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, MSK is a particular case of the sub-family of CPM known as continuous-phase frequency-shift keying ( CPFSK ) which is defined by a rectangular frequency pulse ( i. e. a linearly increasing phase pulse ) of one symbol-time duration ( total response signaling ).

Indeed, the transformation of Newfoundland English offers a case study of the politics of language.

Indeed, in the latter case, it is only defined for non-negative integer arguments.

For the univariate case, Indeed, for random variables X and Y, the expectation of their product is an inner product.

Indeed, as Kotowicz notes, his attention was drawn more to the case presented by Richard Brickner, at the same conference, of a patient who had had his frontal lobes ablated and, while experiencing a flattening of affect, had suffered no apparent decrease in intellect.

Indeed, it is false, because it is not the case that there exists a unique individual who is currently the king of France and is bald — since there is no present king of France ( Bertolet 1999 ).

Indeed, Chief Justice William Rehnquist repeatedly criticized the Court's invention of corporate constitutional " rights ," most famously in his dissenting opinion in the 1978 case First National Bank of Boston v. Bellotti.

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 ).

Indeed, he worked alone ( which is rather rare for a robber ) and carried his machine gun in a violin case.

Indeed several agencies and experts and journals have published concerns about viewing the developments as a case of genocide: Roméo Dallaire, Genocide Watch, Sentinel Project for Genocide Prevention, and the journals War Crimes, Genocide, & Crimes against Humanity and Journal of Genocide Research.

Indeed, one of the common markers of a case of SHC is that the body – or part of it – suffered an extraordinarily large degree of burning while the surroundings or the lower limbs remained comparatively undamaged.

Indeed the approval has little value in any case: it should be noted the subject of the article is not the classic declaration of war, as such a declaration according to doctrine might constitute a war crime by implying a war of aggression forbidden by international law.

Indeed, Fox's generous nature ( helped by his earlier over-indulgence by his father ) made him a rather hopeless political party-leader, often seeming quite unwilling to cajole or discipline his unruly supporters, especially in the case of the young, who were disproportionately represented among the Foxites.

" Indeed defenders of EMH maintain that Behavioral Finance strengthens the case for EMH in that BF highlights biases in individuals and committees and not competitive markets.

Indeed, if that is not the case to start with, a different set of intervals can be picked for which these assumptions hold.

Indeed, it is very frequently the case that one can even predict and explain the kind of mental or psychological deterioration or change that human beings will undergo when specific parts of their brains are damaged.

Indeed, the average intercarrier compensation rate ranges from 0. 1 cents per minute for traffic bound to an information service provider (“ ISP ”) to 5. 1 cents per minute for intrastate traffic bound to a subscriber of a small ( rural ) incumbent local exchange carrier ; individual rates can be as low as zero and as high as 35. 9 cents per minute — even though in each case basically the same transport and switching functions are provided.

An important consequence of the domain invariance theorem is that R < sup > n </ sup > cannot be homeomorphic to R < sup > m </ sup > if m ≠ n. Indeed, no non-empty open subset of R < sup > n </ sup > can be homeomorphic to any open subset of R < sup > m </ sup > in this case.

Indeed, at least one case has been documented of the pro-Nazi and white supremacist Liberty Lobby distributing a pro-Wallace pamphlet entitled " Stand up for America " despite the campaign's denial of such a connection.

Indeed, in this case we introduce the unitary transformation

Indeed, in the case of Kirmani v Captain Cook Cruises Pty Ltd ( No 2 ) ( 1985 ), the court said that it would never again grant a certificate of appeal.

Indeed, the common metaphor for the strongest possible evidence in any case — the " smoking gun "— is an example of proof based on circumstantial evidence.

Indeed, it may be the case that Roméo et Juliettes genesis is intertwined with other works composed before the composer left for his Prix de Rome sojourn of 1830-32.

Indeed, the area of a disk of radius R is πR < sup > 2 </ sup > and the circumference of the circle is 2πR, so both sides of the inequality are equal to 4π < sup > 2 </ sup > R < sup > 2 </ sup > in this case.

i. e., z is a vector orthogonal to the vector v ( Indeed, z is the projection of u onto the plane orthogonal to v .) We can thus apply the Pythagorean theorem to

Indeed, the influence of the Necessary and Proper Clause and its broader interpretation under McCulloch v. Maryland in American jurisprudence can be seen in cases generally thought to simply involve the Commerce Clause.

