A generalization of finite-dimensional Euclidean spaces different from Hilbert spaces
In mathematics, nuclear spaces are topological vector spaces that can be viewed as a generalization of finite-dimensional Euclidean spaces and share many of their desirable properties. Nuclear spaces are however quite different from Hilbert spaces, another generalization of finite-dimensional Euclidean spaces. They were introduced by Alexander Grothendieck.
The topology on nuclear spaces can be defined by a family of seminorms whose unit balls decrease rapidly in size. Vector spaces whose elements are "smooth" in some sense tend to be nuclear spaces; a typical example of a nuclear space is the set of smooth functions on a compact manifold. All finite-dimensional vector spaces are nuclear. There are no Banach spaces that are nuclear, except for the finite-dimensional ones. In practice a sort of converse to this is often true: if a "naturally occurring" topological vector space is not a Banach space, then there is a good chance that it is nuclear.
mathematics, nuclearspaces are topological vector spaces that can be viewed as a generalization of finite-dimensional Euclidean spaces and share many...
Nuclear power in space is the use of nuclear power in outer space, typically either small fission systems or radioactive decay for electricity or heat...
on Space Shuttle development. Although more than ten reactors of varying power output have been built and tested, as of 2023[update], no nuclear thermal...
material. The nuclear envelope consists of two lipid bilayer membranes: an inner nuclear membrane and an outer nuclear membrane. The space between the membranes...
fueled nuclear reactors that can provide propulsion for long periods without refueling. There are also applications in the space sector with nuclear thermal...
list of nuclear power systems in space includes 81 nuclear power systems that were flown to space, or at least launched in an attempt to reach space. Such...
Nuclear weapons tests are experiments carried out to determine the performance, yield, and effects of nuclear weapons. Testing nuclear weapons offers practical...
kernel on a Banach spacePages displaying wikidata descriptions as a fallback Injective tensor product Nuclear operator Nuclearspace – A generalization...
Strategic Defense Initiative (SDI), a space-based system to protect the United States from attack by strategic nuclear missiles. The plan was ridiculed by...
a technology base for nuclear rocket engine systems to be utilized in the design and development of propulsion systems for space mission application"....
(2011), SpaceNuclear Fission Electric Power Systems: Book 3: SpaceNuclear Propulsion and Power Joseph A. Angelo & David Buden (1985), SpaceNuclear Power...
Nuclear marine propulsion is propulsion of a ship or submarine with heat provided by a nuclear reactor. The power plant heats water to produce steam for...
use very different nuclear reactions. Nuclear power reactors (including the miniaturized ones used in space) perform controlled nuclear fission in a chain...
1963 Treaty Banning Nuclear Weapon Tests in the Atmosphere, in Outer Space and Under Water, prohibited all test detonations of nuclear weapons except for...
The United States SpaceNuclear Propulsion Office (SNPO) was a US government agency created in 1961 in response to NASA Marshall Space Flight Center's desire...
In mathematics, nuclear operators between Banach spaces are a linear operators between Banach spaces in infinite dimensions that share some of the properties...
A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission bomb) or a combination of fission...
United States conducted around 1,054 nuclear tests by official count, including 216 atmospheric, underwater, and space tests. Most of the tests took place...
strong dual space are also: complete Hausdorff locally convex spaces, nuclear Montel spaces, It is known that in the dual space of any Montel space, a sequence...
A nuclear holocaust, also known as a nuclear apocalypse, nuclear annihilation, nuclear armageddon, or atomic holocaust, is a theoretical scenario where...
to be demonstrated in space in 2027. The experimental vehicle is planned to be reusable and will utilize next-generation nuclear thermal propulsion technology...
might still have been used as a heavy lift launch vehicle for the nuclear ferry and space station modules. A special "Mars Excursion Module" would be the...
Nuclear power is the use of nuclear reactions to produce electricity. Nuclear power can be obtained from nuclear fission, nuclear decay and nuclear fusion...
vector spaces. For Hilbert spaces or nuclearspaces there is a simple well-behaved theory of tensor products (see Tensor product of Hilbert spaces), but...
from testing nuclear weapons in the atmosphere, underwater, or in outer space. The treaty permitted underground tests. Many other non-nuclear nations acceded...
of two topological vector spaces (TVSs) was introduced by Alexander Grothendieck and was used by him to define nuclearspaces. An injective tensor product...
Global Information