For each element a of a group G, conjugation by a is the operation φ < sub > a </ sub >: G → G given by ( or a < sup >− 1 </ sup > ga ; usage varies ).

Where U and V are tangent vectors and g < sub > ij </ sub > are the components of the metric tensor G,

With the definitions used before 2012, the astronomical unit was dependent on the heliocentric gravitational constant, that is the product of the gravitational constant G and the solar mass M < sub >☉</ sub >.

Neither G nor M < sub >☉</ sub > can be measured to high accuracy in SI units, but the value of their product is known very precisely from observing the relative positions of planets ( Kepler's Third Law expressed in terms of Newtonian gravitation ).

( When measured in decibels it is logarithmically related to the power ratio: G ( dB )= 10 log ( P < sub > out </ sub > /( P < sub > in </ sub >)).

* If G is a locally compact Hausdorff topological group and μ its Haar measure, then the Banach space L < sup > 1 </ sup >( G ) of all μ-integrable functions on G becomes a Banach algebra under the convolution xy ( g ) = ∫ x ( h ) y ( h < sup >− 1 </ sup > g ) dμ ( h ) for x, y in L < sup > 1 </ sup >( G ).

The questions range from counting ( e. g., the number of graphs on n vertices with k edges ) to structural ( e. g., which graphs contain Hamiltonian cycles ) to algebraic questions ( e. g., given a graph G and two numbers x and y, does the Tutte polynomial T < sub > G </ sub >( x, y ) have a combinatorial interpretation ?).

The two functors F and G are called naturally isomorphic if there exists a natural transformation from F to G such that η < sub > X </ sub > is an isomorphism for every object X in C.

The cell cycle consists of four distinct phases: G < sub > 1 </ sub > phase, S phase ( synthesis ), G < sub > 2 </ sub > phase ( collectively known as interphase ) and M phase ( mitosis ).

28 .</ ref > One of the three Milesian philosophers, he is identified as a younger friend or student of Anaximander .< ref > Kirk, G. S., J. E.

124-126 .</ ref > While other philosophers also recognized such transitions in states of matter, Anaximenes was the first to associate the quality pairs hot / dry and cold / wet with the density of a single material and add a quantitative dimension to the Milesian monistic system .< ref > Kirk, G. S., J. E.

While the sun is similarly described as being aflame, it is not composed of rarefied air like the stars but rather of earth like the moon ; its burning comes not from its composition but rather from its rapid motion .< ref > Kirk, G. S., J. E.

In 1978, Joyce G. Baldwin, former principal of Trinity College, Bristol, proposed her view of the chiastic language structure for the Aramaic portion of Daniel chapters 2-7 .</ sup >

: 1 ⊆ G < sub > nil </ sub > ⊆ G < sub > sol </ sub > ⊆ G < sub > con </ sub > ⊆ G.

: G < sub > con </ sub >/ G < sub > sol </ sub > is a central extension of a product of simple connected Lie groups.

: G < sub > sol </ sub >/ G < sub > nil </ sub > is abelian.

When Ravel published his orchestrated version of the Pavane in 1910, he gave the lead melody to the horn, and specified a non-generic instrument: the score calls for " 2 Cors simples en sol " ( two hand-horns in G ).

Simply speaking, if a phthora of nenano is placed on δι, which in Western terms corresponds to the tone " G " ( sol ), then it indicates a chromatic tetrachord, approximated by the notes: D-E flat-F sharp-G.

For loan to the Government of India under subsection ( G ) of Section 104 of the Act, the rupee equivalent of not more than $538 million for financing such projects to promote balanced economic development as may be mutually agreed.

With respect to Article 2,, paragraphs 1 ( B ) and 1 ( C ): Uses of Section 104 ( E ) and Section 104 ( G ) rupees: The Government of India will use the amount of rupees granted or loaned to it by the United States pursuant to paragraphs 1 ( B ) and 1 ( C ) for projects to promote economic development with emphasis upon the agricultural sector including food reserve storage structures and facilities as may from time to time be agreed upon by the authorized representatives of the United States and the authorized representatives of the Government of India, in the following sectors: A.

Additionally, consider for instance the unit circle S, and the action on S by a group G consisting of all rational rotations.

The tones in between are then given by 16: 9 for D, 8: 5 for E, 3: 2 for F, 4: 3 for G, 6: 5 for A, and 16: 15 for B, in ascending order.

