Moreover, as long as the polynomial factors at each stage are relatively prime ( which for polynomials means that they have no common roots ), one can construct a dual algorithm by reversing the process with the Chinese Remainder Theorem.

Moreover these equations have real rather than imaginary roots, so in principle can be solved by geometric construction: this because the work all goes on inside a totally real field.

Moreover, an important emphasis in Methodism is the sense in which it is a grass roots movement.

Moreover, the displayed recursive formula for the ( new ) number r < sub > k + 1 </ sub > in terms of r < sub > k </ sub > is precisely Newton's method for finding roots to equations in the real numbers.

Moreover, by a theorem of Lagrange, the number of solutions modulo p to a congruence of degree q modulo p is at most q ( this follows since the integers modulo p form a field, and a polynomial of degree q has at most q roots ).

Moreover, it seems to be established beyond question that the trains passing along these deep-laid tubes shake the earth to its surface, and the constant jar and quiver will probably have a serious effect upon the trees by loosening their roots.

Moreover, he rejects the contemporary accounts of Englishmen, casually adjudging them to be distorted by prejudice because `` the opinions of Englishmen are of no great value ''.

Moreover, once these steps are taken, they may require years to make themselves felt.

Moreover, from the definitive transformation of intercepts on the generators of Af, it is clear that the only points of Q at which a line can meet its image are the points of Aj.

Moreover, if Af and Af are two planes intersecting in a line l, tangent to Q at a point P, the two free intersections of the image curves Af and Af must coincide at P', the image of P, and at this point Af and Af must have a common tangent l'.

Moreover, the current information on what types of training are needed and possible is too limited and fragmentary.

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, 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 conclusions he draws from the findings are not always the only ones possible.

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, prudence alone would indicate that, unless the local customs are already ready to fall when pushed, the results of direct economic action everywhere upon national chain stores will likely be simply to give undue advantage to local and state stores which conform to these customs, leading to greater decentralization and local autonomy within the company, or even ( as the final self-defeat of an unjust application of economic pressure to correct injustice ) to its going out of business in certain sections of the country ( as, for that matter, the Quakers, who once had many meetings in the pre-Civil War South, largely went out of business in that part of the country over the slavery issue, never to recover a large number of southern adherents ).

Moreover, he said, many qualified young people are not going into medicine and dentistry because they can't afford the schooling costs.

Moreover, her central figures are so busily fulfilling their multitudinous assignments that none emerges as an arresting individual in his own right or as a provocative symbol of mankind's ills.

Moreover, plans are underway to build a-long sub-alpine tunnel connecting the older Lötschberg and Gotthard tunnels built in the 19th century.

Moreover, the slopes of the derivatives of ΔG and ΔH converge and are equal to zero at T = 0.

Individuals who survived to this, the latest and highest stage of evolutionary progress would be “ those in whom the power of self-preservation is the greatest — are the select of their generation .” Moreover, Spencer perceived governmental authority as borrowed from the people to perform the transitory aims of establishing social cohesion, insurance of rights, and security.

Moreover, those failing to do their duty are expected to make up planting requirements, provide funds equivalent to the value of labor required or pay heavy fines.

Moreover they argued that some species have been created for the purpose of being sacrificed and eaten by humans, that it is normal for animals to kill and eat other animals, that agriculture, too, inevitably leads to the death of many animals, that plants are living beings as well and must still be destroyed, that we unintentionally and unknowingly destroy life forms all the time, and that a hunted animal has a fair chance to survive by killing the hunter.

Moreover, the physical changes occurred to the breasts usually are recorded in the stretch marks of the skin envelope ; they are historical indicators of the increments and the decrements of the size and the volume of a woman ’ s breasts throughout the course of her life.

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, in geriatric medicine, if benzodiazepines are necessary, those with short half-lives ( e. g. lorazepam & oxazepam ) are preferred, as they do not require hepatic oxidation.

Moreover the far north remains largely undeveloped as producers await higher prices or new technologies as many operations in this region are not yet cost effective.

Moreover, the ethical philosophies of Utilitarianism ( especially preference utilitarianism ) and Pragmatism commonly are identified as greatly employing casuistic reasoning.

Moreover relatively small sections are not technological for reinforced structures during their production.

Moreover, even when the destructive effects of their work become patently clear, and they are asked to carry out actions incompatible with fundamental standards of morality, relatively few people have the resources needed to resist authority.

Moreover, when position is relatively well defined, the wave is pulse-like and has a very ill-defined wavelength ( and thus momentum ).

Moreover, crystallography can solve structures of arbitrarily large molecules, whereas solution-state NMR is restricted to relatively small ones ( less than 70 kDa ).

Moreover, the built-over area of the city is relatively large, because the buildings are smaller compared with other cities of this size: there is a high ratio of one-family houses and mansions.

Moreover, the merchants in the town felt relatively secure from Mayan attacks and were unwilling to contribute toward the protection of mahogany camps, whereas the landowners felt that they should not be required to pay taxes on lands given inadequate protection.

Moreover, there are relatively few examples of compact positively curved manifolds, leaving a lot of conjectures ( e. g., the Hopf conjecture on whether there is a metric of positive sectional curvature on ).

Moreover, the relatively high clearance between the truck and the ground gave it the more lethal characteristics of an airburst.

Moreover, S. pneumoniae has become a relatively less important cause.

Moreover, the high saving rates and the moral stigma attached to bankruptcy have kept relatively low the level of defaults on mortgages even during the deep recessions after the Asian crisis after 1998 and the SARS epidemic in 2002 / 2003.

Moreover, relatively low income in the rural area compared to the urban area became a major political issue in the late 1980s, one that no government intervention had been able to fully solve.

Moreover, unlike democratic politics in much of the rest of the world, the US has relatively weak parties.

Moreover, NFU remains relatively consistent when augmented with an axiom of infinity and the axiom of choice.

Moreover, their share of the mortgage market held up in the 1990s despite the fact that the Treasury began to steadily reduce MIRAS, which also worked in favour of interest only mortgages, and despite a prolonged period of relatively low inflation ( something which worked against interest only mortgages ).

Moreover, colonial regimes usually have relatively few active supporters, who can often be easily identified, making it possible for guerrilla armies to operate.

Moreover, since 1586, the Orthodox Christian Patriarchate of Constantinople has its headquarters in the relatively modest Church of St. George in the Fener district of Fatih.

Moreover, some of the contemporary Persian language poets and writers, who are relatively well known in the Persian-speaking world, include Khalilullah Khalili, Sufi Ashqari, Sarwar Joya, Qahar Asey, and Parwin Pazhwak.

Moreover, by using relatively narrow widths of lumber, the chance of warping was minimized.

Moreover, relaxation experiments are relatively insensitive to mechanistic details and are thus not typically used for mechanism identification, although they can be under appropriate conditions.