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 a general definition of isomorphism that covers the previous and many other cases is: an isomorphism is a morphism that has an inverse, i. e. there exists a morphism with and.

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 the previous expression is equal to the product of two factors:

Then, using the periodic Bernoulli function P < sub > n </ sub > defined above and repeating the argument on the interval, one can obtain an expression of ƒ ( 1 ).

Then the expression of the fine-structure constant becomes the abbreviated

Then, the relativistic expression for the angular distribution of the bremsstrahlung ( considering only the dominant dipole radiation contribution ), is

Then, still black with smoke and with his uniform in shreds, Nelson went on board Victory where he was received on the quarter-deck by Admiral Jervis – " the Admiral embraced me, said he could not sufficiently thank me, and used every kind expression which could not fail to make me happy.

Then combining the last two expression with Beer's law, molar ellipticity becomes:

Then one faces the problem of expression sin ( θ ) and cos ( θ ) as functions of x.

Then, for this expression, one has

Then for each input to that machine, build a Boolean expression which says that the input is passed to the machine, the machine runs correctly, and the machine halts and answers " yes ".

Then the expression can be satisfied if and only if there is a way for the machine to run correctly and answer " yes ", so the satisfiability of the constructed expression is equivalent to asking whether or not the machine will answer " yes ".

Then expression ( 2 ) becomes:

Then figures become more animated in pose and facial expression, tend to be smaller in relation to the background of scenes, and are arranged more freely in the pictorial space, where there is room.

* How to & Then Some: 27 chapters ( 374 pages ) which discuss the full spectrum of sexual expression and its practical aspects, starting from romance and kissing through the different ways people have sex.

Then, as Wally leaves the room with a parting bon mot and the canned laughter kicks in, the camera catches June's bewildered, dazed, or amused facial expression.

" Fans find the expression useful, too ... Avoidism: Not originally fannish at all, but a philosophy devised in a rather stomach-turning book, In One Head and Out the Other, this doctrine became confused / associated with the Gandhi-following folk of Eric Frank Russell's " And Then There Were None ".

Then, the set of the Hamiltonian's equations given in the introduction can be expressed in a single expression as

Then, the expression given above for is not the only one that is compatible with such distribution for, and.

Then, unless, then number q has a parent in the Stern – Brocot tree given by the continued fraction expression