Phase portraitIn mathematics, a phase portrait is a geometric representation of the trajectories of a dynamical system in the phase plane. Each set of initial conditions is represented by a different point or curve. Phase portraits are an invaluable tool in studying dynamical systems. They consist of a plot of typical trajectories in the phase space. This reveals information such as whether an attractor, a repellor or limit cycle is present for the chosen parameter value.
Bootleg recordingA bootleg recording is an audio or video recording of a performance not officially released by the artist or under other legal authority. Making and distributing such recordings is known as bootlegging. Recordings may be copied and traded among fans without financial exchange, but some bootleggers have sold recordings for profit, sometimes by adding professional-quality sound engineering and packaging to the raw material. Bootlegs usually consist of unreleased studio recordings, live performances or interviews without the quality control of official releases.
Sodium fluorideSodium fluoride (NaF) is an inorganic compound with the formula . It is a colorless or white solid that is readily soluble in water. It is used in trace amounts in the fluoridation of drinking water to prevent tooth decay, and in toothpastes and topical pharmaceuticals for the same purpose. In 2020, it was the 265th most commonly prescribed medication in the United States, with more than 1 million prescriptions. It is also used in metallurgy and in medical imaging.
Sodium iodideSodium iodide (chemical formula NaI) is an ionic compound formed from the chemical reaction of sodium metal and iodine. Under standard conditions, it is a white, water-soluble solid comprising a 1:1 mix of sodium cations (Na+) and iodide anions (I−) in a crystal lattice. It is used mainly as a nutritional supplement and in organic chemistry. It is produced industrially as the salt formed when acidic iodides react with sodium hydroxide. It is a chaotropic salt.
