Genus and Braid Index Associated to Sequences of Renormalizable Lorenz Maps

We describe the Lorenz links generated by renormalizable Lorenz maps with reducible kneading invariant (K(f)(-), = K(f)(+)) = (X, Y) * (S, W) in terms of the links corresponding to each factor. This gives one new kind of operation that permits us to generate new knots and links from the ones corresponding to the factors of the *-product. Using this result we obtain explicit formulas for the genus and the braid index of this renormalizable Lorenz knots and links. Then we obtain explicit formulas for sequences of these invariants, associated to sequences of renormalizable Lorenz maps with kneading invariant (X, Y) * (S,W)*(n), concluding that both grow exponentially. This is specially relevant, since it is known that topological entropy is constant on the archipelagoes of renormalization.

Diagnosis of Tinea pedis and onychomycosis in patients from Portuguese National Institute of Health: a four-year study

ABSTRACT - Tinea pedis and onychomycosis are two rather diverse clinical manifestations of superficial fungal infections, and their etiologic agents may be dermatophytes, non-dermatophyte moulds or yeasts. This study was designed to statistically describe the data obtained as results of analysis conducted during a four year period on the frequency of Tinea pedis and onychomycosis and their etiologic agents. A questionnaire was distributed from 2006 to 2010 and answered by 186 patients, who were subjected to skin and/or nail sampling. Frequencies of the isolated fungal species were cross-linked with the data obtained with the questionnaire, seeking associations and predisposing factors. One hundred and sixty three fungal isolates were obtained, 24.2% of which composed by more than one fungal species. Most studies report the two pathologies as caused primarily by dermatophytes, followed by yeasts and lastly by non-dermatophytic moulds. Our study does not challenge this trend. We found a frequency of 15.6% of infections caused by dermatophytes (with a total of 42 isolates) of which T. rubrum was the most frequent species (41.4%). There was no significant association (p >0.05) among visible injury and the independent variables tested, namely age, gender, owning pet, education, swimming pools attendance, sports activity and clinical information. Unlike other studies, the variables considered did not show the expected influence on dermatomycosis of the lower limbs. It is hence necessary to conduct further studies to specifically identify which variables do in fact influence such infections.