Crystal systemIn crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices. Space groups are classified into crystal systems according to their point groups, and into lattice systems according to their Bravais lattices. Crystal systems that have space groups assigned to a common lattice system are combined into a crystal family. The seven crystal systems are triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic.
Point reflectionIn geometry, a point reflection (also called a point inversion or central inversion) is an transformation of affine space in which every point is reflected across a specific fixed point. A point reflection is an involution: applying it twice is the identity transformation. It is equivalent to a homothetic transformation with scale factor −1. The point of inversion is also called homothetic center. An object that is invariant under a point reflection is said to possess point symmetry; if it is invariant under point reflection through its center, it is said to possess central symmetry or to be centrally symmetric.
Hydrogen fluorideHydrogen fluoride (fluorane) is an inorganic compound with chemical formula . It is a very poisonous, colorless gas or liquid that dissolves in water to yield an aqueous solution termed hydrofluoric acid. It is the principal industrial source of fluorine, often in the form of hydrofluoric acid, and is an important feedstock in the preparation of many important compounds including pharmaceuticals and polymers, e.g. polytetrafluoroethylene (PTFE). HF is also widely used in the petrochemical industry as a component of superacids.
CyclohexaneCyclohexane is a cycloalkane with the molecular formula . Cyclohexane is non-polar. Cyclohexane is a colourless, flammable liquid with a distinctive detergent-like odor, reminiscent of cleaning products (in which it is sometimes used). Cyclohexane is mainly used for the industrial production of adipic acid and caprolactam, which are precursors to nylon. Cyclohexyl () is the alkyl substituent of cyclohexane and is abbreviated Cy. On an industrial scale, cyclohexane is produced by hydrogenation of benzene in the presence of a Raney nickel catalyst.
Newman projectionA Newman projection is a drawing that helps visualize the 3-dimensional structure of a molecule. This projection most commonly sights down a carbon-carbon bond, making it a very useful way to visualize the stereochemistry of alkanes. A Newman projection visualizes the conformation of a chemical bond from front to back, with the front atom represented by the intersection of three lines (a dot) and the back atom as a circle. The front atom is called proximal, while the back atom is called distal.
Flat moduleIn algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion free modules. Formally, a module M over a ring R is flat if taking the tensor product over R with M preserves exact sequences. A module is faithfully flat if taking the tensor product with a sequence produces an exact sequence if and only if the original sequence is exact. Flatness was introduced by in his paper Géometrie Algébrique et Géométrie Analytique.
Coherent sheafIn mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. The definition of coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information. Coherent sheaves can be seen as a generalization of vector bundles. Unlike vector bundles, they form an , and so they are closed under operations such as taking , , and cokernels.
Liquid hydrogenLiquid hydrogen (H2(l)) is the liquid state of the element hydrogen. Hydrogen is found naturally in the molecular H2 form. To exist as a liquid, H2 must be cooled below its critical point of 33 K. However, for it to be in a fully liquid state at atmospheric pressure, H2 needs to be cooled to . A common method of obtaining liquid hydrogen involves a compressor resembling a jet engine in both appearance and principle. Liquid hydrogen is typically used as a concentrated form of hydrogen storage.
Base change theoremsIn mathematics, the base change theorems relate the and the of sheaves. More precisely, they are about the base change map, given by the following natural transformation of sheaves: where is a of topological spaces and is a sheaf on X. Such theorems exist in different branches of geometry: for (essentially arbitrary) topological spaces and proper maps f, in algebraic geometry for (quasi-)coherent sheaves and f proper or g flat, similarly in analytic geometry, but also for étale sheaves for f proper or g smooth.
Hydrogen productionHydrogen production is the family of industrial methods for generating hydrogen gas. As of 2020, the majority of hydrogen (~95%) is produced from fossil fuels by steam reforming of natural gas and other light hydrocarbons, partial oxidation of heavier hydrocarbons, and coal gasification. Other methods of hydrogen production include biomass gasification, methane pyrolysis, and electrolysis of water. Methane pyrolysis and water electrolysis can use any source of electricity including solar power.
