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.

When Archbishop Emmanuel Milingo conferred episcopal ordination on four men in Washington on September 24, 2006, the Holy See's Press Office declared that " the Church does not recognize and does not intend in the future to recognize 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.

When it is necessary to distinguish the first form from generalized continued fractions, the former may be called a simple or regular continued fraction, or said to be in canonical form.

When applied to column vectors, the adjoint can be used to define the canonical inner product on: .< ref group =" note "> This ordering of the inner product ( with the conjugate-linear position on the left ), is preferred by physicists.

When one develops these four states, the Buddha counsels radiating them in all directions, as in the following stock canonical phrase regarding karuā:

When a DNS resolver encounters a CNAME record while looking for a regular resource record, it will restart the query using the canonical name instead of the original name.

When a Hamiltonian is defined on the cotangent bundle, then the generalized coordinates are related to the canonical coordinates by means of the Hamilton – Jacobi equations.

The Picard group of a del Pezzo surface of degree d is the odd unimodular lattice I < sub > 1, 9 − d </ sub >, except when the surface is a product of 2 lines when the Picard group is the even unimodular lattice II < sub > 1, 1 </ sub >. When it is an odd lattice, the canonical element is ( 3, 1, 1, 1, ....), and the exceptional curves are represented by permutations of all but the first coordinate of the following vectors:

When C is a hyperelliptic curve, the canonical curve is a rational normal curve, and C a double cover of its canonical curve.

In particular, this was known to imply the existence of a canonical model, a particular birational model of V with mild singularities that could be constructed by blowing down V. When the canonical ring is finitely generated, the canonical model is Proj of the canonical ring.

When using a distribution function with a canonical parameter, the canonical link function is the function that expresses in terms of, i. e..

When using the canonical link function,, which allows to be a sufficient statistic for.

When there are multiple " official " works or original media, the question of what is and what is not canonical can be unclear.

When viewed in a more general setting, the canonical ensemble is known as the Gibbs measure, where, because it has the Markov property of statistical independence, it occurs in many settings outside of the field of physics.

When he was twenty, Ebu Fadl Ali who was the Sheikh of Wasit province and his teacher awarded him a " Sehadetname " ( which represented writings of evidences including canonical law and order of dervish sciences ), and a nickname that was the father of external and interior sciences, and also dressed him a his own dervish's cloak.

When some object X is said to be embedded in another object Y, the embedding is given by some injective and structure-preserving map.

When the domain manifold is compact, the notion of a smooth embedding is equivalent to that of an injective immersion.

When specializing to the preadditive categories of abelian groups or modules over a ring, this notion of kernel coincides with the ordinary notion of a kernel of a homomorphism, if one identifies the ordinary kernel K of f: A → B with its embedding K → A.

When q ≥ 1, the embedding above has closed timelike curves ; for example, the path parameterized by and all other coordinates zero is such a curve.

When q ≥ 2 these curves are inherent to the geometry ( unsurprisingly, as any space with more than one temporal dimension will contain closed timelike curves ), but when q = 1, they can be eliminated by passing to the universal covering space, effectively " unrolling " the embedding.

When the line bundle is sufficiently ample this construction verifies the Kodaira embedding theorem.

When Heydrich stood up to try to shoot Gabčík, Kubiš threw a modified anti-tank grenade at the vehicle, and its fragments ripped through the car ’ s right-rear fender, embedding shrapnel and fibres from the upholstery into Heydrich ’ s body, even though the grenade failed to enter the car.

When Heydrich stood up to try to shoot Gabčík, Kubiš threw a modified anti-tank grenade at the vehicle, and its fragments ripped through the car ’ s right-rear fender, embedding shrapnel and fibres from the upholstery into Heydrich ’ s body, even though the grenade failed to enter the car.

When Heydrich stood up to try to shoot Gabčík, Kubiš threw a modified anti-tank grenade at the vehicle, and its fragments ripped through the car ’ s right-rear fender, embedding shrapnel and fibres from the upholstery into Heydrich ’ s body, even though the grenade failed to enter the car.