Indeed, following Secretary of State for the Home Department v JJ the House of Lords held that the restrictions imposed within the control would be open to challenge on the basis of incompatibility, with focus on Art 8 ( right to privacy and family life ), Art 10 ( freedom of speech ) and Art 11 ( freedom of assembly ).

Indeed, the fact that in this case, the funding was given to the parents to disburse as they chose, whereas in Lemon v. Kurtzman the funding at question was given directly to the schools, this was a key part of the Private Choice test.

Indeed, in the early case of R v Higgins incitement was defined as being committed when one person counsels, procures or commands another to commit a crime, whether that person commits the crime.

Indeed, in the Bill of Rights case Hogan v. The Queen ( 1978 ), the Supreme Court found the right to be told that one may see a lawyer did not exist even in a penumbra of the Bill of Rights.

: Indeed, in Baker v. Nelson, when faced with a Fourteenth Amendment challenge to a decision by the Supreme Court of Minnesota denying a marriage license to a same-sex couple, the United States Supreme Court dismissed " for want of a substantial federal question.

Indeed, you wouldn't live long, for the females either drive the men they've seized from neighboring islands back to their boats after exploiting them for amatory purposes, or they destroy them by revolting but ingenious methods.

Indeed, the old Jeffersonians were far more atune to the Hamilton-oriented Whigs than they were to the Jacksonian Democrats.

Indeed, it seems that only in today's Southern fiction does Tobacco Road, with all the traditional trimmings of sowbelly and cornbread and mint juleps, continue to live -- but only as a weary, overexploited phantom.

Indeed, it is probable that this point is reached the moment the third level of change begins.

Indeed, in the Halma edition of Theon's presentation of The Hypotheses there is a chart setting out ( under six distinct headings ) otherwise unrelated diagrams for describing the planetary motions.

Indeed, he looked more like a well-fleshed lay brother of the Hospice of St. Bernard.

Indeed, he concluded that `` geographical conditions have exercised a great, possibly a preponderating, influence over man's destiny ''.

Indeed, again and again, the space merchants confirm the prediction of the humanists that the conditioners and behavioral scientists, once they have seen through human nature, will have nothing except their impulses and desires to guide them.

Indeed it might be a more appropriate vehicle than NATO for the development of a parliamentary organ of the Atlantic nations, because it could encompass all of the members of the Atlantic community including those, like Sweden and Switzerland, who are unwilling to be associated with an essentially military alliance like Aj.

Indeed no.

Indeed, as already noted, the Court proceeded on the assumption that the executives involved in the dealings between Du Pont and General Motors acted `` honorably and fairly '' and exercised their business judgment only to serve what they deemed the best interests of their own companies.

Indeed, if pressed, we would say what the late Robert Henri, American painter, said to a pupil, `` Anything will do for a subject: it's what you do with it that counts ''.

Indeed, a lighter weight works much better because a greater, more extensive split can be performed.

Indeed, it has only been a matter of the last few years that reputable schools of art have granted degrees at all.

Indeed it is possible to separate electron paramagnetic from nuclear effects.

Indeed, when the proper inorganic constituents are employed, practically any wetting or surface-active agent will do a reasonably good job when present in sufficient amount in a hard-surface cleaning formulation.

Indeed, the experiment is better viewed as consisting of one binomial trial for the entire family.

Indeed, the spiral Af, with the two endpoints connected by a straight line possesses only one inscribed square.

Indeed their achievement scores were somewhat better on an absolute basis although the difference was not significant.

( Indeed, the set of endings can be replaced by the name of a set of endings.

Indeed, the failure of home-building as a whole to respond this year to somewhat greater availability of mortgage financing, and the increasing reports of pockets of unsold homes and rising vacancy rates in apartment buildings, may also signal in part that the lush days of big backlog demand for housing are reaching an end.

Indeed, the apparent stiffening of the industry's attitude in the recent steel strike has a direct explanation in terms of the model here presented.

Indeed, with developed positivism, the separation of law from justice, or from morality generally, became quite specific.

Indeed, contract was the dominant legal theme of the century, the touchstone of the free society.

Indeed, a study of the individual child is an integral part of the work of the elementary-school teacher, rather than merely an additional chore.