Sentence examples for integer multiplicity from inspiring English sources
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 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.
The speeds are all integer multiples of one number.
Let k and l be positive integers, and let R ( z ) be a rational function, all of whose zeros have multiplicity at least k.
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All through this paper, we will refer to 'fixed points of m-order' simply as 'multipled fixed points'; the integer m is defined as the multiplicity or the order of the multipled fixed point x.
We would like to use the term residue here instead of coefficient, but strictly speaking the coefficient in the pole-term is the residue of the pole only when (multiplicity one); when is any integer other than 1, the residue is zero (see any book on complex analysis and/or Cauchy's Residue Theorem).
Over the past decades, the existence and multiplicity of nontrivial solutions for the integer order Schrödinger equation have been extensively investigated.
