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• The low-level doping present in supposedly undoped MOSFET has a significant effect. • The traditional charge control model is only valid for the nominally intrinsic case. • We present a better approximation of the undoped MOSFET channel surface potential. • We propose a new drain current control model which accounts for series resistance. • The new model agrees well with measurements from GAA Si Nano Sheet MOSFETs. The unwanted low-level doping present in supposedly undoped MOSFET channels has a significant effect on charge control and Lambert W function-based inversion charge MOSFET models, as well as on subsequent drain current models. We show that the hypothetical intrinsic MOSFET channel approximation, often used to describe a nominally undoped channel, produces significant errors, even for the low-level concentrations resulting from unintentional doping. We show that the traditional charge control model, which mathematically describes the gate voltage as the sum of one linear and one logarithmic term of the inversion charge, is only valid for the hypothetically intrinsic case. However, it may still be used for nominally undoped but unintentionally low-doped channel devices within the region of operation where the majority carriers are the dominant charge. With this in mind, we present here a better approximation of the nominally undoped MOSFET channel surface potential. We also propose an improved modified expression that describes the gate voltage as the sum of one linear and two logarithmic terms of the inversion charge. A new approximate drain current control formulation is also proposed to account for parasitic series resistance and/or mobility degradation. The new model agrees reasonably well with measurement data from nominally undoped vertically stacked GAA Si Nano Sheet MOSFETs. [ABSTRACT FROM AUTHOR]

• A first integral of the SIR epidemiological model was solved in terms of the Lambert W function. • The SIR model was solved parametrically by quadratures. • The parametric solution was computed numerically and compared to Runge–Kutta numerical integration. In their article, N. A. Kudryashov, M. A. Chmykhov, M. Vigdorowitsch, "Analytical features of the SIR model and their applications to COVID-19", Applied Mathematical Modelling 90 (2021) 466–473, aimed to establish the relationships among S, I and R populations, as well as to suggest a form for the exact solution of the SIR model. One of the equations given there is not correct, which leads to an error in the solution. The objective of the present letter is to present the correct parametric solution and to discuss its numerical approximation by direct quadrature. [ABSTRACT FROM AUTHOR]

This article describes an efficient and robust algorithm and implementation for the evaluation of the Wright ω function in IEEE double precision arithmetic over the complex plane. [ABSTRACT FROM AUTHOR]

The SIR (Susceptible-Infected-Removed) model is a simple mathematical model of epidemic outbreaks, yet for decades it evaded the efforts of the mathematical community to derive an explicit solution. The present paper reports novel analytical results and numerical algorithms suitable for parametric estimation of the SIR model. Notably, a series solution of the incidence variable of the model is derived. It is proven that the explicit solution of the model requires the introduction of a new transcendental special function, describing the incidence, which is a solution of a non-elementary integral equation. The paper introduces iterative algorithms approximating the incidence variable, which allows for estimation of the model parameters from the numbers of observed cases. The approach is applied to the case study of the ongoing coronavirus disease 2019 (COVID-19) pandemic in five European countries: Belgium, Bulgaria, Germany, Italy and the Netherlands. Incidence and case fatality data obtained from the European Centre for Disease Prevention and Control (ECDC) are analysed and the model parameters are estimated and compared for the period Jan-Dec 2020. [ABSTRACT FROM AUTHOR]