Flatness may refer to:

Flatness may also be expressed using the Tor functors, the left derived functors of the tensor product.

* Flatness and faithful flatness is preserved by base change: If f is flat or faithfully flat and, then the fiber product is flat or faithfully flat, respectively .< ref > EGA IV < sub > 2 </ sub >, Proposition 2. 1. 4, and EGA IV < sub > 2 </ sub >, Corollaire 2. 2. 13 ( i ).</ ref >

Flatness is more easily measured with a co-ordinate measuring machine.

Flatness and parallelism are typically measured with a gauge called an optical flat, a disc of glass or plastic ground with extreme accuracy to have flat, parallel faces, which allows light bands to be counted when the micrometer's anvil and spindle are against it, revealing their amount of geometric inaccuracy.

In August, he submitted his paper, entitled " The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems " to the journal Physical Review.

Flatness was introduced by in his paper Géometrie Algébrique et Géométrie Analytique.

# Flatness.

Martone won the 1998 Associated Writing Programs Award for Creative Nonfiction for his book Flatness and Other Landscapes published by University of Georgia Press.

* Mark D. Roberts, Spacetime Exterior to a Star: Against Asymptotic Flatness.

# Flatness and geometric designs inspired by " non-Western " art forms.

Something was beginning to stir and come alive in her, too ( it may have been there for a good while, since she was twenty now ; ;

Jean Bodin, writing in the sixteenth century, may have been the seminal thinker, but it was the vastly influential John Austin who set out the main lines of the concept as now understood.

Just as now anyone may hurl insults at a citizen of Mars, or even of Tikopia, and no senatorial investigation will result.

I fled, however, not from what might have been the natural fear of being unable to disguise from you that the things about my bridegroom -- in the sense you meant the word `` things '' -- which you had been galvanizing yourself to tell me as a painful part of your maternal duty were things which I had already insisted upon finding out for myself ( despite, I may now say, the unspeakable awkwardness of making the discovery on principle, yes, on principle, and in cold blood ) because I was resolved, as a modern woman, not to be a mollycoddle waiting for Life but to seize Life by the throat.

`` Mais non '', the Interior Ministry man coaxed, `` you may come back to Strasbourg, now, if you wish ''.

But now he knows `` that an intellectual is not only a man to whom books are necessary, he is any man whose reasoning, however elementary it may be, affects and directs his life ''.

what is new and compelling is that the West is now but one of several powerful civilizations, or `` systems '', and that one or more of the others may pose a mortal danger to the West.

This session, for instance, may have insured a financial crisis two years from now.

This may be opera bouffe now, but it will become more serious should the cold war mount in frenzy.

The possibility, as he asserted, that the Russians may get ahead of us or come closer to us because of their tests does not supply the needed ethical premise -- unless, of course, we have unwittingly become so brutalized that nuclear superiority is now taken as a moral demand.

and now, therefore, do I, John A. Notte, Jr., governor of the State of Rhode Island and Providence Plantations, proclaim the week of april 29th to may 7th, 1961, as Rhode Island Heritage Week, advising our citizens that throughout this week many historic houses and beautiful gardens will be open to visitors as well as industrial plants, craft shops, museums and libraries and I earnestly urge all to take advantage of these opportunities to see as many of these places as they can during this outstanding week.

Fortunately, it is the FHA which has arrived at this conclusion, for it means that cooling equipment of all kinds may now be included in a mortgage, and thus acquired with a minimum of financial stress.

Since writing was practiced in the Aegean before the end of the century, we may hope that the details of tradition will now be occasionally useful.

Whatever learning they may have had in their order doesn't disturb them now.

The type of presentation of results used in the deterministic process may be used here, except that now the fourth column is redundant.

This may require imagination and reminding himself that now he can be demanding and self-centered.

We may now take up for consideration a hard case which seems to require either no action employing economic pressure or else action that would seem to violate the principles set forth above.

For the convenience of guests bundle centers have been established throughout the city and suburbs where the donations may be deposited between now and the date of the big event.

Fourteen years is the maximum penalty now faced by the new five, who may have altered history in the 1960s.

and by deriving legitimate decision backward from whatever may conceivably or possibly or probably result, whether by anyone's doing or by accident, it finds itself driven to inaction, to non-political action in politics and non-military action in military affairs, and to the not very surprising discovery that there are now no distinctions on which the defense of justice can possibly be based.

This picture of extreme self-reliant individuation is difficult to reconcile with such Zendo formulas as: `` O you, demons and other spiritual beings, I now offer this to you, and may this food fill up the ten quarters of the world and all the demons and other spiritual beings be fed therewith.

You may do as you please with God now.

This is the tale of one John Enright, an American who has accidentally killed a man in the prize ring and is now trying to forget about it in a quiet place where he may become a quiet man.

