Moreover, the equations are necessary and sufficient conditions for complex differentiation once we assume that its real and imaginary parts are differentiable real functions of two variables.

The first sense of " assume " in the OED is " to take unto ( oneself ), receive, accept, adopt .” The term was originally employed in religious contexts as in “ to receive up into heaven ,” especially “ the reception of the Virgin Mary into heaven, with body preserved from corruption ,” ( 1297 CE ) but it was also simply used to refer to “ receive into association ” or “ adopt into partnership .” Moreover, other senses of assumere included ( i ) “ investing oneself with ( an attribute ), ” ( ii ) “ to undertake ” ( especially in Law ), ( iii ) “ to take to oneself in appearance only, to pretend to possess ,” and ( iv ) “ to suppose a thing to be ” ( all senses from OED entry on “ assume ”; the OED entry for “ assumption ” is almost perfectly symmetrical in senses ).

Moreover, the axioms assume that the vacuum is " cyclic ", i. e., that the set of all vectors which can be obtained by evaluating at the vacuum state elements of the polynomial algebra generated by the smeared field operators is a dense subset of the whole Hilbert space.

Moreover, many Windows software programs have been written since the 1980s which assume that the screen provides 96 PPI.

( Moreover, through normalization, one can assume this projective variety is normal.

Moreover, in a time when individual initiative was a common way to assume the imperial purple, giving important commands to competent generals was asking for trouble.

Moreover, after the biography of Caracalla the ' primary ' biographies, of the emperors themselves, begin to assume the rhetorical and fictive qualities previously confined to the ' secondary ' ones.

Moreover, Senyavin was to assume supreme command of the joint Anglo-Russian fleet ( as the senior officer of the two ).

Moreover, as the chance of any one rod receiving more than one photon is very small, we can assume that it only takes one photon to excite a rod receptor ..

Moreover in scans that were held while Armagan drew, his visual cortex signals seemed as he was seeing to the extent that a naive viewer of his scan might assume Armagan really could see.

Moreover, users unfamiliar with OPAC searching and LCSH, may incorrectly assume their library has no items on their desired topic, if they chose to search by ‘ subject ’ field, and the terms they entered do not strictly conform to a LCSH.

Moreover, his testimony at trial never developed any such facts.

Moreover, C' obviously meets any line Af in a single point.

Moreover, the cost of operations is always high in any new store, as the conservative bankers who act as controllers for retail giants are beginning to discover.

Moreover, the nutritive value of irradiated foods apparently undergoes little, if any, change, although some of the fat-soluble vitamins are affected by sterilization doses.

Moreover, if any coefficient is a fixed power of 2, the multiplication can be replaced by bit shifting.

Moreover, the ansibles Le Guin uses in her stories apparently have a very limited bandwidth which only allows for at most a few hundred characters of text to be communicated in any transaction of a dialog session.

Moreover, for any invertible element and all one has

Moreover, Ogden assumed that any student already should be familiar with ( and thus may only review ) a core subset of around 200 " international " words.

Moreover, spending a total time of five years or more after January 1, 1980 ( to present ), in the above-mentioned countries and / or any country in Europe ( except the former USSR ), also precludes donation.

Moreover, the Banach fixed point theorem states that every contraction mapping on a nonempty complete metric space has a unique fixed point, and that for any x in M the iterated function sequence x, f ( x ), f ( f ( x )), f ( f ( f ( x ))), ... converges to the fixed point.

Moreover, a parent language may spawn several " dialects " which themselves subdivide any number of times, with some " branches " of the tree changing more rapidly than others.

for some natural number n. Moreover, since, the commutator subgroup is normal in G. For any homomorphism f: G → H,

Moreover, any canonical ellipse can be obtained by scaling the unit circle of, defined by the equation

" Moreover, they suggest that if it is wrong in principle for the government to tax in order to fund public education, then one should not accept any portion of the ill-gotten money to fund private education.

Moreover, Godlikeness is an essence of God, since it entails all positive properties, and any nonpositive property is the negation of some positive property, so God cannot have any nonpositive properties.

Moreover, although a lawsuit commenced within the time allowed by a limitations period is valid no matter how long it takes for the action to proceed to trial, laches can sometimes be applied even in a situation where a lawsuit has been commenced and any delays would otherwise be reasonable.

Moreover, any condition affecting the genital area can make women reject the idea of having intercourse.

Moreover, few, if any, children can rely on corrective feedback from adults when they make a grammatical error.

Moreover, any engagements near the sixth berm would threaten to spill over into Mauritania and jeopardize the rail link.

Moreover, is a transcendental number – a number that is not the root of any nonzero polynomial having rational coefficients.

Moreover, the pole itself can be expressed as ( 0, θ ) for any angle θ.

Moreover, it was the third meeting between the two longtime rivals in a Super Bowl ( after Super Bowl X and Super Bowl XIII ), which is currently the most between any two NFL teams.

Moreover, it allows the present management to reassign vehicles so that mileage will be more uniformly distributed throughout the fleet ; ;

Moreover, the larger and more aggressive mass distribution outlets and chain stores have insisted on high quality -- and the customer seems to have caught on.

Moreover, the shortage of treatment resources and the chronically persistent shortage of mental health manpower force us to innovate additional refinements of preventive intervention techniques to make services more widely available -- and on a more effective basis to more people.

Moreover, whereas in Interstate Commerce Commission parlance `` variable cost '' means a cost deemed to vary in direct proportion to changes in rate of output, in the type of analysis now under review `` variable cost '' has been used more broadly, so as to cover costs which, while a function of some one variable ( such as output of energy, or number of customers ), are not necessarily a linear function.

Moreover, all three representations must be squeezed comfortably into little more than the length Brumidi allowed for each one of his.

Moreover, Justin II was moving away from the foreign policy of Justinian, and believed in dealing more strictly with bordering states and peoples.

Moreover, this disposition – concave in relation to the Allied army – gave Marlborough the opportunity to form a more compact line, drawn up in a shorter front between the ‘ horns ’ of the French crescent ; when the Allied blow came it would be more concentrated and carry more weight.

Moreover ( and more embarrassingly, although this is essentially trivial ), mathematicians usually write the dual entity not at the first place, as the physicists do, but at the second one, and they don't use the *- symbol, but an overline ( which the physicists reserve to averages ) to denote conjugate-complex numbers, i. e. for scalar products mathematicians usually write

Moreover, by no means are all mutual managers incompetent, and conversions allows the bank to expand more easily and to grant executive stock options that are valuable to skilled managers ".

Moreover, Mozart also had a taste for more chromatic chords ( and greater contrasts in harmonic language generally ), a greater love for creating a welter of melodies in a single work, and a more Italianate sensibility in music as a whole.

Moreover, computers can easily hatch patterns in colors to give even more options.

Moreover, the study found that the more the school departed from the traditional college preparatory program, the better was the record of the graduates.

Moreover, the original concept of Fourier analysis has been extended over time to apply to more and more abstract and general situations, and the general field is often known as harmonic analysis.

Moreover, the economy and society of northern Finland had modernized more slowly than those of the south.

Moreover, under glasnost, the people were able to learn significantly more about the doings of the administration of Joseph Stalin, including the purges and other previously classified activities.

Moreover, Thucydides developed a historical topic more in keeping with the Greek lifestyle-the polis or city-state-whereas the interplay of civilizations was more relevant to Asiatic Greeks ( such as Herodotus himself ), for whom life under foreign rule was a recent memory.