* In linear algebra, an endomorphism of a vector space V is a linear operator V → V. An automorphism is an invertible linear operator on V. When the vector space is finite-dimensional, the automorphism group of V is the same as the general linear group, GL ( V ).

When more electrons are added to a single atom, the additional electrons tend to more evenly fill in a volume of space around the nucleus so that the resulting collection ( sometimes termed the atom ’ s “ electron cloud ” ) tends toward a generally spherical zone of probability describing where the atom ’ s electrons will be found.

When the wake-up call was issued to the Apollo 16 crew for their final day in space by capsule communicator Tony England, the spacecraft was about out from Earth, traveling just over.

When 301 of the most advanced model, the " Launch Arco ," are built, an " exodus sequence " starts in which all Launch Arcos blast into space.

When compressed at room temperature to 7 GPa, α-berkelium transforms to the beta modification, which has a face-centered cubic ( fcc ) symmetry and space group Fmm.

When the Universe was very young, it was likely infused with dark energy, but with less space and everything closer together, gravity had the upper hand, and it was slowly braking the expansion.

When the Banach algebra A is the algebra L ( X ) of bounded linear operators on a complex Banach space X ( e. g., the algebra of square matrices ), the notion of the spectrum in A coincides with the usual one in the operator theory.

When defined for a topological vector space there is a subspace of this dual space, corresponding to continuous linear functionals, which constitutes a continuous dual space.

When the Soviets launched Sputnik in 1957 he had to play catchup in the space race.

When b = 0, the eigenvalues of A determine the structure of the phase space.

When the evolution map Φ < sup > t </ sup > ( or the vector field it is derived from ) depends on a parameter μ, the structure of the phase space will also depend on this parameter.

When the topological space is homeomorphic to a simplicial complex, its fundamental group can be described explicitly in terms of generators and relations.

When the table is full the code length increases to give space for more strings, up to a maximum code 4095

When his mother returned to work as a lady's maid ( at Uppark, a country house in Sussex ), one of the conditions of work was that she would not be permitted to have living space for her husband and children.

When transformed into Phoenix, Jean's powers escalate to an incalculable level, allowing her to rearrange or disintegrate matter at a subatomic level, fly unaided through space, survive in any atmosphere, and manipulate electromagnetic and cosmic energies for various effects and atmospheric disturbances.

When embedded in Euclidean space the Klein bottle is one-sided.

When items are first presented, they enter short-term memory, but because it has limited space, as new items enter, old ones leave.

When rowing, the crew sat on sea chests ( chests containing their personal possessions ) that would otherwise take up space.

When a longhand note, photograph, memoranda, or other things were placed on the platen, the depression of a lever would cause the item to be photographed onto the next blank space in a section of the memex film.

When one applies this process to nouns such as electrons, energy, contract, happiness, space, time, truth, causality, and God, ontology becomes fundamental to many branches of philosophy.

When order starts to return to the Confederation and Joshua Calvert is questioned as to why he moved the human race to such an isolated space he justified himself by saying that this will allow humanity to avert another " reality dysfunction " as this isolation will force itself to look inwards and re-evaluate itself as a whole.

When the exact chromaticities of the red, green, and blue primaries are defined, the color model then becomes an absolute color space, such as sRGB or Adobe RGB ; see RGB color spaces for more details.

When Heidegger and Sartre speak of a contrast between being and existence, they may be right, I don't know, but their language is too philosophical for me.

When they express themselves it is incandescent hatred that shines forth, the rage of repudiation, the ecstasy of negation.

When I try to work out my reasons for feeling that this passage is of critical significance, I come up with the following ideas, which I shall express very briefly here and revert to in a later essay.

When the proprietor dies, the establishment should become a corporation until it is either acquired by another proprietor or the government decides to drop it.

When the reactionary response is thus bolstered by an intellectual defense, the characteristics of that defense are explicable only in terms of the basic attitudes of unanalyzed reaction.

When I take over Taliesin, the first thing I'll do is fire you ''.

When someone in the audience rose and asked how does it feel to be a celebrity, Carl said, `` A celebrity is a fellow who eats celery with celerity ''.

When decision makers act within this frame they determine whether a claim put forward in the name of religion is to be accepted by the larger community as appropriate to religion.

When we consider the disorganized state of the world community, and the legacy of predispositions adversely directed against all who are identified as Jews, it is obvious that the struggle for the minds and muscles of men needs to be prosecuted with increasing vigor and skill.

When we turn to Aristotle's ideas on the moral measure of literature, it is at once apparent that he is at times equally concerned about the influence of the art.

When their faith in civil liberties is tested against strong pressures of social expediency in specific issues, e.g., suppression of `` dangerous ideas '', many waver and give in.

There is, of course, nothing new about dystopias, for they belong to a literary tradition which, including also the closely related satiric utopias, stretches from at least as far back as the eighteenth century and Swift's Gulliver's Travels to the twentieth century and Zamiatin's We, Capek's War With The Newts, Huxley's Brave New World, E. M. Forster's `` The Machine Stops '', C. S. Lewis's That Hideous Strength, and Orwell's Nineteen Eighty-Four, and which in science fiction is represented before the present deluge as early as Wells's trilogy, The Time Machine, `` A Story Of The Days To Come '', and When The Sleeper Wakes, and as recently as Jack Williamson's `` With Folded Hands '' ( 1947 ), the classic story of men replaced by their own robots.

When I first came across Samuel Johnson's pronouncement, `` the remedy for the ills of life is palliative rather than radical '', it seemed to me to sum up the profoundest of political and social truths.

When all else fails, it is argued that open sessions slow down governmental operations.

When a person has thoughtlessly or deliberately caused us pain or hardship it is not always easy to say, `` Just forget it ''.

When a person meets God's requirements for the experience of forgiveness he is forgiven.

When I hold my son he stiffens his whole body in my arms until he is as straight and stiff as a board.

When different colors are used, she is just as likely to color trees purple, hair green, etc..

When we become firm enough to stand for those ideals which we know to be right, when we become hard enough to refuse to aid nations which do not permit self-determination, when we become strong enough to resist any more drifts towards socialism in our own Nation, when we recognize that our enemy is Communism not war, and when we realize that concessions to Communists do not insure peace or freedom, then, and only then will we no longer be `` soft ''.

When one powerful nation strives to emulate the success of another, it is only natural.

When a man is laid to rest, he is entitled to stay put.

When I talked to Ching about it, he said, Everyone can learn, if he is not a Reactionary or lazy.