Patrice Philippon

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A perfect power is a positive integer of the form ax where a ≥ 1 and x ≥ 2 are rational integers. Subbayya Sivasankaranarayana Pillai wrote several papers on these numbers. In 1936 and again in 1945 he suggested that for any given k ≥ 1, the number of positive integer solutions (a, b, x, y), with x ≥ 2 and y ≥ 2, to the Diophantine equation ax − by = k is(More)
We found a significant decrease of OKT8 + ve cells in silicosis patients (18.1%), but also in unaffected exposed workers (19.0%), when compared with sex- and age-matched controls (22.8%). The proportion of OKT8 + ve cells was significantly lower in subjects with antinuclear antibodies (15.7%) and in those with IgG-rheumatoid factors (16.3%).
A theorem of Kušnirenko and Bernštein shows that the number of isolated roots of a system of polynomials in a torus is bounded above by the mixed volume of the Newton polytopes of the given polynomials, and this upper bound is generically exact. We improve on this result by introducing refined combinatorial invariants of polynomials and a generalization of(More)
We present new lower bounds, proved in [Da–Phi3], for the canonical height of algebraic subvarieties of polarized abelian varieties which are isogeneous to a power of an elliptic curve. Combining these with a geometrical construction we exhibit families of curves defined over a number field, of arbitrary (sufficiently large) genus and satisfying a strong(More)
A survey of silicosis patients and people exposed to silica dust was set up in an effort to look for any relationship between humoral and cell-mediated autoimmune phenomena. It was found that in both sets of subjects, the level of Fc IgG receptor-bearing T lymphocytes was significantly reduced, there was also an inverse correlation between these cell(More)
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