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An inner product is a generalization of the dot product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar. ...

If an integrable quasiperiodic system is slightly perturbed so that it becomes nonintegrable, only a finite number of n-map cycles remain as a result of mode locking. One ...

A Lie algebra over a field of characteristic zero is called semisimple if its Killing form is nondegenerate. The following properties can be proved equivalent for a ...

Let F be a differential field with constant field K. For f in F, suppose that the equation g^'=f (i.e., g=intf) has a solution g in G, where G is an elementary extension of F ...

Matrix diagonalization is the process of taking a square matrix and converting it into a special type of matrix--a so-called diagonal matrix--that shares the same fundamental ...

A space of functions comprising a complete biorthogonal system.

The system of partial differential equations S_t=SxS_(xx).

The system of partial differential equations U_t=U·U_(xx)+U·LambdaU.

Multivariate analysis is the simultaneous statistical consideration of relationships among many measured properties of a given system (Gould 1996, p. 42).

An algorithm for determining the order of an elliptic curve E/F_p over the finite field F_p.