"< ref >, From the Gracchi to Nero: History of Rome from 133 B. C. to A. D. 68, London, 1982 < sup > 5 </ sup >, p. 303 .</ ref >

: From this list we extract an increasing sublist: put m < sub > 0 </ sub >= n < sub > 0 </ sub >, after finitely many steps we find an n < sub > k </ sub > such that n < sub > k </ sub > > m < sub > 0 </ sub >, put m < sub > 1 </ sub >= n < sub > k </ sub >.

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.

From a more advanced perspective, each of these definitions may be interpreted as giving the unique analytic continuation of e < sup > x </ sup > to the complex plane.

From this initial rational point, one can then compute an infinite number of v < sub > i </ sub >.

From the radian frequency, the natural frequency, f < sub > n </ sub >, can be found by simply dividing ω < sub > n </ sub > by 2π.

From this property, one can deduce that h maps the identity element e < sub > G </ sub > of G to the identity element e < sub > H </ sub > of H, and it also maps inverses to inverses in the sense that

From 3. we obtain ( a * b )< sup >− 1 </ sup >

From a geometric perspective, a function f is holomorphic at z < sub > 0 </ sub > if and only if its exterior derivative df in a neighborhood U of z < sub > 0 </ sub > is equal to f ′( z ) dz for some continuous function f ′.

His comment on Numbers 23: 19 has a still more polemical tone: “ God is not a man that he should lie ; neither the son of man, that he should repent ; < font face =" times new roman " size = 3 > if a man says: ‘ I am a god ’ he is a liar ; if he says: ‘ I am a son of man ’ he will have cause to regret it ; and if he says, ‘ I will go up to heaven ’ he has said but will not keep his word ” last phrase is borrowed from B ' midbar 23: 19 ( Yer.

In ultra high fidelity amplifier design, the amp's frequency response should extend considerably beyond this ( one or more octaves either side ) and might have points < 10 Hz and >.

Later evidence indicated that these should be reassigned to < sup > 258 </ sup > 105 and < sup > 258 </ sup > 104 ( see above ).

Some writers, such as James-Charles Noonan, hold that, in the case of cardinals, the form used for signatures should be used also when referring to them, even in English ; and this is the usual but not the only way of referring to cardinals in Latin .< ref > An Internet search will uncover some hundreds of examples of " Cardinalis Ioannes < surname >", examples modern and centuries-old ( such as this from 1620 ), and the phrase " dominus cardinalis Petrus Caputius " is found in a document of 1250.

Since the map d restricts to 0 on I < sub > x </ sub >< sup > 2 </ sup > ( the reader should verify this ), d descends to a map from I < sub > x </ sub > / I < sub > x </ sub >< sup > 2 </ sup > to the dual of the tangent space, ( T < sub > x </ sub > M )< sup >*</ sup >.

In an extrapolation of the chemistries from niobium and tantalum, dubnium should react with oxygen to form an inert pentoxide, Db < sub > 2 </ sub > O < sub > 5 </ sub >.

Reaction with the halogens should readily form the pentahalides, DbX < sub > 5 </ sub >.

Similarly, the pentafluoride, DbF < sub > 5 </ sub >, should be even more volatile.

Thus the halides DbX < sub > 5 </ sub > should react with water to form DbOX < sub > 3 </ sub >.

The @ symbol was not used in continental Europe and the committee expected it would be replaced by an accented À in the French variation, so the @ was placed in position 40 < sub > hex </ sub > next to the letter A.

However, since no equipment existed to show the images in motion, such a series of images cannot be called animation in a true sense of the word .< ref >

In the second example CH < sub > 3 </ sub > COOH undergoes the same transformation, in this case donating a proton to ammonia ( NH < sub > 3 </ sub >), but cannot be described using the Arrhenius definition of an acid because the reaction does not produce hydronium.

Note that the acid can be the charged species and the conjugate base can be neutral in which case the generalized reaction scheme could be written as HA < sup >+</ sup > H < sup >+</ sup > + A.

The stronger of two acids will have a higher K < sub > a </ sub > than the weaker acid ; the ratio of hydrogen ions to acid will be higher for the stronger acid as the stronger acid has a greater tendency to lose its proton.

During the Romantic period, art came to be seen as " a special faculty of the human mind to be classified with religion and science ".< ref >

so it follows that if the voltage is doubled and the power remains the same, the current will be halved .</ ref >

There are millions of asteroids, many thought to be the shattered remnants of planetesimals, bodies within the young Sun ’ s solar nebula that never grew large enough to become planets .< ref >

If the method is applied to an infinite sequence ( X < sub > i </ sub >: i ∈ ω ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.

