Let f : K := [a, a + [eta] (b, a)] [right arrow] R be a

differentiable function on K[degrees] (the interior of K) and a, b [member of] K[degrees] with a < a + [eta] (b, a).

For any

differentiable function h satisfying E[[absolute value of h'(X)]] < [infinity], we have

alpha]) to be a

differentiable function nor a single value mapping (thus allowing for multiple solutions).

We still assume that f is a twice

differentiable function in [OMEGA] satisfying f"([x.

z]) are given n-times

differentiable functions in some closed domain D.

Let w [member of] I be a simple zero of sufficiently

differentiable function f : I [?

Pratt (1964) suggests a formula for comparing two agents' risk aversion: Agent A is more risk averse than agent B if there exists an increasing, strictly concave, and twice

differentiable function |Phi~ such that |U.

15]) Let f: X [right arrow] R be a

differentiable function on a nonempty closed convex subset X of [R.

Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be two Riemannian manifolds and f a positive

differentiable function on [M.

2]), where [PHI] = [PHI] (u) is a

differentiable function of its variable u = [[absolute value of z].

d] and 0 < q [less than or equal to] + [infinity], if there exists an infinitely

differentiable function [eta] satisfying [eta]([xi]) = 1 if [absolute value of [xi]] [less than or equal to] [rho] and [eta]([xi]) = 2[rho] for some 0 < p < 1/2 such that jz([eta]v)/w) belongs to [L.

n]: I [right arrow] K be given continuous functions, let g: I [right arrow] X be a given continuous function, and let y: I [right arrow] X be any n times continuously

differentiable function satisfying the inequality

d], * an infinitely

differentiable function with support in the unit ball such that [DELTA] [phi](x)dx = 1 and a positive real number.

Instead, the physicists' potential energy function (differentiable with respect to particle position components) suggested to economists that they should make Bentham's utility a

differentiable function of consumer good quantities.

Assume the function f: R [right arrow] R is a

differentiable function and g : T [right arrow] R is a delta-

differentiable function.