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Euler's formula is ubiquitous in mathematics, physics, chemistry, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics". [2] When x = π, Euler's formula may be rewritten as e iπ + 1 = 0 or e iπ = −1, which is known as Euler's identity.
The van der Pauw Method is a technique commonly used to measure the resistivity and the Hall coefficient of a sample. Its strength lies in its ability to accurately measure the properties of a sample of any arbitrary shape, as long as the sample is approximately two-dimensional (i.e. it is much thinner than it is wide), solid (no holes), and the electrodes are placed on its perimeter.
A ray trace through a prism with apex angle α. Regions 0, 1, and 2 have indices of refraction, , and , and primed angles ′ indicate the ray's angle after refraction.. Ray angle deviation and dispersion through a prism can be determined by tracing a sample ray through the element and using Snell's law at each interface.
This is an advantage, because sheet resistance of 1 Ω could be taken out of context and misinterpreted as bulk resistance of 1 ohm, whereas sheet resistance of 1 Ω/sq cannot thus be misinterpreted. The reason for the name "ohms per square" is that a square sheet with sheet resistance 10 ohm/square has an actual resistance of 10 ohm ...
Seismic data is sorted by common midpoint and then corrected for normal moveout. In reflection seismology, normal moveout (NMO) describes the effect that the distance between a seismic source and a receiver (the offset) has on the arrival time of a reflection in the form of an increase of time with offset. [1]
The simple Bonferroni correction rejects only null hypotheses with p-value less than or equal to , in order to ensure that the FWER, i.e., the risk of rejecting one or more true null hypotheses (i.e., of committing one or more type I errors) is at most . The cost of this protection against type I errors is an increased risk of failing to reject ...
The Šidák correction is derived by assuming that the individual tests are independent. Let the significance threshold for each test be α 1 {\displaystyle \alpha _{1}} ; then the probability that at least one of the tests is significant under this threshold is (1 - the probability that none of them are significant).
Portable Document Format (PDF), standardized as ISO 32000, is a file format developed by Adobe in 1992 to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems.