( We will drop the ( 0 ) superscripts for the eigenstates, because it is not meaningful to speak of energy levels and eigenstates for the perturbed system.

We can drop the accessibility clause from the latter stipulation because it is trivially true of all S5 frames that w R v.

There is more intergenerational mobility in Australia, Sweden, Norway, Finland, Germany, Spain, France, and Canada than in th U. S. In fact, of affluent countries studied, only Britain and Italy have lower intergenerational mobility than the United States does ( and they are basically even with the U. S .) We know less about the long-term mobility of the top 1 percent, but all indications are that people in this rarefied group usually don ’ t drop very far down the ladder.

We then see Malik and Deja walking at the Peace Fest, with Malik saying he wouldn't drop out because he'd lose her.

When he complained Stengel reportedly leaned over to his first baseman and said, " We was gonna give you a piece but we was afraid you'd drop it!

" Fabius let the fold drop and proclaimed " We give you war.

" Added to the letter was a declaration by the boys in Gloucester's army: " We, your Majesty's subjects, will stand by you while we have a drop of blood.

We weren ’ t going to drop the ball now ,” said Kowalczyk.

" Warner then told the Beach Boys to drop what the company perceived as the weakest track, " We Got Love ," and replace it with the Wilson-Parks tune.

" and " We will drop her first " instead of " Can you drop me off?

" and " We will drop her off first ".

We first define a function b{t} as follows: given the set of squares such that each has three corners on C and vertex at t, b{t} is the corresponding set of positive parametric differences between T and the backward corner points.

We replace r, the number of the stage from the end of the process, by t, a continuous variable which measures the `` distance '' of the point considered from the end of the process.

We have to distinguish between the spectra of di-atomic molecules, which exhibit a pronounced fine structure, and those of larger ( usually tri-atomic ) molecules that don ’ t show such fine structure.

As she confessed later, " We didn ’ t love Papa very much, he was so foreign.

We may solve this by separation of variables ( moving the y terms to one side and the t terms to the other side ),

We shall write the extension of the spring at a time t as x ( t ).

Waiting for a Miracle: Why Schools Can ’ t Solve Our Problems-and How We Can.

We couldn ’ t get on country radio and we couldn ’ t get on rock radio!

We don ’ t know who in particular we are, and therefore can ’ t bias the decision in our own favour.

We really don ’ t think laws and “ imaginary property ” have any place in peoples ’ love or cultural relations.

" We don ’ t decide what men should do with their torso, why then do women have to listen to the men.

We worked together for a few days, weeks maybe, and I decided I didn ’ t really want to do a Roxy thing.

A proponent of Obama ’ s healthcare bill, Turner has said: “ We ’ re the only first world country that doesn ’ t have universal healthcare and it ’ s a disgrace .”

We can begin with the forward wave, whose voltage as a function of time t and of distance x along the transmission line is:

We know, for example, that the Malagasy myth of the ogre Trimo be – " eater of children " is a story brought by the Austronesians and in fact is about the tiger ( from * ( t ) rimau, " tiger " in Proto-MP ) who lives in the forests of the Sunda Islands.

* In God We Tru $ t ( 1980 )

PETA spokesperson Lindsay Rajt told the Huffington Post, “ We try to use absolutely every outlet to stick up for animals ,” adding that “ We are careful about what we do and wouldn ’ t use nudity or some of our flashier tactics if we didn't know they worked .” PETA also used nudity in its " Veggie Love " ad which it prepared for the Super Bowl only to have it banned by the network.

We couldn ’ t believe it.

All The Ways We Don ’ t Tell the Truth, January 6, 2002.

As one Micronesian diplomat said, " We need Israeli expertise, so I don ’ t see a change in our policy anytime soon.

Mackendrick remembered, " We started shooting in Times Square at rush hour, and we had high-powered actors and a camera crane and police help and all the rest of it, but we didn ’ t have any script.

We could, alternatively, choose an encoding for Turing machines, where an encoding is a function which associates to each Turing Machine M a bitstring < M >.

We use the stronger statement that every odd ( antipode-preserving ) mapping h: S < sup > n-1 </ sup > → S < sup > n-1 </ sup > has odd degree.

We can then define the differential map d: C < sup >∞</ sup >( M ) → T < sub > x </ sub >< sup >*</ sup > M at a point x as the map which sends f to df < sub > x </ sub >.

We list the elements of A effectively, n < sub > 0 </ sub >, n < sub > 1 </ sub >, n < sub > 2 </ sub >, n < sub > 3 </ sub >, ...

We repeat this procedure to find m < sub > 2 </ sub > > m < sub > 1 </ sub >, etc.

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

We can use it as basis to say, " a < b " and " b > a ", two judgments which designate the same state of affairs.

We define the periodic Bernoulli functions P < sub > n </ sub > by

We are interested in the following set of continuous functions called loops with base point x < sub > 0 </ sub >.

The ( unique ) representable functor F: → is the Cayley representation of G. In fact, this functor is isomorphic to and so sends to the set which is by definition the " set " G and the morphism g of ( i. e. the element g of G ) to the permutation F < sub > g </ sub > of the set G. We deduce from the Yoneda embedding that the group G is isomorphic to the group

We must also prevent the decoder from using the last code in the upper block, 2 < sup > n + 1 </ sup > − 1, because when the decoder fills that slot, it will increase the code width.

#* We extend this result to more and more complex and lengthy sentences, D < sub > n </ sub > ( n = 1, 2 ...), built out from B, so that either any of them is refutable and therefore so is φ, or all of them are not refutable and therefore each holds in some model.

#* We finally use the models in which the D < sub > n </ sub > hold ( in case all are not refutable ) in order to build a model in which φ holds.

where ω is implicitly a function of k. We assume that the wave packet α is almost monochromatic, so that A ( k ) is nonzero only in the vicinity of a central wavenumber k < sub > 0 </ sub >.

If ƒ is complex differentiable at every point z < sub > 0 </ sub > in an open set U, we say that ƒ is holomorphic on U. We say that ƒ is holomorphic at the point z < sub > 0 </ sub > if it is holomorphic on some neighborhood of z < sub > 0 </ sub >.