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Page "Lac operon" ¶ 48
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We and say
`` We think the governor treated us rather shabbily, to say the least of it.
We often say of a person that he `` looks young for his age '' or `` old for his age ''.
We may say of some unfortunates that they were never young.
We cannot truthfully say of anyone who has succeeded in entering deep into his sixties that he was never old.
We sympathize with Mr. Kennedy, but we feel bound to say that his budget review doesn't please us either, although for very different reasons.
We couldn't be seen together, for the tongue of Scandal was ever ready to link our names, and the tongue of Scandal finds but one thing to say of the association of a man with a girl, no matter how innocent.
We say that N is nilpotent if there is some positive integer R such that Af.
We may say that his problem was diagnosed but that he refused treatment.
We may say that his attitude was foolish, since he may have been a success had he learned some human relations skills ; ;
We should say that we made our point with feeling the first time and little or no feeling the second time, but that it was the same point we were making.
We may carry this sequence one step further and say that at seventy he was a poet at the height of his powers, wanting only the impetus of two tragedies, one personal, the other national, to loose those powers in poetry.
`` We worry '', say the mothers.
We have to tell ourselves that when Parker spoke in this vein, he believed what he said, because he could continue, `` But the truth, which cost me bitter tears to say, I must speak, though it cost other tears hotter than fire ''.
We do not say that a man who takes no interest in politics is a man who minds his own business ; we say that he has no business here at all.
We say A is unital if it contains an element 1 such that
We can say that that relation has being as well.
We say we want to see put on the statute book something which will make our people citizens of the world before they are citizens of this country ".
We might not see any rotation initially, but if we closely look at the right, we see a larger field at, say, x = 4 than at x = 3.
We say that the mutation is recessive because the organism will exhibit the wild type phenotype ( ordinary trait ) unless both chromosomes of a pair have the mutation ( homozygous mutation ).
We say that f is a diffeomorphism if it is bijective, smooth, and if its inverse is smooth.
We can distort a dual polyhedron such that it can no longer be obtained by reciprocating the original in any sphere ; in this case we can say that the two polyhedra are still topologically dual.
We have to also say how to add their elements.
We can use it as basis to say, " a < b " and " b > a ", two judgments which designate the same state of affairs.
: “ We say that it origin of the traditions is polar, and the pole is nomore Western than it is Eastern.

We and operator
We are trying to study a linear operator T on the finite-dimensional space V, by decomposing T into a direct sum of operators which are in some sense elementary.
We know that is opaque and thus follows that is opaque, so in the above equation, each operator can be written as a convex combination:
We now give an operator theoretic proof for the Cauchy – Schwarz inequality which passes to the C *- algebra setting.
We also note that a two-body Dirac equation composed of a Dirac operator for each of the two point particles interacting via the Coulomb interaction can be exactly separated in the ( relativistic ) center of momentum frame and the resulting ground state eigenvalue has been obtained very accurately using the Finite element methods of J. Shertzer.
We can also define a number operator N which has the following property:
We are provided with ( quantum black box ) access to a subroutine in the form of a unitary operator, U < sub > ω </ sub >, which acts as:
He further wrote: " We didn't learn for years — until the reactor vessel was physically opened — that by the time the plant operator called the NRC at about 8 am, roughly ½ of the uranium fuel had already melted.
We now utilize quantum mechanical ladder operators, which are defined for a general angular momentum operator as
We consider generalizations of this operator below.
We see that there is a bijection between symmetric extensions of an operator and isometric extensions of its Cayley transform.
An operator grimly replied, " We put two rounds in their forehead ; the dead don't need handcuffs.
We also define the total number operator for the field which is a sum of number operators of each mode:
Thus we define the representations of G on an Hilbert space H to be those group homomorphisms, ρ, which arise from continuous actions of G on H. We say that a representation ρ is unitary if ρ ( g ) is a unitary operator for all g ∈ G ; i. e., for all v, w ∈ H. ( I. e.
We differentiated according to the product rule and noted that is the time derivative of the operator we started with.
Take X to be a complex manifold with a complex vector bundle V. We let the vector bundles E and F be the sums of the bundles of differential forms with coefficients in V of type ( 0, i ) with i even or odd, and we let the differential operator D be the sum
There were worries that if Arriva Trains Wales were granted this service, it would push Wrexham – London operator Wrexham & Shropshire out of business, with Wrexham & Shropshire Managing Director, Andy Hamilton, saying " We believe that this proposal – if approved – would push the date of profitability of WSMR by at least a year.
We drop the t < sub > 0 </ sub > index in the time evolution operator with the convention that and write it as U ( t ).
And when, the next day, Woodward — this is probably Sunday or maybe Monday, because the burglary was Saturday morning early — called the number and asked to speak to Mr. Hunt, and the operator said, ‘ Well, he's not here now ; he's over at ,’ such-and-such a place, gave him another number, and Woodward called him up, and Hunt answered the phone, and Woodward said,We want to know why your name was in the address book of the Watergate burglars .’ And there is this long, deathly hush, and Hunt said, ‘ Oh my God !’ and hung up.
We call hyperreflexive if there is a constant K such that for every operator T in B ( H ),
We define an operator between two functional spaces of continuous functions, Picard's operator, as follows:
We can measure the spin of this electron's state by applying an operator to the state, and we will always obtain ( or spin 1 / 2 ) since the spin-up and spin-down states are both eigenstates of this operator with the same eigenvalue.
We can also define the functional calculus for not necessarily bounded Borel functions h ; the result is an operator which in general fails to be bounded.

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