For alternative ( equivalent ) formulations of the definition in terms of a bijective function or a surjective function, see the section Formal definition and properties below.

An alternative and equivalent definition of Carmichael numbers is given by Korselt's criterion.

The authors ' caveats and repeated efforts at alternative definition have been echoed in subsequent scholarship: in the more than five decades since, there have been innumerable further attempts at definition, yet in the words of cinema historian Mark Bould, film noir remains an " elusive phenomenon ... always just out of reach ".

Keynes asked his friend Piero Sraffa to respond publicly to Hayek's challenge ; instead of formulating an alternative theory, Sraffa elaborated on the logical inconsistencies of Hayek's argument, especially concerning the effect of inflation-induced " forced savings " on the capital sector and about the definition of a " natural " interest rate in a growing economy.

Another alternative is to give the definition of the word.

Radon measures have an alternative definition in terms of linear functionals on the locally convex space of continuous functions with compact support.

From these three assumptions, neoclassical economists have built a structure to understand the allocation of scarce resources among alternative ends — in fact understanding such allocation is often considered the definition of economics to neoclassical theorists.

An alternative definition for " weakly typed " refers to languages, such as Perl and JavaScript, which permit a large number of implicit type conversions.

A popular alternative definition of chronic pain, involving no arbitrarily fixed durations is " pain that extends beyond the expected period of healing.

* Choice Corollary: People choose for themselves the particular alternative in a dichotomized construct through which they anticipate the greater possibility for extension and definition of their system.

An alternative and disputable definition of QoS, used especially in application layer services such as telephony and streaming video, is requirements on a metric that reflects or predicts the subjectively experienced quality.

In atmosphere science, an alternative definition is usually given, from 3 Hz to 3 kHz.

By this broader definition the two-round system is not the only form of run-off voting, and others include the exhaustive ballot and instant run-off voting ( also known as the alternative vote ).

Like the " dimension of image " characterization this can be generalized to a definition of the rank of a linear map: the rank of a linear map f from V → W is the minimal dimension k of an intermediate space X such that f can be written as the composition of a map V → X and a map X → W. While this definition does not suggest an efficient manner to compute the rank ( for which it is better to use one of the alternative definitions ), it does allow to easily understand many of the properties of the rank, for instance that the rank of the transpose of A is the same as that of A.

The US edition, once again by A & E Home Video, includes the first North American release of an alternative edit of " Arrival " ( in high definition ), as well as " The Alternate Version of ' The Chimes of Big Ben '" from the earlier DVD / VHS releases ( in standard definition due to the degraded source material ) and assorted documentaries and behind-the-scenes footage.

An alternative spelling in English is ' vocal chords ', possibly due to the musical connotations or to confusion with the geometrical definition of the word " chord ".

Swiss psychoanalyst Carl Jung, who studied archetypes, proposed an alternative definition of symbol, distinguishing it from the term sign.

An alternative definition of SNR is as the reciprocal of the coefficient of variation, i. e., the ratio of mean to standard deviation of a signal or measurement:

If the signal data are not constant, then can be calculated from data where the signal is zero or relatively constant .</ ref > Notice that such an alternative definition is only useful for variables that are always non-negative ( such as photon counts and luminance ).

Sometimes SNR is defined as the square of the alternative definition above.

Yet another alternative, very specific and distinct definition of SNR is employed to characterize sensitivity of imaging systems ; see signal to noise ratio ( imaging ).

Convention on the Rights of Persons with Disabilities also defines the communication to include the display of text, Braille, tactile communication, large print, accessible multimedia, as well as written and plain language, human-reader, augmentative and alternative modes, means and formats of communication, including accessible information and communication technology.

An alternative approach defines a polytope as a set of points that admits a simplicial decomposition.

" In the United Kingdom, the Official Chart Company defines a boundary between EP and album classification at 25 minutes of length or four tracks ( not counting alternative versions of featured songs, if present ).

Using an alternative scheme of classification, linguist Michael E. Krauss defines languages as " safe " if it is considered that children will probably be speaking them in 100 years ; " endangered " if children will probably not be speaking them in 100 years ( approximately 60-80 % of languages fall into this category ); and " moribund " if children are not speaking them now.

This book defines and uses an alternative Gödel numbering.

