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Ld(1) IS O(logloglogd) FOR ALMOST ALL SQUARE FREE d
G. S. Mohan Reddy,SS Rau 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.3
Let d be a square free integer.Using Hardy-Ramanujan's value of nor- mal order of w(d) we show that Ld(1) = ○(logloglogd) except on a negligible set. We note that the proof verifies Robin's inequality σ(n) < eϒ nloglogn (equivalent form of Riemann Hypothesis) for such numbers.
G. Lakshmi Vara Prasad,Venkatagurunatham Naidu Kollu,M. Sailaja,S. Radhakrishnan,K. Jagan Mohan,A. Kishore Reddy,G. Rajesh Chandra 한국전기전자재료학회 2024 Transactions on Electrical and Electronic Material Vol.25 No.1
In this paper, we delve into the intriguing realm of Pseudo-morphic High Electron Mobility Transistors (pHEMTs) composed of InAs∕In0.3Al0.7As∕InSb∕In0.3Al0.7As layers, utilizing Silvaco-TCAD for simulation. Our focus centers on the assessment of RF and analog electrical characteristics, with a keen eye on the high-temperature eff ects. The influence of temperature on device performance is meticulously evaluated in comparison to a reference device operating at room temperature. Traditionally, the critical parameters such as threshold voltage ( Vth ), transconductance ( gm ), and Ion∕Ioff ratio have been calculated within the temperature range spanning from 300 K to 700 K. The primary pHEMT device in our study exhibits impressive attributes, featuring a drain current of 950 mA, a threshold voltage of -1.75 V, a high transconductance ( gm ) value of 650 mS/mm, an Ion∕Ioff ratio of 1 × 106 , a transition frequency ( ft ) soaring to 790 GHz, and a maximum frequency ( fmax ) reaching a staggering 1.4 THz. However, as we traverse the temperature spectrum, our findings unveil a compelling narrative. The impact of rising temperature is unequivocal, triggering a cascade of transformations within the device. Notably, as the temperature escalates, we observe a noticeable decrease in current, a reduction in transconductance ( gm ), and a diminishing Ion∕Ioff ratio. To unravel the intricacies of these temperature-induced effects, we introduce the infusion of Machine Learning (ML) into our analysis.