Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

Indeed we have the following result.

Indeed, two roads, which diverged at Othoca ( modern Santa Giusta ) connected Caralis to Turris, the more important keeping inland and the other following the west coast.

Indeed, the following theorem holds true ( provided that the deduction apparatus of the considered fuzzy logic satisfies some obvious effectiveness property ).

Indeed, there are non-Bayesian updating rules that also avoid Dutch books ( as discussed in the literature on " probability kinematics " following the publication of Richard C. Jeffrey's rule, which applies Bayes ' rule to the case where the evidence itself is assigned a probability ).

Observe first the following: if a is a limit point of S, then any finite collection C of open sets, such that each open set U ∈ C is disjoint from some neighborhood V < sub > U </ sub > of a, fails to be a cover of S. Indeed, the intersection of the finite family of sets V < sub > U </ sub > is a neighborhood W of a in R < sup > n </ sup >.

Indeed, in England the word " dollar " was in use for the Thaler for 200 years before the issue of the United States dollar, and until the half crown ceased to be used following decimalisation in 1971, the term " half a dollar " could be heard for " half a crown ".

Indeed, following the 1960s, it increasingly became home to a number of squatters, artists, bohemians and also political radicals.

" Indeed, the act was passed by Parliament on 21 May, the same day as a royal proclamation against seditious writings was issued, and more libel cases would be brought by the government in the following two years than had been in all the preceding years of the eighteenth century.

Indeed, enjoyment of the natural surroundings of the walk is the primary motivating factor for many people following the route.

Indeed, more guilds are known in Thyatira than any other contemporary city in the Roman province of Asia ( inscriptions mention the following: wool-workers, linen-workers, makers of outer garments, dyers, leather-workers, tanners, potters, bakers, slave-dealers, and bronze-smiths ).

Indeed, the concept of self-esteem is approached since then in humanistic psychology as an inalienable right for every person, summarized in the following sentence:

" Indeed, Russian historian Oleg Sokolov noted that Wellington had committed a serious strategic error by following the French into northern Portugal, and that this decision could have had grievous consequences for the Anglo-Portuguese.

Indeed, in 1969 a " Birding Glossary " appeared in Birding Volume 1, No. 2, which stated the following:

Indeed, Against Apion, the writing of Josephus in 95 CE, treated the text of the Hebrew Bible as a closed canon to which "... no one has ventured either to add, or to remove, or to alter a syllable ..." However, we know that for a long time following this date that the divine inspiration of Esther, the Song of Songs, and Ecclesiastes was often under scrutiny.

Indeed, the geometrization of space that would characterize Cubism can already be observed in his works as early as 1905, following the lead of Seurat and Cézanne.

Indeed, the transitional government that ruled the country from the cease-fire agreement ( signed in Lusaka on 7 September 1974 ) to independence ( set for 25 June of the following year ) acted in a very conciliatory fashion.

Indeed, the Wall Street Crash of 1929 and the following Great Depression, which affected France from 1931, caused much anxiety and disturbance, as in other countries.

Indeed, special relativity largely comes down to studying a kind of noneuclidean trigonometry in Minkowski spacetime, as suggested by the following table :< ref group = A >

Indeed, these locally focused routers were often built along existing roads and steam railways with which they competed, sometimes following the latter from terminal to terminal.

Indeed, in the early years following the Scottish Reformation there was actually internal sectarian tension between Church of Scotland Presbyterians and ' High Church ' Anglicans, whom they regarded as having retained too many attitudes and practices from the pre-Reformation Catholic era.

Indeed, following the success of The Deluge, Goehr was commissioned a new cantata, Sutter's Gold for choir, baritone and orchestra.

Indeed, the addition of a couple of key players could have seen Omagh challenge for the following seasons premiership.

Indeed, as a result of the war and the lessons that were learned about the potential of airpower in the region, following the war, the Chief of the Air Staff, Sir Hugh Trenchard, proposed controlling the frontier by air power alone.

Indeed, the 5, 500 public work enterprises in the construction sector comprise 19 percent of all industrial enterprises and engage approximately 10 percent of the entire labor force.

Indeed, becoming aware of the Persian preparations for the coming invasion, the Athenians voted for the construction of more ships than Themistocles had initially asked for.

Indeed, Cubist construction was as influential as any pictorial Cubist innovation.

One important effect of Sentinel construction, he thought, would be to encourage the Soviet Union to enter arms control talks with the U. S. Indeed, before Clifford left office, the Johnson administration made arrangements for negotiations that eventually led to the Anti-Ballistic Missile Treaty of 1972.

Indeed, construction advanced as far as the rebuilding of Edgware Road station to accommodate 4 platforms of 8-car length.

Indeed, his biographers and his correspondence indicate that, during Wyatt's prolonged absences, he took it upon himself to direct the construction of the Abbey, as well as leading the landscaping efforts in his estate.

Indeed in a number of cases it would appear that either the Normans converted existing ringforts into the basis of the future construction of mottes and earthworks, or that the Gaelic Irish, through the use of raised raths, sought to emulate the Norman example.

Indeed it has been thought that the Roman road to the north of the Forth, to Stirling and Perth, dates from the expedition of Severus to beyond the Dee, AD 209 ; it may, however, be doubted whether there was time in that campaign for such a work, and the road may well belong to a period before the construction of the Antonine Wall, AD 140.

Indeed, the latest steel construction specifications published by AISC ( the 13th Edition ) no longer covers their installation.

Indeed, malaria outbreaks have, in the past, occurred in colder climates, for example during the construction of the Rideau Canal in Canada during the 1820s.

Indeed, the initial topology construction can be viewed as a generalization of these.

Indeed, construction grammarians argue that all pairings of form and meaning are constructions including phrase structures, idioms, words and even morphemes.

Indeed this appears to be the style of construction of the dwellings in the excavated Molossian site near Vitsa.

Indeed this is the usual construction to obtain the integers from the natural numbers.

Indeed, cooperative food acquisition, food sharing, and cooperation in other realms such as child rearing, mobility, camp construction, defense, etc., are all part of an integrated system of reciprocal altruism and cooperative promotion of group welfare among the Aché.

Indeed, there is no evidence to show that Santa Marians resented either the construction of the irrigation system in 1813, or the fencing of the town in 1817, both during Fr.

Indeed on January 30, 1861, the construction ended.