* When the subring is isomorphic to the dual number plane, then g acts as a shear mapping and preserves the dual angle.

* When the subring is isomorphic to the ordinary complex number plane, then g acts as a rotation and preserves the Euclidean angle.

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.

When molten antimony is slowly cooled, metallic antimony crystallizes in a trigonal cell, isomorphic with that of the gray allotrope of arsenic.

When n = 0, does not have zero elements ; rather, it is isomorphic to, since.

When n = 2, the dicyclic group is isomorphic to the quaternion group Q.

When the dimension of H is infinite, then S < sub > 1 </ sub >( H ) ( the trace class ) is not reflexive, because it contains a subspace isomorphic to ℓ < sup > 1 </ sup >, and S < sub >∞</ sub >( H ) = L ( H ) ( the bounded operators ) is not reflexive, because it contains a subspace isomorphic to ℓ < sup >∞</ sup > ( in both cases, the subspace can be chosen to be the operators diagonal with respect to a given orthonormal basis of H ).

When the base field is an algebraically closed field of characteristic p, the n-torsion is still isomorphic to ( Z / nZ )< sup > 2g </ sup > when n and p are coprime.

When spoken about graph labeling with unique labels, commonly taken from the integer range 1 ,..., n, where n is the number of the vertices of the graph, two labeled graphs are said to be isomorphic if the corresponding underlying unlabeled graphs are isomorphic.

When we say that any two models of the above axioms are isomorphic, we mean that for any two models ( R, 0 < sub > R </ sub >, 1 < sub > R </ sub >, +< sub > R </ sub >, *< sub > R </ sub >, ≤< sub > R </ sub >) and ( S, 0 < sub > S </ sub >, 1 < sub > S </ sub >, +< sub > S </ sub >, *< sub > S </ sub >, ≤< sub > S </ sub >), there is a bijection f: R → S preserving both the field operations and the order.

When the field is not algebraically closed, the case where the endomorphism ring is as small as possible is of particular interest: A simple module over k-algebra is said to be absolutely simple if its endomorphism ring is isomorphic to k. This is in general stronger than being irreducible over the field k, and implies the module is irreducible even over the algebraic closure of k.

When n is even the algebra Cℓ < sub > n </ sub >( C ) is central simple and so by the Artin-Wedderburn theorem is isomorphic to a matrix algebra over C. When n is odd, the center includes not only the scalars but the pseudoscalars ( degree n elements ) as well.

When Γ is isomorphic to the fundamental group of a hyperbolic 3-manifold, then the quotient space H < sup > 3 </ sup >/ Γ becomes a Kleinian model of the manifold.

When k is strictly less than n then the special orthogonal group SO ( n ) also acts transitively on V < sub > k </ sub >( R < sup > n </ sup >) with stabilizer subgroup isomorphic to SO ( n − k ) so that

When Q = P, however, the line can be any line through P. These lines correspond to the space of directions through P, which is isomorphic to P < sup > 1 </ sup >.

When three dice are tossed repeatedly, what is the probability that the number of aces is 0 ( or 1, or 2, or 3 )??

When each number of successes X is paired with its probability of occurrence Af, the set of pairs Af, is a probability function called a binomial distribution.

When the daily number of deaths jumps to 30, the town is sealed and an outbreak of plague is officially declared.

When the volume of an alcoholic drink is shown in centilitres, determining the number of units in a drink is as simple as < var > volume </ var > × < var > percentage </ var > ( converted into a fraction of 1 ).

When the newly-christened AppleTalk shipped in early 1985, it included a number of compromises.

When the total number of mandates gained by a party has been determined, they are distributed between the Land lists.

When a battleground is the site of more than one battle in the same conflict, the instances are distinguished by ordinal number, such as the First and Second Battles of Bull Run.

When the UK Channel 4 television program " The Bermuda Triangle " ( c. 1992 ) was being produced by John Simmons of Geofilms for the Equinox series, the marine insurance market Lloyd's of London was asked if an unusually large number of ships had sunk in the Bermuda Triangle area.

When harvesting, the needed number of stalks should be cut to the base.

When collecting coins by year, this multiplies the number of specimens needed to complete a collection.

When Chiang was defeated by CPC forces in mainland China in 1949, he retreated to Taiwan with his government and his most disciplined troops, along with most of the KMT leadership and a large number of their supporters ; Chiang Kai-shek had taken effective control of Taiwan at the end of WWII as part of the overall Japanese surrender, when Japanese troops in Taiwan surrendered to Republic of China troops.

However, the story is not yet quite finished: " When the thousand years have expired, Satan will be released from his prison and will go out to deceive the nations which are in the four corners of the earth, Gog and Magog, to gather them together to battle, whose number is as the sand of the sea.

When the condition number is exactly one, then the algorithm may find an approximation of the solution with an arbitrary precision.

When compared with Zebu bulls, Canchim bulls produce the same number of calves, but heavier and of superior quality.

When an order has been defined in this way, a sorting algorithm can be used to put a list of any number of items into that order.

When appropriate, the second line may begin with a ' form ' number — e. g., 1 stands for history and criticism of a subject, 2 for a bibliography, 5 for a dictionary, 6 for an atlas or maps, 7 for a periodical, 8 for a society or university publication, 9 for a collection of works by different authors.

:* When is entered, it is picked up by the scanning unit, the number 25 is encoded and sent to the X register.

* Granularity: When a continuously variable analog value is represented in digital form there is always a decision as to the number of symbols to be assigned to that value.

When the two waves are in phase, i. e. the path difference is equal to an integral number of wavelengths, the summed amplitude, and therefore the summed intensity is maximum, and when they are in anti-phase, i. e. the path difference is equal to half a wavelength, one and a half wavelengths, etc., then the two waves cancel and the summed intensity is zero.

She also returned to number one on the country charts later in 2005 by lending her distinctive harmonies to the Brad Paisley ballad, " When I Get Where I'm Goin '".

When that research was repeated in 2007, the number of senior management posts held by women had fallen to 22 %.

When his preaching companions heard of his death, all save Dominic and a very small number of others returned to their homes.

When a number of officers in George's unit are killed, he is promoted.

When Aldington first published his novel, he redacted a number of passages in order to ensure the publication of his book would not be challenged.

When the hunt is over, prizes may be given for the largest number of eggs collected, or for the largest or the smallest egg.