Afterwards, he does not want to be interviewed by the police, since he has committed a crime by attempting suicide, and fears arrest .</ br > Cottard's personality changes after the outbreak of plague.

While this loss of precision may be tolerable and viewed as a minor flaw of Algorithm I, it is easy to find data that reveal a major flaw in the naive algorithm: Take the sample to be ( 10 < sup > 9 </ sup > + 4, 10 < sup > 9 </ sup > + 7, 10 < sup > 9 </ sup > + 13, 10 < sup > 9 </ sup > + 16 ).

Octal numbers that are used in some programming languages ( C, Perl, PostScript …) for textual / graphical representations of byte strings when some byte values ( unrepresented in a code page, non-graphical, having special meaning in current context or otherwise undesired ) have to be to escaped as < tt >

So, it was argued, the Mediterranean had once opened a passage for itself by the Columns of Hercules into the Atlantic, and perhaps the abundance of sea-shells in Africa, near the Temple of Jupiter Ammon, might also be the deposit of some former inland sea, which had at length forced a passage and escaped .</ p >

< p > In another place, this learned geographer, in alluding to the tradition that Sicily had been separated by a convulsion from Italy, remarks, that at present the land near the sea in those parts was rarely shaken by earthquakes, since there were now open orifices whereby fire and ignited matters and waters escaped ; but formerly, when the volcanoes of Etna, the Lipari Islands, Ischia, and others, were closed up, the imprisoned fire and wind might have produced far more vehement movements.

It is believed that someone was keeping the animal illegally and it had escaped .< ref >' The Beast of Cricklewood is caged '< cite > http :// www. telegraph. co. uk / news / uknews / 1329632 / The-Beast-of-Cricklewood-is-caged. html </ ref > The lynx was taken to London Zoo, and named Lara .< ref >' Captured ' Beast Of Barnet ' Recovers In Zoo '< cite > http :// 100megsfree4. com / farshores / abc_uk85. htm </ ref >

< span lang =" fr "> Moulin </ span > escaped, < span lang =" fr "> Gohier </ span > was taken prisoner, and the two Councils were not immediately intimidated and continued to meet.

Livingstone, < cite > The Oxford Dictionary of the Christian Church </ cite >, ( Oxford: Oxford University Press, 1983 ), 975 sub loco </ ref > He narrowly escaped execution and survived imprisonment.

In 1886, she escaped conviction on another theft charge, but on December 17, Sam Starr was involved in a gunfight with Officer Frank West .< ref >

If one of the arguments is a string that contains a comma, it is escaped by using a backslash or the < tt >

The commandos escaped on board their ALCs .< REF NAME = Sunstar2 > Marthe Rambaud et Jean-Claude Bosquain ( 1995 ).

According to the Book of Mormon, when Jerusalem was destroyed by Babylon during the reign of Zedekiah, all of the sons of Zedekiah were killed except Mulek .< Ref > Helaman 8: 21 Along with " as many as would hearken unto the voice of the Lord ," Mulek escaped into the wilderness and traveled " across the great waters " to the Americas, founding a new nation.

How many inhabitants perished on land and in sea is unknown .< ref > According to Ludolph of Suchem ( which seems exaggeration ): " In Acre and the other places nearly a hundred and six thousand men were slain or taken, and more than two hundred thousand escaped from thence.

From there the family could raise a lantern on a flagpole to signal fleeing slaves in Kentucky when it was safe for them to cross the Ohio River .< sup ></ sup > Rankin also constructed a staircase leading up the hill to the house for slaves to climb up to safety on their way further north .< sup ></ sup > For over forty years leading up to the Civil War, many of the 2000 slaves who escaped to freedom through Ripley stayed at the family's home, and none was ever recaptured there.

Todd ’ s home in Tabor served not only as a ‘ station ’ on the Underground Railroad, complete with a concealed room in which escaped slaves hid until their next ride arrived < ref > Tabor Historical Society, Tabor, Iowa < http :// www. taborhistoricalsociety. org /></ ref >, but also as a storehouse of weapons, ammunition and other supplies for radical abolitionist John Brown.

* < sup > a </ sup > " The advantage of a high school education escaped him, a most fortunate quirk of destiny, for it was that very fact that contributed to his genius ; I always suspected that the lack of a formal education was what made him an authentic original.