Complex convexity is a general term in complex geometry. A set Ω {\displaystyle \Omega } in C n {\displaystyle \mathbb {C} ^{n}} is called C {\displaystyle...

This implies that convexity is invariant under affine transformations. Further, it implies that a convex set in a real or complex topological vector...

This is a list of convexity topics, by Wikipedia page. Alpha blending - the process of combining a translucent foreground color with a background color...

{\displaystyle a+b\leq 1.} The concept of strong convexity extends and parametrizes the notion of strict convexity. Intuitively, a strongly-convex function is...

In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, and is defined as the second derivative...

1923, p. 66). Ahlfors, Lars (1953). Complex Analysis. McGraw-Hill. Bremermann, H. J. (1956). "Complex Convexity". Transactions of the American Mathematical...

the circle, because of the lack of convexity of Lp in this case. Convexity fails but a kind of "complex convexity" remains, namely the fact that z → |z|q...

their extension to arbitrary positive and negative values and even to complex numbers. The sine and cosine functions are commonly used to model periodic...

{P} _{m}} is a projective complex varieties) does not become a Stein manifold, even if it satisfies the holomorphic convexity. The proof method uses an...

referred to as the Riesz–Thorin interpolation theorem or the Riesz–Thorin convexity theorem, is a result about interpolation of operators. It is named after...

^{(1)}} is the polygamma function of order 1. To prove the logarithmic convexity of the gamma function, it therefore suffices to observe that ψ ( 1 ) {\displaystyle...

( B + t C ) ] {\displaystyle F(t)=\operatorname {Tr} [f(B+tC)]} . By convexity and monotonicity of trace functions, F ( t ) {\displaystyle F(t)} is convex...

Holomorphically convex hull Stein manifold Bremermann, H. J. (1956). "Complex Convexity". Transactions of the American Mathematical Society. 82 (1): 17–51...

Stein manifold admits such a function. Bremermann, H. J. (1956). "Complex Convexity". Transactions of the American Mathematical Society. 82 (1): 17–51...

the number of sides. Polygons may be characterized by their convexity or type of non-convexity: Convex: any line drawn through the polygon (and not tangent...

the formal geometrical features are similar. These include: A notion of convexity (supplied by the Levi form) A differential operator, analogous to the...

for ownerships of producers. The assumptions of strict convexity can be relaxed to convexity. This modification changes supply and demand functions from...

{\displaystyle p(0)\leq 0} , any two properties among subadditivity, convexity, and positive homogeneity implies the third. Every sublinear function...

In mathematics, Kostant's convexity theorem, introduced by Bertram Kostant (1973), can be used to derive Lie-theoretical extensions of the Golden–Thompson...

John B. Conway. Functions of One Complex Variable I, second edition. Springer-Verlag, 1995. ISBN 0-387-90328-3. "Convexity, logarithmic", Encyclopedia of...

{\displaystyle \mathbf {x} .} More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite if the real...

(PDF) on 2019-08-25. Retrieved 2018-03-24. Ekeland, Ivar (1990). "One". Convexity methods in Hamiltonian mechanics. Ergebnisse der Mathematik und ihrer...

star domain whose boundary is a sequence of connected line segments. Convexity: any non-empty convex set is a star domain. A set is convex if and only...

In general, the higher the convexity, the more sensitive the bond price is to the change in interest rates. Bond convexity is one of the most basic and...

{R} ^{+}} (for p > 1 {\textstyle p>1} ) and so, by the definition of convexity, | 1 2 f + 1 2 g | p ≤ | 1 2 | f | + 1 2 | g | | p ≤ 1 2 | f | p + 1 2...

made pioneering studies of non-convexity in economics. In economics, non-convexity refers to violations of the convexity assumptions of elementary economics...

compact, the open interval ( − 1 , 1 ) {\displaystyle (-1,1)} is not. Convexity is not strictly necessary for Brouwer's fixed-point theorem. Because the...

{\displaystyle f^{\prime }(-1^{+})=f^{\prime }(0^{+}),} and then the convexity condition implies that f {\displaystyle f} is linear on (−1, 0). Therefore...

significantly decrease the viability of networks, hence making convexity less frequent in complex networks. In the long run, networks tend to converge in the...

said to be quasiconcave. Quasiconvexity is a more general property than convexity in that all convex functions are also quasiconvex, but not all quasiconvex...