Punch had a poem containing the words “ When Ivo comes back with the urn ” and when Ivo Bligh wiped out the defeat Lady Clarke, wife of Sir W. J. Clarke, who entertained the English so lavishly, found a little wooden urn, burnt a bail, put the ashes in the urn, and wrapping it in a red velvet bag, put it into her husband ’ s ( Ivo Bligh ’ s ) hands.

When α is an integer, the Bessel functions J are entire functions of x.

When the functions J < sub > n </ sub >( x ) are plotted on the same graph, though, none of the zeros seem to coincide for different values of n except for the zero at x = 0.

When the eigenvalues of J are not in the unit circle, the dynamics near the fixed point x < sub > 0 </ sub > of F is called hyperbolic and when the eigenvalues are on the unit circle and complex, the dynamics is called elliptic.

When a new student, a rebellious outsider named Jason Dean ( Christian Slater ), or J. D.

When anthropologists David J. Daegling and Daniel O. Schmitt examined the film, they concluded it was impossible to conclusively determine if the subject in the film is nonhuman, and additionally argued that flaws in the studies by Krantz and others invalidated their claims.

When the polar bear was originally documented, two subspecies were identified: Ursus maritimus maritimus by Constantine J. Phipps in 1774, and Ursus maritimus marinus by Peter Simon Pallas in 1776.

When the West End production of Streetcar opened in October 1949, J.

When Dutch physicist J. D. van der Waals received the 1910 Nobel Prize " for his work on the equation of state for gases and liquids " he acknowledged the great influence of Gibbs's work on that subject.

When Clifford Ashley covered the knot in 1944, calling it the lineman's loop, he attributed its first publication to J. M.

When he went to the miller to negotiate about the price, the miller, upon seeing his Lord and military insignia, took interest in the money he was carrying with him, murdered him ; one of Jurij's tools ( compass ) was found in the mill one year after his disappearance and it had " J V " initials on it.

J. Bang-Jensen, G. Gutin and A. Yeo, When the greedy

When a judge of the High Court who is not present is being referred to they are described as " Mr ./ Mrs. Justice N ." In writing, the post-nominal letter " J " is used to denote a Judge ( male or female ) of the High Court: for example, Smith J.

'" When referred to in a decision of a court, judges ' titles are often abbreviated to the suffix " J.

When this effect is taken into account, typical gamma-ray bursts are observed to have a true energy release of about 10 < sup > 44 </ sup > J, or about 1 / 2000 of a Solar mass energy equivalent.

When Christopher Tolkien needed an assistant to edit his father J. R. R. Tolkien's unpublished work, he chose Kay, then a student at the University of Manitoba, whose parents were friends of Baillie Tolkien's parents.

When he had saved enough for England and applied for a pass and a ticket, they arrived in the name of " V. J. Patel ," at Vithalbhai's home, who bore the same initials.

When he recovered enough to travel, the little one-legged hero was put on a boat to the United States, with General John J. Pershing personally seeing Cher Ami off as he departed France.

When police later attempted entry, Philadelphia police officer James J. Ramp was killed by a shot to the back of the head.

When Alan J. W. Bell took over as producer, the plots of Last of the Summer Wine moved away from the original dialogue-packed scenes in the pub and the library ; guest actors were brought in to interact with the trio in new situations.

When he died, Gumbel's papers were made a part of The Emil J. Gumbel Collection, Political Papers of an Anti-Nazi Scholar in Weimar and Exile.

According to R. J. Rummel, " Just consider the Grand Custom in Dahomey: When a ruler died, hundreds, sometimes even thousands, of prisoners would be slain.

When Sharp returns however, Blunt is brought out of retirement by J. Gander Hooter and partnered with Darkwing — a relationship he hates, despite Darkwing's gimmicks, even though he is admired by Darkwing, who claims Blunt was his inspiration.

When the cavalry corps of the Army of the Potomac was reorganized under Maj. Gen. Philip Sheridan in 1864, Custer took part in the various actions of the cavalry in the Overland Campaign, including the Battle of the Wilderness ( after which he ascended to division command ), the Battle of Yellow Tavern, where J. E. B.