In the second example CH < sub > 3 </ sub > COOH undergoes the same transformation, in this case donating a proton to ammonia ( NH < sub > 3 </ sub >), but cannot be described using the Arrhenius definition of an acid because the reaction does not produce hydronium.

* Inverses: by definition every isomorphism has an inverse which is also an isomorphism, and since the inverse is also an endomorphism of the same object it is an automorphism.

Ian Hacking ( 1999, p. 84 ) also uses the same definition.

According to the definition above, two relations with the same graph may be different, if they differ in the sets and.

" With the latter definition, Confucianism is religious, even if non-theistic, in the sense that it " performs some of the basic psycho-social functions of full-fledged religions ", in the same way that non-theistic ideologies like Communism do.

To provide a definition of current that is independent of the type of charge carriers flowing, conventional current is defined to flow in the same direction as positive charges.

Such a definition can be formulated in terms of equivalence classes of smooth functions on M. Informally, we will say that two smooth functions f and g are equivalent at a point x if they have the same first-order behavior near x.

The same definition is used for any consistent norm, i. e. one that satisfies

# a genus ( or family ): An existing definition that serves as a portion of the new definition ; all definitions with the same genus are considered members of that genus.

Dhrystone 2. 1, released in May of the same year, had some minor changes and remains the current definition of Dhrystone.

In his initial argument, Moore concluded that any similar definition of goodness could be criticized in the same way.

This definition holds for most " classical " hormones, but there are also paracrine mechanisms ( chemical communication between cells within a tissue or organ ), autocrine signals ( a chemical that acts on the same cell ), and intracrine signals ( a chemical that acts within the same cell ).

Although this is an independent definition that does not refer to the older basis of ephemeris time, it uses the same quantity as the value of the ephemeris second measured by the cesium clock in 1958.

The term faunal stage is sometimes used, referring to the fact that the same fauna ( animals ) are found throughout the layer ( by definition ).

An FFT is a way to compute the same result more quickly: computing a DFT of N points in the naive way, using the definition, takes O ( N < sup > 2 </ sup >) arithmetical operations, while an FFT can compute the same result in only O ( N log N ) operations.

An FFT computes the DFT and produces exactly the same result as evaluating the DFT definition directly ; the only difference is that an FFT is much faster.

As Tom Shippey points out: " Giles's blunderbuss ... defies the definition and works just the same.

It re-radiates in all directions, both upwards and downwards ; in equilibrium ( by definition ) the same amount as it has absorbed.

A narrow definition would take in roughly the same area as the modern states of Israel, the West Bank, the Gaza Strip, and Jordan, while a wider definition would include Syria.

This is the same as the definition of the derivative for real functions, except that all of the quantities are complex.

I suppose the same emotion holds, if to a lesser degree, with any famous monument.

About the same time the Alleghenies and Poconos in Pennsylvania are magnificent -- Renovo holds its annual Flaming Foliage Festival on Oct. 14, 15.

The evaluation order does not affect the value of such expressions, and it can be shown that the same holds for expressions containing any number of operations .< ref > Thus, when is associative, the evaluation order can be left unspecified without causing ambiguity, by omitting the parentheses and writing simply:

58. 17 ) requires candidates for reception into a Benedictine community to promise solemnly stability ( to remain in the same monastery ), conversatio morum ( an idiomatic Latin phrase suggesting " conversion of manners "), and obedience ( to the superior, because the superior holds the place of Christ in their community ).

At the same time, BONUCA holds seminars in topics such as the relationship between military and civil parts of society.

The same formula holds as before.

In British English it is not necessary to indicate an abbreviation with a full stop ( period ) after the abbreviation, when the last letter of the abbreviation is the same as the unabbreviated word, while the opposite holds true in North American English.

A similar declaration was issued with regard to Archbishop Emmanuel Milingo's conferring of episcopal ordination on four men-all of whom, by virtue of previous Independent Catholic consecrations, claimed already to be bishops-on 24 September 2006: the Holy See, as well as stating that, in accordance with Canon 1382 of the Code of Canon Law, all five men involved incurred automatic (" latae sententiae ") excommunication through their actions, declared that " the Church does not recognise and does not intend in the future to recognise these ordinations or any ordinations derived from them, and she holds that the canonical state of the four alleged bishops is the same as it was prior to the ordination.

Using the principle of equivalence, Einstein concluded that the same thing holds in any gravitational field, that the rate of clocks R at different heights was altered according to the gravitational field g. When g is slowly varying, it gives the fractional rate of change of the ticking rate.

Formula fiction should not be confused with pastiche ( the mimicking of another work or author's style ), though the latter by its nature may include elements of the former ; the same holds true of some parody and satirical works as well, which may well include formulaic elements such as common stereotypes or caricatures, or which may use formulaic elements in order to mock them or point out their supposedly cliché or unrealistic nature.

The elements 2 and 1 + √(− 3 ) are two " maximal common divisors " ( i. e. any common divisor which is a multiple of 2 is associated to 2, the same holds for 1 + √(− 3 )), but they are not associated, so there is no greatest common divisor of a and b.

The same holds for standard GP and other search algorithms.

Breakfast is still very popular and may be elaborated and extended on weekends, with friends invited as guests, the same holds for coffee and cake.

Due to angular momentum conservation, states of the same ℓ but different m have the same energy ( this holds for all problems with rotational symmetry ).

The same holds for the government.

The most widely-held theory is that the military designation of GP begat the term Jeep and holds that the vehicle bore the designation GP ( for Government Purposes or General Purpose ), which was phonetically slurred into the word jeep, in the same way that the contemporary HMMWV ( for High-Mobility Multi-purpose Wheeled Vehicle ) has become known as the humvee.

Meta-ethical theories that imply an empirical epistemology include ethical naturalism, which holds moral facts to be reducible to non-moral facts and thus knowable in the same ways ; and most common forms of ethical subjectivism, which hold that moral facts reduce to facts about individual opinions or cultural conventions and thus are knowable by observation of those conventions.

While the single player tile matching game mahjong solitaire is familiar in the West, in Asia it is the four-player table version which holds predominance and has little in common with the solitaire version other than using the same tiles.

There is an isoelectronic analog of benzene, B < sub > 3 </ sub > N < sub > 3 </ sub > H < sub > 6 </ sub > ( borazine ), for which the same argument holds.

The same rule holds for negative values:

If the foregoing argument holds good, Mary of Bethany and the " sinner " are one and the same.