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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 equivalence of power laws with a particular scaling exponent can have a deeper origin in the dynamical processes that generate the power-law relation. In physics, for example, phase transitions in thermodynamic systems are associated with the emergence of power-law distributions of certain quantities, whose exponents are referred to as the ...
An example is the derivative operator of calculus, /, which is a linear operator acting on functions () to give a new function (/) = ′ (). The n th power of the differentiation operator is the n th derivative:
Rule by an autocracy or oligarchy with a power source predicated on a political party or stratocracy; characterized by the rejection of political plurality. Band society: Rule by a government based on small (usually family) unit with a semi-informal hierarchy, with strongest (either physical strength or strength of character) as leader. Bureaucracy
An example of the relationship between sample size and power levels. Higher power requires larger sample sizes. Statistical power may depend on a number of factors. Some factors may be particular to a specific testing situation, but in normal use, power depends on the following three aspects that can be potentially controlled by the practitioner:
For example, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. [ 2 ] [ 3 ] Thus, in the expression 1 + 2 × 3 , the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7 , and not (1 + 2) × 3 = 9 .
The ancient concept of rule of law can be distinguished from rule by law, according to political science professor Li Shuguang: "The difference ... is that, under the rule of law, the law is preeminent and can serve as a check against the abuse of power. Under rule by law, the law is a mere tool for a government, that suppresses in a legalistic ...
When power passes from one generation to another, it is known as traditional authority. The rule of hereditary monarchs furnishes an obvious example. The Tudor dynasty in England and the ruling families of Mewar in Rajasthan (India) are examples of traditional authority.