The latter definition ignores the direction of the vectors and thus describes the angle between one-dimensional subspaces and spanned by the vectors and correspondingly.

In this process, the former species is oxidized and the latter is reduced, thus the term redox.

In view of the durability of meteoric iron, metal came to be associated with the aether, which is sometimes conflated with Stoic pneuma, as both terms originally referred to air ( the former being higher, brighter, more fiery or celestial and the latter being merely warmer, and thus vital or biogenetic ).

The science that tries to reconstruct phylogenetic trees and thus discover clades is called phylogenetics or cladistics, the latter term being derived from " clade " by Ernst Mayr ( 1965 ).

Although the posts of leader and party president of Fianna Fáil are separate, with the former elected by the Parliamentary Party and the latter elected by the Ardfheis ( thus allowing for the posts to be held by different people, in theory ), in practice they have always been held by the one person.

The latter could thus be thought of as capable of either ' glissando ' or ' portamento ', depending on whether the drum was rolled or not.

The latter two are phonetically indistinguishable ; in writing, capitalization differs: " Ich war am essen " vs. " Ich war am Essen " ( I was eating, compared to the Standard German approximation: " Ich war beim Essen "); yet these forms are not standardized and thus are relatively infrequently written down or printed, even in quotations or direct speech.

Although weakened by his torture, Fawkes managed to jump from the gallows and break his neck, thus avoiding the agony of the gruesome latter part of his execution.

The latter hypothesis seems the more plausible evolution determinant as the surface area of the head is minute compared to the remainder of the body, thus the energy required in producing long hair for the express purpose of " optical " amplification of UV light reflected from the snow seems counterproductive ( however, it's very likely that the trait was sustained due to a nuanced combination of multiple influences, given that human hunting-skills and ingenuity were such by 50, 000 years ago that said benefits in terms of ' comfort ' could have alternatively been derived from constructing head and ear warmers of fur from prey, etc .).

The Khitay conquest of Central Asia can thus be seen as an internecine struggle within the Karluk nomadic tribe, played out as dynastic conflict between the conquering Buddhist Khitay elites and the defending Kara-Khanid princes, resulting in the subjugation of the latter by the former, and in the subjugation of the Muslim Karluks by their Nestorian / Buddhist kin.

After graduating from Rutgers in 1932, Friedman was offered two scholarships to do graduate work ; one being Mathematics at Brown University and the other being Economics at the University of Chicago. Friedman chose the latter, thus earning an M. A.

Before the latter became terminally ill, Bismarck did not expect he would live to see Wilhelm ascend to the throne, and thus had no strategy to deal with him.

Thus followed the line of Lomonosov and the contributions of the Russian school became more frequent through his disciples, and in the nineteenth century we have great geographers as Vasily Dokuchaev who performed works of great importance as a " principle of comprehensive analysis of the territory " and " Russian Chernozem " latter being the most important where introduces the geographical concept of soil, as distinct from a simple geological strata, and thus founding a new geographic area of study: the Pedology.

In the latter work, which examines the subject of paleoanthropology, Bouts developed a teleological and orthogenetical view on a perfecting evolution, from the paleo-encephalical skull shapes of prehistoric man, which he considered still prevalent in criminals and savages, towards a higher form of mankind, thus perpetuating phrenology's problematic racializing of the human frame.

In short, humanity has full control, and thus full responsibility, for obeying the Gospel in addition to full responsibility for every sin ( the latter insisted upon by both proponents and opponents of Pelagianism ).

It turns out that this map is bijective and can thus be used to transfer the vector space operations from R < sup > n </ sup > over to T < sub > x </ sub > M, turning the latter into an n-dimensional real vector space.

These have now been replaced by the defining points in the International Temperature Scale of 1990, though in practice the melting point of water is more commonly used than its triple point, the latter being more difficult to manage and thus restricted to critical standard measurement.

It is comparatively easy to agree on observations of physical phenomena, harder to agree on observations of social or mental phenomena, and difficult in the extreme to reach agreement on matters of theology or ethics ( and thus the latter remain outside the normal purview of science ).

Critics of the latter idea point out that the half-life of Pu-240 is 6, 560 years and Pu-239 is 24, 110 years, and thus the relative enrichment of one isotope to the other with time occurs with a half-life of 9, 000 years ( that is, it takes 9000 years for the fraction of Pu-240 in a sample of mixed plutonium isotopes, to spontaneously decrease by half — a typical enrichment needed to turn reactor-grade into weapons-grade Pu ).

His official title was Chargé d ' un Cours de Science Sociale et de Pédagogie and thus he taught both pedagogy and sociology ( the latter had never been taught in France before ).

** → or a centring diphthong of the type when in final position, with the latter variants being more common in broad Cockney ; thus " saw "-" sore "-" soar ", " law "-" lore ", " war "-" wore ".

