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A section Γ of dπ: TP / G → TM such that Γ: TM → TP / G is a linear morphism of vector bundles over M, can be identified with a principal connection in P. Conversely, a principal connection as defined above gives rise to such a section Γ of TP / G.
Some Related Sentences
section and Γ
Given two tensor bundles E → M and F → M, a map A: Γ ( E ) → Γ ( F ) from the space of sections of E to sections of F can be considered itself as a tensor section of if and only if it satisfies A ( fs ,...) = fA ( s ,...) in each argument, where f is a smooth function on M. Thus a tensor is not only a linear map on the vector space of sections, but a C < sup >∞</ sup >( M )- linear map on the module of sections.
The top left section is separated from the other two sections by a wide divider inscribed with the school's motto ΤΑ Γ ' ΑΡΙΣΤΑ ( Those things that are best ), which conveys the hope that each student and teacher will strive for strong character and the best of their abilities.
section and /
3D scanner | Laser scan section of the four-story Square Tower House, data collected by a CyArk / National Park Service partnership
American National Standards Institute / American Society of Safety Engineers standard ANSI Z359. 1-2007 Safety Requirement for Personal Fall Arrest Systems, Subsystems and Components, section 3. 2. 1. 4 ( for snap hooks and carabiners ) is a voluntary consensus standard.
The general formula is set out in section 38 ( 1 ), known as the " 7 / 50 formula ", requires: ( a ) assent from both the House of Commons and the Senate ; ( b ) the approval of two-thirds of the provincial legislatures ( at least seven provinces ) representing at least 50 % of the population ( effectively, this would include at least Quebec or Ontario, as they are the most populous provinces ).
These versions allowed 25 modules be to inserted into a single 5-1 / 4 inch section of racking, and allowed the high densities needed to build a computer.
Doom, a science fiction / horror themed video game, has a background which is given in the game's instruction manual ; the rest of the story is advanced with short messages displayed between each section of the game ( called episodes ), the action as the player character progresses through the levels, and some visual cues.
Before going further with serious experimentation, it can be convenient to check one ’ s programs at the PC using a suitable cross-assembler, such as the portable PDP-8 / DG Nova cross-assembler listed in the External links section, before attempting execution in the RDOS environment.
The bluegrass bassist is part of the rhythm section, and is responsible for keeping a steady beat, whether fast, slow, in 4 / 4 time, 2 / 4 or 3 / 4 time.
Retrieved from http :// www. wfp. org / food_aid / introduction / index. asp? section = 12 & sub_section = 1 on 2006-09-29.
* 1979 – An intense windstorm strikes western Washington and sinks a 1 / 2-mile-long section of the Hood Canal Bridge.
To accentuate this inherent musical tension, Horn juxtaposed the driving funk / rock rhythm section with a dramatic formal string arrangement and plenty of orchestral stabs, a novel technique that Horn himself had pioneered the previous year in producing Yes's " Owner of a Lonely Heart ".
The standard 7-inch mix ( by the name of " Cowboys & Indians ") featured a pop / radio-oriented production that dispensed with a section of the song's middle eight altogether.
The specification for HTTP / 1. 1 ( RFC 2616 ) specifies three compression methods: " gzip " ( RFC 1952 ; the content wrapped in a gzip stream ), " deflate " ( RFC 1950 ; the content wrapped in a zlib-formatted stream ), and " compress " ( explained in RFC 2616 section 3. 5 as ' The encoding format produced by the common UNIX file compression program " compress ".
For stateless address autoconfiguration ( SLAAC ) to work, subnets require a / 64 address block, as defined in RFC 4291 section 2. 5. 1.
* The University of Guelph Library, Archival and Special Collections, has more than 500 Jacobite pamphlets, histories, and literature in its rare books section introduced at http :// www. lib. uoguelph. ca / resources / archival_ & _special_collections / the_collections / digital_collections / scottish / Jacobite_site_0. htm
section and G
According to anthropologists Todd Sanders and Harry G. West, evidence suggests that a broad cross section of Americans today gives credence to at least some conspiracy theories.
The anti-establishment writer CLR James, in his classic work Beyond a Boundary, included a section " W. G.
Similar marks have been recently rejected by the USPTO citing a " likelihood of confusion " under section 2 ( d ), including ' G NETBOOK ' ( rejected 31 October 2008 ), MSI's ' WIND NETBOOK ' () and Coby Electronics ' ' COBY NETBOOK ' ( rejected 13 January 2009 )
** Monopole ( mathematics ), a connection over a principal bundle G with a section ( the Higgs field ) of the associated adjoint bundle
His first new design for the Germans to be produced in any numbers was the Fokker M. 5, which was little more than a copy of the Morane-Saulnier G, built with steel tube instead of wood for the fuselage, and with minor alterations to the outline of the rudder and undercarriage and a new aerofoil section.
Progress was slowed by mines on the slopes of the bluff, but elements of all three rifle companies, as well as a stray section of G / 116, had gained the top by 09: 00, causing the defenders at WN-62 to mistakenly report that both WN-65 and WN-66 had been taken.
