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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 ...
The consolidation of power by a dominant religious or ethnic minority can be considered a form of oligarchy. [5] Examples include South Africa during apartheid, Liberia under Americo-Liberians, the Sultanate of Zanzibar, [citation needed] and Rhodesia. In these cases, oligarchic rule was often tied to the legacy of colonialism. [5]
In calculus, the power rule is used to differentiate functions of the form () =, whenever is a real number. Since differentiation is a linear operation on the space of differentiable functions, polynomials can also be differentiated using this rule.
The short rule (1494–1498) of Girolamo Savonarola, a Dominican priest, over the city of Florence had features of a theocracy. During his rule, "unchristian" books, statues, poetry, and other items were burned (in the Bonfire of the Vanities), sodomy was made a capital offense, and other Christian practices became law.
Mathematically, the 80/20 rule is roughly described by a power law distribution (also known as a Pareto distribution) for a particular set of parameters. Many natural phenomena are distributed according to power law statistics. [4] It is an adage of business management that "80% of sales come from 20% of clients." [5]
For example, a bequest in a will may be to one's grandchildren, often with a life interest to one's surviving spouse and then to the children, to avoid the payment of multiple death duties or inheritance taxes on the testator's estate. The rule against perpetuities was one of the devices developed to at least limit this tax avoidance strategy.
The rules allow the expression of conjunctions and disjunctions purely in terms of each other via negation. The rules can be expressed in English as: not (A or B) = (not A) and (not B) not (A and B) = (not A) or (not B) where "A or B" is an "inclusive or" meaning at least one of A or B rather than an "exclusive or" that means exactly one of A or B.
In real life, this leads to the practical concepts of computing virtualization and emulation. [ citation needed ] Real computers constructed so far can be functionally analyzed like a single-tape Turing machine (which uses a "tape" for memory); thus the associated mathematics can apply by abstracting their operation far enough.