Sentence examples for the essential solution from inspiring English sources

The advance of metallocene technology provides the essential solution to empower this chemical approach.

In this section, we first introduce the concepts of the essential solution of Ky Fan's section theorem and the essential Ky Fan point with respect to (rho_{s}^{u}) and (rho_{k}^{u}).

Instead of considering the essential solution, Kinoshita [19] introduced the notion of essential components of the set of fixed points and proved that, for any continuous mapping of the Hilbert cube into itself, there exists at least one essential component of the set of its fixed points.

It can be proved that the discretely essential solution of (10), in Example 6.3, is at the same time essential as a fixed point of the Hammerstein-type operator (int_{0}^{2pi} G t,s)[-F_{0}(x t))+cos t],dt), where G t,s):= textstylebegin{cases} frac{e^{-c} t-s+2pi)}{1-e^{-2pi c}},& mbox{frac{e^{-c} t-s+2piq2pi, frac{e^{-c} t-s+2pi-e^{-2pi c}},& mbox{for } 0leq sleq tleq2pi.

The key take-away is the role of home care has as an essential solution for the nations' elder caregiving crisis.

The notation of an essential solution for fixed points was first introduced in [18].

Different from previous works, this paper will provide the necessary and sufficient (essential) solution to linear quadratic (LQ) optimal control problem for continuous-time mean-field systems.

Just as it is a truism that education is an essential solution to the plight of the middle class, we have gotten used to complaining about how badly schools have declined.

It is not just the prevention paradigm that health and environmentalists share; it is some of the same essential solutions.

The 1D fillers may also form percolating paths of "nano-chimneys" that outgas the accumulated helium and other fission gases, providing an essential solution to the gas accumulation problem.

Family planning is one essential solution, albeit not the only one, to solving some of the world's complex problems.