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principal and connection
In process of time the title abbot was extended to clerics who had no connection with the monastic system, as to the principal of a body of parochial clergy ; and under the Carolingians to the chief chaplain of the king,, or military chaplain of the emperor, It even came to be adopted by purely secular officials.
To practice architecture means to offer or render services in connection with the design and construction of a building, or group of buildings and the space within the site surrounding the buildings, that have as their principal purpose human occupancy or use.
This edition both loosened the connection between RuneQuest and Glorantha, introducing ' Fantasy Europe ' as the principal game world for Rune Quest, and much broadened the scope of Glorantha, which was treated as an alternative game world.
This was one of the principal reasons for dissolving the connection with Great Britain.
: The Poem of my Friend has indeed great defects ; first, that the principal person has no distinct character, either in his profession of Mariner, or as a human being who having been long under the control of supernatural impressions might be supposed himself to partake of something supernatural ; secondly, that he does not act, but is continually acted upon ; thirdly, that the events having no necessary connection do not produce each other ; and lastly, that the imagery is somewhat too laboriously accumulated.
** Monopole ( mathematics ), a connection over a principal bundle G with a section ( the Higgs field ) of the associated adjoint bundle
* Curvature form for the appropriate notion of curvature for vector bundles and principal bundles with connection
It typically includes one or more of several features, such as the mystic association of animal and plant species, natural phenomena, or created objects with unilineally related groups ( lineages, clans, tribes, moieties, phratries ) or with local groups and families ; the hereditary transmission of the totems ( patrilineal or matrilineal ); group and personal names that are based either directly or indirectly on the totem ; the use of totemistic emblems and symbols ; taboos and prohibitions that may apply to the species itself or can be limited to parts of animals and plants ( partial taboos instead of partial totems ); and a connection with a large number of animals and natural objects ( multiplex totems ) within which a distinction can be made between principal totems and subsidiary ones ( linked totems ).
Miskito Kings renewed their alliance with Great Britain, and Belize replaced Jamaica as the principal English connection for the kingdom.
An Ehresmann or Cartan connection supplies a lifting of curves from the manifold to the total space of a principal bundle.
Let P → M be a principal bundle over a manifold M with structure Lie group G and a principal connection ω.
As in the case of vector bundles, a principal connection ω on P defines, for each curve γ in M, a mapping
Now, if we're given a vector field Y over M ( but not the principal bundle ) but we also have a connection over the principal bundle, we can define a vector field X over the principal bundle such that its horizontal component matches Y and its vertical component agrees with the connection.
Mathematically, a Yang – Mills instanton is a self-dual or anti-self-dual connection in a principal bundle over a four-dimensional Riemannian manifold that plays the role of physical space-time in non-abelian gauge theory.
The classical Yang – Mills action on a principal bundle with structure group G, base M, connection A, and curvature ( Yang – Mills field tensor ) F is
An Ehresmann connection is a connection in a fibre bundle or a principal bundle by specifying the allowed directions of motion of the field.
In that same year, Charles Ehresmann, a student of Cartan's, presented a variation on the connection as a differential form view in the context of principal bundles and, more generally, fibre bundles.
In Ehresmann's point of view, a connection in a principal bundle consists of a specification of horizontal and vertical vector fields on the total space of the bundle.

principal and α
Fibrinogen, the principal protein of vertebrate blood clotting, is a hexamer containing two sets of three different chains ( α, β, and γ ), linked to each other by disulfide bonds.
Using Log we obtain the principal value of z < sup > α </ sup >, i. e.,
It induces a principal connection α on the associated principal G-bundle P ×< sub > H </ sub > G. This is a Cartan connection.
* a principal G-connection α on Q ( the Cartan connection )
Since α is a principal connection, it induces a connection on any associated bundle to Q.
Suppose that M is a Cartan geometry modelled on G / H, and let ( Q, α ) be the principal G-bundle with connection, and ( P, η ) the corresponding reduction to H with η equal to the pullback of α.
Let V a representation of G, and form the vector bundle V = Q ×< sub > G </ sub > V over M. Then the principal G-connection α on Q induces a covariant derivative on V, which is a first order linear differential operator
When I is a principal ideal αO < sub > K </ sub > then N ( I ) is equal to the absolute value of the norm to Q of α, for α an algebraic integer.
If | α | < δ, the branches are called principal, because they equal their real analogons on the positive real axis.
The norm of a principal ideal generated by α is the ideal generated by the field norm of α.
As a solution to the Hamilton-Jacobi equation, the principal function contains N + 1 undetermined constants, the first N of them denoted as α < sub > 1 </ sub >, α < sub > 2 </ sub > ... α < sub > N </ sub >, and the last one coming from the integration of.

