:“ You who wish to study great and wonderful things, who wonder about the movement of the stars, must read these theorems about triangles.

However, the time hierarchy theorems provide no means to relate deterministic and non-deterministic complexity, or time and space complexity, so they cast no light on the great unsolved questions of computational complexity theory: whether P and NP, NP and PSPACE, PSPACE and EXPTIME, or EXPTIME and NEXPTIME are equal or not.

He was essentially a theorist, and his great merit lay in the capacity of taking over experimental work that others had carried out — without always adequately recognizing their claims — and by a rigorous logical procedure, reinforced by his own quantitative experiments, of expounding the true explanation of the results.

A failure of the aorticopulmonary septum to divide the great vessels results in persistent truncus arteriosus.

Although Communications no longer publishes primary research, and is not considered a prestigious venue, many of the great debates and results in computing history have been published in its pages.

Social harmony — the great goal of Confucianism — therefore results in part from every individual knowing his or her place in the social order, and playing his or her part well.

The imaginary company had produced a proof of the Riemann Hypothesis but then had great difficulties collecting royalties from mathematicians who had proved results assuming the Riemann Hypothesis.

Mendez did teach lip buzzing and got great results.

Indeed, reported results of people generating EDIF 3 0 0 translators was that the writers were now much more difficult to get right, due to the great number of semantic restrictions, and the readers are comparatively trivial to develop.

Its high profile and popularity make it a merchandising environment, which results in great investments from sponsors and budgets in the hundreds of millions for the constructors.

This results in a great reduction in hull drag, and a further corresponding increase in speed.

The combustion process typically results in the production of a great quantity of heat, as well as the production of steam and carbon dioxide and other chemicals at very high temperature ; the temperature reached is determined by the chemical make up of the fuel and oxidisers ( see stoichiometry ), as well as by the compression and other factors.

According to some, results of keno games in great cities were sent to outlying villages and hamlets by carrier pigeons, resulting in its Chinese name 白鸽票 báigē piào, literally “ white dove ticket ”, pronounced baak-gap-piu in Cantonese ( which the Western spelling ' pak-ah-pu ' / ' pakapoo ' was based on ).

One wall of the great tower, various parts of the outer bailey and the battlements were destroyed, but not before the building was surveyed by the antiquarian William Dugdale, who published his results in 1656.

PepsiCo took great advantage of the campaign with television commercials reporting the results to the public.

Sophie had derived the correct differential equation, but her method did not predict experimental results with great accuracy, as she had relied on an incorrect equation from Euler, which led to incorrect boundary conditions.

When the circulatory changes are great enough, vasovagal syncope results.

Trials in the Queen Charlotte Islands ( Haida Gwaii ) of British Columbia using sea water sprayed on the foliage have demonstrated promising results, which may prove to be a viable option for eradication where concerns over herbicide application are too great.

The great majority of patients who met clinics ' screening criteria reported being satisfied in the long-term with the results.

He concluded " The results of my observation are best explained by the assumption that a radiation of very great penetrating power enters our atmosphere from above.

Because of the need for great security, all production facilities and nuclear reactors would be government-owned, while all technical information and research results would be under Commission control.

In a work titled Euclides ab Omni Naevo Vindicatus ( Euclid Freed from All Flaws ), published in 1733, Saccheri quickly discarded elliptic geometry as a possibility ( some others of Euclid's axioms must be modified for elliptic geometry to work ) and set to work proving a great number of results in hyperbolic geometry.

: Nor did he stop here-his searching experiments inspired him with the hope of transmitting messages across rivers and seas without the aid of wires, and he so far perfected his invention as to transmit currents across several small pieces of water-the last occasion on which he publicly experimented with this invention being in Portsmouth, about two years ago, when he was highly successful and the results afforded great satisfaction to the scientific gentlemen who assisted.

This system worked well when a Hetman had great ability and the monarch was weak, but sometimes produced disastrous results in the opposite case, as illustrated by the actions of Mikołaj Potocki in 1648.

Wiener took a great interest in the mathematical theory of Brownian motion ( named after Robert Brown ) proving many results now widely known such as the non-differentiability of the paths.

Morgan immediately saw the great importance of Janssens ' cytological interpretation of chiasmata to the experimental results of his research on the heredity of Drosophila.

The cost effectiveness of these configurations are currently being investigated in great detail and are demonstrating promising results.

