Then ( X × Y, ( π < sub > 1 </ sub >, π < sub > 2 </ sub >)) is a terminal morphism from Δ to the object ( X, Y ) of D × D. This is just a restatement of the above since the pair ( f, g ) represents an ( arbitrary ) morphism from Δ ( Z ) to ( X, Y ).

Then the elements of Z are given by:

Then 2Z has two cosets in Z ( namely the even integers and the odd integers ), so the index of 2Z in Z is two.

Then every cohomology class in H < sup > 2k </ sup >( X, Z ) ∩ H < sup > k, k </ sup >( X ) is the cohomology class of an algebraic cycle with integral coefficients on X.

Then every non-torsion cohomology class in H < sup > 2k </ sup >( X, Z ) ∩ H < sup > k, k </ sup >( X ) is the cohomology class of an algebraic cycle with integral coefficients on X.

Then with " Ichido wa Kekkon Shitai Manbo " from Dragon Ball Z Hit Song Collection 8: Character Special 2 released in 1991.

Then T2 Reads and Writes to object Y and Commits, and finally T3 Reads and Writes to object Z and Commits.

Then Q is not Artinian as a left Z module, but it is Artinian a right Q module.

Then jointly the triple ( X, Y, Z ) has the following probability distribution:

Then X and Y have the same fundamental group, namely Z < sub > 2 </ sub >, and the same universal cover, namely S² × S³ ; thus, they have isomorphic homotopy groups.

" A " And s <= " Z " Then

Then starting with season three and on through season five, McCall drove a Bright Red 1987 Daytona Shelby Z ( Sometimes though, a " Turbo Z " badge on this Daytona is also clearly visible ).

Then, the Z < sub > 2 </ sub > parity of the number of χ particles is well defined and is conserved in time ( even though the number of χ particles itself depends on the choice of which splitting into a free Hamiltonian and an interacting Hamiltonian we make in the interaction picture, which doesn't even exist for interacting theories ( the number is typically infinite )).

If C is the centralizer of H we want to prove that C is contained in H. If not, pick a minimal characteristic subgroup M / Z ( H ) of C / Z ( H ), where Z ( H ) is the center of H, which is the same as the intersection of C and H. Then M / Z ( H ) is a product of simple or cyclic groups as it is characteristically simple.

Suppose that p is an odd prime number and a is a quadratic residue modulo p that is nonzero mod p. Then Hensel's lemma implies that a has a square root in the ring of p-adic integers Z < sub > p </ sub >.

Then, they will start " calling " their ships, which would come, usually all by themselves, back to Z ' ha ' dum, the planet the Shadows have long ago adopted as their home.

Then the coordinates of the d points of intersection are algebraic functions of the Plücker coordinates of U, and by taking a symmetric function of the algebraic functions, a homogeneous polynomial known as the Chow form ( or Cayley form ) of Z is obtained.

Then the unconditional distribution of Z is non-central chi-squared with k degrees of freedom, and non-centrality parameter.

Then the angle between X and Z is ( 2π − α − β ).

) Then X < sub > i </ sub > is the value ( or realization ) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μ < sub > i </ sub > and variance σ < sub > i </ sub >< sup > 2 </ sup > for all times i. Then the definition of the autocorrelation between times s and t is

For about three decades immediately before 1902 it was negative, reaching − 6. 64 s. Then it increased to + 63. 83 s at 2000.

Then s ( t ) can be represented as a recombination of complex exponentials of all possible frequencies:

Let t and s ( t > s ) be the sides of the two inscribed squares in a right triangle with hypotenuse c. Then s < sup > 2 </ sup > equals half the harmonic mean of c < sup > 2 </ sup > and t < sup > 2 </ sup >.

Then Israel laid his right hand on the younger Ephraim ’ s head and his left hand on the eldest Manasseh ’ s head and blessed Joseph.

Then Doe ’ s government declared an amnesty for all political prisoners and exiles, and released sixty political prisoners.

Then in 727, with the Exarchate of Ravenna in chaos over the Byzantine Emperor ’ s iconoclast decrees ( see below ), the Lombards captured and destroyed Classis and overran the Pentapolis.

Then on January 24, eight days before Stephen ’ s death, Afiarta dragged the blinded Sergius from his cell in the Lateran and had him strangled.

Then, in 1905, to explain the photoelectric effect ( 1839 ), i. e., that shining light on certain materials can function to eject electrons from the material, Albert Einstein postulated, based on Planck ’ s quantum hypothesis, that light itself consists of individual quantum particles, which later came to be called photons ( 1926 ).

Then the sufficient condition for exact reconstructability from samples at a uniform sampling rate f < sub > s </ sub > ( in samples per unit time ) is:

Then said Gangleri: Which are the Æsir in whom it is man ’ s duty to believe?

