Sharp local well-posedness for the "good" Boussinesq equation

In the present article, we prove the sharp local well-posedness and ill-posedness results for the "good" Boussinesq equation on $\mathbb{T}$; the initial value problem is locally well-posed in $H^{-1/2}(\mathbb{T})$ and ill-posed in $H^s(\mathbb{T})$ for $s<-1/2$. Well-posedness result is obtained from reduction of the problem into a quadratic nonlinear Schr\"odinger equation and the contraction argument in suitably modified $X^{s,b}$ spaces. The proof of the crucial bilinear estimates in these spaces, especially in the lowest regularity, rely on some bilinear estimates for one dimensional periodic functions in $X^{s,b}$ spaces, which are generalization of the bilinear refinement of the $L^4$ Strichartz estimate on $\mathbb{R}$. Our result improves the known local well-posedness in $H^s(\mathbb{T})$ with $s>-3/8$ given by Oh and Stefanov (2012) to the regularity threshold $H^{-1/2}(\mathbb{T})$. Similar ideas also establish the sharp local well-posedness in $H^{-1/2}(\mathbb{R})$ and ill-posedness below $H^{-1/2}$ for the nonperiodic case, which improves the result of Tsugawa and the author (2010) in $H^s(\mathbb{R})$ with $s>-1/2$ to the limiting regularity.Comment: 40 page

Tratamento da esporotricose cutânea com sski: experiência de 24 anos no estado de São Paulo, Brasil.

BACKGROUND: Sporotrichosis is a subacute or chronic disease caused by a dimorphic fungus, Sporothrix schenckii. The first and most traditional treatment is potassium iodide in satured solution (SSKI) used by DE BEURMANN in 1907. For its effectiveness, it is still used for cutaneous sporotrichosis. OBJECTIVE: To evaluate the treatment of cutaneous sporotrichosis with SSKI in relation to clinical cure, side effects, length of treatment and reactivation. METHODS: We conducted a retrospective analysis of medical records over a 24-year period (1981-2005). Patients of all ages who were treated in the hospital´s division of dermatology were included in the study providing that they had a positive culture of S. schenckii. Satured solution of potassium iodide (3 to 6g per day) was the treatment prescribed. For children, half of the dose was prescribed. RESULTS: The lymphocutaneous disease was prevalent, the cure rate was 94.7%, side effects were described in 5.5% of the cases, mean length of treatment was 3.5 months and possible reactivation was observed in 11.1%. CONCLUSION: SSKI is an effective drug, with many side effects, but with low frequency. Resolution was for maximum six months of treatment. SSKI has been found to be a very effective drug in this retrospective study of culture-proven cases of cutaneous and lymphocutaneous sporotrichosis. It should be used as first drug of choice especially in resource-limited settings.FUNDAMENTOS: Esporotricose é doença subaguda ou crônica causada pelo fungo dimórfico Sporothrix schenckii. O primeiro e mais tradicional tratamento é o iodeto de potássio em solução saturada (SSKI) usado por De Beurmann em 1907. Por ser eficaz,ainda é muito utilizada no nosso meio para o tratamento da esporotricose cutânea. OBJETIVOS: Avaliar o tratamento da esporotricose cutânea com SSKI em relação à cura clínica, efeitos colaterais, tempo de tratamento e recidiva. MÉTODOS: A partir da revisão dos resultados de exames do laboratório de Micologia da Clínica de Dermatologia da Santa Casa de SP, durante 1981 a 2005, foram incluídos pacientes de qualquer idade com lesão cutânea sugestiva de esporotricose e cultura positiva para S. schenckii. Em todos pacientes o tratamento prescrito foi SSKI na dose de 3 a 6g/dia para adultos, por um período de até duas semanas após cura clínica. Em crianças foi utilizada a metade da dose. RESULTADOS: Houve predomínio da forma cutânea localizada, taxa de cura de 94,7%, efeitos colaterais em 5,5%, média de tempo de tratamento de 3,5 meses e 11,1% de provável recidiva. CONCLUSÃO: A SSKI é eficaz, com diversos efeitos colaterais, porém de baixa frequência, permanecendo indicada para as formas cutâneas da esporotricose

Seismic moment of the 1891 Nobi, Japan, earthquake estimated from historical seismograms

The seismic moment of the 1891 Nobi, Japan, earthquake has been evaluated from the historical seismogram recorded at the Central Meteorological Observatory in Tokyo. For this purpose, synthetic seismograms from point and finite source models with various fault parameters have been calculated by a discrete wave-number method, incorporating the instrumental response of the Gray-Milne-Ewing seismograph, and then compared with the original records. Our estimate of the seismic moment (M o) is 1.8×10[20] N m corresponding to a moment magnitude (M w) 7.5. This is significantly smaller than the previous estimates from the distribution of damage, but is consistent with that inferred from geological field survey (Matsuda, 1974) of the surface faults