Functional (mathematics)In mathematics, a functional (as a noun) is a certain type of function. The exact definition of the term varies depending on the subfield (and sometimes even the author). In linear algebra, it is synonymous with linear forms, which are linear mappings from a vector space into its field of scalars (that is, they are elements of the dual space ) In functional analysis and related fields, it refers more generally to a mapping from a space into the field of real or complex numbers.
Formal schemeIn mathematics, specifically in algebraic geometry, a formal scheme is a type of space which includes data about its surroundings. Unlike an ordinary scheme, a formal scheme includes infinitesimal data that, in effect, points in a direction off of the scheme. For this reason, formal schemes frequently appear in topics such as deformation theory. But the concept is also used to prove a theorem such as the theorem on formal functions, which is used to deduce theorems of interest for usual schemes.
Linear formIn mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars (often, the real numbers or the complex numbers). If V is a vector space over a field k, the set of all linear functionals from V to k is itself a vector space over k with addition and scalar multiplication defined pointwise. This space is called the dual space of V, or sometimes the algebraic dual space, when a topological dual space is also considered.
Fiber product of schemesIn mathematics, specifically in algebraic geometry, the fiber product of schemes is a fundamental construction. It has many interpretations and special cases. For example, the fiber product describes how an algebraic variety over one field determines a variety over a bigger field, or the pullback of a family of varieties, or a fiber of a family of varieties. Base change is a closely related notion. The of schemes is a broad setting for algebraic geometry.
Hybrid trainA hybrid train is a locomotive, railcar or train that uses an onboard rechargeable energy storage system (RESS), placed between the power source (often a diesel engine prime mover) and the traction transmission system connected to the wheels. Since most diesel locomotives are diesel-electric, they have all the components of a series hybrid transmission except the storage battery, making this a relatively simple prospect. Surplus energy from the power source, or energy derived from regenerative braking, charges the storage system.
Electrode potentialIn electrochemistry, electrode potential is the electromotive force of a galvanic cell built from a standard reference electrode and another electrode to be characterized. By convention, the reference electrode is the standard hydrogen electrode (SHE). It is defined to have a potential of zero volts. It may also be defined as the potential difference between the charged metallic rods and salt solution. The electrode potential has its origin in the potential difference developed at the interface between the electrode and the electrolyte.
Hybrid (biology)In biology, a hybrid is the offspring resulting from combining the qualities of two organisms of different varieties, species or genera through sexual reproduction. Generally, it means that each cell has genetic material from two different organisms, whereas an individual where some cells are derived from a different organism is called a chimera. Hybrids are not always intermediates between their parents (such as in blending inheritance), but can show hybrid vigor, sometimes growing larger or taller than either parent.
Foreign exchange reservesForeign exchange reserves (also called forex reserves or FX reserves) are cash and other reserve assets such as gold held by a central bank or other monetary authority that are primarily available to balance payments of the country, influence the foreign exchange rate of its currency, and to maintain confidence in financial markets. Reserves are held in one or more reserve currencies, nowadays mostly the United States dollar and to a lesser extent the euro.
Bell's theoremBell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement. "Local" here refers to the principle of locality, the idea that a particle can only be influenced by its immediate surroundings, and that interactions mediated by physical fields cannot propagate faster than the speed of light.
Ion exchangeIon exchange is a reversible interchange of one kind of ion present in an insoluble solid with another of like charge present in a solution surrounding the solid with the reaction being used especially for softening or making water demineralised, the purification of chemicals and separation of substances. Ion exchange usually describes a process of purification of aqueous solutions using solid polymeric ion-exchange resin. More precisely, the term encompasses a large variety of processes where ions are exchanged between two electrolytes.
