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  2. Banzhaf power index - Wikipedia

    en.wikipedia.org/wiki/Banzhaf_power_index

    Computer model of the Banzhaf power index from the Wolfram Demonstrations Project. The Banzhaf power index, named after John Banzhaf (originally invented by Lionel Penrose in 1946 and sometimes called Penrose–Banzhaf index; also known as the Banzhaf–Coleman index after James Samuel Coleman), is a power index defined by the probability of changing an outcome of a vote where voting rights ...

  3. Raising and lowering indices - Wikipedia

    en.wikipedia.org/wiki/Raising_and_lowering_indices

    It is common convention to use greek indices when writing expressions involving tensors in Minkowski space, while Latin indices are reserved for Euclidean space. Well-formulated expressions are constrained by the rules of Einstein summation : any index may appear at most twice and furthermore a raised index must contract with a lowered index.

  4. Exponentiation - Wikipedia

    en.wikipedia.org/wiki/Exponentiation

    Powers of 2 appear in set theory, since a set with n members has a power set, the set of all of its subsets, which has 2 n members. Integer powers of 2 are important in computer science. The positive integer powers 2 n give the number of possible values for an n-bit integer binary number; for example, a byte may take 2 8 = 256 different values.

  5. Exponentiation by squaring - Wikipedia

    en.wikipedia.org/wiki/Exponentiation_by_squaring

    Yao's method collects in u first those x i that appear to the highest power ⁠ ⁠; in the next round those with power ⁠ ⁠ are collected in u as well etc. The variable y is multiplied ⁠ h − 1 {\displaystyle h-1} ⁠ times with the initial u , ⁠ h − 2 {\displaystyle h-2} ⁠ times with the next highest powers, and so on.

  6. nth root - Wikipedia

    en.wikipedia.org/wiki/Nth_root

    The integer n is called the index or degree, and the number x of which the root is taken is the radicand. A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred by using ordinal numbers, as in fourth root, twentieth root, etc. The computation of an n th root is a root extraction.

  7. Faulhaber's formula - Wikipedia

    en.wikipedia.org/wiki/Faulhaber's_formula

    Faulhaber also knew that if a sum for an odd power is given by = + = + + + + then the sum for the even power just below is given by = = + + (+ + + (+)). Note that the polynomial in parentheses is the derivative of the polynomial above with respect to a .

  8. Binomial approximation - Wikipedia

    en.wikipedia.org/wiki/Binomial_approximation

    The binomial approximation for the square root, + + /, can be applied for the following expression, + where and are real but .. The mathematical form for the binomial approximation can be recovered by factoring out the large term and recalling that a square root is the same as a power of one half.

  9. Shapley–Shubik power index - Wikipedia

    en.wikipedia.org/wiki/Shapley–Shubik_power_index

    A power of 0 means that a coalition has no effect at all on the outcome of the game; and a power of 1 means a coalition determines the outcome by its vote. Also the sum of the powers of all the players is always equal to 1. There are some algorithms for calculating the power index, e.g., dynamic programming techniques, enumeration methods and ...