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.

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.

The exact definition of racism is controversial both because there is little scholarly agreement about the meaning of the concept " race ", and because there is also little agreement about what does and doesn't constitute discrimination.

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.

He had noticed how formal and irritably exact Rachel had grown.

This expression is the exact parallel of mias gunaikos andra and illuminates how that expression is to be understood.

The following examples show how to solve differential equations in a few simple cases when an exact solution exists.

All that matters is which vertices are connected to which others by how many edges and not the exact layout.

The exact, detailed origin for how this lake became the name for the province is unknown.

However, the missile failed shortly after launch, so it is unknown what its exact capabilities are or how close North Korea is to perfecting the technology.

The exact timescale for how long this smoke remains, and thus how severely this smoke affects the climate once it reaches the stratosphere, is dependent on both chemical and physical removal processes.

* The Ptolemaic model of planetary motion: Based on the geometrical model of Eudoxus of Cnidus, Ptolemy's Almagest, demonstrated that calculations could compute the exact positions of the Sun, Moon, stars, and planets in the future and in the past, and showed how these computational models were derived from astronomical observations.

The exact number that was agreed to, along with how the series ended, is disputed by different sources.

The differences between Husserl and Heidegger are significant, but if we do not see how much it is the case that Husserlian phenomenology provides the framework for Heidegger's approach, we will not be able to appreciate the exact nature of Heidegger's project in Being and Time or why he let it unfinished.

In addition, records as to the specific reasons for internment are non-existent in many areas, making it hard to put an exact number on exactly how many gay men perished in death camps.

This was done with the reluctant help of Geordi LaForge who voiced concerns about how this could cause B-4 to be nothing more than an exact duplicate of Data.

Subway uses the advertising slogan " Eat Fresh ", and focuses on how their sandwiches are made from freshly baked bread and fresh ingredients, in front of customers to their exact specifications, by employees whom Subway calls " Subway Sandwich Artists ".

The story of Zeuxis deals with this exact question: how would an artist immortalize ideal beauty?

There were also distinct variations of the writing system in different parts of Greece, primarily in how the Phoenician characters which did not have an exact match to Greek sounds were employed.

The exact dates are those on which the Sun is at the points where the horizon is tangential to the analemma, which in turn depend on how much the analemma, or the north-south meridian passing through it, is tilted from the vertical.

A photographer uses a contract to sell the " license " or use of his or her photograph with exact controls regarding how often the photograph will be used, in what territory it will be used ( for example U. S. or U. K. or other ), and exactly for which products.

The exact manner that many scholars in Islam describe how high the hands should be raised during a regular Du ' a is up to the shoulders with palms placed together.

The exact details of how TMS functions are still being explored.

The homology groups of X therefore measure " how far " the chain complex associated to X is from being exact.

With sarcastic disbelief, Dundee challenges Corwin to produce a bottle of cherry brandy, vintage 1903 and, as he continues to berate Flaherty ("... how dare you drag me here at the busiest time of the year ..."), Corwin comments " Oh, that's a good year " and reaches into the bag to hand Dundee his exact request.