Search results for "Lambert W function"
showing 3 items of 3 documents
A summary of expressions for central performance parameters of high efficiency solar cell concepts
2019
This work reviews expressions for central performance parameters of various types of PV-concepts when operating at the radiative limit. Some new expressions not published elsewhere are also included. The performance parameters include the short circuit current density, the open circuit voltage, the maximum power density and the optimal voltage. The cell concepts include single junction cells, cells optically coupled to up- and down-converters, intermediate band solar cells and a couple of implementations of multijunction devices. The Lambert W function is used to express the maximum power density.
Beyond Viner: Smoothed Cost Curves and Co-Detetermination of Output and Production Capacity
2017
We address two problems of traditional cost functions: the discontinuity caused by the production capacity (the marginal cost abruptly becomes infinite when production capacity is reached) and the production capacity is artificially exogenous. So, we introduce a smoothed form of marginal cost function. It progressively tends to infinity when it approaches to the production capacity. Then, we prove that it is perfectly possible to determine directly output, fixed costs and production capacity simultaneously, even if this could lead to a system of equations that is not so elementary to solve because it includes a Lambert function. We also show that the smoothed cost function prevails in both …
Computing Difficulties for Deriving Poverty Indices from Some Functional Forms of Lorenz Curves
2014
We examine three families of classical one-parameter functional forms for estimating a Lorenz curve: the power form (Pareto, elementary form), the exponential form (Gupta, elementary form) and fractional form (Rohde). For the first time, we systematically study these functions not for their ability to be estimated but on the point of view of the possibility of deriving poverty indices, which implies first determining the headcount ratio (i.e., the percentage of poor). We show that computing difficulties have been largely underestimated. Two forms, the most simple ones, pose no problem: the elementary power and exponential forms. However, the Pareto functional form poses problem with a restr…