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.

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 ).

The alternative to this is that if a conservative candidate is nominated the national committee will have to appeal to the trusts for their campaign funds, and in doing this will incur obligations which would make a Democratic victory absolutely fruitless.

The Dominican people have known no democratic institutions and precious little freedom for a generation, and all alternative leadership has been suppressed.

Expressed differently: if the price for becoming a faithful follower of Jesus Christ is some form of self-destruction, whether of the body or of the mind -- sacrificium corporis, sacrificium intellectus -- then there is no alternative but that the price remain unpaid.

It will be recalled from the discussion in Section 7 that the position of the `` right '', as represented by Barth, rests on the following thesis: The only tenable alternative to Bultmann's position is a theology that ( 1 ) rejects or at least qualifies his unconditioned demand for demythologization and existential interpretation ; ;

Anthropology has been used in Britain to provide an alternative explanation for the Financial crisis of 2007 – 2010 to the technical explanations rooted in economic and political theory.

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.

The alternative name for the family, Umbelliferae, derives from the inflorescence being generally in the form of a compound umbel.

While resistant to most beta lactam antibiotics commonly used for skin infections, it remains sensitive to alternative antibiotics, e. g., clindamycin ( Cleocin ), trimethoprim-sulfamethoxazole ( Bactrim ), and doxycycline ( unlike hospital-acquired MRSA that may only be sensitive to vancomycin IV ).

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.

By the conditions accepted in the treaty, the Avars were to take possession of Pannonia and the Lombards were promised military support in Italy should the need arise ; also, for a period of 200 years the Lombards were to maintain the right to reclaim their former territories if the plan to conquer Italy failed, thus leaving Alboin with an alternative open.

Sometimes, Roman numerals are still used for enumeration of lists ( as an alternative to alphabetical enumeration ), for sequential volumes, to differentiate monarchs or family members with the same first names, and ( in lower case ) to number pages in prefatory material in books.

Although a phoneme's allophones are all alternative pronunciations for a phoneme, the specific allophone selected in a given situation is often predictable.

Ayurveda, Chinese medicine, Homeopathy and Naturopathy are cited as examples The term appears to have entered into usage through the National Institute of Health's National Center for Complementary and Alternative Medicine ( NCCAM ), which began to employ it as a substitute for alternative medical systems as a way of differentiating widely comprehensive systems of medicine, such as Ayurvedic medicine, from specialized alternative approaches.

It was commonly thought that most individuals were homozygous for the " wild type " allele at most gene loci, and that any alternative ' mutant ' allele was found in homozygous form in a small minority of " affected " individuals, often as genetic diseases, and more frequently in heterozygous form in " carriers " for the mutant allele.

Then, p < sup > 2 </ sup > is the fraction of the population homozygous for the first allele, 2pq is the fraction of heterozygotes, and q < sup > 2 </ sup > is the fraction homozygous for the alternative allele.

As resistance towards antibiotics becomes more common, a greater need for alternative treatments arises.

Private and alternative education institutions for children in preschool-12th grade include Regents School of Austin, Redeemer Lutheran School, Garza ( public ), Austin Discovery School ( public charter ), Austin Jewish Academy, The Austin Waldorf School, The Griffin School, The Khabele School, Concordia Academy, St. Ignatius Martyr Catholic School, Holy Family Catholic School, San Juan Diego Catholic High School, Brentwood Christian School, St. Austin Catholic School, St. Stephen's Episcopal School, St. Mary's, St. Theresa's, St. Michael's Catholic Academy, St. Gabriel's Catholic School, St. Andrew's Episcopal School, St. Francis Episcopal School, Saint Paul Lutheran School, Trinity Episcopal School, Huntington-Surrey, Cleaview Sudbury School, The Inside Outside School, ACE Academy, Paragon Preparatory Middle School, Austin International School, The Progress School and a number of Montessori schools.

An alternative name for the ACC is the West Wind Drift.

( via their ARA / ARA2 / ASR products ) allowed ' Sideways ROM ' capability, that allowed the standard Acorn ROM space to be programmatically mapped out for alternative EPROMs, either physically via ZIF Sockets, or ' virtually ' via ROM-images loaded into ( Battery-backed ) RAM in the same ROM memory space.

Carbonless copy paper ( CCP ), non-carbon copy paper, or NCR paper is an alternative to carbon paper, used to make a copy of an original, handwritten ( or mechanically typed ) document without the use of any electronics.

