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

Various definitions of its exact composition exist, and no one definition is universally accepted.

No widely accepted exact definition exists for DBMS.

However, there is no exact, universally agreed, definition of the term " discrete mathematics.

The definition of an extreme sport is not exact and the origin of the term is unclear, but it gained popularity in the 1990s when it was picked up by marketing companies to promote the X Games.

While the exact definition and what is included as extreme sport is debatable, some attempted to make classification for extreme sports.

Authorities disagree on the exact definition of fractal, but most usually elaborate on the basic ideas of self-similarity and an unusual relationship with the space a fractal is embedded in.

An exact definition of how GWP is calculated is to be found in the IPCC's 2001 Third Assessment Report.

There are also a few nations in which the exact title and definition of the office of head of state have been vague.

This definition is not exact because " non-leptonic " may also signify " photonic ".

The exact legal definition of " incest ," including the nature of the relationship between persons, and the types sexual activity, varies by country, and by even individual states or provinces within a country.

The phrase is not a term of art in the law ; it has no exact meaning, nor does it have a legal definition.

In 1964, at the 12th CGPM conference, the original definition was reverted to, and thus the litre was once again defined in exact relation to the metre, as another name for the cubic decimetre, that is, exactly 1 dm < sup > 3 </ sup >.

The exact number of known living languages will vary from 5, 000 to 10, 000, depending generally on the precision of one's definition of " language ", and in particular on how one classifies dialects.

The exact definition of a mineral is under debate, especially with respect to the requirement a valid species be abiogenic, and to a lesser extent with regards to it having an ordered atomic structure.

It is important to note that what exactly constitutes a machine gun, and whether volley guns are a type of machine gun, and to what extent some earlier types of devices are considered to be like machine guns, is a matter of debate in many cases and can vary depending which language and exact definition is used.

A military academy or service academy ( in American English ) is an educational institution which prepares candidates for service in the officer corps of the army, the navy, air force or coast guard, which normally provides education in a service environment, the exact definition depending on the country concerned.

Though the exact definition varies between scholars, natural language can broadly be defined in contrast on the one hand to artificial or constructed languages, such as computer programming languages like Python and international auxiliary languages like Esperanto, and on the other hand to other communication systems in nature, such as the waggle dance of bees.

* The Islamic calendar has retained an observational definition of the new moon, marking the new month when the first crescent moon is actually seen, and making it impossible to be certain in advance of when a specific month will begin ( in particular, the exact date on which Ramadan will begin is not known in advance ).

The exact point of intersection of the Earth's axis and the Earth's surface, at any given moment, is called the " instantaneous pole ", but because of the " wobble " this cannot be used as a definition of a fixed North Pole ( or South Pole ) when metre-scale precision is required.

All schools agree this implies the cessation of worldly desires and freedom from the cycle of birth and death, though the exact definition differs.

Since the terms are administrative political subdivisions of the local regional government their exact relationship and definitions are subject to home rule considerations, tradition, as well as state statute law and local governmental ( administrative ) definition and control.

Classic Islamic law details the exact definition of the fast, the times of fasting, how a fast may be broken, who must fast, and permitted exceptions to the fast.

The exact mathematical definition is given below.

There is every reason to recognize that in the very last years of his life, as we shall see, Thompson did take the drug in carefully rationed doses to ease the pains of his illness, but the exact date at which this began has never been determined.

On most drill presses, it is impossible to get the exact speed, but you can come close by adjusting the drive belt on the step-cone pulleys.

The collective by which I address you in the title above is neither patronizing nor jocose but an exact industrial term in use among professional thieves.

In free-burning electric arcs, for instance, approximately 90% of the total arc power is transferred to the anode giving rise to local heat fluxes in excess of Af as measured by the authors -- the exact value depending on the arc atmosphere.

If work is substituted for things ( with more exact contribution to meaning ), it will have dominant stress.

Authorities hesitate to quote exact figures, however, believing that any sum they come up with is only a surface manifestation -- turned up by their inevitably limited policing -- of the real loot of the medical racketeer.

A difference of opinion arose between Mr. Martinelli and John P. Bourcier, town solicitor, over the exact manner in which the vote is handled.

This is an exact description of what Mr. Sansom does.

The exact number and placement of Endosymbiotic theory | endosymbiotic events is currently unknown, so this diagram can be taken only as a general guide It represents the most parsimonious way of explaining the three types of endosymbiotic origins of plastids.

In New Jersey, for example, the Administrative Office of the Court has promulgated a form of notice of appeal for use by appellants, though using this exact form is not mandatory and the failure to use it is not a jurisdictional defect provided that all pertinent information is set forth in whatever form of notice of appeal is used.

: " It is true that I can speak the exact, the idiomatic English.

It is instrumental for keeping time, in that UTC is basically the atomic time synchronized to Earth's rotation by means of exact observations.

At the exact midpoint between the two pKa values, the trace amount of net negative and trace of net positive ions exactly balance, so that average net charge of all forms present is zero.

This is known through the writings of John of Salisbury, who is thought to have been a near exact contemporary student of Alan of Lille.

The exact number and extent of these pagi is unclear and probably changed over time.

Most of those who identify themselves as Ainu still live in this same region, though the exact number of living Ainu is unknown.

His exact birth site is unclear because he was born about the time his mother was making a difficult trip home from burying Jackson's father.

" Biographer Trefousse indicates that Johnson's drinking on the occasion was the result of ill health which began before his arrival in Washington, though the exact nature of the ailment is not specified.

In addition to being married to Jochebed, Amram is also described in the Bible as having been related to Jochebed prior to the marriage, although the exact relationship is uncertain ; some Greek and Latin manuscripts of the Septuagint state that Jochebed was Amram's father's cousin, and others state that Amram was Jochebed's cousin, but the Masoretic text states that he was Jochebed's nephew.