Then, following the programme he outlined in his talk at the 1958 International Congress of Mathematicians, he introduced the theory of schemes, developing it in detail in his Éléments de géométrie algébrique ( EGA ) and providing the new more flexible and general foundations for algebraic geometry that has been adopted in the field since that time.

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 after-depolarization this effect leads initially to bigeminy: regular ectopic beats following each ventricular contraction.

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

Then, for any given sequence of integers a < sub > 1 </ sub >, a < sub > 2 </ sub >, …, a < sub > k </ sub >, there exists an integer x solving the following system of simultaneous congruences.

Then the following three connected theorems hold:

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

Then the following month, on May 31st 1902, in a letter to William Blackwood, Conrad remarks:

Then the generation following them received it, thus conveying it to those after them and so on.

It is frequently stated in the following equivalent form: Suppose that is continuous and that u is a real number satisfying or Then for some c ∈ b, f ( c ) = u.

This melding of scientific and social speculation is clearly present in the novel Voyage from Yesteryear ( strongly influenced by Eric Frank Russell's famous story " And Then There Were None ") about a high-tech anarchist society in the Alpha Centauri system, a starship sent from Earth by a dictatorial government, and the events following their first contact.

Then the following formula is an axiom:

Then the following are equivalent.

Then a subset is called a σ-algebra if it satisfies the following three properties:

Let U be a functor from D to C, and let X be an object of C. Then the following statements are equivalent:

Then in March of the same year, following the insurrection of the Paris Commune the French government under Thiers relocated to Versailles, from where the insurrection was militarily quelled.

Then the following dynamical system describes PLL behavior

Then the priest blesses kolyva ( boiled wheat with honey and raisins ) which is distributed to the faithful in commemoration of the following miracle worked by St. Theodore on the First Saturday of Great Lent: Fifty years after the death of St Theodore, the emperor Julian the Apostate ( 361-363 ), as a part of his general policy of persecution of Christians, commanded the governor of Constantinople during the first week of Great Lent to sprinkle all the food provisions in the marketplaces with the blood offered to pagan idols, knowing that the people would be hungry after the strict fasting of the first week.

Then, Cicero had the incriminating letters read before the Senate the following day, and shortly thereafter these five conspirators were condemned to death without a trial despite an eloquent protest by Julius Caesar.

Then, to construct the elements of following rows, add the number above and to the left with the number above and to the right to find the new value.

Then, each person decorates their page following the theme.

Then the following regression equation is postulated as a description of the process that generated the data:

Then write a review without using any of the following words: " Progressive rock ", " Genesis ", " Fish ", " heavy metal ", " dinosaurs ", " predictable ", " concept album ".

Then on September 22, 1862, George McClellan defeated Robert E. Lee at Antietam ; the second draft of the Emancipation Proclamation was issued to the public the following day.

In a few of her novels, including Death Comes as the End and And Then There Were None, there are multiple victims.

# Then at the operating system level ( to let system software access multiple address spaces and utilize larger address spaces )

Then, as more features are added to support each viewpoint, it might be necessary to have cross-conversion features between the multiple viewpoints, further complicating the total features.

Then Li Chunfeng ( 李淳風 ) of the Tang dynasty created one in 633 CE with three spherical layers to calibrate multiple aspects of astronomical observations, calling them ' nests ' ( chhung ).

Then multiple internal compartment / bulkheads accessed by separate hatches and ladders, reminiscent of the interior structure of bamboo were built in.

Then the Sundays ' daughter, the only child actually raised by Nell, died in 1932 of what seems to have been multiple sclerosis.

Then the latest entry to the quotient, 2, is multiplied by the divisor 4 to get 8, which is the largest multiple of 4 that does not exceed 10 ; so 8 is written below 10, and the subtraction 10 minus 8 is performed to get the remainder 2, which is placed below the 8.

) Then the kernel is the space of multiples of exp ( λx ) if λ is an integral multiple of 2πi and is 0 otherwise, and the kernel of the adjoint is a similar space with λ replaced by its complex conjugate.

Then in April 2004 On2 announced that negotiations with E-World had broken down and that On2 would file multiple breach of contract claims against E-World in arbitration proceedings.

Then the surgeon makes multiple palmar puncture wounds with small nicks.

Then he took multiple copies of the message and laid them one-above-another, each one shifted left by the length of the key.

Then the matrix defines an automorphism of ρ, which is clearly not a scalar multiple of the identity matrix.

Then in April 2004, On2 announced that its business relationship with E-World had soured, and that On2 would file multiple breach of contract claims against E-World in arbitration proceedings.

Then, we can have punctures in the plane, holes so to speak so that if γ is a closed path which winds once around the puncture, is only an integer multiple of 2π.

Then he deals with the matters " directly concerned with the birth ", explaining how to judge such issues as whether the child will be male or female ( ch. 6 ); whether the birth will produce twins or multiple children ( ch. 7 ); and whether it will involve physical defects or monstrous forms ; if so, whether these are accompanied by mental deficiency, notability or honour ( ch. 8 ).

Then any odd prime p divides whenever M is a multiple of, where

Then, two or multiple man sets are practiced to train responses and applications of techniques learned from the sets.

Then next season, Dennis returned for three races, before being replaced by multiple drivers.

Then next season, Dennis returned for three races, before being replaced by multiple drivers.