Sentence examples for has a critical functional from inspiring English sources

The bulk of evidence suggests that in human leukemia cells, PEITC-induced Akt inactivation has a critical functional role in mediating PEITC lethality.

The finding that pharmacological and genetic interruption of the JNK pathway attenuated PEITC-mediated lethality indicates that stress pathways have a critical functional role in apoptosis induction by this agent.

Because of the key role of p53 in UVB-induced apoptosis, cell cycle arrest and skin cancer, we reasoned that lincRNA-p21 could have a critical functional role in UVB-induced apoptosis and/or cell cycle arrest in keratinocytes and its loss in the evasion of apoptosis and/or defective cell cycle control and the pathogenesis of skin cancer.

Then, the functional has a critical point in.

By Lemmas 2.32.4 and the mountain pass theorem, the functional has a critical point satisfying.

Hence, Lemma 3.3 implies that the operator equation has a solution in if and only if the functional has a critical point in.

Then the functional φ has a critical point in H.

By Remarks 2.1 and 2.3 and the mountain pass theorem, the functional (I_) has a critical point (u_{1}) satisfying (I_ u_{1} geqbeta).

By Lemma 2.2, Lemma 2.3, Lemma 2.4, and the mountain pass theorem, the functional (I_) has a critical point (u_{1}) satisfying (I_ u_{1} geqbeta).

By Lemmas 2.2 and 2.3 and the mountain pass theorem, the functional I+ has a critical point ul satisfying I+ ul) ≥ β.

This formula implies that the functional T has a critical point (mu_{2}:=inf_{nuinmathcal{B}} max_{t inmathbb{R}} T nu(t))), which is the second solution for (5).