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Let delta=z>=z_(observed). A value 0<=alpha<=1 such that P(delta)<=alpha is considered "significant" (i.e., is not simply due to chance) is known as an alpha value. The ...

Calculus I

The m×n knight graph is a graph on mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a knight (which may ...

The objective of global optimization is to find the globally best solution of (possibly nonlinear) models, in the (possible or known) presence of multiple local optima. ...

Any square matrix T has a canonical form without any need to extend the field of its coefficients. For instance, if the entries of T are rational numbers, then so are the ...

The Sobolev embedding theorem is a result in functional analysis which proves that certain Sobolev spaces W^(k,p)(Omega) can be embedded in various spaces including ...

The conjugate gradient method can be viewed as a special variant of the Lanczos method for positive definite symmetric systems. The minimal residual method and symmetric LQ ...

Conditions at an initial time t=t_0 from which a given set of mathematical equations or physical system evolves. A system with initial conditions specified is known as an ...

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

The principal branch of an analytic multivalued function, also called a principal sheet, is a single-valued "slice" (i.e., branch) of the function chosen that is for ...