CONVERGENCE

In the absence of a more specific context, 'convergence' denotes the approach toward a definite value, as time goes on; or to a definite point, a common view or opinion, or toward a fixed or equilibrium state.

Contents

Mathematics

Natural sciences

Computing and technology

Social sciences

Religion

See also

Mathematics

In mathematics, 'convergence' describes limiting behaviour, particularly of an infinite sequence or series toward ''some'' limit. To assert convergence is to claim the existence of such a limit, which may be itself unknown. For any fixed standard of accuracy, however, you can always be sure to be within that limit, provided you have gone ''far enough''. The following lists more specific usages of this word:

★ Convergent sequence, a sequence which has a limit, see limit of a sequence.

★ Convergent series, a sequence of which the partial sums have a limit.

★ Convergent of a (possibly infinite) continued fraction.

★ Convergent net - a generalization of a convergent sequence.

★ Convergent filter - a generalization of a convergent net.

★ Integral test for convergence is a technique used to test infinite series of nonnegative terms for convergence.

★ Radius of convergence pertains to a domain interval over which a power series converges.

★ Uniform convergence pertains to pointwise convergence where the speed of convergence is independent of any value in the domain.

★ Monotone convergence theorem pertains to any one of several such theorems defined over a monotone sequence of numbers.

★ Convergence of random variables pertains to any one of several notions of convergence in probability theory.

★ Rate of convergence pertains to the "speed" at which a convergent sequence approaches its limit.

★ Absolute convergence pertains to whether the absolute value of the limit of a series or integral is finite.

★ Pointwise convergence is the convergence of functions' values at each specific input individually.

★ Gromov-Hausdorff convergence pertains to metric spaces and is a generalization of Hausdorff distance.

★ Convergence of Fourier series pertains to whether the Fourier series of a periodic function converges. Also known as classic harmonic analysis.

★ Dominated convergence theorem pertains to a theorem by Henri Lebesgue.

★ Convergence of a numerical method for solving differential equations.
The opposite of convergence is divergence. Divergence may be some kind of oscillation, unrestricted growth (recognised as the case of an infinite limit), or chaotic behavior. An infinite series that is divergent cannot be used for meaningful computations of its value. Nevertheless, divergent series can be summed formally, as generating functions or asymptotic series, or via some summation method.

Natural sciences

★ Convergent evolution pertains to organisms not closely related that independently acquire similar characteristics while evolving in separate and sometimes varying ecosystems.

★ Convergent synthesisis a strategy that aims to improve the efficiency of multi-step chemical synthesis.

★ Convergent boundary is a fault boundary defined in the specialty of geology known as plate tectonics.

★ Convergence zone in meteorology is an area where the horizontal wind produces a net in-flow of air

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★ South Pacific convergence zone is a belt of low pressure from the west Pacific warm pool

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★ Intertropical convergence zone is a belt of low pressure at the equator.

★ Convergence is the simultaneous inward movement of both eyes toward each other, usually in an effort to maintain single binocular vision when viewing an object.

Computing and technology

★ Convergence (converged environments/networks) defines a multi-media environment and/or network where signals regardless of type (i.e. voice, quality audio, video, data, etc.) and encoding methodology may be seamlessly exchanged between independent endpoints with similar characteristics. Convergence in this case requires the overall environment have two primary characteristics: 1) the intelligence to provide translation between disparate signal types and multipoint routing to establish connectivity between requested endpoints 2) The ability to dynamically allocate required bandwidth to support endpoint requirements for each requested session. Convergence as defined by this is independent of signal format and transport media.
:Convergence (converged environments/networks), as such, was formally defined in January 1992 by Phillip A. Coombs, Manager of Systems Integration for McGraw Broadcast Communications and President of the Gemini Group, Cincinnati, Ohio. This environment is fully described in US Patent 5,577,042.

★ Convergence and "convergence time" are a process and a measure, respectively, of the adaptation of a computer network to unplanned changes in its topology or structure. For example, a routing protocol's convergence time is how long it takes between when a link is broken to when all of the routers (nodes) in the network have restructured their routing tables to take the next most optimal path.

★ Convergence (evolutionary computing) is a means of modelling the tendency for genetic characteristics of populations to stabilize over time.

★ Premature convergence is an anomaly in Evolutionary computation in which the population evolved to some stable yet sub-optimal state.

★ Technological convergence refers to a trend where some technologies having distinct functionalities evolve to technologies that overlap, i.e. multiple products come together to form one product, with the advantages of each initial component.

★ Convergence culture, according to Henry Jenkins [1], is "where old and new media collide, where grassroots and corporate media intersect, where the power of the media producer and the power of the media consumer interact in unpredictable ways." (Jenkins, H. (2006). Convergence Culture. New York: New York UniversityPress. "Introduction," pp.1-24.) Blogging, YouTube, Wikipedia, and other social networking sites are all examples of how this convergence culture is playing out in the networked world.

Social sciences

★ Language convergence pertains to the blending of two languages that are perceived as having equal social status. Opposite of Non-convergent discourse.

★ Non-convergent discourse pertains to the persistence of asymmetric or bilingual discourse in natural languages.

★ Catch-up effect is otherwise known as the 'Theory of convergence' in economic theory.

★ In the context of bargaining, 'Convergence' pertains to a behavior in which the price offered by a buyer may increase while the price acceptable to a seller may decrease until both prices approach equality, in which case they are said to ''converge''.

★ Convergence criteria are requirements specified by the European Union that stipulate the membership qualifications each state must fulfill.

★ Media convergence refers to the removal of entry barriers across the IT, telecoms, media and consumer electronics industries, creating one large 'converged' industry. In recent years it has also come to refer specifically to the ongoing 'bundling' of services by telecoms players, resulting in 'triple play' (one company offering combined fixed line phone, TV and broadband services) and more recently 'quad play' (triple play plus mobile phone). The 2006 acquisition of Virgin Mobile by NTL is often cited as an exemplar of the move in this direction.

★ Economic convergence refers to the phenomena in which lesser developed countries supposedly catch up to developed countries in terms of economic productivity and growth. Many theorists agree that economic growth in the United States peaked in the first half of the 20th century allowing it to diverge from other nations and leapfrogging to its status as a world leader in nearly every area. However, other countries are starting to gain on the United States. One of the sources or causes of growth in the past, especially the 19th century was the accumulation of factors of production. Today, economic growth and productivity seems to be tied to innovation and technology.

★ Convergence as popularized by Franz Boas, as an historical particularist, states that two societies may contain like traits that are the result of different antecedant events. Refuted cultural evolution that stated that similar traits found in a society were a result of a society being at the same point in the evolutionary trajectory.

Religion

Convergence may also refer to the act of converging two Faiths together. For instance in Christianity an act of Convergence would be the blending of a Charismatic church celebration with Roman Catholic beliefs.

See also

★ Divergent / Divergence (disambiguation)