* 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 split-complex number plane, then g acts as a squeeze mapping and preserves the hyperbolic 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 an ordinary free man accepted Islam, despite opposition, he would enjoy the protection of his tribe.

When this gene was inserted into tomato and tobacco cells ( see RNA interference ), the cells were able to withstand environmental stresses like salt, drought, cold and heat, far more than ordinary cells.

When the Greek astronomer Ptolemy's Almagest was translated from Greek to Arabic, the translator Johannitius ( following Alberuni ) did not know the Greek word and rendered it as the nearest-looking Arabic word, writing العصى ذات الكلاب in ordinary unvowelled Arabic text " al -` aşā dhāt al-kullāb ", which means " the spearshaft having a hook ".

When the nets were inspected, the " rods " were no more than regular moths and other ordinary flying insects.

When matter ( ordinary material particles ) is changed into energy ( such as energy of motion, or into radiation ), the mass of the system does not change through the transformation process.

When the domain of the input function is time ( t ), and the domain of the output function is ordinary frequency, the transform of function s ( t ) at frequency ƒ is given by the complex number:

When you had trade unions, ordinary people, rank and file, never been on television, never been interviewed, and they're not allowed to be heard, that's scandalous.

* When conducted by an ordinary electric cable, RF current has a tendency to reflect from discontinuities in the cable such as connectors and travel back down the cable toward the source, causing a condition called standing waves, so RF current must be carried by specialized types of cable called transmission line.

When dealing with situations on an ordinary human scale, Newtonian physics has been so enormously successful that it has no competition.

When n < sub > e </ sub > < n < sub > o </ sub >, as in calcite, the extraordinary axis is called the fast axis and the ordinary axis is called the slow axis.

When an antihydrogen atom comes into contact with ordinary matter, its constituents quickly annihilate.

In the 1983 " Liber Hymnarius " from Solesmes, it is stated that, " When an ordinary syllable is set to one note, this represents the fundamental rhythmic value used in Gregorian chant ( i. e. valor syllabicus medius ).

The latter example leads to a generalization of modules over rings: If C is a preadditive category, then Mod ( C ) := Add ( C, Ab ) is called the module category over C. When C is the one-object preadditive category corresponding to the ring R, this reduces to the ordinary category of ( left ) R-modules.

When specializing to the preadditive categories of abelian groups or modules over a ring, this notion of kernel coincides with the ordinary notion of a kernel of a homomorphism, if one identifies the ordinary kernel K of f: A → B with its embedding K → A.

When travelling, a priest could take one with him and place it on an ordinary table for saying Mass.

When a substantial number of copies of an electrical transcription were required, as for the distribution of a syndicated program, they were produced by the same process used to make ordinary records.

When the ordinary citizen of Ancient Greece read inscriptions and the educated Greek read literature, what they saw was an all upper case Ionic alphabet: Α, Β, Γ, Δ, etc.

When the term generating function is used without qualification, it is usually taken to mean an ordinary generating function.

When lu kan shih ( zinc carbonate, calamine ) or wo chhein ( zinc metal ) is mixed and combined with chih thung ( copper ), one gets ' yellow bronze ' ( ordinary brass ).

When something out of the ordinary occurs, usually something unfortunate, to an individual, the Azande may blame witchcraft, just as non-Zande people might blame " bad luck ".

When criticized, the U. S. military's response was to point out that these men were no ordinary combatants, and to express hope that confirmation of the deaths would bring closure to the Iraqi people.

When ordinary citizens are confronted with tyranny, he wrote, ordinary citizens have to suffer it ( whereas in the Mandate of Heaven and in the theology of the Jesuits Bellarmine and Mariana, they have the right to rebellion and tyrannicide ), but magistrates have the duty to " curb the tyranny of kings ," as had the Tribunes in ancient Rome, the Ephori in Sparta, and the Demarchs in ancient Athens -- and indeed the Censorate of China.