Sentence examples for an integer multiplicity from inspiring English sources

The second largest region of phase locking occurs for periods of stimulus that are an integer multiplicity of the intrinsic period.

We found that only when the extrinsic period is close to an integer multiplicity of the averaged intrinsic period can the collective behaviors be induced/enhanced; otherwise, the stimulus possibly ruins the achieved collective behaviors.

On the other hand, in the case of sinusoidal stimulus, the condition under which the external stimulus induces a collective behavior is basically similar to that in the case of periodic impulsive stimulus, that is, only when the extrinsic period is close to an integer multiplicity of the intrinsic period, can the synchronization be achieved.

Such functions play a crucial role in the study of area minimizing submanifolds at branch point singularities, at which at least one tangent cone is a plane with integer multiplicity > 1.

This is even more true in the case of the asymmetry index  (varvec{alpha }(Gamma )) whose precise definition is more technical and requires the use of a certain seminorm defined for integer multiplicity currents [18, Sect. 2].

The ideal is a collection of all algebraic integer multiples of a given algebraic integer.

Suppose that d(≥ 0) is an integer, p z) is an analytic function in D, and the multiplicity of its all zeros is at most d.

An automorphic number is an integer whose square ends with the given integer, as (25)2 = 625, and (76 2 = 5776.

Theorem D Suppose that d (≥0) is an integer, p ( z ) is an analytic function in D, and the multiplicity of its all zeros is at most d.

Theorem 1.1 Suppose that d ≥ 0 is an integer, p ( z ) ≢ 0 is a holomorphic function in D, and the multiplicity of its all zeros is at most d.

Theorem 1.1 Let k ≥ 2 be an integer, and let ℱ be a family of meromorphic functions in D, all of whose zeros have multiplicity at least k + 1.