The exact definition of an automorphism depends on the type of " mathematical object " in question and what, precisely, constitutes an " isomorphism " of that object.

( The definition of a homomorphism depends on the type of algebraic structure ; see, for example: group homomorphism, ring homomorphism, and linear operator ).

In fact anode polarity depends on the device type, and sometimes even in which mode it operates, as per the above electric current direction-based universal definition.

The definition of ballroom dance also depends on the era: balls have featured popular dances of the day such as the Minuet, Quadrille, Polonaise, Polka, Mazurka, and others, which are now considered to be historical dances.

The definition of " addictive " depends on each individual but most Buddhists consider alcohol, tobacco and contraband drugs to be addictive.

Of course, this definition depends on the choice of norm:

However, whether this is possible depends on how the field of complex numbers is derived in the first place: it may not be possible to distinguish a complex number from its conjugate ( say, 3 + i from 3-i ), since it is impossible to find a property of one that is not also a property of the other, without falling back on the underlying set-theoretic definition.

A bit, or a group of malfunctioning physical bits ( not always the specific defective bit is known ; group definition depends on specific storage device ) is typically automatically fenced-out, taken out of use by the device, and replaced with another functioning equivalent group in the device, where the corrected bit values are restored ( if possible ).

The entries can be numbers or expressions ( as happens when the determinant is used to define a characteristic polynomial ); the definition of the determinant depends only on the fact that they can be added and multiplied together in a commutative manner.

A bit, or a group of malfunctioning physical bits ( not always the specific defective bit is known ; group definition depends on specific storage device ) is typically automatically fenced-out, taken out of use by the device, and replaced with another functioning equivalent group in the device, where the corrected bit values are restored ( if possible ).

The identity of the longest word in English depends upon the definition of what constitutes a word in the English language, as well as how length should be compared.

The definition of homomorphism depends on the type of algebraic structure under consideration.

Latency is a measure of time delay experienced in a system, the precise definition of which depends on the system and the time being measured.

In generative grammar, the definition of a morpheme depends heavily on whether syntactic trees have morphemes as leafs or features as leafs.

The precise definition of " class " depends on foundational context.

The " right " definition depends on the context in which the scheme will be deployed.

The relationship between religion and myth depends on what definition of " myth " one uses.

The definition of a road depends on the definition of a highway, however there is no formal definition for a highway in the relevant Act.

Within this context, the definition of an apneic event depends on several factors ( e. g. patient's age ) and account for this variability through a multi-criteria decision rule described in several, sometimes conflicting, guidelines.

A suitable definition of the entropy of a small local region depends on the physically insightful and judicious selection of the independent local non-equilibrium macroscopic state variables, and different selections provide different generalized or extended thermodynamical accounts of one and the same given physical process.

The notion of simultaneity depends on the frame of reference ( see relativity of simultaneity ), so switching between frames requires an adjustment in the definition of the present.

As regards animals, to what extent different animals think depends on the exact definition of the word that is given, so it may be taken literally or regarded as anthropomorphic.

First, we can encourage responsibility by establishing as conditions for assistance on a substantial and sustained scale the definition of objectives and the assessment of costs.

Used in several sets of high reps once or twice each week it will not be long before your entire upper leg takes on a razor-sharp definition in which the muscles look like wire cables writhing and twisting under the skin!!

If Af is the operator induced on Af by T, then evidently Af, because by definition Af is 0 on the subspace Af.

It might be contended, of course, that Eichmann in stubbornly denying anti-Semitic feelings was lying or insisting on a private definition of anti-Semitism.

One definition of paternalism is `` The principle or practice, on the part of a government, of managing the affairs of a country in the manner of a father dealing with his children ''.

The appellate court will typically be deferential to the lower court's findings of fact ( such as whether a defendant committed a particular act ), unless clearly erroneous, and so will focus on the court's application of the law to those facts ( such as whether the act found by the court to have occurred fits a legal definition at issue ).

The new definition is expected to be formally proposed at the 25th General Conference on Weights and Measures ( CGPM ) in 2014.

Its domain is the powerset of A ( with the empty set removed ), and so makes sense for any set A, whereas with the definition used elsewhere in this article, the domain of a choice function on a collection of sets is that collection, and so only makes sense for sets of sets.

* The Logicians or the School of Names, which focused on definition and logic.

This definition was adopted by the United Nations Sub-Commission on the Promotion and Protection of Human Rights in The Despouy Report on Human Rights and Extreme Poverty.

