Sentence examples for extends the existence from inspiring English sources

Especially, our Theorem 3.1 extends the existence of solution in the literature to the case of generalized extended nonlinear variational inequality (2.1).

Daniel E. Lieberman, a human evolutionary biologist at Harvard who was not involved in the research, wrote in a commentary for the journal that the hominin foot "is a valuable addition to the fossil record as it extends the existence of Ardipithecus-like feet by a million years".

Such enzyme is the first example of a DING protein in Archaea, and this finding extends the existence of DINGGG proteins into all the biological kingdoms [9].

Our result gives both the existence and approximation of solutions to Caputo fractional order hybrid differential equations and also extends the existence results for ordinary hybrid differential equations.

This novel protein extends the existence of anti-infectious molecules in monotreme milk and adds to the complexity of species-specific antibacterial activity to protect immunocompromised hatchlings.

Vitimopsyche pristina sp. nov. extends the existence of the genus Vitimopsyche Novokshonov and Sukacheva, 2001, from the mid Lower Cretaceous to the latest Middle Jurassic.

In this section, we extend the existence results presented in Section 3 to the global situation.

Recently, Dhage [9] extended the existence of PPF dependent fixed points to PPF common dependent fixed points for mappings satisfying the weaker contractive conditions.

We try to extend the existence of solutions for semilinear Dirichlet problems on the Heisenberg balls in [9] to general Carnot domains.

After that Dhage [11] extended the existence of PPF dependent fixed points to PPF common dependent fixed points for mappings satisfying the weaker contractive conditions.

We extend the existence of solution by the upper and lower solution methods and generalized monotone method for first-order impulsive hybrid equation.