Gemstone irradiation produce mixtures of blue and yellow-to-brown colors, so heating is required as an additional procedure to remove the yellowish color. In some cases, the new colors induced by artificial irradiation may fade rapidly when exposed to light or gentle heat, so some laboratories submit them to a "fade test" to determine color stability. Sometimes colorless or pink beryls become deep blue upon irradiation, which are called Maxixe-type beryl. However, the color easily fades when exposed to heat or light, so it has no practical jewelry application. Gemstone irradiation The gemstone irradiation is a process in which a gemstone is artificially
History of manifolds and varieties History of manifolds and varieties The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology. Certain special classes of manifolds also have additional algebraic structure; they may behave like groups, for instance. In that case, they are called Lie Groups. Alternatively, they may be described by polynomial equations, in which case they are called algebraic varieties, and if they additionally carry a group structure, they are called algebraic groups. The term "manifold" comes from German "Mannigfaltigkeit," by Riemann. In English, "manifold" refers to