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follows and two
Another less ambiguous case read as follows: `` The bearer of this letter has served me for two years to his complete satisfaction.
A final class of exceptional lines is identifiable from the following considerations: Since no two generators of Af can intersect, it follows that their image curves can have no free intersections.
Since two curves of symbol Af on Q intersect in Af points, it follows that there are Af lines of Af which are tangent to Aj.
Using the F-distribution is a natural candidate because the test statistic is the ratio of two scaled sums of squares each of which follows a scaled chi-squared distribution.
* There then follows the Frühjahrsmarkt ( Spring market ) two weeks before Easter, when all the shops in the town are permitted to open on Sunday ( which is normally prohibited in Bavaria ).
In mathematics, the arithmetic – geometric mean ( AGM ) of two positive real numbers and is defined as follows:
It follows that expressions involving only two variables can be written without parenthesis unambiguously in an alternative algebra.
The film follows two juxtaposed families: the Northern Stonemans, consisting of the abolitionist Congressman Austin Stoneman ( based on the Reconstruction-era Congressman Thaddeus Stevens
The leaching of CuFeS < sub > 2 </ sub > follows the two stages of being dissolved and then further oxidised, with Cu < sup > 2 +</ sup > ions being left in solution.
Jean Froissart states as follows: " Now will I name some of the principal lords and knights ( men-at-arms ) that were there with the prince: the earl of Warwick, the earl of Suffolk, the earl of Salisbury, the earl of Oxford, the lord Raynold Cobham, the lord Spencer, the lord James Audley, the lord Peter his brother, the lord Berkeley, the lord Basset, the lord Warin, the lord Delaware, the lord Manne, the lord Willoughby, the lord Bartholomew de Burghersh, the lord of Felton, the lord Richard of Pembroke, the lord Stephen of Cosington, the lord Bradetane and other Englishmen ; and of Gascon there was the lord of Pommiers, the lord of Languiran, the captal of Buch, the lord John of Caumont, the lord de Lesparre, the lord of Rauzan, the lord of Condon, the lord of Montferrand, the lord of Landiras, the lord Soudic of Latrau and other ( men-at-arms ) that I cannot name ; and of Hainowes the lord Eustace d ' Aubrecicourt, the lord John of Ghistelles, and two other strangers, the lord Daniel Pasele and the lord Denis of Amposta, a fortress in Catalonia ".
Richard T. Cox showed that Bayesian updating follows from several axioms, including two functional equations and a controversial hypothesis of differentiability.
Using terms from formal language theory, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets, respectively.
Source code is written in a programming language that usually follows one of two main paradigms: imperative or declarative programming.
The relation he there gives of the miracle is as follows: " On the nones ( or 7th ) of May, about the third hour, ( or nine in the morning ,) a vast luminous body, in the form of a cross, appeared in the heavens, just over the holy Golgotha, reaching as far as the holy mount of Olivet, ( that is, almost two English miles in length ,) seen not by one or two persons, but clearly and evidently by the whole city.
It follows from this theorem that all Carmichael numbers are odd, since any even composite number that is square-free ( and hence has only one prime factor of two ) will have at least one odd prime factor, and thus results in an even dividing an odd, a contradiction.
From the criterion it also follows that Carmichael numbers are cyclic .< ref > Proof sketch: If is square-free but not cyclic, for two prime factors and of.
The table below is constructed as follows: the second column contains the values of the polynomial, the third column contains the differences of the two left neighbors in the second column, and the fourth column contains the differences of the two neighbors in the third column:
Another product rule for the cross product of two vector fields F and G in three dimensions involves the curl and reads as follows:
Of course, if two stations transmit on the same frequency, it is practically impossible for the receiver to separate them ; so instead of all stations transmitting at the same frequency, each chain was allocated a nominal frequency, 1f, and each station in the chain transmitted at a harmonic of this base frequency, as follows:
The tangential components of the electric and magnetic fields as they relate on the boundary of two media are as follows:
It was " set in Argentina, with the reunion of two brothers, the story follows the rivalries born out of creative differences passed down through generations of an artistic Italian immigrant family.
In the Ynglinga Saga of Snorri Sturluson the entire story is told as follows: " Othin had two brothers.
The film follows the lives of two seemingly disparate teenage girls who begin a tentative romantic relationship.

