Fermi's interactionIn particle physics, Fermi's interaction (also the Fermi theory of beta decay or the Fermi four-fermion interaction) is an explanation of the beta decay, proposed by Enrico Fermi in 1933. The theory posits four fermions directly interacting with one another (at one vertex of the associated Feynman diagram). This interaction explains beta decay of a neutron by direct coupling of a neutron with an electron, a neutrino (later determined to be an antineutrino) and a proton.
Symmetric matrixIn linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, Because equal matrices have equal dimensions, only square matrices can be symmetric. The entries of a symmetric matrix are symmetric with respect to the main diagonal. So if denotes the entry in the th row and th column then for all indices and Every square diagonal matrix is symmetric, since all off-diagonal elements are zero. Similarly in characteristic different from 2, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative.
Standard solar modelThe standard solar model (SSM) is a mathematical treatment of the Sun as a spherical ball of gas (in varying states of ionisation, with the hydrogen in the deep interior being a completely ionised plasma). This model, technically the spherically symmetric quasi-static model of a star, has stellar structure described by several differential equations derived from basic physical principles. The model is constrained by boundary conditions, namely the luminosity, radius, age and composition of the Sun, which are well determined.
Electron captureElectron capture (K-electron capture, also K-capture, or L-electron capture, L-capture) is a process in which the proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron, usually from the K or L electron shells. This process thereby changes a nuclear proton to a neutron and simultaneously causes the emission of an electron neutrino. Proton + Electron → Neutron + Electron Neutrino or when written as a nuclear reaction equation, ^{0}{-1}e + ^{1}{1}p -> ^{1}{0}n + ^{0}{0} ν Since this single emitted neutrino carries the entire decay energy, it has this single characteristic energy.
Matrix decompositionIn the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems. In numerical analysis, different decompositions are used to implement efficient matrix algorithms. For instance, when solving a system of linear equations , the matrix A can be decomposed via the LU decomposition.
Unitary groupIn mathematics, the unitary group of degree n, denoted U(n), is the group of n × n unitary matrices, with the group operation of matrix multiplication. The unitary group is a subgroup of the general linear group GL(n, C). Hyperorthogonal group is an archaic name for the unitary group, especially over finite fields. For the group of unitary matrices with determinant 1, see Special unitary group. In the simple case n = 1, the group U(1) corresponds to the circle group, consisting of all complex numbers with absolute value 1, under multiplication.
Decay chainIn nuclear science, the decay chain refers to a series of radioactive decays of different radioactive decay products as a sequential series of transformations. It is also known as a "radioactive cascade". The typical radioisotope does not decay directly to a stable state, but rather it decays to another radioisotope. Thus there is usually a series of decays until the atom has become a stable isotope, meaning that the nucleus of the atom has reached a stable state. Decay stages are referred to by their relationship to previous or subsequent stages.
Diagonalizable matrixIn linear algebra, a square matrix is called diagonalizable or non-defective if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix and a diagonal matrix such that , or equivalently . (Such , are not unique.) For a finite-dimensional vector space , a linear map is called diagonalizable if there exists an ordered basis of consisting of eigenvectors of .
Neutrino astronomyNeutrino astronomy is the branch of astronomy that observes astronomical objects with neutrino detectors in special observatories. Neutrinos are created as a result of certain types of radioactive decay, nuclear reactions such as those that take place in the Sun or high energy astrophysical phenomena, in nuclear reactors, or when cosmic rays hit atoms in the atmosphere. Neutrinos rarely interact with matter, meaning that it is unlikely for them to scatter along their trajectory, unlike photons.
Square root of a matrixIn mathematics, the square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if the matrix product BB is equal to A. Some authors use the name square root or the notation A1/2 only for the specific case when A is positive semidefinite, to denote the unique matrix B that is positive semidefinite and such that BB = BTB = A (for real-valued matrices, where BT is the transpose of B).
Sino-Tibetan languagesSino-Tibetan, also cited as Trans-Himalayan in a few sources, is a family of more than 400 languages, second only to Indo-European in number of native speakers. The vast majority of these are the 1.3 billion native speakers of Sinitic languages. Other Sino-Tibetan languages with large numbers of speakers include Burmese (33 million) and the Tibetic languages (6 million). Other languages of the family are spoken in the Himalayas, the Southeast Asian Massif, and the eastern edge of the Tibetan Plateau.
Basis (linear algebra)In mathematics, a set B of vectors in a vector space V is called a basis (: bases) if every element of V may be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B. The elements of a basis are called . Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B.
