Considering vector fields as infinitesimal generators of flows ( active diffeomorphisms ) on M, the Lie derivatives are the infinitesimal representation of the representation of the diffeomorphism group on tensor fields, analogous to Lie algebra representations as infinitesimal representations associated to group representation in Lie group theory.

Considering not only the English proficiency but also the pedagogical skills requires of teachers, the Center offers all instruction required of English education professionals including teaching methods and application of theory to the field, as well as the evaluation, review, and production of learning materials in addition to English language training.

Considering subgroups, and in particular maximal subgroups, of semigroups often allows one to apply group-theoretic techniques in semigroup theory.

Considering such a program, Douglas herself thought it unworkable, saying that “ f we were invited to make a coalition between group-grid theory and psychometrics, it would be like going to heaven .” Such deeply ironic statements are scattered through her work as indicating an unattainable mirage of ' postionlessness ': understanding and knowledge must, for Douglas, always emerge from a particular, partial, position, as is evident from the opening chapters of her 1982 book with Wildavsky.

He comments: " Considering the fact that Darwin's theory of natural selection takes generations and that successful varieties must sustain a survival advantage over others, the only way Mr. Burns can prove his assertion the fish is the next step in evolution through natural selection is by tracking Blinky over time to see if the third eye allows the mutant fish to find food more quickly or dodge predators.

Considering " a series of landmark publications concerning ethnobiological classification, Berlin has remained a prime architect of the descriptive and analytic frameworks now widely regarded as standard and major theory.

1. 5 Considering it from all aspects, the Commission is not inclined to give serious credence to the theory that dis – proportionately large number of Muslim deaths in December 1992 was necessarily indicative of an attempt on the part of the police to target and liquidate Muslims because of bias.

Considering the " color-of-the-shape " function above, the set X is the domain consisting of the four shapes, while Y is the codomain consisting of five colors.

Considering the 10 / 0 example above, let's set x

Considering more precisely the intervals,, and, we see that every number above 99 gets strictly smaller under this process.

Considering that Bangkok is a low-lying plain which is prone to flooding, all of the Metro's station entrances are raised about one metre above the ground level and are equipped with built-in floodgates in order to avoid water inundating the system.

Considering the steps of Patton and Sawicki model as in Figure 1 above, this paper only follows components 1 to 5 of the rationalist policy analysis model:

Considering her height ( five feet, seven inches ) and the length of the tub ( five feet ), the upper part of her body would have been pushed up the sloping head of the tub, far above the level of the water.

Considering the example above, each time an additional if-then-else statement is added, the number of possible paths doubles.

Considering its geological evolution, the lake periphery now has crystal bands of salt and remarkable white gypsum above which are the distinct overlay of black basalt formations.

Considering the above mentioned theories about the possible origin of the clan in Ireland, it is relevant to report that the clan seems to have no male line with the DNA signature associated with Uí Néill families in Ireland.

Considering that many of the Federation's other members have several interplanetary colonies just as Earth does, the full number of planets which the Federation encompasses may be impossible to determine ; it is presumed that colony worlds are directly subsidiary to the planetary governments of their homeworlds ( much like individual states / provinces in a nation ), but this has never been clearly established.

Considering Morrison's past as a police officer, several men he had arrested were at first considered suspects ; 12 people were arrested in the case before Hill was arrested and charged with the murder.

Considering that most bank clients in the developed world need several active accounts to keep their affairs in order, these figures indicate that the task the microfinance movement has set for itself is still very far from finished.

Considering that the trained singers had imbibed an oral tradition that was several centuries old, singing a small part of the chant repertory in straightforward heterophony of parallel harmony or other ways of ' singing by the ear ' would come naturally.

" Considering situation in Chechnya, the Moscow Times quoted election officials in the republic's capital, Grozny, as acknowledging that they had filled in several thousand ballots for Putin.

Considering that many pulp mills require several thousand tonnes of fiber source per day, storage of the fiber source can be a major issue.