follows and other
in addition to the miscellaneous pamphlets and other printed matter which it issues, the College maintains regular publications, as follows:
These publications may be secured as follows: The Annual Catalog from the Director of Admissions and other issues from the Publications Office.
This follows naturally since frontage on an ocean, stream, or lake provides scenic values and opportunities for the very popular recreation activities of bathing, fishing, boating, and other water sports.
Makes necessary purchases, places contracts, supervises construction, installation, finishing and placement of furniture, fixtures and other correlated furnishings, and follows through to completion of project ''.
For finite sets X, the axiom of choice follows from the other axioms of set theory.
In dogma he follows Basil of Caesarea and other Greek authors, but nevertheless gives a distinctly Western cast to the speculations of which he treats.
This conservation law mathematically follows from continuous directional symmetry of space ( no direction in space is any different from any other direction ).
In " A Village Sketch ," author Miss Mitford wrote: " Then comes a sun-burnt gipsy of six, beginning to grow tall and thin and to find the cares of the world gathering about her ; with a pitcher in one hand, a mop in the other, an old straw bonnet of ambiguous shape, half hiding her tangled hair ; a tattered stuff petticoat once green, hanging below an equally tattered cotton frock, once purple ; her longing eyes fixed on a game of baseball at the corner of the green till she reaches the cottage door, flings down the mop and pitcher and darts off to her companions quite regardless of the storm of scolding with which the mother follows her runaway steps.
At the end, however, he follows other gods and oppresses Israel.
The exact expression " the Day of the Lord ”, from Obadiah 1: 15, has been used by other authors throughout the Old and New Testaments, as follows:
Essentially, every country that was colonised at some time by England, Great Britain, or the United Kingdom uses common law except those that were formerly colonised by other nations, such as Quebec ( which follows the law of France in part ), South Africa and Sri Lanka ( which follow Roman Dutch law ), where the prior civil law system was retained to respect the civil rights of the local colonists.
On the other hand, some cosmologists insist that energy is conserved in some sense ; this follows the law of conservation of energy.
The doctrinal acts are as follows: after reaffirming the Niceno-Constantinopolitan Creed ( third session ), the decree was passed ( fourth session ) confirming that the deuterocanonical books were on a par with the other books of the canon ( against Luther's placement of these books in the Apocrypha of his edition ) and coordinating church tradition with the Scriptures as a rule of faith.
Intuitively, the process can be pictured as follows: first shrink the real line to the open interval (- π, π ) on the x-axis ; then bend the ends of this interval upwards ( in positive y-direction ) and move them towards each other, until you get a circle with one point ( the topmost one ) missing.
Chapter 11 follows the same priority scheme as other bankruptcy chapters.
In May 1955 McCarthy threatened to issue subpoenas to White House personnel ; Eisenhower was furious, and issued an order as follows: " It is essential to efficient and effective administration that employees of the Executive Branch be in a position to be completely candid in advising with each other on official matters ... it is not in the public interest that any of their conversations or communications, or any documents or reproductions, concerning such advice be disclosed.
The rule is deterministic ; in other words, for a given time interval only one future state follows from the current state.
New World's budget breakdown for Godzilla 1985 is as follows: $ 500, 000 to lease the film from Toho, $ 200, 000 for filming the new scenes and other revisions, and $ 2, 500, 000 for prints and advertising, adding up to a grand total of approximately $ 3, 200, 000.
The purpose of these shafts is not clear: they appear to be aligned on stars or areas of the northern and southern skies, but on the other hand one of them follows a dog-leg course through the masonry so there was not intention to directly sight stars through them.
" The Constitution grants the Governor-General a wide range of powers, but in practice he or she follows the conventions of the Westminster system and ( with rare exceptions ) acts only on the advice of the Prime Minister of Australia or other ministers.
Notable among them are: ( 1 ) whether the word " eden " means a steppe or plain, or instead means " delight " or some similar term ; ( 2 ) whether the garden was in the east of Eden, or Eden itself was in the east, or whether " east " is not the correct word at all and the Hebrew means the garden was " of old "; ( 3 ) whether the river in Genesis 2: 10 " follows from " or " rises in " Eden, and the relationship, if any, of the four rivers to each other ; and ( 4 ) whether Cush, where one of the four rivers flows, means Ethiopia ( in Africa ) or Elam ( just east of Mesopotamia ).
In the important special case of module homomorphisms, and for some other classes of homomorphisms, there are much simpler descriptions, as follows:

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