Lang's Conjecture and Sharp Height Estimates for the elliptic curves y2=x3+axy^{2}=x^{3}+ax

For elliptic curves given by the equation $E_{a}: y^{2}=x^{3}+ax$, we establish the best-possible version of Lang's conjecture on the lower bound of the canonical height of non-torsion points along with best-possible upper and lower bounds for the difference between the canonical and logarithmic height.Comment: published version. Lemmas 5.1 and 6.1 now precise (with resultant refinement to Theorem 1.2). Small corrections to

Subacute sclerosing leucoencephalitis: an epidemiological, clinical and biochemical study of 31 cases

Thirty-one cases of SSLE are reported. The diagnosis was based on the clinical picture, the marked increase of gammaglobulins in the cerebrospinal fluid, the typical electroencephalographic pattern, and the pathological examination. Intracellular inclusion bodies were found at the postmortem examination of 8 among 13 cases and in 1 of 7 cerebral biopsies. The mean age was 11.7 years, with the limits of 3 and 22 years. Males prevailed markedly over females (23:8). Patients from rural regions were the bulk of the series (77.4%). No definite regional predominance was demonstrated by the analysis of the geographic distribution. A seasonal influence was not evidenced. In 16 patients followed up to death, the average duration of the disease was 7 months, with a range from 2 to 20 months. In the clinical picture the constancy of myoclonus or losses of tonus, and psychiatric disorders was evidenced. The first symptom was the psychiatric alteration in 55.6% of the cases, myoclonus in 35.5% and grand mal seizures in 33.3%. Rigidity and pyramidal signs were very frequent, while the cerebellar syndrome was rare. Ophtalmoscopic alterations (edematous or pale disk, choroidits) were found in a third of the cases. In two cases an epizootic of household chicken was coincident with the onset of the disease. The blood copper concentrations determined in 8 cases were always above the normal range, while ceruloplasmin remained within the normal limits. The blood sulfur levels were high in 3 patients studied. The blood magnesium levels were variable in 6 patients studied