Stephen Barrett, who runs the alternative medicine watchdog website, Quackwatch, a consumer information organization with several websites dedicated to exposing quackery, defines the practice this way:

In The Future of Art in a Postdigital Age Mel Alexenberg defines " postdigital art " as artworks that address the humanization of digital technologies through interplay between digital, biological, cultural, and spiritual systems, between cyberspace and real space, between embodied media and mixed reality in social and physical communication, between high tech and high touch experiences, between visual, haptic, auditory, and kinesthetic media experiences, between virtual and augmented reality, between roots and globalization, between autoethnography and community narrative, and between web-enabled peer-produced wikiart and artworks created with alternative media through participation, interaction, and collaboration in which the role of the artist is redefined.

Victor H. Vroom ( 1964 ) defines motivation as a process governing choices among alternative forms of voluntary activities, a process controlled by the individual.

The alternative to a commodity money system is fiat money which is defined by a central bank and government law, or " fiat ", which defines legal tender.

Additionally the ICS defines an alternative type of benchmark and criteria called Global Standard Stratigraphic Ages ( GSSAs ) where the characteristics and dating criteria set solely by physical sciences methods ( such as magnetic alignment sequences, radiological criteria, etcetera.

This is different from the alternative definition where, using a fixed Grassmann algebra generated by a countable number of generators Λ, one defines a supermanifold as a point set space using charts with the " even coordinates " taking values in the linear combination of elements of Λ with even grading and the " odd coordinates " taking values which are linear combinations of elements of Λ with odd grading.

The WPAD standard defines two alternative methods the system administrator can use to publish the location of the proxy configuration file, using the Dynamic Host Configuration Protocol ( DHCP ) or the Domain Name System ( DNS ):

rabble. ca defines itself on numerous times throughout its site as an “ alternative ” medium, which consequently sets it apart from other Canadian mainstream media.

The 2000 edition of the American Heritage Dictionary also defines jennet, with the alternative spelling genet, as a small Spanish saddle horse.

An alternative news agency ( or alternative news service ) operates in a similar fashion to a commercial news agency, but defines itself as an alternative to commercial or " mainstream " operations.

In the alternative partitioning, one defines

Also common in telecom ( especially VoIP ) is the term grey route, which defines a route that is legal for one country or the party on one end, but illegal on the alternative end.

Under the influence of Habermas's Structural Transformation of the Public Sphere, she proposes an alternative division that defines women as belonging to an authentic public sphere of government critique through salons, Masonic lodges, academies, and the press.

Augmentative and alternative communication ( AAC ) is an umbrella term that encompasses methods of communication for those with impairments or restrictions on the production or comprehension of spoken or written language.

With regard to historic properties ( those properties that are listed or that are eligible for listing in the National Register of Historic Places, or properties designated as historic under State or local law ), those facilities must still comply with the provisions of Title III of the ADA to the " maximum extent feasible " but if following the usual standards would " threaten to destroy the historic significance of a feature of the building " then alternative standards may be used.

A generalization of Artin's theorem states that whenever three elements in an alternative algebra associate ( i. e. ) the subalgebra generated by those elements is associative.

The situation is complex, however, because the relatively free Russian media is allowed to transmit television programming, sell newspapers and conduct journalistic activities in Belarus ( though some Russian journalists have been expelled by the Belarusian government ) thus giving some members of the public, typically those in large cities with many Russian residents, access to an alternative point of view in the Russian language ( nearly all Belarusians understand and most of them speak Russian ).

While the scientific community was once divided between supporters of the Big Bang and those of alternative cosmological models, most scientists became convinced that some version of the Big Bang scenario best fit observations after the discovery of the cosmic microwave background radiation in 1964, and especially when its spectrum ( i. e., the amount of radiation measured at each wavelength ) was found to match that of thermal radiation from a black body.

This view has the advantage of anchoring Numbers to the Pentateuch as a whole, but an alternative is to see it as structured around the two generations of those condemned to die in the wilderness and the new generation who will enter Canaan, making a theological distinction between the disobedience of the first generation and the obedience of the second.

