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A CONDITIONAL DENSITY FOR CARMICHAEL NUMBERS
Bulletin of the Australian Mathematical Society, 2020Under sufficiently strong assumptions about the first prime in an arithmetic progression, we prove that the number of Carmichael numbers up to$X$is$\gg X^{1-R}$, where$R=(2+o(1))\log \log \log \log X/\text{log}\log \log X$. This is close to Pomerance’s conjectured density of$X^{1-R}$with$R=(1+o(1))\log \log \log X/\text{log}\log X$.
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Controllability Index Based on Conditioning Number
Journal of Dynamic Systems, Measurement, and Control, 1975Use of the conditioning number k(F) = ∥ F ∥ • ∥ F−1 ∥ where F is a symmetric matrix related to the controllability (observability) matrix is suggested as basis for index of controllability (observability). This index has advantages of being independent of scaling of state variables and being a continuous function of parameters of process.
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The role of the microbiome in cancer development and therapy
Ca-A Cancer Journal for Clinicians, 2017Aadra P Bhatt, Matthew R Redinbo
exaly