Random variableA random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. The term 'random variable' can be misleading as it is not actually random nor a variable, but rather it is a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads and tails ) in a sample space (e.g., the set ) to a measurable space (e.g., in which 1 corresponding to and −1 corresponding to ), often to the real numbers.
LU decompositionIn numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination. Computers usually solve square systems of linear equations using LU decomposition, and it is also a key step when inverting a matrix or computing the determinant of a matrix.
Peaceful nuclear explosionPeaceful nuclear explosions (PNEs) are nuclear explosions conducted for non-military purposes. Proposed uses include excavation for the building of canals and harbours, electrical generation, the use of nuclear explosions to drive spacecraft, and as a form of wide-area fracking. PNEs were an area of some research from the late 1950s into the 1980s, primarily in the United States and Soviet Union. In the U.S., a series of tests were carried out under Project Plowshare.
Nuclear weapon yieldThe explosive yield of a nuclear weapon is the amount of energy released such as blast, thermal, and nuclear radiation, when that particular nuclear weapon is detonated, usually expressed as a TNT equivalent (the standardized equivalent mass of trinitrotoluene which, if detonated, would produce the same energy discharge), either in kilotonnes (kt—thousands of tonnes of TNT), in megatonnes (Mt—millions of tonnes of TNT), or sometimes in terajoules (TJ). An explosive yield of one terajoule is equal to .
Nuclear powerNuclear power is the use of nuclear reactions to produce electricity. Nuclear power can be obtained from nuclear fission, nuclear decay and nuclear fusion reactions. Presently, the vast majority of electricity from nuclear power is produced by nuclear fission of uranium and plutonium in nuclear power plants. Nuclear decay processes are used in niche applications such as radioisotope thermoelectric generators in some space probes such as Voyager 2. Generating electricity from fusion power remains the focus of international research.
Nuclear weapons testingNuclear weapons tests are experiments carried out to determine the performance, yield, and effects of nuclear weapons. Testing nuclear weapons offers practical information about how the weapons function, how detonations are affected by different conditions, and how personnel, structures, and equipment are affected when subjected to nuclear explosions. However, nuclear testing has often been used as an indicator of scientific and military strength.
Complex random variableIn probability theory and statistics, complex random variables are a generalization of real-valued random variables to complex numbers, i.e. the possible values a complex random variable may take are complex numbers. Complex random variables can always be considered as pairs of real random variables: their real and imaginary parts. Therefore, the distribution of one complex random variable may be interpreted as the joint distribution of two real random variables.
Uncertainty principleIn quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the product of the accuracy of certain related pairs of measurements on a quantum system, such as position, x, and momentum, p. Such paired-variables are known as complementary variables or canonically conjugate variables.
Uncertainty quantificationUncertainty quantification (UQ) is the science of quantitative characterization and estimation of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known. An example would be to predict the acceleration of a human body in a head-on crash with another car: even if the speed was exactly known, small differences in the manufacturing of individual cars, how tightly every bolt has been tightened, etc.
Nuclear falloutNuclear fallout is the residual radioactive material propelled into the upper atmosphere following a nuclear blast, so called because it "falls out" of the sky after the explosion and the shock wave has passed. It commonly refers to the radioactive dust and ash created when a nuclear weapon explodes. The amount and spread of fallout is a product of the size of the weapon and the altitude at which it is detonated.
