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* It is essential for U to be simply connected for the function f to be globally invertible ( under the sole condition that its derivative is a bijective map at each point ).
Some Related Sentences
is and essential
I think it is essential, however, to pinpoint here the difference between the two concepts of sovereignty that went to war in 1861 -- if only to see better how imperative is our need today to clarify completely our far worse confusion on this subject.
Often it is recognized that all the details of the pattern may not be essential to the outcome but, because the pattern was empirically determined and not developed through theoretical understanding, one is never quite certain which behavior elements are effective, and the whole pattern becomes ritualized.
And if I have gone into so much detail about so small a work, that is because it is also so typical a work, representing the germinal form of a conflict which remains essential in Mann's writing: the crude sketch of Piepsam contains, in its critical, destructive and self-destructive tendencies, much that is enlarged and illuminated in the figures of, for instance, Naphta and Leverkuhn.
Hence government must establish greater controls upon corporations so that their activities promote what is deemed essential to the national interest.
There is essential pleasantness in reading the writing of men who are not angry, who can contend without quarreling.
Thus, circular motion is itself one of the essential characteristics of completely perfect celestial existence.
Because of these involvements in the matter at stake, Boniface lacked the impartiality that is supposed to be an essential qualification for the position of arbiter, and in retrospect that would seem to be sufficient reason why the English embassies to the Curia proved so fruitless.
A requirement of reasonably honest administration may be politically uncomfortable in the short run, but it is politically essential in the long run.
The Merchant Marine is the `` Fourth Arm of Defense '', for a strong and effective American Merchant Marine is essential to the economy and security of our Nation.
The movement of events is so fast, the pace so severe, that an attempt to peer into the future is essential if we are to think accurately about the present.
A substantial increase is estimated in the cost of operating additional communications systems in the air defense program, as well as in all programs where speed and security of communications are essential.
The second capability is represented by our deployed ground, naval, and air forces in essential forward areas, together with ready reserves capable of effecting early emergency reinforcement.
However, it is essential that the various mathematical symbols used in the equations be understood so that the mathematical processes can be done properly and in their correct order.
In analyzing the watercolors of Roy Mason, the first thing that comes to mind is their essential decorativeness, yet this word has such a varied connotation that it needs some elaboration here.
Consultation with architects, clients, real estate men, fabric houses and furniture companies is essential to the proper development of class problems just as in actual work.
is and for
It is possible, although highly doubtful, that he killed none at all but merely let his reputation work for him by privately claiming every unsolved murder in the state.
( The best evidence is that he received a monthly wage of about $125, very good money in an era when top hands worked for $30 and found.
this is not so, for education offers all kinds of dividends, including how to pull the wool over a husband's eyes while you are having an affair with his wife.
He speaks your language too, for he is the grandson of a chieftain on Taui who made much magic and was strong and cunning.
`` And if the dive goes OK he has the exclusive import rights to your line for this country, is that right ''??
I want the room in the attic prepared for him He is a most unusual lad, quite precocious in many ways.
-- liberal considers that the need for a national economy with controls that will assure his conception of social justice is so great that individual and local liberties as well as democratic processes may have to yield before it.
In fact it has caused us to give serious thought to moving our residence south, because it is not easy for the most objective Southerner to sit calmly by when his host is telling a roomful of people that the only way to deal with Southerners who oppose integration is to send in troops and shoot the bastards down.
but for this discussion the most important division is between those who have been reconstructed and those who haven't.
Had the situation been reversed, had, for instance, England been the enemy in 1898 because of issues of concern chiefly to New England, there is little doubt that large numbers of Southerners would have happily put on their old Confederate uniforms to fight as allies of Britain.
Of greater importance, however, is the content of those programs, which have had and are having enormous consequences for the American people.
The general acceptance of the idea of governmental ( i.e., societal ) responsibility for the economic well-being of the American people is surely one of the two most significant watersheds in American constitutional history.
Reduced to its simplest terms, it is an assumption of a collective duty to compensate for the inability of individuals to cope with the rigors of the era.
National responsibility for individual welfare is a concept not limited to the United States or even to the Western nations.
For better or for worse, we all now live in welfare states, the organizing principle of which is collective responsibility for individual well-being.
( Since the time-span of the nation-state coincides roughly with the separate existence of the United States as an independent entity, it is perhaps natural for Americans to think of the nation as representative of the highest form of order, something permanent and unchanging.
There is little time for the men in the command centers to reflect about the implications of these clocks.
Only recently new `` holes '' were discovered in our safety measures, and a search is now on for more.