With increasing level of generality, it turns out, an increasing amount of technical background is helpful or necessary to understand these theorems: the modern formulation of both these dualities can be done using derived categories and certain direct and inverse image functors of sheaves, applied to locally constant sheaves ( with respect to the classical analytical topology in the first case, and with respect to the étale topology in the second case ).

With helpful assistant Tip, the player must navigate to the Aquadome in the new untested two-person submarine Scimitar and investigate the problem.

With approximately half of potable water in urban areas being used for irrigation, and many homeowners either not taking the time to regularly adjust the programming on their controllers or simply not knowing how, these " smart controllers " have been shown to be helpful in achieving water conservation.

With further education on the symptoms and implications of child psychopathology, psychologists and physicians will improve their accuracy in diagnosing children-giving the right diagnosis and discovering the most helpful treatment and therapies for children.

With EPIC, the compiler determines in advance which instructions can be executed at the same time, so the microprocessor simply executes the instructions and does not need elaborate mechanisms to determine which instructions to execute in parallel.

With the advent of higher level languages, computer architects also started to create dedicated instructions to directly implement certain central mechanisms of such languages.

With very few exceptions, the 80486 and subsequent x86 processors then integrated this x87 functionality on chip which made the x87 instructions a de facto integral part of the x86 instruction set.

With the instructions from his father, he extended his arms.

With no byte addressing instructions at all, code had to be written to pack and shift characters into words.

With a 12 MHz clock frequency, the 8051 could thus execute 1 million one-cycle instructions per second or 500, 000 two-cycle instructions per second.

* Various constructions using compass and straightedge With interactive animated step-by-step instructions

With the help of interpreters and pictures which he carried with him, he gave basic instructions and assured the slaves of their human dignity and God's saving love.

With the combination of video and audio, the expert can mimic the one on one experience of the classroom and deliver clear, complete instructions.

With chaining, this could be coded as " A 700, 850 ", " A ", " A "-omitting data address from the 2nd and 3rd instructions.

With a judicious choice for the single instruction and given infinite resources, an OISC is capable of being a universal computer in the same manner as traditional computers that have multiple instructions.

With these last instructions, the expedition crossed the Atlantic and founded the first settlement at St. Mary's in 1634 on land purchased from the native Yaocomico.

With branch predication, all possible branch paths are coded inline, but some instructions execute while others do not.

With Villers-Bocage in British hands A Squadron 4CLY motored ahead to Point 213 without additional reconnaissance, according to their instructions.

With the settlement now solidly behind him, Riel proposed the formation of a new convention of forty representatives, split evenly between French-and English-speaking settlers, to consider Smith's instructions.

With the support of the Premier Edward Stafford, Grey evaded instructions from the Colonial Office to finalise the return of the regiments, which had commenced in 1865 and 1866.

With no orders from Mathews and a lack of clear instructions or command structure, the British line broke, and began to flee to the northwest.

With a four stage pipeline, the rate at which instructions are executed is four times that of sequential execution.

With the accession of Peter III of Russia, formerly Duke of Holstein, formerly elected King of Sweden by the Swedish Parliament, former King of Finland by his aunt decision, the Russian Empress, soon to be assassinated after only 6 months of being " promoted " to new Emperor of Russia, he received instructions ( May 1762 ) to join his forces with the former enemies, the Prussians.

With moving block, lineside signals are not provided, and instructions are passed direct to the trains.

With the new instructions, the R5000 CPU could perform coordinate transformations faster than the XZ graphics board.

With only minutes of supplemental oxygen left in the pod, Jack follows Tuck's instructions to eject the pod from his lungs by making himself sneeze.

With his wife and three or more children he arrived in Boston in March, 1637, and soon found it was no place for anyone looking for liberty of conscience.

With that act of Parliament the opponents of the stage won the day, and for more than two decades after that England had no legitimate public drama.

With this no loyal citizen can quarrel.

`` With no strong men and no parliament to dispute his will, he was the government ''.

With no set standards, there is the tendency to promote to the next highest level when the top of a salary band is reached regardless of performance.

With the source of light behind the copy, there is no loss of lumen output, as with conventional boards illuminated by means of reflected light.

With few exceptions, your car will be waiting for you at dockside, airport, railroad station or hotel when you arrive, oftentimes at no additional cost.

With a few important and a few more unimportant exceptions, no expression can be deemed le mot juste for its context, because each was very probably the only expression that long-established practice and ease of rapid recitation would allow.

With the exception of the Roman Catholic and the Orthodox Catholic Churches, most churches make no moral distinction between rhythm and mechanical or chemical contraceptives, allowing the couple free choice.

With infinite patience she responded to every call, no matter at what cost to herself, and to her all went, for she was sure to have the needed information or word of cheer.

With capital largely squandered, there seemed to them no other course to pursue.

With no company to interfere, he kept close control over all the traders.

With the loss of the Emperor diety in Japan, the people are left in confusion with no God or moral teachings that have strength.

With almost no support in the South, Lincoln swept the North and was elected president in 1860.

With the axiom of dependent choice ( which is a weakened form of the axiom of choice ), this result can be reversed: if there are no such infinite sequences, then the axiom of regularity is true.

* 1713 – With no living male heirs, Charles VI, Holy Roman Emperor, issues the Pragmatic Sanction of 1713 to ensure that Habsburg lands and the Austrian throne would be inherited by his daughter, Maria Theresa of Austria ( not actually born until 1717 ).

With no place for his team to play, Rhodes ' effort came to nothing.

With 32 bytes, France would have been able to implement an ATM-based voice network with calls from one end of France to the other requiring no echo cancellation.

With only minor opposition in the primary and no opposition at all in the general election, Clinton was elected Arkansas Attorney General in 1976.

With no major Southern state remaining, Clinton targeted New York, which had many delegates.

With no serious external or internal threats, the armed forces are searching for a new role.

With the collapse of the Warsaw Pact and the end of the Cold war, Bulgaria could no longer support a vast military.

With no effective long-range weapon the original Blue Steel served on after a crash programme of minor modifications to permit a low-level launch at, even though its usefulness in a hot war was likely limited.

With Switzerland joining the Schengen Area on December 12, 2008, immigration checks were no longer carried out at the crossings.