Consequently, we can assert that a complex function f, whose real and imaginary parts u and v are real-differentiable functions, is holomorphic if and only if, equations ( 1a ) and ( 1b ) are satisfied throughout the domain we are dealing with.

Chief Justice William Rehnquist Chief Justice William Rehnquist's majority opinion relied upon Roberts v. United States Jaycees, 468 U. S. 609, 622 ( 1984 ), in which the Supreme Court said: " Consequently, we have long understood as implicit in the right to engage in activities protected by the First Amendment a corresponding right to associate with others in pursuit of a wide variety of political, social, economic, educational, religious, and cultural ends.

Consequently, substituting these functions into the consistent conditions on four distinct trials, u, v, w, and s shown above, they are able to obtain the following four equations concerning one and the same value λ:

Consequently, the principle is universal in the United States either in Model Penal Code jurisdictions ( 40 states ) or those remaining common law jurisdictions influenced by the reasoning in R v Brown.

Consequently, in R v Constanza, the court found a stalker's threats could constitute assault.

Consequently, for any complex u, v ≠ 0,

Consequently, v < sub > 2 </ sub > cannot be adjacent to v < sub > 4 </ sub >, which lies outside this face.

Consequently, each legitimises the other. he was born in 1703 died: 1792 88-89 18th century school: hanbali region = Arabian Peninsula

Consequently, a conversion equation like " 1 C = N statC " can be misleading: the units on the two sides are not consistent.

Consequently, ( ƒ g ) g ' = f < sub >− 1 </ sub > g < sup >− 1 </ sup > g ' + ( F ' g ) g ' = ƒ < sub >− 1 </ sub > g '/ g + ( F g )' and ( iv ) follows from ( i ) and ( iii ).

Consequently it was proposed that the pyramid was originally that of Ankhnespepi IV ( ˁnḫ-n = s ppj, " Pepi lives for her ") a wife of Pepi II, and was only later appropriated by Ibi.

Consequently, in the case of an inscribed quadrilateral, θ = 90 °, whence the term

Consequently, its fundamental group Γ = π < sub > 1 </ sub >( M ) is Gromov hyperbolic.

Consequently the organising committee was the first to rely heavily on corporate sponsorship for funding .< ref name = ioc >

Consequently, the equation E = mc < sup > 2 </ sup > was not originally written as a formula but as a sentence in German that meant if a body gives off the energy L in the form of radiation, its mass diminishes by L / V < sup > 2 </ sup >.< ref > See the sentence on the last page ( p. 641 ) of the original edition of Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?

Consequently, rescaling by the fraction ( 235-16 )/( 240-16 ) = 219 / 224 is sometimes required when doing color matrixing or processing in YCbCr space, resulting in quantization distortions when the subsequent processing is not performed using higher bit depths.

Consequently m < sub > 0 </ sub > = 0.

Consequently bids of 1 < font color = red >♦</ font >, 1 < font color = red >♥</ font > and 1 ♠ are limited to about 18HCP, and also 1 < font color = red >♦</ font > shows at least four diamonds ( five in some versions of the system ).

Consequently, writing a Gaussian integer ω = x + iy with x, y ∈ Z and applying the Frobenius automorphism in Z /( p ), one finds

Consequently total cost is fixed costs ( FC ) plus variable cost ( VC ) or TC =

Consequently it allowed symbols like " ½ " for ". 5 " and the superscript < sup > 2 </ sup > for " to the power of 2 ".

Consequently, most commercial explosives are organic compounds containing-NO < sub > 2 </ sub >,-ONO < sub > 2 </ sub > and-NHNO < sub > 2 </ sub > groups that, when detonated, release gases like the aforementioned ( e. g., nitroglycerin, TNT, HMX, PETN, nitrocellulose ).

In this expression, a is a constant, not a variable, so f < sub > a </ sub > is a function of only one real variable, that being y. Consequently, the definition of the derivative for a function of one variable applies:

Consequently, the Roman surface is a quotient of the real projective plane RP < sup > 2 </ sup >

Consequently, a lightning strike observed at a very close distance will be accompanied by a sudden clap of thunder, with almost no perceptible time lapse, and the smell of ozone ( O < sub > 3 </ sub >).

