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Let A and B_j be sets. Conditional probability requires that P(A intersection B_j)=P(A)P(B_j|A), (1) where intersection denotes intersection ("and"), and also that P(A ...

The term Bol loop refers to either of two classes of algebraic loops satisfying the so-called Bol identities. In particular, a left Bol loop is an algebraic loop L which, for ...

A bounded operator T:V->W between two Banach spaces satisfies the inequality ||Tv||<=C||v||, (1) where C is a constant independent of the choice of v in V. The inequality is ...

The rank of a vector bundle is the dimension of its fiber. Equivalently, it is the maximum number of linearly independent local bundle sections in a trivialization. ...

In general, the pedal curve of the cardioid is a slightly complicated function. The pedal curve of the cardioid with respect to the center of its conchoidal circle is the ...

A multiway system that generates causal networks which are all isomorphic as acyclic digraphs is said to exhibit causal invariance, and the causal network itself is also said ...

A causal network is an acyclic digraph arising from an evolution of a substitution system, and representing its history. The illustration above shows a causal network ...

Let P be a finite partially ordered set. A chain in P is a set of pairwise comparable elements (i.e., a totally ordered subset). The partial order length of P is the maximum ...

Given a symmetric positive definite matrix A, the Cholesky decomposition is an upper triangular matrix U with strictly positive diagonal entries such that A=U^(T)U. Cholesky ...

One of the quantities lambda_i appearing in the Gauss-Jacobi mechanical quadrature. They satisfy lambda_1+lambda_2+...+lambda_n = int_a^bdalpha(x) (1) = alpha(b)-alpha(a) (2) ...