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 following multiple protest from Jews in the new world and Holland and after his death they were even granted the right to pray, besides just trade.

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 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.

) Then, the transitions can proceed through the technifermion's dynamical mass by the emission and reabsorption of ETC bosons whose masses M < sub > ETC </ sub > ≅ g < sub > ETC </ sub > Λ < sub > ETC </ sub > are much greater than Λ < sub > TC </ sub >.

Then fill the system and add a rust inhibitor.

Then, standard tools such as ls, cp, and rm can be used to manipulate files on the remote system.

Then the pair (( A < sub > i </ sub >)< sub > i ∈ I </ sub >, ( f < sub > ij </ sub >)< sub > i ≤ j ∈ I </ sub >) is called an inverse system of groups and morphisms over I, and the morphisms f < sub > ij </ sub > are called the transition morphisms of the system.

* Let the index set I of an inverse system ( X < sub > i </ sub >, f < sub > ij </ sub >) have a greatest element m. Then the natural projection π < sub > m </ sub >: X → X < sub > m </ sub > is an isomorphism.

Then on Oct 23, 1972, Balliett's student, Dr. Juno Jordan, changed Numerology further and helped it to become the system known today under the title " Pythagorean ", although Pythagoras himself had nothing to do with the system.

Then, as the number of users increases, the system becomes even more valuable and is able to attract a wider user base.

Then, on August 15, 1971, United States President Richard Nixon announced that the United States dollar would no longer be convertible to gold, effectively ending the system.

Then we can translate this system into fuzzy program in such a way that f is the interpretation of a vague predicate Good ( x, y ) in the least fuzzy Herbrand model of this program.

Then hypothiocyanite, OSCN, cannot be produced by immune defense system.

Then the system is in state

Then, using physical arguments, one derives a suitable " fundamental volume " for the particular system to reflect the fact that quantum mechanical microstates are discretely distributed on the phase space.

Then the solutions to the homogeneous system given in parametric form with x < sub > 3 </ sub >, x < sub > 5 </ sub >, and x < sub > 6 </ sub > as free variables are

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

Then the density matrix for this system is

Then the matrices would progress through the machine, where a special keying system on one end of the matrix, unique for each character, would allow the matrix to drop only into the correct storage slot, ready for future use.

Then we will study the coordinate transformations between this coordinate and the fixed " laboratory " system.

Then there is the type of activity that uses the network to waste time, as indicated in SurfControl's advice on writing AUPs, of technical staff to troubleshoot a problem for which the user is the cause, corrupting or destroying other user's data, violating the privacy of others online, using the network in such a way that it denies the service to others, continuing to use software or other system for which the user has already been warned about using, and any other misuse of the network such as introduction of viruses.

Then, oxygen is added to the system.

Then, as community sentiment favored forming a public school system, the college was closed, and the property deeded to the Pea Ridge Public School.