Sentence examples for be a concave mapping from inspiring English sources

In this paper, we aim at proving several criteria for the function (finSigma) to be a concave mapping.

A conformal, meromorphic function f on the punctured unit disk {mathbb{U}}^:= bigl{ zin{mathbb{C}}: 0< vert z vert <1 bigr} =: mathbb{U}backslash{0} is said to be a concave mapping if (f(mathbb{U}^)) is the complement of a compact, convex set.

We show that, for a meromorphic function f ( z ), the sufficient condition for concavity is Re { z f ‴ ( z ) f ″ ( z ) } < 0, z ∈ U. A conformal, meromorphic function f on the punctured unit disk U ˆ : = { z ∈ C : 0 < | z | < 1 } is said to be a concave mapping if f ( U ˆ ) is the complement of a convex, compact set.

Thus, for example, we know that if (f"(x)>0) for all x in the domain of f, then f is a convex mapping, whereas if (f"(x)<0) on the domain of f, then f is a concave mapping.

Similarly, (Delta^{2}y(t)<0) for each (tinmathbb{N}_{a}) if and only if y is a concave map on (mathbb{N}_{a}).

Because the logarithm is a concave function, the interval containing these yields is mapped to a smaller interval than an interval of the same size containing small yields.

If φ is a concave function on I and ψ is an increasing concave function on φ ( I ), then ψ ∘ φ is concave on I.

However, among these only the Laplace distribution is log-concave, i.e. has a log-concave density function, leading to a posterior whose log density is a concave function, thus has a single local maximum.

Since is a concave operator, it is easy to verify that is also a concave operator.

The articular surface is a concave facet.

If is a convex (concave) function, then the function (417). is Schur-convex (Schur-concave).