Goitre in iodine in the soil. For example, in the English Midlands, the condition was known as Derbyshire Neck. In the United States, goitre was found in the Great Lakes, Midwest, and Intermountain regions. The condition now is practically absent in affluent nations, where table salt is supplemented with iodine. However, it is still prevalent in India, China, Central Asia, and Central Africa. Goitre had been prevalent in the alpine countries for a long time. Switzerland reduced the condition by introducing iodised salt in 1922. The Bavarian tracht in the Miesbach and Salzburg regions, which appeared in the 19th century, includes
Trace field of a representation that for Fuchsian groups. One big difference is that the trace field of a group of finite covolume is always a number field. When considering subgroups of general Lie groups (which are not necessarily defined as a matrix groups) one has to use a linear representation of the group to take traces of elements. The most natural one is the adjoint representation. It turns out that for applications it is better, even for groups which have a natural lower-dimensional linear representation (such as the special linear groups formula_30), to always define the trace field using the adjoint representation. Thus we