Considering the prevalence of a number of genetic diseases in both the Ashkenazi and Sephardi communities, several organisations ( most notably Dor Yeshorim ) routinely screen large groups of young people anonymously, only handing them a telephone number and a PIN.

Considering the use of Spidrons Daniel Erdély enumerated several possible applications:

Considering only the participants who could recall the source of the news, ongoing activity, and place, researchers reported that less than 35 % had detailed memories.

Considering the ready availability of television broadcasts for the majority of baseball games, plus instant access to information through the Internet, some have called into question why the BBWAA has not broadened its membership rules to include broadcasters and researchers.

Considering then the optimism which has permeated science fiction for so long, what is really remarkable is that during the last twelve years many science-fiction writers have turned about and attacked their own cherished vision of the future, have attacked the Childhood's End kind of faith that science and technology will inevitably better the human condition.

Considering that the current school-age potential is 23 million youths, the project and its message on hunting and shooting education have many more to reach.

Considering Dio must have read Tacitus, it is worth noting he mentions nothing about suicide ( which was also how Postumus and Nero ended their lives ).

Considering these references to Robin Hood, it is not surprising that the people of both South and West Yorkshire lay some claim to Robin Hood, who, if he existed, could easily have roamed between Nottingham, Lincoln, Doncaster and right into West Yorkshire.

Considering a bipolar NRZ transmission, we have

Considering that they formed the nucleus of the tribe later known as the Wyandot, they too may have called themselves Wendat.

Considering these fluids have boiling points of 77. 36 K and 4. 22 K respectively, the technology is clearly not cost-and energy-efficient for home appliances, but for experimental, laboratory, and industrial use only.

Considering what kind of person it would be who would have dedicated his life to this peculiar task of being a Watcher, and what would be the unique characteristics of somebody who had made those decisions, and then was taken out of that environment and put into Sunnydale.

Considering the high operational costs of the vessels ( containerships have daily operational costs of approximately US $ 40, 000 ), the long queues that occur during the high season ( sometimes up to a seven-day delay ), and the high value of some of the cargo transported through the canal, the ACP implemented a congestion pricing scheme to allow a better management of the scarce capacity available and to increase the level of service offered to the shipping companies.

Considering mtDNA D-loop sequence data, they may have evolved in the general area of Siberia ; Mallard bones rather abruptly appear in food remains of ancient humans and other deposits of fossil bones in Europe, without a good candidate for a local predecessor species.

Considering the time at which it was written ( 1650 ), it was a meritorious work, but philology was then in the empirical stage, and many of Ménage's derivations ( such as that of " rat " from the Latin " mus ," or of " haricot " from " faba ") have since become bywords among philologists.

Considering that the only Christian poet before Bede was Caedmon, Stephens makes the point that there could have been no one else during this time period or living in the same area that could have authored the poem other than Caedmon.

Considering that unions have sometimes won rights by defying unjust laws, what should be the attitude of unionists toward that legislation?

Considering such achievements in digital imaging, the artist has the ability to " paint " the image, thus the names " colorist " or " color painter " have become most applicable.

Considering the period in which the cartoon was produced ( the Red Scare was in full swing during the 1950s era ), some scholars have used the cartoon to parallel the futility of the Cold War and the arms race.

Considering his later achievements, many analysts have called Brady the best NFL draft pick of all time.

Considering that the Lesser Kestrel would in fact have an advantage if some would-be predators confuse it with the larger species and consequently avoid it, it might be a case of Müllerian mimicry.

Considering also the prophecy in Psalms 69: 12, his place of crucifixion would have been near enough to the gate that Jesus could hear what the people were saying about him there.

Considering that about 80, 000 men were garrisoned in Alesia, together with the local civilian population, this would not have taken long.

Considering Russian historical practices, this would have made the Church officially a department of the government.

Considering the considerable commercial potentials of hydro-pneumatic technology ( Corolla, 1996 ), interconnected hydropneumatic suspensions have also been explored in some recent studies, and their potential benefits in enhancing vehicle ride and handling have been demonstrated.