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Page "Spectrum (functional analysis)" ¶ 53
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For and λ
For every a ∈ A, there is λ ∈ C such that
For example, the character ' λ ' can be represented as, or.
For example, ' λ ' can also be encoded as in an HTML document.
* For every λ in C and every x in A:
For any alphabet there is only one word of length 0, the empty word, which is often denoted by e, ε or λ.
For light, the refractive index n, vacuum wavelength λ < sub > 0 </ sub >, and wavelength in the medium λ, are related by
For example, suppose the state space is the n-dimensional complex Hilbert space C < sup > n </ sup > and A is a Hermitian matrix with eigenvalues λ < sub > i </ sub >, with corresponding eigenvectors ψ < sub > i </ sub >.
For example, one talks about " a Poisson distribution with mean value λ ".
For a beam of wavelength λ at a distance z along the beam from the beam waist, the variation of the spot size is given by
For example, for λ < sub > 0 </ sub >= 1550 nm, n < sup >*</ sup >= 1. 5, Δλ
For many optical fiber materials, M ( λ ) approaches zero at a specific wavelength λ < sub > 0 </ sub > between 1. 3 and 1. 5 μm.
For a half-wave plate, the relationship between L, Δn, and λ < sub > 0 </ sub > is chosen so that the phase shift between polarization components is Γ = π.
For a quarter-wave plate, the relationship between L, Δn, and λ < sub > 0 </ sub > is chosen so that the phase shift between polarization components is Γ = π / 2.
For example, 3 + 1 can be calculated by evaluating ( λ x → x + 1 )( 3 ):
For example, component failures typically occur at some constant failure rate λ ( a constant hazard function ).
For example, a λ DNA-HindIII Digest: a common lambda DNA ladder that has band sizes ( in base pairs ) of 23, 130 ; 9, 416 ; 6, 557 ; 4, 361 ; 2, 322 ; 2, 027 ; 564 ; and 125 bp
For visible light, refraction indices n of most transparent materials ( e. g., air, glasses ) decrease with increasing wavelength λ:
For a 1 × 1 matrix A = ( a ), the characteristic polynomial is given by p ( λ )= λ a, and so p ( A )=( a )− a ( 1 )=( 0 ) is obvious.
For instance, in the above 2 × 2 matrix example, the coefficient c < sub > 1 </ sub >= a + d of λ above is just the trace of A, trA, while the constant coefficient c < sub > 0 </ sub >= ad bc can be written as ½ (( trA )< sup > 2 </ sup >− tr ( A < sup > 2 </ sup >)).
For a simple plane-mirror cavity, the allowed modes are those for which the separation distance of the mirrors L is an exact multiple of half the wavelength of the light λ, such that, where q is an integer known as the mode order.
For wavelength λ, it is:

For and be
For less than a dozen miles from the unplowed land of the dead man lived another settler who had ignored the warnings that his existence might be foreclosed on -- a blatant and defiant rustler named Fred Powell.
For three straight years, Tom Horn patrolled the southern Wyoming pastures, and how many men he killed after Lewis and Powell ( if he killed Lewis and Powell ) will never be known.
Plays more highly formalized than `` Waiting For Godot '', `` Endgame '', and `` Krapp's Last Tape '' would be hard to find.
For this reason, he appears as an independent and self-reliant figure, whose rugged individualism need not be pressed into the mold of a 9 to 5 routine.
For the answer cannot be derived from any socially cohesive element in the disrupting community.
For Rachel, conceded to be the prettiest of the Szold girls -- and she did make a pretty picture sitting in the grape-arbor strumming her guitar and singing in her silvery tones -- there was no particular March counterpart ; ;
For innocence, of all the graces of the spirit, is I believe the one most to be prayed for.
William Wimsatt and Cleanth Brooks, it seems to me, have a penetrating insight into the way in which this control is effected: `` For if we say poetry is to talk of beauty and love ( and yet not aim at exciting erotic emotion or even an emotion of Platonic esteem ) and if it is to talk of anger and murder ( and yet not aim at arousing anger and indignation ) -- then it may be that the poetic way of dealing with these emotions will not be any kind of intensification, compounding, or magnification, or any direct assault upon the affections at all.
For his part, Thompson had explained in a previous letter that there would be nothing but an honorable friendship between Katie and himself.
For them a box will be lodgment enough.
For them only a little more needed to be learned, and then all physical knowledge could be neatly sorted, packaged and put in the inventory to be drawn on for the solution of any human problem.
For this reason, then, poetry tends to weaken the power of control, the reason, because it tempts one to indulge his passions, and even the best of men, he maintains, may be corrupted by this subtle influence.
For him to divorce God and wife simultaneously would be bad publicity.
For a time it appeared that a common European army might be created, but the project for a European Defense Community was rejected by the French National Assembly in 1954.
For one thing, there wasn't going to be any ceremony at all this year.
For the young child this may be no more than providing food, light or movement.
For the most part, however, the new version is contemporary and, as such, should be the means for many to attain a clearer comprehension of the meaning of those words recorded so many hundreds of years ago by the first followers of Christ.
For those who `` like poetry but never get around to reading it '', the Library of Congress makes it possible for poets to be heard reading their own work.
For it is such a distinguished place, with such fine works of art and such a big library, that there can be little doubt but that the owner has become depraved by all this culture.
For the first time, he be sad about the move.
For both economic and political reasons all segments of the population must be able to share in the growth of a country.
The Industrial Division published, in 1960, a new, attractive industrial brochure, `` Rhode Island -- Right For Industry '', and prepared copy for a new edition of the Directory Of Manufacturers ( to be printed shortly ), and for a new space catalogue.

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