Fixed Points (mathematics)
Fixed point may refer to: * Fixed point (mathematics), a value that does not change under a given transformation * Fixed-point arithmetic, a manner of doing arithmetic on computers * Fixed point, a benchmark (surveying) used by geodesists * Fixed point join, also called a recursive join * Fixed point, in quantum field theory, a coupling where the beta function vanishes – see * Temperature reference point, usually defined by a phase change or triple point In thermodynamics, the triple point of a substance is the temperature and pressure at which the three Phase (matter), phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium.. It is that temperature and pressure at ...

Fixed Point (mathematics)
In mathematics, a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation (mathematics), transformation. Specifically, for function (mathematics), functions, a fixed point is an element that is mapped to itself by the function. Any set of fixed points of a transformation is also an invariant set. Fixed point of a function Formally, is a fixed point of a function if belongs to both the domain of a function, domain and the codomain of , and . In particular, cannot have any fixed point if its domain is disjoint from its codomain. If is defined on the real numbers, it corresponds, in graphical terms, to a curve in the Euclidean plane, and each fixed-point corresponds to an intersection of the curve with the line , cf. picture. For example, if is defined on the real numbers by f(x) = x^2 - 3 x + 4, then 2 is a fixed point of , because . Not all functions have fixed points: for example, ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Fixed-point Arithmetic
In computing, fixed-point is a method of representing fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. Dollar amounts, for example, are often stored with exactly two fractional digits, representing the cents (1/100 of dollar). More generally, the term may refer to representing fractional values as integer multiples of some fixed small unit, e.g. a fractional amount of hours as an integer multiple of ten-minute intervals. Fixed-point number representation is often contrasted to the more complicated and computationally demanding floating-point representation. In the fixed-point representation, the fraction is often expressed in the same number base as the integer part, but using negative powers of the base ''b''. The most common variants are decimal (base 10) and binary (base 2). The latter is commonly known also as binary scaling. Thus, if ''n'' fraction digits are stored, the value will always be an integer multiple of ' ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Benchmark (surveying)
The term benchmark, bench mark, or survey benchmark originates from the chiseled horizontal marks that surveyors made in stone structures, into which an angle iron could be placed to form a "bench" for a leveling rod, thus ensuring that a leveling rod could be accurately repositioned in the same place in the future. These marks were usually indicated with a chiseled arrow – specifically a broad arrow – below the horizontal line. A benchmark is a type of survey marker. The term is generally applied to any item used to mark a point as an elevation reference. Frequently, bronze or aluminum disks are set in stone or concrete, or on rods driven deeply into the earth to provide a stable elevation point. If an elevation is marked on a map, but there is no physical mark on the ground, it is a spot height. Purpose The height of a benchmark is calculated relative to the heights of nearby benchmarks in a network extending from a ''fundamental benchmark''. A fundamental benchma ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Recursive Join
The recursive join is an operation used in relational databases, also sometimes called a "fixed-point join". It is a compound operation that involves repeating the join operation, typically accumulating more records each time, until a repetition makes no change to the results (as compared to the results of the previous iteration). For example, if a database of family relationships is to be searched, and the record for each person has "mother" and "father" fields, a recursive join would be one way to retrieve all of a person's known ancestors: first the person's direct parents' records would be retrieved, then the parents' information would be used to retrieve the grandparents' records, and so on until no new records are being found. In this example, as in many real cases, the repetition involves only a single database table, and so is more specifically a "recursive self-join". Recursive joins can be very time-consuming unless optimized through indexing, the addition of extra key ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Temperature Reference Point
Scale of temperature is a methodology of calibrating the physical quantity temperature in metrology. Empirical scales measure temperature in relation to convenient and stable parameters or reference points, such as the freezing and boiling point of water. Absolute temperature is based on thermodynamic principles: using the lowest possible temperature as the zero point, and selecting a convenient incremental unit. Celsius, Kelvin, and Fahrenheit are common temperature scales. Other scales used throughout history include Rankine, Rømer, Newton, Delisle, Réaumur, Gas mark, Leiden, and Wedgwood. Technical definition The zeroth law of thermodynamics describes thermal equilibrium between thermodynamic systems in form of an equivalence relation. Accordingly, the set of all thermal systems may be divided into a quotient set of equivalence classes, denoted as M, where any element of M collects all systems that are in thermal equilibrium with one another. If the set M has cardina ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]