(32a) and (32b), as these equations show that for f ≈ 0 the parameter S is always negative and therefore, the essential condition for existence of solitary solution cannot be satisfied at f ≈ 0.
The ability to produce antibiotics to inhibit competitors or to inactivate organisms that serve as potential nutrient sources is a critical factor for the existence of a soil-inhabiting, non-pathogenic organism, just as virulence against a host is essential for the existence of a pathogenic organism factor.
"This book is essential for our existence," Rabbi Steinsaltz said.
Extracellular matrix (ECM) is essential for multicellular existence.
Water and energy are essential for human existence, and its rational use should be encouraged.
Alkaline groundwater is considered essential for the existence of low-productive fen plants.
In Theorem 3.1, the monotonicity of F is not essential for the existence of a fixed point.
Water is a chief natural resource essential for the existence of life and is a basic human entity.
As we all know Lazer type conditions are essential for the existence and uniqueness of periodic solutions of equations [1 4].
This way of putting the point, however, gives rise to the question of whether both relata of this relation are equally essential for its existence.