According to scholar Colin G. Crisp, " Anxiety about resuscitating the flow of silent films was frequently expressed in the industrial press, and a large section of the industry still saw the silent as a viable artistic and commercial prospect till about 1935.
Rewatched today, the original Kid, directed by Rockys John G. Avildsen, feels smart and fresh, with a wealth of small character details and a leisurely middle section that explores the boy's developing respect for his teacher.
Many airs end a section on a G or A note in the first octave, at which point a piper will often play one of these hand chords for dramatic effect.
The First String Quartet No. 1 in G minor ( 1889 ) was innovative in the " Résumé " section which Nielsen included in the finale, bringing together themes from the first, third and fourth movements.
Madison was the site of a battle in the American Civil War on March 16, 1864, when Col. Josiah Patterson's 5th Alabama Cavalry, supported by Col. James H. Stuart's cavalry battalion and a section of horse artillery, drove Col. Adam G. Gorgas's 13th Illinois Infantry Regiment from the city.
In 1830, land entries were recorded for William Harris for the southwest quarter of section 17 and Major G. Van Dwyer for the southwest quarter of section 13 ( the eastern portion of the section is now part of Galesburg ).
The quarter section of land on which the original city was built, was entered by Henry G. Beard, in 1892.
The eastern section connects Sayner and Star Lake via CTH K, and provides a connection to CTH G and Eagle River.
( For the actual catalogs, go to these websites: http :// psychclassics. yorku. ca / Jastrow / section. htm and http :// psychclassics. yorku. ca / Munster / Lab /) In a similar attempt to inform the public, the 1904 Louisiana Purchase Exposition in St. Louis included ( among others ) presentations from G. Stanley Hall, Edward B. Titchener, Mary Whiton Calkins, John B. Watson, and Adolph Meyer.
The entire middle section resides primarily in C major, with forays into G major ( the dominant relation ).
This movement remains mostly in G major, but does modulate to D minor, E minor and E major ; the B2 section has a rather unstable tonality, being more chromatic and moving through many keys.
Miranda reminisces over her previous life throughout this section of the novel, and many of her diary entries are written either to her sister, or to a man named G. P., whom she respected and admired as an artist.
The overtone series is an octave above that of the F horn, exactly like playing the lower portion of a horn in F. Many drum and bugle corps, however, use mellophones pitched in G, although the number has dwindled somewhat since the two major United States drum and bugle corps circuits ( first Drum Corps International and then Drum Corps Associates ) passed rule changes allowing use of bell-front instruments in any key ( although corps using mellophones pitched in G typically have the whole of their brass section also using G instruments, whereas those using mellophones pitched in F generally have the remainder of their brass section using B ♭).
section and →
* Style → There is a sudden change in style and theology after chapter 40 ; numerous key words and phrases found in one section are not found in the other.
Hence a measurement of any dramatic change to the H → γγ cross section predicted by the Standard Model is crucial in probing the physics beyond it.
This second sum is a Riemann sum, and so by letting T → ∞ it will converge to the integral for the inverse Fourier transform given in the definition section.
By contrast, the previous section shows that in natural ( unformalized ) language, for every natural language statement Y there is a natural language statement Z such that Z is equivalent to ( Z → Y ) in natural language.
For each neighborhood U of x, the canonical morphism F ( U ) → F < sub > x </ sub > associates to a section s of F over U an element s < sub > x </ sub > of the stalk F < sub > x </ sub > called the germ of s at x.
Itagaki and Ishiwara chose to sabotage the rail section in an area near Liǔtiáo Lake ( → liǔtiáohú ).
In addition, to make the sabotage appear more convincingly as a calculated Chinese attack on an essential target – thereby masking the Japanese action as a legitimate measure to protect a vital railway of industrial and economic importance – the Japanese press labeled the site " Liǔtiáo Ditch " ( → liǔtiáogōu ) or " Liǔtiáo Bridge " ( → liǔtiáoqiáo ), when in reality, the site was a small railway section laid on an area of flat land.
A global section of L is a function s: X → L such that if p: L → X is the natural projection, then ps = id < sub > X </ sub >.
In a small neighborhood U in X in which L is trivial, the total space of the line bundle is the product of U and the underlying field k, and the section s restricts to a function U → k. However, the values of s depend on the choice of trivialization, and so they are determined only up to multiplication by a nowhere-vanishing function.
A local section of a fiber bundle is a continuous map s: U → E where U is an open set in B and π ( s ( x )) = x for all x in U. If ( U, φ ) is a local trivialization of E, where φ is a homeomorphism from π < sup >− 1 </ sup >( U ) to U × F ( where F is the fiber ), then local sections always exist over U in bijective correspondence with continuous maps from U to F. The ( local ) sections form a sheaf over B called the sheaf of sections of E.
A connection ∇ on a vector bundle E → M defines a notion of parallel transport on E along a curve in M. Let γ: → M be a smooth path in M. A section σ of E along γ is said to be parallel if
Recall that a section v of the induced vector bundle V over M can be thought of as an H-equivariant map P → V. This is the point of view we shall adopt.
In the remainder of this section, it will be set to zero, but in order for all the integrations over intermediate states to be well defined, the limit ε → 0 is to be only taken after the final state is calculated.