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A method for predicting the onset of widespread chaos.

A scalar is a one-component quantity that is invariant under rotations of the coordinate system.

The functional equation phi(f(x))=sphi(x), with s!=0,1.

The sinusoidal projection is an equal-area projection given by the transformation x = (lambda-lambda_0)cosphi (1) y = phi. (2) The inverse formulas are phi = y (3) lambda = ...

A diagonal of a square matrix which is traversed in the "northeast" direction. "The" skew diagonal (or "secondary diagonal") of an n×n square matrix is the skew diagonal from ...

Let (K,|·|) be a complete non-Archimedean valuated field, with valuation ring R, and let f(X) be a power series with coefficients in R. Suppose at least one of the ...

If a subset S of the elements of a field F satisfies the field axioms with the same operations of F, then S is called a subfield of F. In a finite field of field order p^n, ...

Subtraction is the operation of taking the difference d=x-y of two numbers x and y. Here, x is called the minuend, y is called the subtrahend, and the symbol between the x ...

Let h>=2 and let A_1, A_2, ..., A_h be sets of integers. The sumset A_1+A_2+...+A_h is the set of all integers of the form a_1+a_2+...+a_h, where a_i is a member of A_i for ...

An (n,k)-talisman hexagon is an arrangement of nested hexagons containing the integers 1, 2, ..., H_n=3n(n-1)+1, where H_n is the nth hex number, such that the difference ...