Alternative medicine is frequently grouped with complementary medicine or integrative medicine, which, in general, refers to the same interventions when used in conjunction with mainstream techniques, under the umbrella term complementary and alternative medicine, or CAM.

Complementary medicine usually refers to methods and substances used along with conventional medicine, while alternative medicine refers to compounds used instead of conventional medicine.

Here the term " races " is used as an alternative for " varieties " and does not carry the modern connotation of human races — the first use in the book refers to " the several races, for instance, of the cabbage " and proceeds to a discussion of " the hereditary varieties or races of our domestic animals and plants ".

As an alternative, Kripke outlined a causal theory of reference, according to which a name refers to an object by virtue of a causal connection with the object as mediated through communities of speakers.

Knossos ( alternative spellings Knossus, Cnossus, Greek Κνωσός, currently refers to the main Bronze Age archaeological site at Heraklion, a modern port city on the north central coast of Crete.

Hughes ' autobiography A London Home in the 1890s repeatedly refers to halma as an alternative to chess for relaxation, though the actual playing is never described.

Several alternative names have been proposed by various people: Generation We, Global Generation, Generation Next, the Net Generation, The name " Echo Boomers " refers to the size of the generation and its relation to the Baby Boomer generation.

" stone boat "), while sleigh typically refers to a moderate-to large-sized, usually open-topped vehicle equipped with one or more passenger seats, essentially a cold-season alternative to a carriage or wagon, typically drawn by horses or ( at least in the Santa Claus legend or in reference to Scandinavia ) by reindeer.

Josephus refers to the queen at the time ( corresponding to the Nitocris of Herodotus ) as the grandmother of Belshazzar which corroborates the alternative view that the younger " Labynetos " ( son of Nitocris ) is Nabonidus.

The term " Go-Kart ", which exists since 1959, also shortened as " Kart ", an alternative spelling of " cart ", refers to a tiny race car with frame and two-stroke engine ; the old term go-cart originally meant a sedan chair or an infant walker

Full cost accounting ( FCA ) generally refers to the process of collecting and presenting information — about environmental, social, and economic costs and benefits / advantages ( collectively known as the " triple bottom line ")-for each proposed alternative when a decision is necessary.

The private equity secondary market ( also often called private equity secondaries ) refers to the buying and selling of pre-existing investor commitments to private equity and other alternative investment funds.

The prefix " alt " refers to the fact that it is a " hierarchy that is ' alternative ' to the ' mainstream ' ( comp, misc, news, rec, soc, sci and talk ) hierarchies ".

Sometimes called " true bugs ", that name more commonly refers to Hemiptera as a whole, and " typical bugs " might be used as a more unequivocal alternative since among the Hemiptera the heteropterans are most consistently and universally termed " bugs ".

An alternative explanation is that the name refers to a " holding " to the South of New Haven, from whence the original settlers hailed.

An alternative explanation is that the town's name refers to a " holding " to the south New Haven ), from whence the original settlers hailed.

The alternative name great rhombicuboctahedron refers to the fact that the 12 square faces lie in the same planes as the 12 faces of the rhombic dodecahedron which is dual to the cuboctahedron.

Out of Box refers to the act of assembling a kit only from what is contained in the box supplied, whereas a Modifier will employ after-market products such as alternative decals, photo-etched metal detail parts, and cast resin detail or conversion parts to enhance or change the model in some way.

Pseudoarchaeology — also known as alternative archaeology, fringe archaeology, fantastic archaeology, or cult archaeology — refers to interpretations of the past from outside of the academic archaeological community, which typically also reject the accepted scientific and analytical methods of the discipline.

The alternative term antiquities commonly refers to the remains of ancient art and everyday items from antiquity, which themselves are often archaeological artifacts.

It has been suggested that the Aramaic name is actually Gol Goatha, meaning mount of execution, possibly the same location as the Goatha mentioned in a Book of Jeremiah passage, describing the geography of Jerusalem An alternative explanation is that the location was a place of public execution, and the name refers to abandoned skulls that would be found there, or that the location was near a cemetery, and the name refers to the bones buried there.

It is important to note that the crux of Kane's position is grounded not in a defense of alternative possibilities ( AP ) but in the notion of what Kane refers to as ultimate responsibility ( UR ).