Sentence examples similar to many functions exist from inspiring English sources
Remark 1.3 There exist many functions I j and f ( t, u ) satisfying conditions (I1 - I2) and (H1 - H3), respectively.
(i) It is not difficult to see that there exist many functions, which, respectively, satisfy Theorem 1.1 and Theorem 1.2.
A ( x ) ≢ 0. There exist many functions h ( x, t ) satisfying condition (H), for example, h ( x, t ) = P ( x ) | t | p − 2 t, where P ( x ) is a positive and bounded function.
We should point out that Theorem 2.3 is different from the previous results of [9], [10] in three main directions: (i) A ( x ) ≢ 0. There exist many functions h ( x, t ) satisfying condition (H), for example, h ( x, t ) = P ( x ) | t | p − 2 t, where P ( x ) is a positive and bounded function.
Many functions of our brain exist to protect us from the uncomfortable reality that we are far more limited than we like to think we are.
Many functions throughout their SDK can just crash the program because they don't exist on older OS versions.
Very small BESs do exist and many functioning BESs do not contain the full complement of expression site associated genes (ESAGs).
The enzyme has many functions.
Therefore water serves many functions.
Many proteins exist and function as multimeric complexes, in which subunits noncovalently interact with each other.
