Beginning with chapter 27, they consider such topics as special ancient solutions, compact two-dimensional ancient solutions, hyperbolic geometry and three-manifolds, constant mean curvature surfaces and harmonic maps by the

implicit function theorem, and type II singularities and degenerate neckpinches.

The gyroid structure was described by

implicit function 1.

Imdad: An

implicit function implies several contraction conditions, Sarajevo J.

OriginPro adds tools for

implicit function fitting and IIR filter design.

The aim of implicit surface reconstruction is to obtain an

implicit function from unconstructed scattered data using interpolation or approximation.

After critical study of Pakistan's E-Government strategy as well as framework, it reveals that the strategy adopted and being implemented by GOP is an

implicit function of variables including policy advocacy, organizational development, capacity building and linkage between state and non-state actors.

b] and using the

implicit function rule, one gets [dX.

1), we can solve, for instance, for x and y in terms of z; according to the

implicit function theorem, it is enough to assume that the Jacobian [partial derivative]([[phi].

In this paper, we define a new class of

implicit function and utilize the same to prove our results because of their versatility of deducing several known and unknown contraction conditions in one go.

If the improvement of the solution for an one-criterion sub-problem in the complex optimisation, using special mathematical tools for acceleration of the computing process GMRG, is called complex optimal correction of ESS of EPS, the improvement of the solution of multi-objective sub-problems of the complex optimisation using special mathematical tools for acceleration of the computing process [application instead of the gradient of the one

implicit function the array of the multi-objective descent or rise (dependent on the minimisation or maximisation of the partners objective functions)], is called complex multiobjective or Pareto-optimal correction of ESS of IPS.

d]J(c) [not equal to] 0, there exists a holomorphic function g guaranteed by the

implicit function theorem such that in some open ball around c, J(X, g(X)) = 0.

14) This

implicit function can conceptually be rearranged to an explicit form of Firm i's reaction function.