Consequently surface tension can be also measured in SI system as joules per square meter and in the cgs system as ergs per cm < sup > 2 </ sup >.

Consequently, a phrase such as " the energy is 300 wavenumbers " should be interpreted or restated as " the energy corresponds to a wavenumber of 300 cm < sup >− 1 </ sup >.

Consequently, in the Middle Ages, a less severe penance was imposed for the sin of abortion < nowiki >" before foetus has life ".</ nowiki >

Every measurable cardinal κ is a 0-huge cardinal because < sup > κ </ sup > M ⊂ M, that is, every function from κ to M is in M. Consequently, V < sub > κ + 1 </ sub >⊂ M.

Consequently, under the influence of Moabite culture, the Israelites begin whoring after the Moabite gods, and join themselves to Baal Peor ( Hebrew בעל פעור Ba ‘ al P < sup > ə </ sup >‘ ôr ), in the Septuagint Beelphegôr, a baal associated with Mount Pe ‘ or.

Consequently no file could be larger than 2 < sup > 32 </ sup > bytes ( 4 GiB ).

where I < sub > n </ sub > is the n × n identity matrix and H < sup > T </ sup > is the transpose of H. Consequently the determinant of H equals ± n < sup > n / 2 </ sup >.

Consequently, the voltage drop across Q < sub > 1 </ sub > is V < sub > BE </ sub >, that is, this voltage is set by the diode law and Q < sub > 1 </ sub > is said to be diode connected.

Consequently, the k-fold product of W ′ with itself, W ′< sup > k </ sup >, is one-dimensional.

In mathematics, given a subset S of a totally or partially ordered set T, the supremum ( sup ) of S, if it exists, is the least element of T that is greater than or equal to every element of S. Consequently, the supremum is also referred to as the least upper bound ( lub or LUB ).

Consequently, if the shear angle **yf is replaced by the rupture angle Af, the relationships as described in eqns. ( 1 ), ( 2 ), ( 4 ), and ( 6 ) will directly apply.

Consequently, the traditional usage of the terms is based on the orbit ’ s semi-major axis, and includes objects situated between the 2: 3 and 1: 2 resonances, that is between 39. 4 and 47. 8 AU ( with exclusion of these resonances and the minor ones in-between ).

Consequently, he decided to switch from federal to state politics: He was appointed Prime Minister ( Ministerpräsident ) of the state of Baden-Württemberg on 17 December 1958, an office in which he served until 1 December 1966.

Consequently, Hitler postponed his planned 26 August invasion of Poland to 1 September.

Consequently, the number of m-faces of an n-simplex may be found in column ( m + 1 ) of row ( n + 1 ) of Pascal's triangle.

Consequently, the wavelength will be approximately two-thirds that in free space, and the electrical length approximately 1. 5 times the physical length.

Consequently, the waveforms used to represent a 0 and a 1 bit differ by exactly half a carrier period.

Consequently, from 1975 to 1990 the real wages of black manufacturing workers rose by 50 %, that of whites by 1 %.

Consequently, the recommended average intake of omega-3 for adult men in the United States is only 1. 6 grams / day, or less than 2 % of total fat ; the actual average consumption of omega-3 in the United States is around 1. 3 grams / day, almost all of it in the form of ALA ; EPA and DHA contributed less than 0. 1 grams / day.

Consequently, the ionosphere consists of a rapid increase in density of free electrons, beginning at ~ 70 km, reaching a peak at ~ 300 km, and then falling off again as the atmosphere disappears entirely by ~ 1, 000 km.

Consequently, Cave 1 was rediscovered on 28 January 1949, by Belgian United Nations observer Captain Phillipe Lippens and Arab Legion Captain Akkash el-Zebn.

Consequently one year since the Incarnation would have meant 25 March 1, meaning that Dionysius placed the Incarnation on 25 March 1 BC.

Consequently, it was re-granted in 1749 by Governor Benning Wentworth as Monadnock No. 1, or South Monadnock.

Consequently, a distance measurement of only a few meters would still have an accuracy of ± 1 mm in this example .< sub > </ sub ></ ref >