group O(1, 5) of signature (1+, 5-). Given a definite quaternion algebra B over ℚ, the orthogonal group is attached to the indefinite quadratic space of rank 6 with the anisotropic part defined by the reduced norm of B. As well as the explicit construction we study the cuspidal representations generated by our cusp forms in detail. We determine all local components of the cuspidal representations and show that our cusp forms are CAP forms. Our construction can be viewed as a generalization of [8]to the case of any definite quaternion algebras, for which we note that [8] takes up the case where the discriminant of B is two. Unlike [8] the method of the construction is to consider the theta lifting from Maass cusp forms to O(1, 5), following the formulation by Borcherds

Isolated Protein S Deficiency

Isolated protein S deficiency is an inherited condition having proven association with venous thromboembolism. There is controversy regarding clear association between protein S deficiency and arterial thrombosis. It is therefore necessary to bring focus to this uncommon clinical condition and highlight the probable association with arterial thrombosis facilitating timely diagnosis of this condition. We describe a 48-year-old male with stroke and pulmonary thromboembolism with chronic deep vein thrombosis secondary to isolated protein S deficiency, managed with thrombolysis and long-term anticoagulation.

COVID-19: New Challenge in 21st Century

COVID-19 pandemic turned into the proven existence-threatening virus in-line with World Health Organization (WHO) has declared a public health emergency of International Concerned and our healthcare system found a challenge to save human civilization. This evaluation gives a brief idea of COVID-19 epidemiology, pathophysiology, treatment, and prevention of COVID-19. Exclusive drugs like Dexamethasone and Remdesivir were found effective to treat the virus was covered in this review article. Pathophysiology of virus in the body of diabetes and cancer patients, there mechanism of action and risk involved in that patients were studied. This review turned to conduct on data found in science direct, various information sources on the internet and different review articles were studied. The major objective is to provide a brief overview of this disease, study infectious virus effect on   human beings proves to be an existence-threat to the world population and brief overview of COVID-19 was covered in this review article. Keywords: SARS-CoV-2, MERS, Vaccine, Dexamethasone, Remdesivir

Bifunctional nanoparticulated nickel ferrite thin films:Resistive memory and aqueous battery applications

Herein, excellent non-volatile memory and aqueous battery properties of solution-processable nickel ferrite (NFO) nanomaterial were demonstrated. In the case of non-volatile memory property, the device operates on ±2 V resistive switching voltage and shows double valued charge-magnetic flux characteristics. Excellent endurance (103) and retention (104 s) non-volatile memory properties with a good memory window (103) were observed for NFO memristive device. The conduction and resistive switching mechanisms based on experimental data are provided. Furthermore, the present work investigates the electrochemical performance of the NFO thin film electrode in the different electrolytes (viz. Na2SO4, Li2SO4, and Na2SO4: Li2SO4). It was revealed that the NFO thin film shows improved electrochemical performance in Na2SO4 electrolyte with a high specific capacity of 18.56 mAh/g at 1 mA/cm2 current density. The electrochemical impedance spectroscopic results reveal that the NFO thin film electrode shows low series and charge transfer resistance values for Na2SO4 electrolyte than other electrolytes. The diffusion coefficient of different ions (DNa+, DLi+ and DNa+:Li+) were found to be 9.975 × 10−10 cm2 s−1, 3.292 × 10−11 cm2 s−1, 2 × 10−10 cm2 s−1, respectively. A high diffusion coefficient was found for Na+ ions, indicating rapid Na+ transport with NFO thin-film electrodes</p