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.
Continuous functionIn mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value, known as discontinuities. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is .
Electric arc furnaceAn electric arc furnace (EAF) is a furnace that heats material by means of an electric arc. Industrial arc furnaces range in size from small units of approximately one-tonne capacity (used in foundries for producing cast iron products) up to about 400-tonne units used for secondary steelmaking. Arc furnaces used in research laboratories and by dentists may have a capacity of only a few dozen grams. Industrial electric arc furnace temperatures can reach , while laboratory units can exceed .
Sequence spaceIn functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers. The set of all such functions is naturally identified with the set of all possible infinite sequences with elements in K, and can be turned into a vector space under the operations of pointwise addition of functions and pointwise scalar multiplication.
Electromagnetic interferenceElectromagnetic interference (EMI), also called radio-frequency interference (RFI) when in the radio frequency spectrum, is a disturbance generated by an external source that affects an electrical circuit by electromagnetic induction, electrostatic coupling, or conduction. The disturbance may degrade the performance of the circuit or even stop it from functioning. In the case of a data path, these effects can range from an increase in error rate to a total loss of the data.
Transcendental functionIn mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function. In other words, a transcendental function "transcends" algebra in that it cannot be expressed algebraically. Examples of transcendental functions include the exponential function, the logarithm, and the trigonometric functions. Formally, an analytic function f (z) of one real or complex variable z is transcendental if it is algebraically independent of that variable.
Standard basisIn mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as or ) is the set of vectors, each of whose components are all zero, except one that equals 1. For example, in the case of the Euclidean plane formed by the pairs (x, y) of real numbers, the standard basis is formed by the vectors Similarly, the standard basis for the three-dimensional space is formed by vectors Here the vector ex points in the x direction, the vector ey points in the y direction, and the vector ez points in the z direction.
Cross section (physics)In physics, the cross section is a measure of the probability that a specific process will take place when some kind of radiant excitation (e.g. a particle beam, sound wave, light, or an X-ray) intersects a localized phenomenon (e.g. a particle or density fluctuation). For example, the Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus. Cross section is typically denoted σ (sigma) and is expressed in units of area, more specifically in barns.
AluminiumAluminium (aluminum in North American English) is a chemical element with the symbol Al and atomic number 13. Aluminium has a density lower than those of other common metals; about one-third that of steel. It has a great affinity towards oxygen, forming a protective layer of oxide on the surface when exposed to air. Aluminium visually resembles silver, both in its color and in its great ability to reflect light. It is soft, nonmagnetic and ductile.
Experimental evolutionExperimental evolution is the use of laboratory experiments or controlled field manipulations to explore evolutionary dynamics. Evolution may be observed in the laboratory as individuals/populations adapt to new environmental conditions by natural selection. There are two different ways in which adaptation can arise in experimental evolution. One is via an individual organism gaining a novel beneficial mutation. The other is from allele frequency change in standing genetic variation already present in a population of organisms.
Beta functionIn mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial coefficients. It is defined by the integral for complex number inputs such that . The beta function was studied by Leonhard Euler and Adrien-Marie Legendre and was given its name by Jacques Binet; its symbol Β is a Greek capital beta. The beta function is symmetric, meaning that for all inputs and .
Neutron cross sectionIn nuclear physics, the concept of a neutron cross section is used to express the likelihood of interaction between an incident neutron and a target nucleus. The neutron cross section σ can be defined as the area in cm2 for which the number of neutron-nuclei reactions taking place is equal to the product of the number of incident neutrons that would pass through the area and the number of target nuclei. In conjunction with the neutron flux, it enables the calculation of the reaction rate, for example to derive the thermal power of a nuclear power plant.
