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The fourth power law (also known as the fourth power rule) states that the stress on the road caused by a motor vehicle increases in proportion to the fourth power of its axle load. This law was discovered in the course of a series of scientific experiments in the United States in the late 1950s and was decisive for the development of standard ...
Fermat knew that a fourth power cannot be the sum of two other fourth powers (the n = 4 case of Fermat's Last Theorem; see Fermat's right triangle theorem). Euler conjectured that a fourth power cannot be written as the sum of three fourth powers, but 200 years later, in 1986, this was disproven by Elkies with: 20615673 4 = 18796760 4 ...
The distributions of a wide variety of physical, biological, and human-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, [2] cloud sizes, [3] the foraging pattern of various species, [4] the sizes of activity patterns of neuronal populations, [5] the frequencies of words in most languages ...
In numerical analysis, inverse iteration (also known as the inverse power method) is an iterative eigenvalue algorithm. It allows one to find an approximate eigenvector when an approximation to a corresponding eigenvalue is already known. The method is conceptually similar to the power method. It appears to have originally been developed to ...
A user will input a number and the Calculator will use an algorithm to search for and calculate closed-form expressions or suitable functions that have roots near this number. Hence, the calculator is of great importance for those working in numerical areas of experimental mathematics. The ISC contains 54 million mathematical constants.
The dimensions that can be formed from a given collection of basic physical dimensions, such as T, L, and M, form an abelian group: The identity is written as 1; [citation needed] L 0 = 1, and the inverse of L is 1/L or L −1. L raised to any integer power p is a member of the group, having an inverse of L −p or 1/L p.
However, Newton's theorem shows that an inverse-cubic force may be applied to a particle moving under a linear or inverse-square force such that its orbit remains closed, provided that k equals a rational number. (A number is called "rational" if it can be written as a fraction m/n, where m and n are integers.)
By contrast, the near-field ' s E and B strengths decrease more rapidly with distance: The radiative field decreases by the inverse-distance squared, the reactive field by an inverse-cube law, resulting in a diminished power in the parts of the electric field by an inverse fourth-power and sixth-power, respectively. The rapid drop in power ...