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Then and general
Then in 1875, apparently in response to the nationalizing influence of the Civil War, Congress first gave the lower federal courts general authority -- concurrently with state tribunals -- to decide cases involving federal-right questions.
Then she catapults into `` everything and everybody '', putting particular violence on `` everybody '', indicating to the linguist that this is a spot to flag -- that is, it is not congruent to the patient's general style of speech up to this point.
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 he writes the music to the title and the general feeling of the song is established.
Then is a derivation and is linear, i. e., and, and a Lie algebra homomorphism, i. e.,, but it is not always an algebra homomorphism, i. e. the identity does not hold in general.
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 he announced to the world: " The independence of Austria, for which he has fallen, is a principle that has been defended and will be defended by Italy even more strenuously ", and then replaced in the main square of Bolzano the statue of Walther von der Vogelweide, a Germanic troubadour, with that of Drusus, a Roman general who conquered part of Germany.
Then, at around 1960 a critical resurgence in interest occurred which has resulted in making general relativity central to physics and astronomy.
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, other than general support, Milford left Foss largely to his own devices.
Then general officers in tall Astrakhan hats appeared, carrying the late leader's 21 decorations and medals on small red cushions.
Then general Augereau ( he of the Fructidor-coup ), now commander-in-chief of the French forces in the Netherlands, routinely closed the doors of the Assembly ( by previous arrangement with Pijman ) on September 19, and arrested the dissident Directors.
Then however Maniakes fell out with his Lombard allies, while his Norman mercenaries, unhappy with their pay, abandoned the Byzantine general and raised a revolt on the Italian mainland, resulting in the temporary loss of Bari.
Then a general invitation was given to all who desired to partake, which many did until the keg was emptied … In the evening they reassembled, burning Prof. Humiston in effigy about 10 p. m.
Abstractly, we can say that D is a linear transformation from some vector space V to another one, W. We know that D ( c ) = 0 for any constant function c. We can by general theory ( mean value theorem ) identify the subspace C of V, consisting of all constant functions as the whole kernel of D. Then by linear algebra we can establish that D < sup >− 1 </ sup > is a well-defined linear transformation that is bijective on Im D and takes values in V / C.
Then products like Platform Builder ( an integrated environment for Windows CE OS image creation and integration, or customized operating system designs based on CE ) offered several components in source code form to the general public.
Then in 580, the general Maurice launched a new offensive, raiding well beyond the Tigris.
Then governor general Adrienne Clarkson ( right ) meets with President of Russia Vladimir Putin in the governor general's study
Then general Soult decided to go around the mountainous border of the Upper Minho and make his penetration across the dry border of Trás-os-Montes.
Then, it briefly sets forth the underlying idea of a general relativity-like spacetime.
Then it discusses how de Sitter space describes a distinct variant of the ordinary spacetime of general relativity ( called Minkowski space ) related to the cosmological constant, and how anti de Sitter space differs from de Sitter space.
Then, he sent Manuel Villagrán, a relative of Artigas, to offer him the pardon and appoint him general and military leader of the Banda Oriental if he gave up the rebellion.
Then this can be seen by a direct computation for n any integer, and the general case reduces to this case without much difficulty.
Then, in January 1919, the Admiralty sent the officers whose training had been interrupted by the war to Cambridge University for a course of general duties.

Then and definition
) 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
Then the equivalence class of the pair can be identified with the rational number, and this equivalence relation and its equivalence classes can be used to give a formal definition of the set of rational numbers.
Then, the definition of a square may be recast with that abstraction as its genus:
Then, the definition of a square may be recast with that abstraction as its genus:
Then suppose definition B contains 32 instances of A ; C contains 32 instances of B ; D contains 32 instances of C ; and E contains 32 instances of D. The design now contains 5 definitions ( A through E ) and 128 instances.
The algorithm for deciding this is conceptually simple: it constructs ( the description of ) a new program t taking an argument n which ( 1 ) first executes program a on input i ( both a and i being hard-coded into the definition of t ), and ( 2 ) then returns the square of n. If a ( i ) runs forever, then t will never get to step ( 2 ), regardless of n. Then clearly, t is a function for computing squares if and only if step ( 1 ) terminates.
* Then extend the definition of truth to include sentences that predicate truth or falsity of one of the original subset of sentences.
Then by definition, torque τ = r × F.
Then, thus by T, which means w R w using the definition of.
Then x is an interior point of S if there exists a neighbourhood of x which is contained in S. Note that this definition does not depend upon whether neighbourhoods are required to be open.
Then the dasher writes the definition of the word ( as supplied on the card ) on a piece of paper.
Then n is palindromic if and only if a < sub > i </ sub > = a < sub > k − i </ sub > for all i. Zero is written 0 in any base and is also palindromic by definition.
Then by the definition of h.
Then we obtain the definition of a product.
Then a C-valued presheaf on X is the same as a contravariant functor from O ( X ) to C. This definition can be generalized to the case when the source category is not of the form O ( X ) for any X ; see presheaf ( category theory ).
Then follows a lengthened elucidation of the axiom that nothing can be produced from nothing, and that nothing can be reduced to nothing ( Nil fieri ex nihilo, in nihilum nil posse reverti ); which is succeeded by a definition of the Ultimate Atoms, infinite in number, which, together with Void Space ( Inane ), infinite in extent, constitute the universe.
Then, recalling the definition of:
Then the intersection number of two closed curves on X has a simple definition in terms of an integral.
Then one sets,, so that by definition, is the ratio of dy by dx.
Then using the rules in the definition, we find that for general vector fields and we get
Then, by the definition of.
Then followed 23 anathemas directed against Arius and his doctrines, succeeded by the creeds of Nicaea and Constantinople and the definition of Chalcedon, the whole being subscribed by 8 Arian bishops with their clergy, and by all the Gothic nobles.
Then, and, where is the set of curves given by the first definition at the beginning of this document.

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