We discussed some related terms like completeness, total degree and

constant function and exemplified them.

The random HR in (2) is a

constant function of time for each widowed person, with expected value [[beta].sub.0] + [[beta].sub.1].

Furthermore, its leaves are geodesics in ([bar.M], [bar.g]), if and only if, f is a

constant function, i.e., [bar.g] is a bundle-like metric.

The fractional differential of

constant function f(x) = C, (C is a constant) is different under different definitions:

In the following [1.sub.[bar.X]] denotes the

constant function 1 on [bar.X].

Then the function <[p.sub.1] [omicron] F, [p.sub.2] [omicron] F, ..., [p.sub.m] [omicron] F> is a

constant function if and only if the following conditions are equivalent.

Obviously, the situation becomes more complicated when time-delay is a piecewise

constant function.

That is, [f.sub.2] is the

constant function with ouput being the entire vertex set X.

Applying the lemma for the function g, we obtain that / is a

constant function, then, by (c), we have, for any x [member of] R, g(x) = g(0) = f(0) - 0 = 0, i.e.

Neither the signed distance function nor the piecewise

constant function is used, the level set function is initialized to a

constant function and this method eliminates the need for initial contours and re-initialization.

For simplicity, the piecewise

constant function [theta]([eta]) defined on [GAMMA] by (1.3) will be denoted by

The present paper is organized as follows: In Section 2, we give our strategy for proving Theorem 1.2, that is, we show it is enough to prove a mapping F defined by (2.2) maps a small neighborhood of a

constant function c in [C.sup.[alpha]][(0, 1).sub.0] homeomorphically onto a neighborhood of [square root of (2)]c' in [C.sup.a + 1/2][(0,1).sub.0].