Micronutrient deficiency Micronutrient deficiency Micronutrient deficiency or dietary deficiency is not enough of one or more of the micronutrients required for optimal plant or animal health. In humans and other animals they include both vitamin deficiencies and mineral deficiencies, whereas in plants the term refers to deficiencies of essential trace minerals. Micronutrient deficiencies affect more than two billion people of all ages in both developing and industrialized countries. They are the cause of some diseases, exacerbate others and are recognized as having an important impact on worldwide health. Important micronutrients include iodine, iron, zinc, calcium, selenium, fluorine, and vitamins A, B, B,
Trace field of a representation Trace field of a representation In mathematics, the trace field of a linear group is the field generated by the traces of its elements. It is mostly studied for Kleinian and Fuchsian groups, though related objects are used in the theory of lattices in Lie groups, often under the name "field of definition". Fuchsian groups are discrete subgroups of formula_1. The trace of an element in formula_1 is well-defined up to sign (by taking the trace of an arbitrary preimage in formula_3) and the "trace field" of formula_4 is the field generated over formula_5 by the traces of all elements