And although the universe may forever defy understanding, it might even now be finding its match in the imagination of man.

Although the driving force for both sexes is reproductive success, the two genders have different concerns: males may seek to monopolize access to a group of fertile females, while the females want to maximize return on the energy they invest in reproduction, seeing their offspring grow into healthy adults-and especially into alpha males with well-developed, sexually attractive features that sire them many descendants.

Predatory pricing practices may result in antitrust claims of monopolization or attempts to monopolize.

That aside, Marxist economists such as Ernest Mandel have argued that owners of new, more productive fixed equipment ( which the owners may monopolize with the aid of patents ) can obtain extra income from its use, representing effectively an economic rent ( so-called " technological rents ").

The presence of two Tarquins, the last of whom was ousted as a tyrant, may indicate that the family attempted to monopolize power within the family contrary to Roman custom.

Position may not be everything, but in the case of a pool it can certainly contribute difficulties, social and/or physical.

All this emphasis on Centrality and on the number 5 as a symbolic expression of the Center, which seems to have begun as far back as 400 B.C., also may conceivably have led to the development of the Five-Elements School and the subsequent efforts to fit everything into numerical categories of five.

Errors in technical terminology suggest that the over-all translation from the German may not convey quite everything Mr. Remarque hoped to tell us.

The emotional effects of anxiety may include " feelings of apprehension or dread, trouble concentrating, feeling tense or jumpy, anticipating the worst, irritability, restlessness, watching ( and waiting ) for signs ( and occurrences ) of danger, and, feeling like your mind's gone blank " as well as " nightmares / bad dreams, obsessions about sensations, deja vu, a trapped in your mind feeling, and feeling like everything is scary.

Where being, the noun, is readily accessible to experience and classifiable, being, the participle, is not :" In short ... philosophy may perhaps be able to tell us everything about that which reality is, but nothing at all concerning this not unimportant detail: the actual existence, or non-existence, of what we call reality ....

Therefore dharma may encompass ideas such as duty, vocation, religion and everything that is considered correct, proper or decent behaviour.

Contarini thus openly concludes that the Doge is a combination of myth and reality, saying that “ in everything you may see the show of a king, but his authority is nothing ”.

:" Since you desire to know everything, I have written this ' book of notes ,' that you may learn of what the universe and its elements consist, what the world contains, and what the human race has done.

The habitats studied by marine biology include everything from the tiny layers of surface water in which organisms and abiotic items may be trapped in surface tension between the ocean and atmosphere, to the depths of the oceanic trenches, sometimes 10, 000 meters or more beneath the surface of the ocean.

:" My thesis is ," says, " That if we start with the supposition that there is only one primal stuff or material in the world, a stuff of which everything is composed, and if we call that stuff ' pure experience ,' then knowing can easily be explained as a particular sort of relation towards one another into which portions of pure experience may enter.

The Islamic religious tradition, in particular Sufism and Alevism has a strong belief in the unitary nature of the universe and the concept that everything in it is an aspect of God itself, although this perspective leans closer to panentheism and may also be termed Theopanism.

And He was saying to them, " To you has been given the mystery of the kingdom of God, but those who are outside get everything in parables, so that while seeing, they may see and not perceive, and while hearing, they may hear and not understand, otherwise they might return and be forgiven.

They were unaware that, although Singer believes that some lives are so blighted from the beginning that their parents may decide their lives are not worth living, in other cases, once the decision is made to keep them alive, everything that can be done to improve the quality of their life should, to Singer's mind, be done.

When people possess places to which the public has access, it may be difficult to know whether they intend to possess everything within those places.

This fact is summarized in the commonly heard phrase " In Smalltalk everything is an object ", which may be more accurately expressed as " all values are objects ", as variables are not.

Spirituality in this context may be a matter of nurturing thoughts, emotions, words and actions that are in harmony with a belief that everything in the universe is mutually dependent ; this stance has much in common with some versions of Buddhist spirituality.

Following this view, we may reasonably hope for a theory of everything which self-consistently incorporates all currently known forces, but we should not expect it to be the final answer.

It is an age of revolutions, in which everything may be looked for.

The story ends with Alice recalling the speculation of the Tweedle brothers, that everything may have, in fact, been a dream of the Red King and that Alice might herself be no more than a figment of his imagination.

A place perhaps, at which once everything may have started rationally, then however, became more and more irrational and totally out of control until a return to sanity — or was it still emotion ?— made a humanitarian encounter come true.

In some cases, it may be possible to have more of everything by making different choices ; for instance, when an economy is within its production possibility frontier.

As everything in the field of consciousness assumes unusual importance, feelings become magnified ; love, gratitude, joy, sympathy, lust, anger, pain, terror, despair, or loneliness may become overwhelming, or two seemingly incompatible feelings may be experienced at once.