Lloyd George offered a degree of support to the Labour government in the hope of winning concessions, including a degree of electoral reform to introduce the alternative vote, but this support was to prove bitterly divisive as the Liberals increasingly divided between those seeking to gain what Liberal goals they could achieve, those who preferred a Conservative government to a Labour one and vice-versa.

An alternative for those people may however be sailing near the coast, which still gives a certain amount of safety.

From 1904, however, he instead termed those ' original disease conditions ', and introduced the new alternative category of psychopathic personalities.

* a layer derived from earlier source materials, almost certainly transmitted to the vernacular author / translator in Latin ; and comprising, at the least, those extensive passages in the Gospel of Barnabas that closely parallel pericopes in the canonical gospels ; but whose underlying text appears markedly distinct from that of the late medieval Latin Vulgate ( as for instance in the alternative version of the Lord's Prayer in chapter 37, which includes a concluding doxology, contrary to the Vulgate text, but in accordance with the Diatessaron and many other early variant traditions );

Slaw, the Canadian legal co-operative, offered this advice to lawyers just starting out in practice, especially those who are trying to pay off student loans, " The GnuCash software ... should present a great alternative for lawyers looking for a solid accounting system at low cost.

For those Orthodox Christians who follow the Julian Calendar, this day falls on December 25 of the Gregorian Calendar, and thus provides a spiritual alternative to what some believe to be the increasingly secularized celebration of Christmas.

* an unsustainably flexible movement of ... everything to everyone: an alternative social provider to the poor masses ; an angry platform for the disillusioned young ; a loud trumpet-call announcing ` a return to the pure religion ` to those seeking an identity ; a " progressive, moderate religious platform ` for the affluent and liberal ; ... and at the extremes, a violent vehicle for rejectionists and radicals.

It included a review of alternative theories, such as those of Thomas Burnet and Georges-Louis Leclerc, Comte de Buffon.

In severe cases and those involving multiple conditions in addition to the cause of the neuralgia, there is no substitute for comprehensive palliative therapy including systemic NSAIDs, opioids, muscle relaxants, intermittent corticosteroids and other agents if needed and adjuncts and potentiators to increase the power of the analgesics in addition to the topical preparation and physical and alternative modalities such as physiotherapy, acupuncture, biofeedback and related modalities, nutritional approaches and many others relevant to each case.

As with the anarchists, they too saw the Bolshevik take-over of the soviets ( like that of the trade unions ) as subverting the revolution and beginning the restoration of domination and exploitation ... Over the years this emphasis on working class autonomy has resulted in a reinterpretation of Marxist theory that has brought out the two-sided character of the class struggle and shifted the focus from capital ( the preoccupation of orthodox Marxism ) to the workers ... As a result, not only has there been a recognition that capitalism seeks to subordinate everyone's life ( from the traditional factory proletariat to peasants, housewives and students ) but that all those peoples ' struggles involve both the resistance to this subordination and the effort to construct alternative ways of being.

With their ideas rooted in Marxism and the 20th century European artistic avant-gardes, they advocated experiences of life being alternative to those admitted by the capitalist order, for the fulfillment of human primitive desires and the pursuing of a superior passional quality.

The alternative, " Wycliffite ", is generally accepted to be a more neutral term covering those of similar opinions, but having an academic background.

Other classification schemes may be used in non-western cultures, for example the Chinese Classification of Mental Disorders, and other manuals may be used by those of alternative theoretical persuasions, for example the Psychodynamic Diagnostic Manual.

In the past, MAOIs were prescribed for those resistant to tricyclic antidepressant therapy, but newer MAOIs such as selegiline ( typically used in the treatment of Parkinson's disease ) and the reversible MAOI moclobemide provide a safer alternative and are now sometimes used as first-line therapy, although these substances are not always as effective as their predecessors.

In particular, his stories — together with those of C. S. Lewis — were among the first to establish the convention of an alternative world or universe as the setting for speculative fiction.

Most programming languages describe computation in an imperative style, i. e., as a sequence of commands, although some languages, such as those that support functional programming or logic programming, use alternative forms of description.

While contemporary biomedicine has distanced itself from its ancient roots in religion and magic, many forms of traditional medicine and complementary and alternative medicine ( CAM ) continue to espouse vitalism in various guises: ' As long as life had its own secret properties, it was possible to have sciences and medicines based on those properties ' ( Grossinger 1980 ).