What is joint convexity?
What is joint convexity?
A real valued function f(A, B) defined on B(H) × B(H) is said to be. jointly convex in (A, B) if. f(λA1 + (1 − λ)A2, λB1 + (1 − λ)B2) ⩽ λf(A1,B1) + (1 − λ)f(A2,B2) for all Ai,Bi ∈ B(H), 1 ⩽ i ⩽ 2 and λ ∈ [0,1]. f(A, B) is said to be jointly concave if −f(A, B) is jointly convex in (A, B).
Can a discontinuous function be convex?
Thus, a discontinuous convex function is unbounded on any interior interval and is not measurable. If, for some function f, inequality (2) is true for any two points x1 and x2 in some interval and any p1>0 and p2>0, the function f is continuous and, of course, convex on this interval.
What is Superadditive effect?
A superadditive effect means that memory structures in the brain are producing additional input, which, combined with the inputs of the separate modalities, produces an integrated input greater than the sum of those separate modalities.
Does strong convexity imply strict convexity?
These conditions are given in increasing order of strength; strong convexity implies strict convexity which implies convexity. Geometrically, convexity means that the line segment between two points on the graph of f lies on or above the graph itself.
What is convex in science?
Definition of Convex A convex shape is the opposite of a concave shape. It curves outward, and its middle is thicker than its edges.
How do you define a convex function?
In mathematics, a real-valued function is called convex if the line segment between any two points on the graph of the function does not lie below the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set.
Can a discontinuous function be concave?
A concave function can be discontinuous only at an endpoint of the interval of definition.
Is convex function continuous?
A convex function is a continuous function whose value at the midpoint of every interval in its domain does not exceed the arithmetic mean of its values at the ends of the interval.
What is Superadditivity in psychology?
Although all multisensory enhancements may have perceptual/behavioral consequences, superadditivity, which suggests a nonlinear combination of modality-specific influences, seems to have had a disproportionate influence within the multisensory literature.
What does it mean if two drugs have synergistic effects?
An interaction between two or more drugs that causes the total effect of the drugs to be greater than the sum of the individual effects of each drug. A synergistic effect can be beneficial or harmful.
