Examples of differentiable

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Since vote shares are differentiable, we can consider critical points of these functions.
The method of characteristics gives a continuously differentiable solution for short time, since the initial data are smooth.
The regression function m 1 is two times continuously differentiable+ v i !
If is continuously differentiable, the following are equivalent.
Application of implicit-function theorems should be able to prove if the value function is locally differentiable.
We then construct a domain for differentiable real-valued functions of a real variable by pairing consistent information about the function and information about its derivative.
In this process the position of the corner layer gives to leading order a differentiable solution which is a necessity for elliptic problems.
We speak of a bifurcation, or a bifurcating random differentiable map, if at least one of these properties is violated.
Two smooth mapping families are boundedly conjugate if there exists a differentiable conjugating map which induces a bounded equivalence of the metrics.
This means they can be used to define equivalence relations on sets, and to give the analogue of differentiable structures.
Then the set of solutions to (5.1) for all positive forms a nonempty differentiable path, called the central path.
However, twice differentiable property of cubic splines was not a requirement in our approach.
However, this requires that the function f (k) be thrice differentiable.
As the sequence is generated by a continuous-although not everywhere differentiable-map, it should converge to a fixed point of the map.
To have a smooth movement, the trajectory must be twice differentiable to give a continuous velocity and acceleration.
This prevents corners from occurring there; we require that 0 be everywhere continuously differentiable.
If forcing were added to the second equation rather than to the first, then sample paths would be continuous and differentiable.

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