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Generator (mathematics) The 5th roots of unity in the complex plane under multiplication form a group of order 5. Each non-identity element by itself is a generator for the whole group. In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. The underlying concept in each case is that ...
Generating functions are sometimes called generating series, in that a series of terms can be said to be the generator of its sequence of term coefficients. Definitions [ edit ] A generating function is a device somewhat similar to a bag.
In electricity generation, a generator [1] is a device that converts motion-based power ( potential and kinetic energy) or fuel-based power ( chemical energy) into electric power for use in an external circuit. Sources of mechanical energy include steam turbines, gas turbines, water turbines, internal combustion engines, wind turbines and even ...
In abstract algebra, a generating set of a group is a subset of the group set such that every element of the group can be expressed as a combination (under the group operation) of finitely many elements of the subset and their inverses . In other words, if is a subset of a group , then , the subgroup generated by , is the smallest subgroup of ...
The affine group of one dimension is a two-dimensional matrix Lie group, consisting of. 2 × 2 {\displaystyle 2\times 2} real, upper-triangular matrices, with the first diagonal entry being positive and the second diagonal entry being 1. Thus, the group consists of matrices of the form.
Faraday's law of induction (or simply Faraday's law) is a law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (emf). This phenomenon, known as electromagnetic induction, is the fundamental operating principle of transformers, inductors, and many types of electric ...
Term Explanation and discussion References and related terms Labyrinth seal Strips and grooves on a shaft that provide a torturous path for sealing steam. Used in sealing of steam on turbine shafts, and sealing of oil and hydrogen on generator shafts. Gland seal
In mathematics, a Lie algebra (pronounced / liː / LEE) is a vector space together with an operation called the Lie bracket, an alternating bilinear map , that satisfies the Jacobi identity. In other words, a Lie algebra is an algebra over a field for which the multiplication operation (called the Lie bracket) is alternating and satisfies the ...