1) Without assuming the boundedness, monotonicity and differentiability of the activation functions, the conditions ensuring existence and uniqueness of the equilibrium are obtained.

2) The continuity and differentiability are achieved by using cubic polynomial interpolation based on hard thresholding.

3) The paper probes into the relation between functional differentiability and the derivative function limit, and the relation between asymptote of function and the derivative function limit.

4) This is a much stronger condition than real differentiability and implies that the function is infinitely often differentiable and can be described by its Taylor series.

5) Two new notions of continuous differentiability and uniformly continuous differentiability are introduced in this paper.

6) The relationship between the differentiability of solution of Cauchy problem of weak—hyperbolic differential equationand its lower term is studied in this paper.

7) The uniform differentiability of characteristic function and conditional characteristic function and reversion formula of conditional eigenfunction are obtained in this paper.

8) Differentiability of the interpolated function was dropped really through solving the problem and some approximation results were obtained.

9) The differentiability of the initial stresses and elastic constants of the surrounding rocks of tunnels is discussed firstly from the point of view of finite element method.

10) Without requiring the differentiability of the functions and with implicit parallelism,[http:///differentiability.html] evolutionary algorithms are often used to solve some difficult problems which the classical algorithms can't.

11) The example that ultimately drove home the distinction between continuity and differentiability was given by him.

12) This algorithm has a strong global - searching performance and has no requests for the continuity and differentiability of object function.

13) Argument functions are defined by set and its existence , Continuity and differentiability are discussed.

14) In the case of complete recourse matrix, we prove the continuity and the differentiability of the objective.

15) This mark can even be dependent on the ingress interface so that higher differentiability can be achieved.

16) The Relation between the Continuity, the Partial Derivatives, the Directional Derivatives and the Differentiability of a Function.

17) The thesis mainly discusses the value of the theory of differentiability in natural science to the system of product identification.

18) A discussion of the relations between continuity, partial derivative, directional derivative and differentiability of binary function is helpful for us to study binary function.

19) In the second half of the semester we go back and examine the notions that you already 'know' of differentiability of functions and integration.

20) Compared with the existing results for this network, the given stability conditions do not require the differentiability of the mappings, and the symmetric of the sum of the mappings.

21) As to their applications, the continuity and uniformly continuity of derivative mapping are characterized by the two new notions of differentiability.