Then, in December 1965 and March 1966, Nature and The Lancet published the first preliminary reports by British cytogeneticist Patricia Jacobs and colleagues at the MRC Human Genetics Unit at Western General Hospital in Edinburgh of a chromosome survey of 315 male patients at The State Hospital outside Carstairs, Lanarkshire — Scotland ’ s only special security hospital for the developmentally disabled — that found nine patients, ages 17 to 36, averaging almost 6 ft. in height ( avg.

Then burr holes are created into the patient ’ s skull using a drill.

Then, in 1704 James Louis Sobieski and his brother Alexander were seized by Augustus II ’ s troops and imprisoned.

Then a fuzzy subset s: S of a set S is recursively enumerable if a recursive map h: S × N Ü exists such that, for every x in S, the function h ( x, n ) is increasing with respect to n and s ( x ) = lim h ( x, n ).

Then there ’ s freestyle where you come off the top of the head ".

Then, as now, potatoes were the area ’ s primary cash crop.

Then the set of satisficing options S ( ε ) can be defined as all those options s such that.

Then, on April 11, 1034, Zoe ’ s husband, Romanos III was found dead in his bath.

) There are also numerous instances where the killer is not brought to justice in the legal sense but instead dies ( death usually being presented as a more ' sympathetic ' outcome ), for example Death Comes as the End, And Then There Were None, Death on the Nile, Dumb Witness, The Murder of Roger Ackroyd, Crooked House, Appointment with Death, The Hollow, Nemesis, Cat Among the Pigeons, and The Secret Adversary.

Then comes the choripán ( a kind of spiced sausage made with pork or lamb and placed between two slices of bread ), and lastly meat such as asado de tira, vacío ( hindquarter ), lomo ( tenderloin ), colita de cuadril ( rump ), matambre ( rolled stuffed steak cut into slices and served cold ), entraña ( innards ); the list is never-ending.

Then in 1702 the French astronomer Philippe de la Hire used a year he labeled at the end of years labeled ante Christum ( BC ), and immediately before years labeled post Christum ( AD ) on the mean motion pages in his Tabulæ Astronomicæ, thus adding the designation 0 to Kepler's Christi.

Then they suggested Mu ' awiya ( founder of the Umayyad Caliphate ), but the Caliph again said no.

Then they suggested Abd al-Malik ibn Marwan ( one the greatest of the Umayyad caliphs ), but again no.

Then, following the battle, the Athenian army marched the 40 ( 25 miles ) or so kilometers back to Athens at a very high pace ( considering the quantity of armour, and the fatigue after the battle ), in order to head off the Persian force sailing around Cape Sounion.

Then the Greek army counter-attacked and defeated the Bulgarians at Kilkis-Lahanas ( Kukush ), after which the mostly Bulgarian town was destroyed and its population expelled.

Then followed Woolwich Common ( 1907 – 1908 ), Pound Park ( 1908 – 1913 ), and Angerstein Lane ( 1913 – 1915 ).

Then, according to Adkins ( 1975 ), it can be shown that one can write a further thermodynamic version of the above calorimetric rules:

Then being employed by the De Laurentiis Entertainment Group, he proceeded to make two films: the science-fiction epic Dune ( 1984 ), which proved to be a critical and commercial failure, and then a neo-noir crime film, Blue Velvet ( 1986 ), which was critically acclaimed.

Then deforestation rates accelerate ( HFHD, high forest cover – high deforestation rate ), and forest cover is reduced ( LFHD.

Christie's novels include, Murder on the Orient Express ( 1934 ), Death on the Nile ( 1937 ), and And Then There Were None ( 1939 ).

Then in 1743 he further alienated his father by marrying Antoinette Champion ( 1710 – 1796 ), a devout Roman Catholic.

Then, considering all three colour channels, and assuming that the colour channels are expressed in a γ = 1 colour space ( that is to say, the measured values are proportional to light intensity ), we have:

Then G is a group under composition, meaning that ∀ x ∈ A ∀ g ∈ G ( = ), because G satisfies the following four conditions:

Then, in terms of P < sub > n </ sub >( x ), the remainder

Then, in the time of Pope Gregory VII ( 1073 – 1085 ), canonists who in the Investiture Controversy quoted the prohibition in canon 22 of the Council of Constantinople of 869 – 870 against laymen influencing the appointment of prelates elevated this council to the rank of ecumenical council.

Then, in the grand final against Melbourne, Essendon set a grand final record score of 22. 18 ( 150 ) to Melbourne 13. 9 ( 87 ), with 7 goal centre half forward Gordon Lane.