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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 ...
The power rule for differentiation was derived by Isaac Newton and Gottfried Wilhelm Leibniz, each independently, for rational power functions in the mid 17th century, who both then used it to derive the power rule for integrals as the inverse operation. This mirrors the conventional way the related theorems are presented in modern basic ...
The elementary power rule generalizes considerably. The most general power rule is the functional power rule: for any functions f and g, ′ = () ′ = (′ + ′ ), wherever both sides are well defined. Special cases
A common form for the rate equation is a power law: [6] = [] [] The constant is called the rate constant.The exponents, which can be fractional, [6] are called partial orders of reaction and their sum is the overall order of reaction.
In general I is an order-2 tensor, see above for its components. The dot · indicates tensor contraction. Force and Newton's 2nd law: Resultant force acts on a system at the center of mass, equal to the rate of change of momentum:
Thermal conduction rate, thermal current, thermal/heat flux, thermal power transfer P = / W ML 2 T −3: Thermal intensity I = / W⋅m −2: MT −3: Thermal/heat flux density (vector analogue of thermal intensity above) q
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field.
In mathematics, a law is a formula that is always true within a given context. [1] Laws describe a relationship , between two or more expressions or terms (which may contain variables ), usually using equality or inequality , [ 2 ] or between formulas themselves, for instance, in mathematical logic .