Nonnegative

A function is said to be absolutely monotonic over an interval if the derivatives of all orders of are nonnegative or all nonpositive at all points on the interval.

A Hermitian matrix is positive semidefinite if and only if all of its principal minors are nonnegative.

All ASCII codes stored within an eight-bit byte had nonnegative values on systems such as the PDP-11 that treated bytes as signed quantities.

Generalisations Newton's generalised binomial theorem main Around 1665, Isaac Newton generalised the binomial theorem to allow real exponents other than nonnegative integers.

If the domain of the function is restricted to the nonnegative reals then the function is injective and invertible.

Note that in the final property above, the square need not be nonnegative if g is not positive definite.

Polyadic or multiary means n-ary for some nonnegative integer n. A 0-ary, or nullary, quasigroup is just a constant element of Q. A 1-ary, or unary, quasigroup is a bijection of Q to itself.

Since the degree is a nonnegative integer, and since it decreases with every step, the Euclidean algorithm concludes in a finite number of steps.

Such mixture problem are often formulated with normalized constraints, so that the nonnegative components sum to one, in which case the feasible region forms a simplex.

The probability density function is nonnegative everywhere, and its integral over the entire space is equal to one.

The properties of binomial coefficients have led to extending the meaning of the symbol beyond the basic case where n and k are nonnegative integers with k ≤ n ; such expressions are still called binomial coefficients.

The solution for subset sum also provides the solution for the original subset sum problem in the case where the numbers are small (again, for nonnegative numbers).

This agrees with the usual definitions when r is a nonnegative integer.

Thus, if the two piles consist of x and y stones, where x is larger than y, the next player can reduce the larger pile from x stones to x − my stones, as long as the latter is a nonnegative integer.

Von Neumann's method used a pivoting algorithm between simplices, with the pivoting decision determined by a nonnegative least squares subproblem with a convexity constraint ( projecting the zero-vector onto the convex hull of the active simplex ).