He was aware of insistent inner beatings, as if prisoners within sought release from his rigid body.

I don't know if I can get you into the inner camp.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

However, if the excited atom has been previously ionized, in particular if one of its inner shell electrons has been removed, a phenomenon known as the Auger effect may take place where the quantity of energy is transferred to one of the bound electrons causing it to go into the continuum.

Every Hilbert space X is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.

His brow was low and broad, his eyes a volcanic blue that smoldered as if with some inner fire.

If the earlier completion procedure is applied to a normed vector space, the result is a Banach space containing the original space as a dense subspace, and if it is applied to an inner product space, the result is a Hilbert space containing the original space as a dense subspace.

The parallel postulate: If two lines intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.

However, if one additionally prescribes a smoothly varying inner product on the manifold's tangent spaces, then the result is what is called a Riemannian manifold.

All cuticular structures are shed at ecdysis, including the inner parts of the exoskeleton, which includes terminal linings of the alimentary tract and of the tracheae if they are present.

The centrifugal force from the Earth's rotation would pull a person ( on the inner surface ) outwards if the person was traveling at the same velocity as the Earth's interior and was in contact with the ground on the interior, but even the maximum centrifugal force at the equator is only 1 / 300 of ordinary Earth gravity.

Eventually, harpsichords came to be built with just a single case, though an intermediate stage also existed: the " false inner – outer ", which for purely aesthetic reasons was built to look as if the outer case contained an inner one, in the old style.

In long track speed skating, almost any infringement on the pairmate is punished, though skaters are permitted to change from the inner to the outer lane out of the final curve if they are not able to hold the inner curve, as long as they are not interfering with the other skater.

This inner necessity is the right of the artist to unlimited freedom, but this freedom becomes licence if it is not founded on necessity.

Assign z to z < sup > 2 </ sup > minus the conjugate of z, plus the original value of the pixel for each pixel, then count how many cycles it took when the absolute value of z exceeds two ; inversion ( borders are inner set ), so that you can see that it threatens to fail that third condition, even if it meets condition two.

and the fact that equality holds only when u and v are linearly dependent ( the fact that conversely one has equality if u and v are linearly dependent is immediate from the properties of the inner product ).

" He was preparing a bull that would excommunicate the King of France and put the interdict over France, and to depose the entire clergy of France, when in September 1303, William Nogaret, the strongest critic of the Papacy in the French inner circle, led a delegation to Rome, with intentionally loose orders by the king to bring the pope, if necessary by force, before a council to rule on the charges brought against him.

For example, if one said " The inner city youth orchestra has been a remarkably successful initiative in that it has kept young people off the streets after school and exposed them to culture and discipline, thereby improving their self esteem and future prospects.

Therefore the form is an inner product on if and only if is real and positive for all nonzero z ; that is if an only if M is positive definite.

Cut a notch in lid for spoon handle if desired.

Once it was Osiris's turn to see if he could fit in the box, Set closed the lid on him so that the box was now a coffin for Osiris.

The safety comes from a secure screw-on metal lid, and two flat sides which prevent it from rolling if knocked over.

The boot lid includes an integrated rear spoiler which designed to look as if it was impossible to make on the orders of Aston Martin Chief Executive, Dr. Ulrich Bez.

The lid of the now opened can is lifted, most often with the P-38 cutting edge, and the P-38 is wiped clean, and the cutting point is rotated back to its stowed, folded position ; then, the P-38 is returned to its stored location, whether that is dangling on a dog tag chain around one's neck, or in one's pocket if the P-38 is attached to a key ring.

1993 and 1994 models also had a slim armrest lid, however, if an optional leather armrest was selected, it brought the height up to about.

* The battery pack ( if included ) is designed to fit four AA batteries, yet is often under-sized slightly such that four AA's will not fit and the battery pack lid cannot be closed.

Almost all modern food processors have safety devices which prevent the motor from operating if the bowl isn't properly affixed to the base or if the lid isn't properly affixed to the bowl.

The advantage of an aquarium closed with a lid ( rather than a permanently sealed plug, which is found in the base of an EcoSphere ) is that if the system goes out of equilibrium, the owner can remedy conditions and prevent a complete die-off.

The automaker said the fuel-filler lid and owner's manual warn that the engine should not be worked hard if regular fuel is used.

They are usually made out of pewter, and are usually equipped with a lever that is in reach of the thumb, so that it is possible to grab the mug and open and close the lid with a single hand ( if one can hold the weight, that is ).

Jars of food items soon started appearing with a metal bubble-top lid, commonly known as a " safety button ", which popped out if the jar had ever been opened and stayed flat if the jar was in pristine condition.

The W140 introduced innovations such as double-pane window glazing, power-assisted closing for doors and boot lid, electric windows which lowered back down upon encountering an obstruction, rear-parking markers which rose from the rear wings ( discontinued on later vehicles, and replaced with sonar-assisted parking ) and a heating system which, if desired, continued to emit warm air after the engine was turned off.

He notes, correctly anticipating foreign specimens " As there is now no vexatious delay or trouble experienced by Custom-house regulations, specimens of natural history being admitted free of duty, it is recommended that all packages may be entered in the ship ’ s papers, and if a list of all the contents of each package could, with convenience, be attached inside the lid of the box or cover, the risk of injury to the specimens, by examination at the Custom-house, would in great measure be avoided ".

`` That is, if we can be sure this is Colcord's money '' --

Let me pass over the trip to Sante Fe with something of the same speed which made Mrs. Roebuck `` wonduh if the wahtahm speed limit '' ( 35 m.p.h. ) `` is still in ee-faket ''.

It is the last of the three tests of manhood which the women impose, to discover if a male is worthy of survival there.

There was a measure of protection in its concrete walls and ceiling, but the engineers who hastily installed it were well aware that concrete is not much better than prayer, if as efficacious, when a direct hit comes along.

`` And if the dive goes OK he has the exclusive import rights to your line for this country, is that right ''??

`` All right, if you can't do your arithmetic during school hours you can do it after school is out '', Miss Langford said firmly, not smiling.

Why, in the first place, call himself a liberal if he is against laissez-faire and favors an authoritarian central government with womb-to-tomb controls over everybody??

And if he is so scornful of the rights of states, why not advocate a different sort of constitution that he could more sincerely support??

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

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.

Unruly hair goes straight up from his forehead, standing so high that the top falls gently over, as if to show that it really is hair and not bristle.

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

He will not curb his instinctual desires but release the energy within him that makes him feel truly and fully alive, even if it is only for this brief moment before the apocalypse of annihilation explodes on earth.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

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.

All such imitations of negative quality have given rise to a compensatory response in the form of a heroic and highly individualistic humanism: if man can neither know nor love reality as it is, he can at least invent an artistic `` reality '' which is its own world and which can speak to man of purely personal and subjective qualities capable of being known and worthy of being loved.

But Aristotle kept the principle of levels and even augmented it by describing in the Poetics what kinds of character and action must be imitated if the play is to be a vehicle of serious and important human truths.

Operating as a one man police force in fact if not in name, he is at once more independent and more dedicated than the police themselves.