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We investigate the sets of uniform limits A ( B ‾ n ) , A ( D ‾ I ) of polynomials on the closed unit ball B ‾ n of C n and on the cartesian product D ‾ I where I is an arbitrary set, maybe finite, infinite denumerable or non-denumerable and D ‾ is the closed unit disc in C . The class A ( D ‾ I ) contains exactly all functions f : D ‾ I → C continuous with respect to the product topology on D ‾ I and separately holomorphic. We consider sets of uniqueness for A ( D ‾ I ) (respectively for A ( B ‾ n ) ) to be compact subsets K of T I (respectively of ∂ B ‾ n ) where T = ∂ D is the unit circle. If K has positive measure then K is a set of uniqueness. The converse does not hold. Finally, we do a similar study when the uniform convergence is not meant with respect to the usual Euclidean metric in C , but with respect to the chordal metric χ on C ∪ { ∞ } . [ABSTRACT FROM AUTHOR]

This article, published in the journal Neuropediatrics, discusses a case study of a 12-year-old boy with drug-resistant autoimmune epilepsy caused by glutamate decarboxylase 1 (GAD65) antibodies. GAD65 antibodies are associated with autoimmune diseases and can also lead to neurological disorders such as autoimmune encephalitis and cerebellar ataxia. The patient's seizures were initially treated with medication but recurred, leading to confusion and amnesia. Aggressive immunotherapy, including intravenous methylprednisolone and immunoadsorption, along with the use of the GABA receptor modulator cenobamate, resulted in sustained resolution of symptoms. This case highlights the importance of early intervention and aggressive treatment for GAD65-mediated neurological disorders and suggests cenobamate as a promising treatment option for GAD65-associated autoimmune epilepsy. [Extracted from the article]

We prove concurrent universal Padé approximation for several universal Padé approximants of several types. Our results are generic in the space of holomorphic functions, in the space of formal power series as well as in a subspace of A ∞. These results are valid for one center of expansion or for several centers as well. The Padé approximants allow generic approximation on arbitrary compact sets, not necessarily having connected component, in contrast with the partial sums of power series. We also establish affine genericity for a class of universal functions. [ABSTRACT FROM AUTHOR]