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The concept of strong convexity extends and parametrizes the notion of strict convexity. Intuitively, a strongly-convex function is a function that grows as fast as a quadratic function. [11] A strongly convex function is also strictly convex, but not vice versa.
Complex convexity — extends the notion of convexity to complex numbers. Convex analysis - the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex minimization. Convex combination - a linear combination of points where all coefficients are non-negative and sum to 1 ...
In statistical quality control, the ¯ and s chart is a type of control chart used to monitor variables data when samples are collected at regular intervals from a business or industrial process. [1] This is connected to traditional statistical quality control (SQC) and statistical process control (SPC).
The classes of s-convex measures form a nested increasing family as s decreases to −∞" . or, equivalently {} {}.Thus, the collection of −∞-convex measures is the largest such class, whereas the 0-convex measures (the logarithmically concave measures) are the smallest class.
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 of the price of the bond with respect to interest rates (duration is the first derivative). In general, the higher the duration, the more sensitive the bond price is to the change in ...
Then convexity guarantees that the curves cannot intercept other than at the point of tangency, and the box is accordingly divided into 3 regions. The pale blue area is preferable to the point of tangency for Octavio but worse for Abby; the pale orange area is preferable for Abby but worse for Octavio; and the white area is worse for both.
A plane curve is the image of any continuous function from an interval to the Euclidean plane.Intuitively, it is a set of points that could be traced out by a moving point. More specifically, smooth curves generally at least require that the function from the interval to the plane be continuously differentiable, and in some contexts are defined to require higher derivative
In mathematical finance, convexity refers to non-linearities in a financial model.In other words, if the price of an underlying variable changes, the price of an output does not change linearly, but depends on the second derivative (or, loosely speaking, higher-order terms) of the modeling function.