## Concave

The word **concave** means curving in or hollowed inward , as opposed to convex . The former may be used in reference to: **Concave** lens , a lens with inward-curving **concave** ) surfaces. **Concave** polygon , a polygon which is not convex. **Concave** function , a type of function which is related

**wikipedia.org**| 2010/9/25 9:32:06

## Concave function

In mathematics , a **concave** function is the negative of a convex function . A **concave** function is also synonymously called **concave** downwards , **concave** down , convex cap or upper convex . Contents 1 Definition 2 Properties 3 Examples 4 See also 5 References [ edit

**wikipedia.org**| 2011/7/12 6:35:53

## Concave set

In mathematics , the notion of a **concave** set" is not correct. [ citation needed ] A set that is not convex, is a non-convex set. [ edit ] See also Convex set **Concave** function [ edit ] References

**wikipedia.org**| 2011/10/2 3:42:00

## Log-concave

Log **concave** From Wikipedia, the free encyclopedia Jump to: navigation , search Log **concave** may refer to: Logarithmically **concave** function Logarithmically **concave** measure Logarithmically **concave** sequence This disambiguation page lists articles associated with the

**wikipedia.org**| 2011/3/22 18:37:07

## Virtual image

not necessary for the image to form. [ 1 ] When we look through a diverging lens (at least one **concave** surface) or look into a convex mirror , what we see is a virtual image. However, if we observe a focused image on a screen inside or behind a converging lens (at least one convex side

**wikipedia.org**| 2011/4/30 2:44:52

## Logarithmically concave measure

In mathematics , a Borel measure μ on n - dimensional Euclidean space R n is called logarithmically **concave** (or log **concave** for short) if, for any compact subsets A and B of R n and 0 λ 1, one has where λ A + (1 − λ ) B denotes the Minkowski sum

**wikipedia.org**| 2011/9/6 2:30:01

## Logarithmically concave function

In convex analysis , a non-negative function f : R n → R + is logarithmically **concave** (or log **concave** for short) if its domain is a convex set , and if it satisfies the inequality for all x , y ∈ dom f and 0 θ 1 . If f is strictly positive, this is equivalent

**wikipedia.org**| 2011/9/6 0:46:37

## Schur-convex function

majorization . Every function that is convex and symmetric is also Schur-convex. [ edit ] Schur **concave** function A function f is 'Schur **concave** ' if − f is Schur-convex. [ edit ] Examples Entropy function is Schur **concave** is Schur-convex This mathematical analysis

**wikipedia.org**| 2010/9/26 21:59:39