However even when this term is not identically 0, it is often negligibly small and thus in practice is usually ignored giving us the standard nonlinear wave-equation:

However, almost any nonlinear electronic component will also multiply signals applied to it, producing heterodyne frequencies in its output, so these are most often used as mixers.

However, in 1992, Bernhard E. Boser, Isabelle M. Guyon and Vladimir N. Vapnik suggested a way to create nonlinear classifiers by applying the kernel trick ( originally proposed by Aizerman et al.

However, dispersion also has an effect in many other circumstances: for example, GVD causes pulses to spread in optical fibers, degrading signals over long distances ; also, a cancellation between group-velocity dispersion and nonlinear effects leads to soliton waves.

However, most Mira variables exhibit slight cycle-to-cycle changes in period, probably caused by nonlinear behavior in the stellar envelope including deviations from spherical symmetry.

However elasticity is nonlinear in these materials.

However, in nonlinear cases, optimum minimum-variance performance guarantees no longer apply.

However, more importantly, empirical investigations can indicate the advantage of using predictions derived from non-linear models, over those from linear models, as for example in nonlinear autoregressive exogenous models.

However, within each day play may be nonlinear.

However, some inputs may cause the algorithm to backtrack many times, each time performing many steps before backtracking, so its overall complexity may be nonlinear.

However, both color spaces are nonlinear in terms of psychovisually perceived color differences.

However, this nonlinear formula, obtained from data in only 39 young men, is not accurate, and over-corrects at high heart rates and under-corrects at low heart rates.

However most optical materials have a relatively weak nonlinear response, meaning that their properties only change by a small amount for large changes in the intensity of the electromagnetic field.

However, singularities are places where the equations break down, and Einstein believed that in an ultimate theory the laws should apply everywhere, with particles being soliton-like solutions to the ( highly nonlinear ) field equations.

However, use of a nonlinear transformation requires caution.

However, more complex equivalent circuits are used that approximate the nonlinear behavior of the original circuit as well.

However, when the crystal is in contact with a rough surface, stress can easily become a nonlinear function of strain ( and speed ) because the stress is transmitted across a finite number of rather small load-bearing asperities.

However, perturbation expansions are generally not reliable for questions of long-term existence and stability, in the case of nonlinear equations.

However, they are based on linear elastic response and hence the applicability decreases with increasing nonlinear behaviour, which is approximated by global force reduction factors.

However, the multiple reflection causes a nonlinear phase shift.

However, as can be seen, when R is increased, the nonlinear phase shift gives the nonlinear response to and shows step-like behavior.

However, it has since been extended to weakly nonlinear systems, time varying systems, distributed parameter systems, multi-input multi-output ( MIMO ) systems ( Horowitz, 1991 ), discrete systems ( these using the Z-Transform as transfer function ), and non minimum phase systems.

However, studies in vertebrate nervous systems of ventral midline crossing axons, has shown that modulatory cues play a crucial part in tuning axon responses to other cues, suggesting that the process of axon guidance is nonlinear.

However, the term ' bankruptcy ' is often used when referring to companies in the media and in general conversation.

However, as multimedia has largely shifted to digital media, the need for some form of SIMD in general-purpose CPUs has become significant.

However, revenues fell far short of optimistic predictions by church managers, who had ignored early warnings by members and media experts.

However, in certain applications where discs will not be distributed or exchanged outside a private group and will not be archived for a long time, a proprietary format may be an acceptable way to obtain greater capacity ( up to 1. 2 GB with GigaRec or 1. 8 GB with HD-BURN on 99 minute media ).

However, there are also many computer magazines or newspapers that provide ratings for freeware and include compact discs or other storage media containing freeware.

However, from the political scene following the post-1968 radicalization, the Soviet adaptation spread to the editors of mass media, sparking strong forms of self-control, self-censorship and pro-Soviet attitudes.

However, it is hard to ignore the similarities between Thompson's gonzo journalism and today's growing popularity of citizen journalism through new media like blogs and Twitter.

However, over time East Germany's abbreviation DDR became colloquial also among most West Germans and West German media.

However, since network news use of the term pertained primarily to the criminal activities despite this attempt by the technical community to preserve and distinguish the original meaning, the mainstream media and general public continue to describe computer criminals with all levels of technical sophistication as " hackers " and does not generally make use of the word in any of its non-criminal connotations.

However, when in 1906 two city teams chose the city's Roman amphitheatre as a venue to showcase the game, crowd enthusiasm and media interest began to rise.

However, by this time Tintin had begun to move into other media.

However, the legal and political climate continued to encourage self-censorship in online media.

However, rather than in factories and sweatshops, most child labour occurs in the informal sector, " selling on the street, at work in agriculture or hidden away in houses — far from the reach of official inspectors and from media scrutiny.

However, the news media also show a remarkable degree of centrism, just because all outlets but one are located – from an ideological point of view-between the average Democrat and average Republican in Congress.

However, it would be a mistake to consider media studies a specialism of communication sciences, since media make up just a small portion of the overall course.

However, the focus of such programs sometimes excludes certain media — film, book publishing, video games, etc.

However the Fine Gael candidate felt shortchanged by this deal as the media was more interested in the Robinson campaign, and privately he did not like Robinson.

However, regional cultural differences, like regional dialects, have been breaking down under the influence of centralized education, nationwide media, and the several decades of population movement since the Korean War.

However, pre-war claims of wide scale, long-lasting, and significant global environmental impacts were not borne out and found to be significantly exaggerated by the media and speculators, with climate models at the time of the fires predicting only more localized effects such as a daytime temperature drop of ~ 10 ° C within ~ 200 km of the source.

However, studies by the Drug Abuse Warning Network in the 1970s show that media reports of PCP-induced violence are greatly exaggerated and that incidents of violence were unusual and often ( but not always ) limited to individuals with reputations for aggression regardless of drug use.

However, whenever there was a significant lack of media coverage or concern with racial profiling, the amount of arrests and traffic stops for the African-American community would significantly rise again.

However, since the 1960s, a greater permissiveness towards allowing regional English varieties has taken hold in education and the media in Britain ; in some contexts conservative RP is now perceived negatively.

However, the ruling party then lost its majority in by-elections in 2005, as discontinued reform plans, continual labor unrest, Roh's personal feuds with the media, diplomatic friction with the United States and Japan, caused criticism of the government's incompetence of political, socioeconomical issues and foreign affairs.