A universal exponent for homeomorphs

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On the range of Carmichael’s universal-exponent function

Let λ denote Carmichael’s function, so λ(n) is the universal exponent for the multiplicative group modulo n. It is closely related to Euler’s φ-function, but we show here that the image of λ is much denser than the image of φ. In particular the number of λ-values to x exceeds x/(log x).36 for all large x, while for φ it is equal to x/(log x)1+o(1), an old result of Erdős. We also improve on an ...

Universal scaling of Lyapunov-exponent fluctuations in space-time chaos.

Finite-time Lyapunov exponents of generic chaotic dynamical systems fluctuate in time. These fluctuations are due to the different degree of stability across the accessible phase space. A recent numerical study of spatially extended systems has revealed that the diffusion coefficient D of the Lyapunov exponents (LEs) exhibits a nontrivial scaling behavior, D(L)~L(-γ), with the system size L. He...

Homeomorphs and amallamorphs of the Petersen graph

Let P be the Petersen graph. The main results of this paper are the discovery of infinite families of chromatically equivalent pairs of P homeomorphs and the discovery of infinite families of flow equivalent pairs of P amallamorphs. In particular, three families of P homeomorphs with 8 parameters, five families with 7 parameters and many families with fewer parameters are obtained. Also one fam...

Universal Pharmacare in Canada: A Prescription for Equity in Healthcare

Despite progressive universal drug coverage and pharmaceutical policies found in other countries, Canada remains the only developed nation with a publicly funded healthcare system that does not include universal coverage for prescription drugs. In the absence of a national pharmacare plan, a province may choose to cover a specific sub-population for certain drugs. Altho...