It is not within the scope of this report to elaborate in any great detail upon special districts in Rhode Island.

The downtown store continues to offer the great inducement of variety, both within its gates and across the street, where other department stores are immediately convenient for the shopper who wants to see what is available before making up her mind.

Since the land he desired lay within the great northern empire of the Hudson's Bay Company, he purchased great blocks of the Comany's stock with the view to controlling its policies.

The executive paid tribute to research and development and technology for their great contributions in the past, but he also cautioned industry that they tend to be great equalizers because they move at a fairly even pace within an industry and fail to give it the short-term advantage which it often needs.

Schweitzer found many New Testament references to apparently show that 1st-century Christians believed literally in the imminent fulfillment of the promise of the World's ending, within the lifetime of Jesus's original followers, He noted that in the gospel of Mark, Jesus speaks of a " tribulation ", with his coming in the clouds with great power and glory " ( St Mark ), and states when it will happen: " This generation shall not pass, till all these things be fulfilled " ( St Matthew, 24: 34 ) ( or, " have taken place " ( Luke 21: 32 )): " All these things shall come upon this generation " ( Matthew 23: 36 ).

One of the most fascinating and intriguing aspects of Ancestral Puebloan infrastructure is at Chaco Canyon and is the Chaco Road, a system of roads radiating out from many great house sites such as Pueblo Bonito, Chetro Ketl and Una Vida, and leading towards small outlier sites and natural features within and beyond the canyon limits.

Kiva walls show marks from great fires set within them, which probably required removal of the massive roof-a task which would require significant effort.

Pentecostals believe that physical healing is within the anointing and so there is often great expectation or at least great hope that a miraculous cure or improvement will occur when someone is being prayed over for healing.

The clouds which strike Kathiawar and Kutch are deprived of a great deal of their moisture by the hills in those countries ( now the majority of this region is in Gujarat state within independent India ), and the greater part of the remainder is deposited on Mount Abu and the higher slopes of the Aravalli Range, leaving but little for Merwara, where the hills are lower, and still less for Ajmer.

It is likely for instance that within a decade, a great deal of trade between West Africa and Southern Africa will be moving on the network through Yaoundé.

Some forms of Islamic law, as in Saudi Arabia, may require capital punishment, but there is great variation within Islamic nations as to actual capital punishment.

Corcovado hill lies just west of the city center but is wholly within the city limits and visible from great distances.

He composed a number of sonnets for special occasions within the Colonna family, including " Colonna the Glorious, the great Latin name upon which all our hopes rest ".

The discovery that the comet was likely to collide with Jupiter caused great excitement within the astronomical community and beyond, as astronomers had never before seen two significant Solar System bodies collide.

He has used this program to great effect with composers such as Bach and Mozart ( his program Experiments in Musical Intelligence is famous for creating " Mozart's 42nd Symphony "), and also within his own pieces, combining his own creations with that of the computer.

Even within a type of fiber, there can be great variety in the length and thickness of the fibers ; for example, Merino wool and Egyptian cotton are favored because they produce exceptionally long, thin ( fine ) fibers for their type.

Because Judaism focuses on this life, many questions to do with survival and conflict ( such as the classic moral dilemma of two people in a desert with only enough water for one to survive ) were analysed in great depth by the rabbis within the Talmud, in the attempt to understand the principles a godly person should draw upon in such a circumstance.

Despite his leanings toward Deism, Alexander has retained a respect for the Catholic Church, believing it to embody a great deal of accumulated human truth within its rituals.

Eisenhower's stint as president of Columbia University was punctuated by his activity within the Council on Foreign Relations, a study group he led as president concerning the political and military implications of the Marshall Plan, and The American Assembly, Eisenhower's " vision of a great cultural center where business, professional and governmental leaders could meet from time to time to discuss and reach conclusions concerning problems of a social and political nature ".

The blacks killed or enslaved the native males and married the females, and within a generation they constituted a population of zambos that resisted Spanish authority until the end of the century and afterwards managed to retain a great deal of political and cultural independence.

Even the dialectal differences within Alutiiq and Central Alaskan Yup ' ik sometimes are relatively great for locations that are relatively close geographically.

This approach was favoured by Toho and to this end, King Kong vs. Godzilla has a much lighter tone than the previous two Godzilla films and contains a great deal of humor within the action sequences.