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Informally, a situation in which a decision must be made from several alternatives, none of which is obviously the optimal one. In formal logic, a dilemma is a specific type ...

A pointed space is a topological space X together with a choice of a basepoint x in X. The notation for a pointed space is (X,x). Maps between two pointed spaces must take ...

Given a homogeneous linear second-order ordinary differential equation, y^('')+P(x)y^'+Q(x)y=0, (1) call the two linearly independent solutions y_1(x) and y_2(x). Then ...

Let a distribution to be approximated be the distribution F_n of standardized sums Y_n=(sum_(i=1)^(n)(X_i-X^_))/(sqrt(sum_(i=1)^(n)sigma_X^2)). (1) In the Charlier series, ...

An illusion studied by the psychologist Walter Ehrenstein in which the sides of a square placed inside a pattern of concentric circles take an apparent curved shape. The name ...

A map which uses a set of rules to transform elements of a sequence into a new sequence using a set of rules which "translate" from the original sequence to its ...

A robust nonparametric test which is an alternative to the paired t-test. This test makes the basic assumption that there is information only in the signs of the differences ...

If f:D->Y is a map (a.k.a. function, transformation, etc.) over a domain D, then the image of f, also called the range of D under f, is defined as the set of all values that ...

Consider a horse rider who wishes to feed his horse at a field, gather water from a river, and then return to his tent, all in the smallest overall distance possible. The ...

An exchange of two elements of an ordered list with all others staying the same. A transposition is therefore a permutation of two elements. For example, the swapping of 2 ...