Total orderIn mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation on some set , which satisfies the following for all and in : (reflexive). If and then (transitive). If and then (antisymmetric). or (strongly connected, formerly called total). Reflexivity (1.) already follows from connectedness (4.), but is required explicitly by many authors nevertheless, to indicate the kinship to partial orders.
Lexicographic orderIn mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences of different lengths by comparing the lengths of the sequences before considering their elements.
FerricyanideFerricyanide is the anion [Fe(CN)6]3−. It is also called hexacyanoferrate(III) and in rare, but systematic nomenclature, hexacyanidoferrate(III). The most common salt of this anion is potassium ferricyanide, a red crystalline material that is used as an oxidant in organic chemistry. [Fe(CN)6]3− consists of a Fe3+ center bound in octahedral geometry to six cyanide ligands. The complex has Oh symmetry. The iron is low spin and easily reduced to the related ferrocyanide ion [Fe(CN)6]4−, which is a ferrous (Fe2+) derivative.
Order isomorphismIn the mathematical field of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets (posets). Whenever two posets are order isomorphic, they can be considered to be "essentially the same" in the sense that either of the orders can be obtained from the other just by renaming of elements. Two strictly weaker notions that relate to order isomorphisms are order embeddings and Galois connections.
Steady-state modelIn cosmology, the steady-state model or steady state theory is an alternative to the Big Bang theory of evolution of the universe. In the steady-state model, the density of matter in the expanding universe remains unchanged due to a continuous creation of matter, thus adhering to the perfect cosmological principle, a principle that says that the observable universe is always the same at any time and any place. From the 1940s to the 1960s, the astrophysical community was divided between supporters of the Big Bang theory and supporters of the steady-state theory.
Photocatalytic water splittingPhotocatalytic water splitting is a process that uses photocatalysis for the dissociation of water (H2O) into hydrogen (H2) and oxygen (O2). Only light energy (photons), water, and a catalyst(s) are needed, since this is what naturally occurs in natural photosynthetic oxygen production and CO2 fixation. Photocatalytic water splitting is done by dispersing photocatalyst particles in water or depositing them on a substrate, unlike Photoelectrochemical cell, which are assembled into a cell with a photoelectrode.
Prussian bluePrussian blue also known as Berlin blue, Brandenburg blue, Parisian and Paris blue is a dark blue pigment produced by oxidation of ferrous ferrocyanide salts. It has the chemical formula Fe[Fe(CN)]. Turnbull's blue is chemically identical, but is made from different reagents, and its slightly different color stems from different impurities and particle sizes. Prussian blue was created in the early 18th century and is the first modern synthetic pigment. It is prepared as a very fine colloidal dispersion, because the compound is not soluble in water.
Equilibrium constantThe equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency towards further change. For a given set of reaction conditions, the equilibrium constant is independent of the initial analytical concentrations of the reactant and product species in the mixture.
Order topologyIn mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets. If X is a totally ordered set, the order topology on X is generated by the subbase of "open rays" for all a, b in X. Provided X has at least two elements, this is equivalent to saying that the open intervals together with the above rays form a base for the order topology.
Electrolysis of waterElectrolysis of water is using electricity to split water into oxygen (O2) and hydrogen (H2) gas by electrolysis. Hydrogen gas released in this way can be used as hydrogen fuel, but must be kept apart from the oxygen as the mixture would be extremely explosive. Separately pressurised into convenient 'tanks' or 'gas bottles', hydrogen can be used for oxyhydrogen welding and other applications, as the hydrogen / oxygen flame can reach circa 2,800°C. Water electrolysis requires a minimum potential difference of 1.
