" From these principles and some additional constraints —( 1a ) a lower bound on the linear dimensions of any of the parts, ( 1b ) an upper bound on speed of propagation ( the velocity of light ), ( 2 ) discrete progress of the machine, and ( 3 ) deterministic behavior — he produces a theorem that " What can be calculated by a device satisfying principles I – IV is computable.

From 552 to 745, Göktürk leadership bound together the nomadic Turkic tribes into an empire, which eventually collapsed due to a series of dynastic conflicts.

From Dublin, he crossed to Liverpool to become an ordinary seaman on the British merchant ship Tangier ( also recorded as Tanjore ), bound for China.

From the House of the Interpreter, Christian finally reaches the " place of deliverance " ( allegorically, the cross of Calvary and the open sepulcher of Christ ), where the " straps " that bound Christian's burden to him break, and it rolls away into the open sepulchre.

From there, about 3, 000 were sent to America either directly or through England, bound for William Penn's colony.

From 1833 to 1835, Livingston was minister plenipotentiary to France, charged with procuring the fulfilment by the French government of the treaty negotiated by W. C. Rives in 1831, by which France had bound herself to pay an indemnity of twenty-five millions of francs for French spoliations of American shipping chiefly under the Berlin and Milan decrees, and the United States in turn agreed to pay to France 1, 500, 000 francs in satisfaction of French claims.

A scene with Emma Peel bound and threatened with a death ray in the episode From Venus with Love is a direct parallel to James Bond's confrontation with a laser in the film Goldfinger.

From 1700 he initiated what has been called a " successful racket " where he would write occasional poems, typically eulogistic or nuptial verse, have them bound up in notably ostentatious armorial bindings, which he would send to the wealthy person whose arms he used.

From the late 12th century, the office was considered to be bound with the Earldom of Leicester.

From 1847 to 1862, most Chinese contract laborers (" coolies ") bound for Cuba were shipped on American vessels, and numbered about 600, 000 per year.

From there he transferred to another ship bound for the Madeira Islands, located 535 miles from mainland Europe.

From 1955 to 1963 Prouty was the " Focal Point Officer " for contacts between the CIA and the Pentagon on matters relating to military support for " special operations " but he was not assigned to the CIA and was not bound by any oath of secrecy.

From 2 November 1944 until 2 January 1945 at such time as Fifteenth Army left Ft. Sam Houston, Texas, bound for movement overseas, Colonel Louis Compton was designated commander of Fifteenth Army .< ref >< cite > History of the Fifteenth United States Army, page 10 </ ref > From New York, on 3 November, they sailed bound for Greenock, Scotland on the Queen Mary, arriving 10 November 1944.

From the time of the acquisition of Macau in 1557, and their formal recognition as trade partners by the Chinese, the Portuguese Crown started to regulate trade to Japan, by selling to the highest bidder the annual " Capitaincy " to Japan, in effect conferring exclusive trading rights for a single carrack bound for Japan every year.

From the 1950s through the 1960s the song was given to Vermont school children in a soft bound booklet titled Vermont Sings.

From highest to lowest, they were bound to the palace economy by indissoluble bonds of involuntary servitide or patronage.

From then on all white men were bound to be their enemies and yet their own fighting power had been severely reduced.

From its creation until 1984, the road was the main entrance for cars bound for boarding the car ferry.

) From this norm we are able to establish a lower bound on the sum of the ( differential ) Rényi entropies where For simplicity, we consider this inequality only in one dimension ; the extension to multiple dimensions is straightforward and can be found in the literature cited.

From the time of the acquisition of Macau in 1557, and their formal recognition as trade partners by the Chinese, the Portuguese Crown started to regulate trade to Japan, by selling to the highest bidder the annual " Captaincy " to Japan, in effect conferring exclusive trading rights for a single carrack bound for Japan every year.

From an initial investment of $1,200 in 1943, it has grown, with no additional capital investment, to a present value estimated by some as exceeding $10,000,000 ( we don't disclose financial figures to the public ).

From the records we keep -- Susan is the only Junior who has placed in the Junior Classes in both United States and Canada.

From the wealth of material and the wide variety of different electronic techniques perfected in the past few years we have selected a few examples which appear to be headed for use in the immediate future and which offer completely new tools in medical research.

From the dated poems we can venture certain conclusions about Hardy's career in poetry, always remembering that conclusions based on a fraction of the whole must remain tentative.

From all this we can now see that two streams of development run through the history of twentieth-century American folklore.

From this taste of the 1920s, we leaped way out to Stan Getz's private brand of progressive jazz, which did lovely, subtle things for `` Baubles, Bangles And Beads '', and a couple of ballards.

From the outset, these were not intended to displace the autonomy of the emerging provinces of the Communion, but to " discuss matters of practical interest, and pronounce what we deem expedient in resolutions which may serve as safe guides to future action.

From the assumption of small disturbances we have

From there we see Jesus ' ministry move from Galilee ( chapters 4 – 9 ), through Samaria and Judea ( chs.

From the sources and from inlay-work we have also representations of palaces and houses.

From that work we learn that the higher education of the youth of Baghdad consisted principally in a minute and careful study of the rules and principles of grammar, and in their committing to memory the whole of the Qur ' an, a treatise or two on philology and jurisprudence, and the choicest Arabic poetry.

From Acts 18: 24-28 we deduce that Apollos had an ' accurate ' understanding of Jesus most likely derived from the Scriptures.

From basic functional analysis we know that any ket can be written as

From the end of the 15th century we have printed ballads that suggest a rich tradition of popular music.

Nelson publicly encouraged this close bond with his officers and on 29 September 1798 described them as " We few, we happy few, we band of brothers ", echoing William Shakespeare's play Henry V. From this grew the notion of the Nelsonic Band of Brothers, a cadre of high-quality naval officers that served with Nelson for the remainder of his life.

From the formula, we can see the standard deviation is proportional to the square root of the number of rounds played, while the expected loss is proportional to the number of rounds played.

: 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 Suetonius, we know that she at least accompanied the Emperor to the amphitheatre, while the Jewish writer Josephus speaks of benefits he received from her.

From Weierstrass he derives the idea that we generate the concept of number by counting a certain collection of objects.

From this relation we see that the increase in enthalpy of a system is equal to the added heat

Many new words can be derived simply by changing these suffixes, just as-ly derives adverbs from adjectives in English: From vidi ( to see ), we get vida ( visual ), vide ( visually ), and vido ( sight ).

From now on, we can fire thousands of these rockets all over the world with very little cost.

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