By construction, h is antipode-preserving, and thus has non-zero degree.

By construction, h extends to the whole upper hemisphere of S < sup > n </ sup >, and as such is null-homotopic.

By 1972, however, with only a minimum of work done on the I-95 right of way and none on the potentially massively disruptive Inner Belt, Governor Francis Sargent put a moratorium on highway construction within the MA-128 corridor, except for a short stretch of Interstate 93.

By 1985, construction was completed and the World Financial Center saw its first tenants.

By the turn of the 21st century, Battery Park City was mostly completed, with the exception of some ongoing construction on West Street.

By the autumn of 1855, the royal apartments were ready, though the tower was still under construction and the servants had to be lodged in the old house.

By the same construction, every locally compact Hausdorff space X is a dense subspace of a compact Hausdorff space having at most one point more than X ..

By 1827, construction on the Dayton-Cincinnati canal began as a way to better transport goods from Dayton to Cincinnati.

By 1973, construction of the Naval Communications Station ( NAVCOMMSTA ) was completed.

By construction, each point on the curve shows productive efficiency in maximizing output for given total inputs.

By 2007, the Falkland Islands had a road network of with a further roads planned for construction link to all occupied mainland settlements by 2013.

By the 16th century the vihuela's construction had more in common with the modern guitar, with its curved one-piece ribs, than with the viols, and more like a larger version of the contemporary four-course guitars.

By applying his construction to the sequence of real algebraic numbers, Cantor produces a transcendental number.

By June construction had reached the second level platform, and on Bastille Day this was used for a fireworks display, and Eiffel held a celebratory banquet for the press on the first level platform.

By 1953 nearly one-quarter of the government's budget was devoted to road construction.

By 1907, the product had become successful enough to warrant construction of a second factory at Camberwell Green in London.

By 1947, there would be approximately 22, 000 motor courts in operation in the US alone ; a typical 50-room motel in that era cost $ 3000 per room in initial construction costs, compared to $ 12, 000 per room for metropolitan city hotel construction.

By the construction of ~, this definition is independent of the chosen representatives and the corresponding relation is indeed well-defined.

By construction, d * e = 1 mod φ ( n ).

By 1981 overseas construction projects, most of them in the Middle East, accounted for 60 percent of the work undertaken by South Korean construction companies.

By 1989 there were signs of a revival of the overseas construction market — the Dong Ah Construction Company signed a US $ 5. 3 billion contract with Libya for the second phase of Libya's Great Man-Made River Project, which, when all five phases were completed, was projected to cost US $ 27 billion.

By the 8th century, a navigable canal existed between Old Cairo and the Red Sea, but accounts vary as to who ordered its construction — either Trajan or ' Amr ibn al -' As, or Omar the Great.

By the induction hypothesis,

By the de Broglie hypothesis, we see that

By the above hypothesis, the graph indicates one of the major criticisms of deficit spending as a way to stimulate the economy: rising interest rates lead to crowding out – i. e., discouragement – of private fixed investment, which in turn may hurt long-term growth of the supply side ( potential output ).

By using Song state-gathered statistics, Edward A. Kracke, Sudō Yoshiyuki, and Ho Ping-ti supported the hypothesis that simply because one had a father, grandfather, or great-grandfather who had served as an official of state, it did not guarantee that one would obtain the same level of authority.

By the inductive hypothesis,

By the 18th century the problems with Augustine's idea led Johann Jakob Griesbach to put forward the Griesbach hypothesis, which was that Luke had revised Matthew and that Mark had then written a shorter gospel using material on which both Matthew and Luke agreed ( Matthew → Luke → Mark ).

By this hypothesis, creation of the fictional poetess capitalized on the period's literary fascination with the classical poet Sappho and on a publication ( 1533 ) of poems attributed to Petrarch's " Laura " ( Laura de Sade ; the poems were in fact the work of a descendant of Laura ).

By his method of observation and induction as thus explained, his philosophy will be found to be marked off very clearly, on the one hand from the deductive construction of notions of an absolute system, as represented either by Schelling or Hegel, which Cousin regards as based simply on hypothesis and abstraction, illegitimately obtained ; and on the other, from that of Kant, and in a sense, of Sir W. Hamilton, both of which in the view of Cousin are limited to psychology, and merely relative or phenomenal knowledge, and issue in scepticism so far as the great realities of ontology are concerned.

By pointing to differences in organization among other things, Ward Jones Jr. casts doubt on Baswell ’ s earlier hypothesis.

By the second half of the twentieth century, however, observations had failed to confirm this hypothesis, and an alternative hypothesis was proposed that something must instead suppress the diurnal tide.

By the inductive hypothesis R ( r − 1, s ) and R ( r, s − 1 ) exist.

By the inductive hypothesis, it contains either a K < sub > n </ sub >< sub >< sub > i </ sub ></ sub > monochromatically coloured with colour i for some 1 ≤ i ≤ ( c − 2 ) or a K < sub > R ( n </ sub >< sub >< sub > c − 1 </ sub >, n < sub > c </ sub >)</ sub >- coloured in the ' blurred colour '.

By the late 20th century the hypothesis that the Moriori were different from the Māori had fallen out of favour amongst archeologists, who believed that the Moriori were Maori who settled on the Chatham Islands in the 16th century.

Also, since λ is an eigenvalue of A, the dimension Ran ( A − λ I ), r, is strictly less than n. Let A ' denote the restriction of A to Ran ( A − λ I ), By inductive hypothesis, there exists a basis

By the end of the 19th century, there was a hypothesis that the Annals had been fabricated by 15th century Italian author Poggio Bracciolini ( 1380-1459 ).

By taking quantum physics into account, the gravastar hypothesis attempts to resolve contradictions caused by conventional black hole theories.

By that time Hodgkin and Lister had already published research on tissue samples, based on observations made with Lister's innovative microscope, in particular on the " globule hypothesis " of the time which was held in particular by Henri Milne Edwards.

By current standards, the indications seem odd but may be explained by the hypothesis that children may fail to thrive if they have chronically sore throats or severe obstructive sleep apnea ( OSA ).

By induction, the hypothesis implies that M < sup > k </ sup > T

By concluding that complex life is uncommon, the Rare Earth hypothesis is a possible solution to the Fermi paradox: " If extraterrestrial aliens are common, why aren't they obvious?

By the 1970s, Michael H. Hart's 1979 paper " Atmospheric Evolution, the Drake Equation and DNA: Sparse Life in an Infinite Universe " outlined the first evolutionary model for a habitable zone and hist pessimistic conclusions on the distribution of extraterrestrial life fuelled the Rare Earth hypothesis.

By going through hundreds or thousands of potential similarities between John and Mary, each having a low probability of being true, we may eventually find proof of virtually any hypothesis.

By hypothesis, a welfare recipient is destitute, without funds or assets.