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The Einstein field equations (EFE) may be written in the form: [5] [1] + = EFE on a wall in Leiden, Netherlands. where is the Einstein tensor, is the metric tensor, is the stress–energy tensor, is the cosmological constant and is the Einstein gravitational constant.
In optics, Cauchy's transmission equation is an empirical relationship between the refractive index and wavelength of light for a particular transparent material. It is named for the mathematician Augustin-Louis Cauchy , who originally defined it in 1830 in his article "The refraction and reflection of light".
From the parabolic partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price given the risk of the security and its expected return (instead replacing the ...
Darcy's law is an equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on results of experiments [1] on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences.
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
In 1905, "Einstein believed that Planck's theory could not be made to agree with the idea of light quanta, a mistake he corrected in 1906." [133] Contrary to Planck's beliefs of the time, Einstein proposed a model and formula whereby light was emitted, absorbed, and propagated in free space in energy quanta localized in points of space. [132]
The difference between the two sample means, each denoted by X i, which appears in the numerator for all the two-sample testing approaches discussed above, is ¯ ¯ = The sample standard deviations for the two samples are approximately 0.05 and 0.11, respectively. For such small samples, a test of equality between the two population variances ...
Figure 1: Typical plot of crack growth rate versus the stress intensity range. The Paris–Erdogan equation fits the central linear region of Regime B. A crack growth equation is used for calculating the size of a fatigue crack growing from cyclic loads. The growth of a fatigue crack can result in catastrophic failure, particularly in the case ...