The structures of Hausdorff metric in non-Archimedean spaces

For non-Archimedean spaces $X$ and $Y,$ let $\mathcal{M}_{\flat } (X), \mathfrak{M}(V \rightarrow W)$ and $\mathfrak{D}_{\flat }(X, Y)$ be the ballean of $X$ (the family of the balls in $X$), the space of mappings from $X$ to $Y,$ and the space of mappings from the ballen of $X$ to $Y,$ respectively. By studying explicitly the Hausdorff metric structures related to these spaces, we construct several families of new metric structures (e.g., $\widehat{\rho } _{u}, \widehat{\beta }_{X, Y}^{\lambda }, \widehat{\beta }_{X, Y}^{\ast \lambda }$) on the corresponding spaces, and study their convergence, structural relation, law of variation in the variable $\lambda,$ including some normed algebra structure. To some extent, the class $\widehat{\beta }_{X, Y}^{\lambda }$ is a counterpart of the usual Levy-Prohorov metric in the probability measure spaces, but it behaves very differently, and is interesting in itself. Moreover, when $X$ is compact and $Y = K$ is a complete non-Archimedean field, we construct and study a Dudly type metric of the space of $K-$valued measures on $X.$Comment: 43 pages; this is the final version. Thanks to the anonymous referee's helpful comments, the original Theorem 2.10 is removed, Proposition 2.10 is stated now in a stronger form, the abstact is rewritten, the Monna-Springer is used in Section 5, and Theorem 5.2 is written in a more general for

A girl with cutaneous hyperpigmentation, cafe au lait spots and ring chromosome 15 without significant deletion.

Ring chromosome 15 [r(15)] syndrome is characterised by specific facial features, cafe au lait spots, failure to thrive, mental retardation and typically with a terminal deletion of the long arm of chromosome 15. We report a 2.5 year old girl showing normal growth and development, large hyperpigmented skin changes showing hypopigmentated areas inside, multiple cafe au lait spots and premature graying-like hypopigmentation of scalp hair. She had a karyotype of r(15) in peripheral lymphocytes and fibroblasts. By FISH analysis the breakpoint was located distal to locus D15S936 (15q26.3) and within 300 kb of the end of the chromosome, indicating no deletion of functional genes on 15q. Hyperpigmentation and cafe au lait spots are rare signs in ring chromosome syndromes, but with r(15) syndrome, cafe au lait spots have been described in about 30% of patients and have been considered to result from the deletion of gene(s) on distal 15q. Based on the frequent observation of patchy hyperpigmentation with the r(15) syndrome, absent hyperpigmentation in cases of distal 15q deletion without a ring chromosome, and the telomeric breakpoint location in our patient indicating no significant deletion, we propose that the cutaneous hyperpigmentation and cafe au lait spots in our proband represent effects of the r(15) chromosome but are not caused by the deletion of specific gene(s) on distal 15q. Patchy skin hypopigmentation is a well known nonspecific sign in cytogenetic mosaicism which is commonly seen in ring syndrome

Small inherited terminal duplication of 7q with hydrocephalus, cleft palate, joint contractures, and severe hypotonia.

We report a 14-month-old girl with submucous cleft palate, resolving mild hydrocephalus, severe hypotonia and joint contractures. The finding of extreme hydrocephalus, cleft palate and club feet in a fetus of the mother's previous pregnancy suggested an inherited defect. Chromosome analysis and FISH studies in the proband revealed an abnormal homolog 13 resulting in a duplication of distal chromosome 7q, 7q35-qter, and a very small associated deletion of distal chromosome 13q, 13q34-qter. The mother showed the balanced translocation. Similar clinical signs have been described with larger distal 7q duplications. Our findings suggest that 7q35-qter, and possibly the gene for sonic hedgehog (SHH) on 7q36, is the critical region for the typical facial features and the profound hypotonia observed in the 'trisomy of distal 7q' syndrome

Clin. Dysmorphol.

We report a 14-month-old girl with submucous cleft palate, resolving mild hydrocephalus, severe hypotonia and joint contractures. The finding of extreme hydrocephalus, cleft palate and club feet in a fetus of the mother's previous pregnancy suggested an inherited defect. Chromosome analysis and FISH studies in the proband revealed an abnormal homolog 13 resulting in a duplication of distal chromosome 7q, 7q35-qter, and a very small associated deletion of distal chromosome 13q 13q34-qter. The mother showed the balanced translocation. Similar clinical signs have been described with larger distal 7q duplications. Our findings suggest that 7q35-qter, and possibly the gene for sonic hedgehog (SHH) on 7q36, is the critical region for the typical facial features and the profound hypotonia observed in the 'trisomy of distal 7q' syndrome

Small inherited terminal duplication of 7q with hydrocephalus, cleft palate, joint contractures, and severe hypotonia

We report a 14-month-old girl with submucous cleft palate, resolving mild hydrocephalus, severe hypotonia and joint contractures. The finding of extreme hydrocephalus, cleft palate and club feet in a fetus of the mother's previous pregnancy suggested an inherited defect. Chromosome analysis and FISH studies in the proband revealed an abnormal homolog 13 resulting in a duplication of distal chromosome 7q, 7q35-qter, and a very small associated deletion of distal chromosome 13q 13q34-qter. The mother showed the balanced translocation. Similar clinical signs have been described with larger distal 7q duplications. Our findings suggest that 7q35-qter, and possibly the gene for sonic hedgehog (SHH) on 7q36, is the critical region for the typical facial features and the profound hypotonia observed in the 'trisomy of distal 7q' syndrome

Retorno da ciclicidade de ovelhas lactantes da raça Santa Inês até 105 dias pós-parto com amamentação contínua dos cordeiros em clima tropical quente úmido.

[Return od cyclicity of Santa Ines lactating ewes to 105 days after birth continued suckling of lambs in warm and tropical climate]