The Catholic Church does recognise as valid ( though illicit ) ordinations done by breakaway Catholic, Old Catholic or Oriental bishops, and groups descended from them ; it also regards as both valid and licit those ordinations done by bishops of the Eastern churches, so long as those receiving the ordination conform to other canonical requirements ( for example, is an adult male ) and an orthodox rite of episcopal ordination, expressing the proper functions and sacramental status of a bishop, is used ; this has given rise to the phenomenon of episcopi vagantes ( for example, clergy of the Independent Catholic groups which claim apostolic succession, though this claim is rejected by both Orthodoxy and Catholicism ).

The canonical example of a context free grammar is parenthesis matching, which is representative of the general case.

A second canonical example is two different kinds of matching nested parentheses, described by the productions:

The Cauchy distribution is often used in statistics as the canonical example of a " pathological " distribution.

* It is not difficult to construct spacetimes which have naked singularities, but which are not " physically reasonable ;" the canonical example of such a spacetime is perhaps the " superextremal " < math > M <| Q |</ math > Reissner-Nordstrom solution, which contains a singularity at that is not surrounded by a horizon.

This is a canonical example of the PDP-1, with the console typewriter on the left, CPU and main control panel in the center, the Type 30 display on the right.

Overgrazing is used as the canonical example of the Tragedy of the commons.

The canonical example of a ligand-binding protein is haemoglobin, which transports oxygen from the lungs to other organs and tissues in all vertebrates and has close homologs in every biological kingdom.

The canonical example is the linked list.

For the example, we have a canonical form available that reduces any string to one of length at most three, by decreasing the length monotonically.

The canonical example is the Slashdot effect when receiving traffic from Slashdot.

The prisoner's dilemma is a canonical example of a game analyzed in game theory that shows why two individuals might not cooperate, even if it appears that it is in their best interests to do so.

This is a powerful criterion: for example, all axioms listed above as canonical are ( equivalent to ) Sahlqvist formulas.

The algorithm provides no cryptographic security, and is often cited as a canonical example of weak encryption.

The earliest, and still the canonical example of an esoteric language was INTERCAL, designed in 1972 by Don Woods and James M. Lyon, with the stated intention of being unlike any other programming language the authors were familiar with.

For example, the phase space measure of the microcanonical ensemble ( see below ) is different from that of the canonical ensemble.

For example, one can specify the density operators describing microcanonical, canonical, and grand canonical ensembles of quantum mechanical systems, in a mathematically rigorous fashion.

This set of endomorphisms is a canonical example of a near-ring which is not a ring.

The canonical example of extrinsic curvature is that of a circle, which everywhere has curvature equal to the reciprocal of its radius.

For example, he developed a theory of canonical transformations which allowed changing coordinates so that some coordinates disappeared from the Lagrangian, as above, resulting in conserved canonical momenta.

The canonical example of this is the sham ruin: a folly which pretends to be the remains of an old building but which was in fact constructed in that state.

The can be used in Applesoft BASIC as a shortcut for " PRINT ", though spelling out the word is not only acceptable but canonical — Applesoft converted "?

For a detailed discussion of the differences including a more comprehensive table ( several essential tables are given below ) of Biblical scripture for both Testaments and the intertestamental period with regard to canonical acceptance in Christendom's various major traditions, see Wikipedia's article on " Biblical canon ".

The canonical age for the ordination of a deacon was 25 ; Bede's early ordination may mean that his abilities were considered exceptional, but it is also possible that the minimum age requirement was often disregarded.

The only canonical information we have comes from the book that is named for him.

A breviary ( from Latin brevis, ' short ' or ' concise ') is a liturgical book of the Latin liturgical rites of the Catholic Church containing the public or canonical prayers, hymns, the Psalms, readings, and notations for everyday use, especially by bishops, priests, and deacons in the Divine Office ( i. e., at the canonical hours or Liturgy of the Hours, the Christians ' daily prayer ).

In liturgical language Breviary has a special meaning, indicating a book furnishing the regulations for the celebration of Mass or the canonical Office, and may be met with under the titles Breviarium Ecclesiastici Ordinis, or Breviarium Ecclesiæ Rominsæ ( Romanæ ).

Jean Beleth, a 12th-century liturgical author, gives the following list of books necessary for the right conduct of the canonical office: the Antiphonarium, the Old and New Testaments, the Passionarius ( liber ) and the Legendarius ( dealing respectively with martyrs and saints ), the Homiliarius ( homilies on the Gospels ), the Sermologus ( collection of sermons ) and the works of the Fathers, besides, of course, the Psalterium and the Collectarium.

Indeed, Catullus was never considered one of the canonical school authors, although his body of work is on the reading lists for American Ph. D. programs in the classics, and is still taught at secondary school level in the United Kingdom.

The bishop of the diocese in which the martyrdom took place set up a canonical process for conducting the inquiry with the utmost severity.

As usual for objects defined by universal mapping properties, this shows the uniqueness of the abelianization G < sup > ab </ sup > up to canonical isomorphism, whereas the explicit construction G → G / shows existence.

Parametric equation for the ellipse ( red ) in canonical position.

After the establishment of the canonical classic Greek alphabet, new glyph variants for Ε were introduced through handwriting.

When it declared devoid of canonical effect the consecration ceremony conducted by Archbishop Pierre Martin Ngô Đình Thục for the Carmelite Order of the Holy Face group at midnight of 31 December 1975, the Holy See refrained from pronouncing on its validity.

The canonical Book of Ezra and Book of Nehemiah are the oldest sources for the activity of Ezra, whereas many of the other books ascribed to Ezra ( First Esdras, 3-6 Ezra ) are later literary works dependent on the canonical books of Ezra and Nehemiah.

To extend what may have once been ten Labours to the canonical dozen, it was said that Eurystheus didn't count the Hydra, as he was assisted, nor the Augean stables, as Heracles received payment for his work.

The permanent criteria of church structure for the Orthodox Church today, outside the New Testament writings, are found in the canons ( regulation and decrees ) of the first seven ecumenical councils ; the canons of several local or provincial councils, whose authority was recognized by the whole church ; the Apostolic Canons, dating from the 4th century ); and the " canons of the Fathers " or selected extracts from prominent church leaders having canonical importance.

The canonical source for the document is in the philosophy section of the GNU Project website.

Author Lin Carter later created a son for Dr. Petrie and Kara, but this is not considered canonical.

Allowing negative exponents provides a canonical form for positive rational numbers.

* a layer derived from earlier source materials, almost certainly transmitted to the vernacular author / translator in Latin ; and comprising, at the least, those extensive passages in the Gospel of Barnabas that closely parallel pericopes in the canonical gospels ; but whose underlying text appears markedly distinct from that of the late medieval Latin Vulgate ( as for instance in the alternative version of the Lord's Prayer in chapter 37, which includes a concluding doxology, contrary to the Vulgate text, but in accordance with the Diatessaron and many other early variant traditions );