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We describe a parameter synthesis algorithm for planar mechanical systems comprised of higher kinematic pairs in which each part translates along a fixed axis or rotates around a fixed point.
The physical manifestation of a wave is familiar – a material (water, metal, air etc) deforms back and forth around a fixed point.
In fact, if we make a great number of records to investigate the dynamic behavior of a permanent population system, we may find that a single record may fluctuate around a fixed point even if the number of records is large.
The authors aimed to quantify gene expression heterogeneity and establish whether it constitutes noise around a fixed point or the presence of multiple subpopulations that could correspond to functional states.
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So, has a fixed point.
By Schauder fixed point theorem, has a fixed point.
Then A has a fixed point.
(3.1) Then T has a fixed point.
Hence, T has a fixed point.
From Remark 3.3 has a fixed point.
Hence, f has a fixed point.
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