We consider an inverse problem of identifying an unknown cavity within an elastic material by a single boundary measurement. For this problem we show a conditional stability estimate.

In this note we determine explicitly the dimension of Kohnen's spaces of half integral weight with odd square free level and arbitrary character $\chi$, and show that it coincides with that of spaces of modular cusp forms of weight $2k$ with square free level and character $\chi^2$.

We present a new type of rational octic reciprocity law, which is different from the one discovered by Williams.

Simplified proof of an order preserving operator inequality is given.