Additional addresses ( say, 10. 0. 0. 230-10. 0. 0. 240 ) are aliased to the loopback interface of the server ( or assigned to special interfaces, the latter typically being the case with VMware / UML / jails / vservers / other virtual server environments ) and ' published ' on the 10. 0. 0. 2 interface ( although many operating systems allow direct allocation of multiple addresses to one interface, thus eliminating the need for such tricks ).

The latter thus continued to rule in Dalmatia as Emperor, recognized as such in Dalmatia and in the eastern court.

The latter were far more geographically accessible, and thus had more dealings with the foreign powers.

When it started in 1970, the Universal Press Syndicate gave cartoonists a 50-percent share on the ownership of their works, while the Creators Syndicate ( founded in 1987 ) granted artists full rights to the strips, something that Universal Press did in 1990. followed by King Features in 1995, while before 1999 both the Tribune and United Feature services began granting rights to creators over their works ; however the latter three syndicates only applied this to new strips, or to ones popular enough.

The most important English chronicles are the Anglo-Saxon Chronicle, started under the patronage of King Alfred in the 9th century and continued until the 12th century, and the Chronicles of England, Scotland and Ireland ( 1577 – 87 ) by Raphael Holinshed and other writers ; the latter documents were important sources of materials for Elizabethan drama.

The judge concluded that it was only in " the last months of 1977 Berg started counseling the members that it was permissible for proselyting reasons to offer sexual contacts and services to perspective members, the more so when the latter were potentially good financial contributors to the cult ".

The latter was so much pleased with Abeken's work that officials started to call Abeken " the quill the scribe of Bismarck.

Industries like textile mills and railways companies had started in India in the latter half of the 19th century.

Furthermore, it was only around 1500 that lute players started the transition from plectrum technique to that of the right hand: the latter allowed for complex polyphony, for which notation had to be developed.

The latter group of refugees started to impose their view of Hinduism upon the Magars, while the former group were given the status of Chettri by the latter group in accordance with their view of Hinduism.

The Christian population of the empire, owing to their higher educational levels, started to pull ahead of the Muslim majority, leading to much resentment on the part of the latter.

The hippie culture, which started in the latter half of the 1960s, waned by the early 1970s and faded towards the middle part of the decade, which involved opposition to the Vietnam War, opposition to nuclear weapons, the advocacy of world peace, and hostility to the authority of government and big business.

The economic developments in the latter third of the decade were dominated by a worldwide economic downturn, which started with the crisis in housing and credit in the United States in late 2007, and led to the bankruptcy of major banks and other financial institutions.

Still, it was during the latter half of the 18th century that Tórshavn started to develop into a small town.

The strength in the Dow occurred despite a brief recession in 1949 and other global conflicts which started a short time later including the latter stages of the Chinese Civil War, the Greek Civil War, the Indo-Pakistani War of 1947 and the 1948 Arab-Israeli War.

Writing in 2000, David Roffe argued that the inquest ( the survey ) and the construction of the book were two distinct exercises ; the latter being completed, if not started, by William II following his assumption of the English throne and quashing of the rebellion that followed and based on, though not consequent on, the findings of the inquest.

At the turn of the 20th century, electricity had been mastered well enough to become a commercially viable alternative to gas and slowly started replacing the latter.

Denmark started colonies on St. Thomas in 1665 and St. John in 1683 ( though control of the latter was disputed with Great Britain until 1718 ), and purchased St. Croix from France in 1733.

He changes into a monstrous creature who kills Ridge before the latter can murder Linda, who has started to suspect Damian.

To stop the gossiping which started shortly afterwards, Huygens write the poem Cluijs-werck, in which he shows a glimpse of the latter stages of his life.

Mr. Milne (" Billy " to one and all who knew him ) started at once with his idea and by the latter part of the summer of 1909 had formed a troop of Boy Scouts with about a dozen boys from the Sunday School Class of the First Baptist Church, Barre, Vermont, Mr. James Grearson, teacher.

The latter was started in the 1820s by the planter Joseph E. Davis, who intended to create a model slave community on his plantation.

Early growth in the township started in the 1950s, starting with the construction of large resort communities of Beach Haven West and Ocean Acres, which were built around the same time as the completion of the Garden State Parkway and the expansion of Route 72, the latter which formerly ran along the two-lane Bay Avenue.

The latter immediately started construction of two forts: Campus Martius, whose former site is now occupied by the museum of the same name, and Picketed Point Stockade, at the confluence of the Muskingum and Ohio rivers.

Second, a decline of idealism and hedonism occured as many notable counterculture figures died, the rest settled into mainstream society and started their own families, and the " magic economy " of the 1960s gave way to the stagflation of the 1970s — the latter costing many middle-class Americans the luxury of being able to live outside conventional social institutions.

On June 14, 2011, Yoshinoya in Japan started serving eel bowls ( unadon, 鰻丼 ) as a standard seasonal menu to be offered until the latter part of July.