( See G. F. Hill, The Development of Arabic Numerals in Europe for more examples.

The manuscript, which is being edited for publication by G. Maltsiniotis, later led to another of his monumental works, Les Dérivateurs.

In this case, the 0. 5 value for the G channel actually indicates 100 % green intensity ( with 50 % opacity ).

The AVL tree is named after its two Soviet inventors, G. M. Adelson-Velskii and E. M. Landis, who published it in their 1962 paper " An algorithm for the organization of information.

The standard tuning for an acoustic guitar is E-A-D-G-B-E ( low to high ), although many players, particularly fingerpickers, use alternate tunings ( scordatura ), such as " open G " ( D-G-D-G-B-D ), " open D " ( D-A-D-F-A-D ), or " drop D " ( D-A-D-G-B-E ).

* awb-AMR-WB audio, used primarily for speech, same as the ITU-T's G. 722. 2 specification.

If F is an antiderivative of f, and the function f is defined on some interval, then every other antiderivative G of f differs from F by a constant: there exists a number C such that G ( x ) = F ( x ) + C for all x.

Its title is a literal English translation of the German name for Mozart's Serenade No. 13 for strings in G major, Eine kleine Nachtmusik.

There is a Mozart reference in the title — A Little Night Music is an occasionally used translation of Eine kleine Nachtmusik, the nickname of Mozart's Serenade No. 13 for strings in G major, K. 525.

The latter notation corresponds to viewing R as the characteristic function on " X " x " Y " for the set of pairs of G.

The incident resulting in the single largest loss of life in the history of the US Navy not related to combat occurred when USS Cyclops, under the command of Lt Cdr G. W.

Over the next 6 days, 21 distinct impacts were observed, with the largest coming on July 18 at 07: 33 UTC when fragment G struck Jupiter.

Together, these two Chianti zones produce the largest volume of DOC / G wines in Italy.

These G proteins are made from three subunits, with the G domain located on the largest one ( the α unit ); together with the two smaller subunits ( β and γ units ), they form a tightly associated protein complex.

: G < sub > nil </ sub > for the largest connected normal nilpotent subgroup

* Siemens A. G., Europe's largest engineering company has its Dutch headquarters there

* July 1 – 3 – American Civil War: Union forces under George G. Meade turn back a Confederate invasion by Robert E. Lee at the Battle of Gettysburg, the largest battle of the war ( 28, 000 Confederate casualties, 23, 000 Union ).

Several large U. S. Department of Defense installations and R & D facilities surround Columbia, the largest being the National Security Agency at Fort George G. Meade, and the Applied Physics Laboratory, both pre-dating the establishment of Columbia.

Murray gained access to the largest chess library in the world, that of John G. White of Cleveland, Ohio, and also used the collection of J. W. Rimington Wilson in England.

A. G. Mazourek organized the producers into an egg producers cooperative, the Hernando Egg Producers, Inc., possibly the largest egg cooperative in the southeastern United States.

One of the largest fruit farms in Norton Township was operated by G. N. Cobb who also operated a box factory for fifteen years beginning in 1869.

* 1960-Kenneth Strachan starts Evangelism-in-Depth in Central America ; 18, 000 people in Morocco reply to newspaper ad by Gospel Missionary Union offering free correspondence course on Christianity ; Loren Cunningham founds Youth with a Mission ; The Asia Evangelistic Fellowship ( AEF ), one of the largest Asian indigenous missionary organisations, is launched in Singapore by G. D. James

Part of the airport's South Terminal project, the concourse was designed by Carlos Zapata and M. G. E., one of the largest Hispanic-owned architecture firms in Florida.

The cannabinoid receptor is a typical member of the largest known family of receptors called a G protein-coupled receptor.

* E < sup > p </ sup >( G ) is the intersection of all index p normal subgroups ; G / E < sup > p </ sup >( G ) is an elementary abelian group, and is the largest elementary abelian p-group onto which G surjects.

* A < sup > p </ sup >( G ) is the intersection of all normal subgroups K such that G / K is an abelian p-group ( i. e., K is an index normal subgroup that contains the derived group ): G / A < sup > p </ sup >( G ) is the largest abelian p-group ( not necessarily elementary ) onto which G surjects.