Information on GH in relation to epilepsy is sparse, and to our knowledge there is no information on GH levels during status epilepticus in man. We studied GH in serum in six patients during status epilepticus, and in a control group of six seizure-free patients with epilepsy, before and after injection of TRH. The baseline GH values before TRH administration were within the normal range in all...

Abstract When $k\geqslant 4$ and $0\leqslant d\leqslant (k-2)/4$ , we consider the system of Diophantine equations \begin{align*}x_1^j+\ldots +x_k^j=y_1^j+\ldots +y_k^j\quad (1\leqslant j\leqslant k,\, j\ne k-d).\end{align*} We show that in this cousin a Vinogradov system, there is paucity non-diagonal positive integral solutions. Our quantitative estimates are particularly sharp when $d=o\!\le...

Given a family $$\varphi = (\varphi_1, \ldots, \varphi_d)\in \mathbb{Z}[T]^d$$ of d distinct nonconstant polynomials, positive integer $$k\le d$$ and real parameter $$\rho$$ , we consider the mean value $$M_{k, \rho} (\varphi, N) \int_{{\rm x} \in [0,1]^k} \sup_{{\rm y} [0,1]^{d-k}} | S_{\varphi}({\rm x}, {\rm y}; |^\rho \,d{\rm $$ of exponential sums $$S_{\varphi}({\rm \sum_{n=1}^{N} \...