Then every linear operator T in V can be written as the sum of a diagonalizable operator D and a nilpotent operator N which commute.

Then we can express the variables as the sum of the ( time averaged ) mean field () that varies in space and a small fluctuating field () that varies in space and time.

Then the sum total of all the maintenance actions are bundled into maintenance intervals so that maintenance is not occurring around the clock, but rather, at regular intervals.

Then, calculate the flow rate for each and sum the flows.

Since they are even, they can be written as x = 2a and y = 2b respectively for integers a and b. Then the sum.

Then the resultant perturbation can be written as a linear sum of the individual types of perturbations,

Then it will be spontaneously re-emitted, either in the same frequency as the original or in a cascade, where the sum of the energies of the photons emitted will be equal to the energy of the one absorbed ( assuming the system returns to its original state ).

Then the zero vector of this space can be expressed as a linear combination of no elements, which again is an empty sum.

Then any linear functional can be written in these coordinates as a sum of the form:

Since they are even, they can be written as x = 2a and y = 2b respectively for integers a and b. Then the sum.

Then negotiations began over how much money U. S. businesses owed Iran — Iran believing the sum to be $ 20 to $ 60 billion and the United States estimating it at " closer to $ 20 to 60 million ".— and how much Iran owed U. S. businesses.

* Let ρ be a unitary representation of a compact group G on a complex Hilbert space H. Then H splits into an orthogonal direct sum of irreducible finite-dimensional unitary representations of G.

If we take E to be the sum of the even exterior powers of the cotangent bundle, and F to be the sum of the odd powers, define D = d + d *, considered as a map from E to F. Then the topological index of D is the Euler characteristic of the Hodge cohomology of M, and the analytical index is the Euler class of the manifold.

Then came chivalry to Rome, and the sum of learning, which now is come to France.

Then, luminance is calculated as a weighted sum of the three linear-intensity values.

Then continue the sequence, where each subsequent term is the sum of the previous n terms.

Then χ ( M, N ), defined as the alternating sum of the lengths of the modules Tor < sub > i </ sub >< sup > R </ sup >( M, N ) is 0 if dim M + dim N < d, and positive if the sum is equal to d. ( N. B.

Then the statement is that the sum of delta-functions at each point of Λ, and at each point of Λ ′, are again Fourier transforms as distributions, subject to correct normalization.

# Then decide the input connections of OR matrix to generate the sum terms.

Then the Gauss sum mod p, g ( a ; p ), is the following sum of the pth roots of unity:

Then A ( G ) splits as a sum over characters λ of T of the subrepresentations A ( G )< sup > λ </ sup > of elements transforming according to λ.

Then, in 1502 James signed the Treaty of Perpetual Peace with Henry VII.

Then President George Bush signed a presidential finding directing the Central Intelligence Agency to create conditions for Hussein's removal in May 1991.

Then in 1935, under the accord signed between He Yingqin, the commander of Kuomintang armies in Northern China, and Yoshijiro Umezu, the commander of Japanese troops in Northern China, elite Kuomintang troops related to the group Blue Shirts Society, core of Chiang ’ s Whampoa Clique, had to evacuate from Beijing and Northern China, which put the whole of Northern China under direct threat of Japanese invasion.

Then, after Stax's bankruptcy in 1975, they signed to Curtis Mayfield's label, Curtom Records, and released " Let's Do It Again ", produced by Mayfield ; the song became their second # 1 pop hit in the US and the album also.

Then, on 7 May 2008, Borland and Embarcadero Technologies announced that Embarcadero had " signed a definitive asset purchase agreement to purchase CodeGear.

Then he returned to Pennsylvania and signed a contract with the Christy Minstrels.

Then came Napoleon's contemptuous violation of Prussian territory by marching three French corps through Ansbach ; King Frederick William's pride overcame his weakness, and on November 3 he signed with Tsar Alexander I of Russia the terms of an ultimatum to be laid before the French emperor.

Then, on 15 September 2000, Nauru withdraw the recognition of the SADR, and signed accords with Morocco on the phosphates area, which are running out in the island.

Then on January 26, Lalime signed a contract with the Penguins, who then assigned him to the Cleveland Lumberjacks of the IHL.

In 1969, the group signed with Warner Bros. Records and recorded their fourth studio album Then Play On that year, featuring the group's newly recruited third guitarist Danny Kirwan, who featured prominently on the album.

Then State Senator Harold Montgomery, State Representative, Parey Branton, Mayor Frank T. Norman, and other local officials presented Hennigan with a signed document of his accomplishments.

Then, despite the fact that many legislators expected the bill to be vetoed, Dow met with the new Governor, John Hubbard, who signed the bill into law on June 2.

Then, visiting Australia, at a ceremony held in Government House, Canberra, on 2 March 1986 the Queen signed a proclamation that the Australia Act ( Cth ) would come into force at 5 am Greenwich Mean Time on the following day.

Then, on July 22, 2004, after five seasons with D. C. United, Convey signed a three-year contract with Reading, who were then playing in the Championship, on the highest transfer fee paid by Reading up to that date.

Then in 2005, Nejmeh released the player, where he sign-up with Al-Mabarrah, In 2008 Houjeij signed for Lebanese Second Division club Al Khayoul, In summer of 2009 Houjeij signed with Shabab Al-Sahel, in August 2011 the nejmeh fans celebrated the return of moussa as a coach and a player and at his first season match against mabarrah he scored a goal.

The President Costa e Silva signed a decree on August 23 of 1968 Authorizing the project for the bridge, designed by Mario Andreazza Then Minister of Transport, under the management of whom the bridge was begun and completed.

Then after everybody signed on they rewrote it five times and it ended up nothing like the same movie.

Then, the total variation of the signed measure μ is equal to the total variation, in the above sense, of the function φ.

Then she signed to become " Jeannie ," a genie in a bottle rescued by an astronaut in the television sitcom I Dream of Jeannie.

Then, he signed with Detroit ( 1988 ), before being dealt back to San Diego.

Then, the two military leaders signed a peace treaty, which complicated the political situation further.

Then in August 843, they signed probably the most important treaty in European history, the Treaty of Verdun.

Then got the rest of the group signed.