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In complex geometry and analysis, the notion of convexity and its generalizations play an important role in understanding function behavior. Examples of classes of functions with a rich structure are, in addition to the convex functions, the subharmonic functions and the plurisubharmonic functions.
It is also strongly convex (and hence strictly convex too), with strong convexity constant 2. The function () = has ″ =, so f is a convex function. It is strictly convex, even though the second derivative is not strictly positive at all points. It is not strongly convex.
A mesoscale convective complex (MCC) is a unique kind of mesoscale convective system which is defined by characteristics observed in infrared satellite imagery. Their area of cold cloud tops exceeds 100,000 square kilometres (39,000 sq mi) with temperature less than or equal to −32 °C (−26 °F); and an area of cloud top of 50,000 square ...
If the relative compact subset of a arbitrary complex manifold M is a strongly pseudoconvex on M, then M is a holomorphically convex (i.e. Stein manifold). Also, D is itself a Stein manifold. And Narasimhan [ 99 ] [ 100 ] extended Levi's problem to complex analytic space , a generalized in the singular case of complex manifolds.
In mathematics, the modulus of convexity and the characteristic of convexity are measures of "how convex" the unit ball in a Banach space is. In some sense, the modulus of convexity has the same relationship to the ε-δ definition of uniform convexity as the modulus of continuity does to the ε-δ definition of continuity.
A mesoscale convective complex (MCC) is a unique kind of mesoscale convective system which is defined by characteristics observed in infrared satellite imagery. They are long-lived, often form nocturnally, and commonly contain heavy rainfall , wind , hail , lightning , and possibly tornadoes .
A conical combination is a linear combination with nonnegative coefficients. When a point is to be used as the reference origin for defining displacement vectors, then is a convex combination of points ,, …, if and only if the zero displacement is a non-trivial conical combination of their respective displacement vectors relative to .
In mathematics, a strictly convex space is a normed vector space (X, || ||) for which the closed unit ball is a strictly convex set. Put another way, a strictly convex space is one for which, given any two distinct points x and y on the unit sphere ∂ B (i.e. the boundary of the unit ball B of X ), the segment joining x and y meets ∂ B only ...