In this definition, it is implicitly assumed that storing a value into a variable U has no effect on the state of a distinct variable V. To make this assumption explicit, one could add the constraint that

Also running on a JOHANNIAC, the Logic Theory Machine constructed proofs from a small set of propositional axioms and three deduction rules: modus ponens, ( propositional ) variable substitution, and the replacement of formulas by their definition.

Celsius was the first to perform and publish careful experiments aiming at the definition of an international temperature scale on scientific grounds.

Heschel then goes on to explore the problems of doubts and faith ; what Judaism means by teaching that God is one ; the essence of humanity and the problem of human needs ; the definition of religion in general and of Judaism in particular ; and human yearning for spirituality.

This definition was proposed by Justus von Liebig circa 1838, based on his extensive works on the chemical composition of organic acids.

Meteorologists ( and most of the temperate countries in the southern hemisphere ) use a definition based on months, with autumn being September, October and November in the northern hemisphere, According to United States tradition, autumn runs from the day after Labor Day ( i. e. the Tuesday following the first Monday of September ) through Thanksgiving ( i. e. the fourth Thursday in November ), after which the holiday season that demarcates the unofficial beginning of winter begins.

Based on this definition, the drain efficiency cannot exceed 25 % for a class A amplifier that is supplied drain bias current through resistors ( because RF signal has its zero level at about 50 % of the input DC ).

He goes on to define error as self-contradiction of definition (" an absurdity, or senselesse Speech ") or conclusions that do not follow the definitions on which they are supposed to be based.

According to United Nation's Food and Agriculture Organization the term bean should include only species of Phaseolus ; however, a strict consensus definition has proven difficult because in the past, several species such as Vigna ( angularis ( azuki bean ), mungo ( black gram ), radiata ( mung bean ), aconitifolia ( moth bean )) were classified as Phaseolus and later reclassified.

This was the approach that Bessel used, and from this definition he derived several properties of the function.

The word cannon is derived from several languages, in which the original definition can usually be translated as tube, cane, or reed.

In addition to fundamental contributions in several branches of theoretical computer science, Knuth is the creator of the TeX computer typesetting system, the related METAFONT font definition language and rendering system, and the Computer Modern family of typefaces.

Standard definition TV ( SDTV ), by comparison, may use one of several different formats taking the form of various aspect ratios depending on the technology used in the country of broadcast.

The widespread adoption of digital video has also drastically reduced the bandwidth needed for a high-definition video signal ( with HDV and AVCHD, as well as several commercial variants such as DVCPRO-HD, all using less bandwidth than a standard definition analog signal ) and tapeless camcorders based on flash memory and often a variant of MPEG-4.

Often the complete definition for a class does not exist in a single module, but is spread across several that are optionally collected together.

The Roman Catholic Church does not consider the validity of an ecumenical council's teaching to be in any way dependent on where it is held or on the granting or withholding of prior authorization or legal status by any state, in line with the attitude of the 5th-century bishops who " saw the definition of the church's faith and canons as supremely their affair, with or without the leave of the Emperor " and who " needed no one to remind them that Synodical process pre-dated the Christianisation of the royal court by several centuries ".

It should, however, be emphasized that Faivre's definition is one of several divergent understandings of the most appropriate use of the term.

The frequentist interpretation is a philosophical approach to the definition and use of probabilities ; it is one of several, and, historically, the earliest to challenge the classical interpretation.

Note that with this definition, two elements a and b may very well have several greatest common divisors, or none at all.

There have been several recent proposals to amend the definition to consider biogenic or amorphous substances as minerals.

The definition of Macedonia has changed several times throughout history.

According to Margaret Bent ( 1997 ), " a piece of music in several parts with words " is as precise a definition of the motet as will serve from the 13th to the late 16th century and beyond.

A " folded " hierarchy allows a single definition to be represented several times by instances.

The definition given here is one of several possible oracle machine definitions.

The term " classical education " has been used in English for several centuries, with each era modifying the definition and adding its own selection of topics.

There are several things to notice about this definition:

Nevertheless, the teaspoon, usually under its Latin name, continued to be used in Apothecaries ' measures for several more decades, with the original definition of one fluid dram.

In several years, an entry was submitted that was so patently absurd that it required a new definition of some of the rules for the next year.

The distinction between vellum and parchment has been made in several different ways, and no one definition can be considered correct, but vellum has always denoted the better quality.

No exact definition of borders can be given, because the name " Westphalia " was applied to several different entities in history.