First, since the function is a

concave function from Proposition 2.1, it guarantees existence of a global optimal point.

Since the upper formula is a strictly

concave function of [x.sub.N-1], we can obtain the optimal execution strategy by taking its partial derivative with respect to [x.sub.N-1] and solving for its zero

while the inequalities are reversed for a

concave function f.

Key words and phrases : Meromorphic function,

Concave function, Starlike function, Dirichlet finite integral, Integral mean.

Given K, P, and [s.sub.p], the profit function PR is a

concave function of S.

The distributional function has three forms:

concave function, convex function, and linearity function.

Lemma 1: Let f : [R.sup.2] [right arrow] R be a

concave function in the variables (y, s), that is, [f.sub.yy] < 0 and [f.sub.yy] [f.sub.ss] - [f.sup.2.sub.ys] > 0, which is maximal at ([y.sup.*], [s.sup.*]).

In general, the residual--the difference between "true" (simulated using a

concave function) attendance due to the quality of a team and the theoretical value--will surely be concave (convex) in quality if it increases (decreases) in quality and the approximation of quality is convex.

The first two conditions ensure that the probability density function will map a

concave function onto another

concave function.

F(d) is a convex function then H(d') is a

concave function ([[partial derivative].sup.2]H(d') / [[partial derivative].sup.2]d'[less than or equal to] 0).

As we can see in the next section, throughput is a

concave function of payload size, and then there exists the optimal payload size, which maximizes throughput under a given condition.

Hence it is a nondecreasing

concave function up to [d.sub.i] point.