V2 June 2014. To say that the subject of VTE prophylaxis in orthopaedic surgery is a thorny issue may be understating the case. Debate and difference of opinion is something which is part and parcel of orthopaedic surgery and one of the many. components that makes this specialty fascinating.
Note that just monotonic transformation of a concave function isnot necessarily concave: consider, for example f (x) = x and g (z) = z 3 .Thus the concavity of a function is not ordinal, it is cardinal property.Economic ExampleSuppose production function f (x) is concave and the cost function c (x) is convex.ote that just monotonic transformation of a concave function isnot necessarily concave: consider, for example f (x) = x and g (z) = z 3 .Thus the concavity of a function is not ordinal, it is cardinal property.Economic ExampleSuppose production function f (x) is concave and the cost function c (x) is convex.
Two facts about these functions are: 1  if is a monotonic function defined on an interval, then is differentiable almost everywhere on, i.e. the set of numbers in such that is not differentiable in has Lebesgue measure zero.2  In addition, this result cannot be improved to countable: see Cantor function.f the order in the definition of monotonicity is replaced by the strict order, then one obtains a stronger requirement. A function with this property is called strictly increasing. Again, by inverting the order symbol, one finds a corresponding concept called strictly decreasing.