principal and on
The promenade, for example, continues to take place on the Chahar Bagh, a mile-long garden of plane and poplar trees that now serves as the city's principal street.
Potemkin's Army of Ekaterinoslav, totaling, it was claimed, 40,000 regular troops and 6,000 irregulars of the Cossack Corps, had invested Islam's principal stronghold on the north shore of the Black Sea, the fortress town of Oczakov, and was preparing to test the Turk by land and sea.
Two of the principal addresses were delivered by prominent Protestants, and when the speaker was a Catholic, one `` discussant '' on the dais tended to be of another religious persuasion.
We had a couple of schools in this country, the principal one being on the Marshall Field estate out in Lloyd's Neck.
Subject to the limitations hereinafter provided, the Secretary of the Treasury is authorized and directed to pay, as prescribed by Section 8 of this Title, an amount not exceeding the principal of each award, plus accrued interests on such awards as bear interest, certified pursuant to Section 5 of this Title, in accordance with the award.
to make payments of $1,000 on the principal of each award of more than $1,000 in principal amount, certified pursuant to Section 5 of this Title ; ;
after completing the payments prescribed by paragraphs ( 2 ) and ( 3 ) of this subsection, to make payments, from time to time in ratable proportions, on account of the unpaid principal of all awards in the principal amount of more than $1,000, according to the proportions which the unpaid principal of such awards bear to the total amount in the fund available for distribution at the time such payments are made ; ;
after payment has been made of the principal amounts of all such awards, to make pro rata payments on account of accrued interest on such awards as bear interest.
The extent of such interference -- which may be so slight as to be undetectable at any point where either of the stations renders a usable signal, or may be so great as to virtually destroy the service areas of both stations -- depends on many factors, among the principal ones being the distance between the stations, their respective radiated power, and, of particular significance here, the time of day.
Barco, his state of apprehension gone, never to return, had assumed a matter-of-factness which remained his principal attitude from that time on.
In their very first collages, Braque and Picasso draw or paint over and on the affixed paper or cloth, so that certain of the principal features of their subjects as depicted seem to thrust out into real, bas-relief space -- or to be about to do so -- while the rest of the subject remains imbedded in, or flat upon, the surface.
If it is owned, taxes must be paid, and if the place is not free of mortgage, there will be interest and payments on the principal to take care of.
The Ainus were a primitive people, already living on the island before the principal ancestors of the Japanese came from Southern Asia.
Ships from the West Coast rotated on six-month tours of duty with the Seventh Fleet, and Yokosuka was the Seventh Fleet's principal port for maintenance, upkeep and shore liberty.
Mr. Willis bought Zenith Plastic Products, a skeleton corporation of sorts which had undergone many vicissitudes and whose principal assets were a couple of electronics plants on Long Island engaged in working out government contracts, and installed Freddy in an executive position.
There are three principal families of abugidas, depending on whether vowels are indicated by modifying consonants by diacritics, distortion, or orientation.
Sultan Ahmed III had become unpopular by reason of the excessive pomp and costly luxury in which he and his principal officers indulged ; on September 20, 1730, a mutinous riot of seventeen janissaries, led by the Albanian Patrona Halil, was aided by the citizens as well as the military until it swelled into an insurrection in front of which the Sultan was forced to give up the throne.
Most notably, Ajax is not wounded in any of the battles described in the Iliad, and he is the only principal character on either side who does not receive personal assistance from any of the gods who take part in the battles.
His principal theological works are a commentary in three volumes on the Books of the Sentences of Peter Lombard ( Magister Sententiarum ), and the Summa Theologiae in two volumes.
Opposition to the union seemed to subside somewhat for a time upon the publication of Tsar Nicholas II's congratulations to the king on his engagement and of his acceptance to act as the principal witness at the wedding.
However we are told by Longinus that Ammonius wrote nothing, and if Ammonius was the principal influence on Plotinus, then it is unlikely that Ammonius would have been a Christian.

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