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Therefore Fermat is right
(2014)
It was Fernat's idea to investigate how many numbers would fulfill the equation according to the Pythagorean Theorem if the exponent were increased to random, e.g. to a3 + b3 = c3. His question became therefore: are there two whole numbers the cubes of which add up to the volume of the cube of a third whole number? He posed this same question, of course, for all kinds of higher exponents, so that the equation could be generalized: is there an integral solution for the equation an + bn = cn, if the exponent n is higher than 2? Although in 1993, the English mathematician Andrew Wiles was able to produce an arithmetical proof for Fermat's famous theorem, I will show that there is a simple logical explanation which is also pragmatic and plausible and what is the result of a fundamental alternative idea how our world seems to be constructed.
The light-addressable potentiometric sensor (LAPS) is a semiconductor-based potentiometric sensor using a light probe with an ability of detecting the concentration of biochemical species in a spatially resolved manner. As an important biomedical sensor, research has been conducted to improve its performance, for instance, to realize high-speed measurement. In this work, the idea of facilitating the device-level simulation, instead of using an equivalent-circuit model, is presented for detailed analysis and optimization of the performance of the LAPS. Both carrier distribution and photocurrent response have been simulated to provide new insight into both amplitude-mode and phase-mode operations of the LAPS. Various device parameters can be examined to effectively design and optimize the LAPS structures and setups for enhanced performance.