Sentence examples for both the minimum function from inspiring English sources

If (f_{i}: Rtimes Rrightarrow R) ((i=1,2,ldots,m)) are Lipschitz continuous functions relative to their two arguments, then both the minimum function (min{f_{i}:i=1,2,ldots,m}) and the maximum function (max{f_{i}:i=1,2,ldots,m}) are also Lipschitz continuous functions.

Thus, the minimum function (min{f_{i}:i=1,2,ldots,m}) is a Lipschitz continuous function.

For the resource allocation problem with the minimum function, this was not obvious.

For the polyphase code design problem, HdABC obtains the minimum function value compared with the other algorithms over 25 trials.

In a following step, the other rate in the minimum function might become worse and the subcarrier assignments can change.

which is due to the nature of the maximization of the minimum function and the continuity of the two terms.

By suitable approximation of the "minimum" function we then obtain from Corollary 4.1 the following analogue of Theorem 1.4.

As mentioned, the integral in (13) is split into a sum of integrals where the minimum function is substituted by the corresponding minimum distance.

Instead, a sum of integrals is used where the minimum function is substituted by the corresponding minimum distance at each interval (see Section 5).

Let minF{ f 1 x),f 2 x),…,f n (x)} be the minimum function of functions f 1 x),f 2 x),…,f n (x).

Co-limitation can be identified along a vector through the bend in the L-shaped contours of the minimum function (Figure 1a).