Exterior square gamma factors for cuspidal representations of $$\mathrm {GL}_n$$ GL n : simple supercuspidal representations

We compute the local twisted exterior square gamma factors for simple supercuspidal representations, using which we prove a local converse theorem for simple supercuspidal representations.

     

Sodium acetate tri-hydrate whiskers

A new kind of whisker, which has not been previously reported in the literature, was grown on membranes which were in contact with a saturated aqueous solution of sodium acetate, using several techniques. Cellulose acetate membranes were used in all the cases and growth was successful at 25 ± 2°C and 45–55% relative humidity. A dense colony of whiskers, sometimes stuck together in bundles, usually up to 5 cm in length and ranging in width from 0.3–100 μm, developed within 72 h of growth. The whiskers were identified as sodium acetate tri-hydrate by means of Debye-Scherrer X-ray powder method. Laue transmission photographs indicated the existence of twin crystals within the individual single crystal whiskers as proved by electron diffraction in TEM. Some whiskers included internal and external channels, and there were several secondary effects, such as thickening in the middle of a whisker, formation of arrow-heads or spirals at the tips and various modes of branching. The whisker morphology and the various growth phenomena may be explained as a whisker growth process from their bases, when we consider a continuous crystallization from material which is supplied through and over the membrane.