Therefore, to reduce the computational complexity, AKS makes use of the related congruence

Therefore, pp-waves belong to the Kundt class ( the class of Lorentzian manifolds admitting a null congruence with vanishing optical scalars ).

Therefore, if the target can significantly change its location in something less than 30 minutes, the probability of having destroyed it is drastically lowered.

Therefore the second principle of the plan must be that, while providing for all-out hostilities, its effectiveness is not dependent on general war.

Therefore, all primordial americium ( americium that was present on Earth during its formation ) should have decayed by now.

Therefore each pearl, natural or cultured, will have its own unique collage of colours.

Therefore, this group is generally now either included in the Brassicaceae or as its own family, Cleomaceae.

Therefore its status as a species is still questionable.

Therefore, a liquid will normally catch fire only above a certain temperature: its flash point.

Therefore, a company must analyze its business workflows and processes before choosing a technology platform ; some will likely need re-engineering to better serve the overall goal of winning and satisfying clients.

Therefore the quiet Sun always coincides with the equatorial zone and its surface is lower during the maximum of the solar cycle.

Therefore, the distillate will not be pure – its composition will be identical to the composition of the vapors at the given temperature and pressure, and can be computed from Raoult's law.

Therefore, each image engenders its opposite.

Therefore, a country's ability to learn from the leader is a function of its stock of " human capital ".

Therefore, the idea was born that only the elite should know the truth in its complete form and the rulers, Plato said, must tell the people of the city " The Noble Lie " to keep them passive and content, without the risk of upheaval and unrest.

Therefore, the most probable date for its composition is the second half of the year 63 or the beginning of 64, according to the Catholic Encyclopedia.

Therefore, earthquakes lower the Earth's available elastic potential energy and raise its temperature, though these changes are negligible compared to the conductive and convective flow of heat out from the Earth's deep interior.

Therefore, General Niazi and Air Marshal Enamul Haque, Commander of Eastern Air Force Command ( EAFC ), were failed to launch any operation in East Pakistan against Indian or its allies.

Therefore, it seems important to make the rules and focus of a discussion forum public to avoid misconceptions about its accepted use.

Therefore, the FDP wasn't able to form a coalition with its preferred partners, the CDU / CSU parties.

Therefore landing on a gas giant may or may not be possible, depending on the size and composition of its core.

Therefore, Hong Kong continues to play an active role in the international arena and maintains close contact with its international partners. Furthermore, Hong Kong continues to be an active, independent member of the World Trade Organization ( WTO ) and the Asia-Pacific Economic Cooperation ( APEC ) forum in the name of Hong Kong, China.

Therefore, with British permission, the Va ' ad raised its own taxes and ran independent services for the Jewish population.

Therefore, in spite of its condemnation by religious authorities, homosexuality persisted in a subterranean manner.

Therefore, to keep its economy afloat, Japan ran massive budget deficits ( added trillions in Yen to Japanese financial system ) to finance large public works programs.

Therefore, the underlying reason for gay behavior, he argues, must be to rebel against God, to wish to do something forbidden ( perhaps, implying some innate knowledge of its forbidden nature ).

Therefore, it is plain that the clear distinctions of the nineteenth century are no longer with us.

Therefore, what we must prove or disprove is that there were Saxons, in the broad sense in which we must construe the word, in the area of the Saxon Shore at the time it was called the Saxon Shore.

Therefore, under our longstanding allocation rules, on some of these channels no station other than the dominant ( class 1 ) -- A ) station is permitted to operate at night, so that the 1, -- A station can render service, interference free, wherever it can be received.

Therefore, the lumber is bought in planks and ripped to size for battens, etc., on a table saw.

Therefore, neglecting the extreme outbursts, reflected solar radiation is not expected to cause sizable errors in the measurements of planetary radiation in the centimeter- and decimeter-wave-length range.

Therefore, N is inversely proportional to the radius cubed and in fair agreement with the inverse 7/2 power derived from 1958 Alpha and 1959 Eta data.

Therefore, Af is single-valued near Q.

Therefore, for any value of T the number of values of f{t} is equal to the ( finite ) number of tangent points corresponding to the argument T plus an odd number.

Therefore, it is not only a question of honor but of life and death for the Soviet state ''.

Therefore, if the sense of touch is functioning normally and there is a complete absence of spatial awareness in a psychically-blind person when the eyes are closed and an object is handled, the conclusion seems unavoidable that touch by itself cannot focus and take possession of the third-dimensionality of things and that actual sight or visual representations are necessary.

Whereas, John Brown has cheerfully risked his life in endeavoring to deliver those who are denied all rights and is this day doomed to suffer death for his efforts in behalf of those who have no helper: Therefore,

Therefore, a broad concept of over-all submarine defense is needed for co-ordination of the Navy's efforts, for a logical presentation to the public, for industry's guidance, and as a basis for a program to the Congress.

Therefore, it is recommended that in such cases the sample be replaced, or if used, the results of dimensional change or dimensional restorability tests be considered as indicative only.

Therefore, her wardrobe is largely mobile, to be packed at a moment's notice and to shake out without a wrinkle.

Therefore, by contraposition, a necessary condition for unit-treatment additivity is that the variance is constant.

Therefore the perfect of these verbs would be ich bin gesessen, ich bin gelegen and ich bin geschlafen respectively ( note: ich bin geschlafen is a very rare form, usually you will hear ich habe geschlafen ; but ich bin eingeschlafen fell asleep is quite normal ).

Therefore, pure antimony is not used to make hard objects: coins made of antimony were issued in China's Guizhou province in 1931, but because of their rapid wear, their minting was discontinued.