X-linked lissencephaly with abnormal genitalia (XLAG) is a rare disorder caused by mutations in the aristaless-related homeobox (ARX) gene. We report on the clinical data of a boy with a 1-bp deletion (790 delC) resulting in a frame shift in the ARX gene and prolonged survival until age 18 months. Similar to other patients, the boy showed postnatal microcephaly, hypothalamic dysfunction, intractable neonatal seizures, and chronic diarrhoea. In addition, he suffered from exocrine pancreatic insufficiency and renal phosphate wasting became apparent from age 5 months, both of which have not been described previously in XLAG. This allows us to speculate that the phenotype of XLAG is more complex than hitherto known and may include renal phosphate wasting which might not have been observed in other patients due to early death.

While the use of finite element methods for the numerical approximation of eigenvalues is a well-studied problem, the use of serendipity elements for this purpose has received little attention in the literature. We show by numerical experiments that serendipity elements, which are defined on a square reference geometry, can attain the same order of accuracy as their tensor product counterparts while using dramatically fewer degrees of freedom. In some cases, the serendipity method uses only 50% as many basis functions as the tensor product method while still producing the same numerical approximation of an eigenvalue. To encourage the further use and study of serendipity elements, we provide a table of serendipity basis functions for low order cases and a Mathematica file that can be used to generate the basis functions for higher order cases.

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