Imaginary expression

Definitions

  • Webster's Revised Unabridged Dictionary
    • Imaginary expression (Alg) an algebraic expression which involves the impossible operation of taking the square root of a negative quantity; as, √-9 a + b √-1.
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Usage

In literature:

A SIMILE or COMPARISON is when the resemblance between two objects, whether real or imaginary, is expressed in form.
"English Grammar in Familiar Lectures" by Samuel Kirkham
Then he had promised Paul an organ in a cathedral of dreams, where the imaginary self which was his greater self might find expression.
"Destiny" by Charles Neville Buck
In naval architecture, an imaginary timber, expressed by vertical lines in the sheer-draught, to prove the fairness of the body.
"The Sailor's Word-Book" by William Henry Smyth
All through the direct testimony of our imaginary witness, it will be remembered, we were watching his every movement and expression.
"The Art of Cross-Examination" by Francis L. Wellman
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In science:

We discussed how such asymmetries, which measure the imaginary part of the two-photon exchange amplitude, can be expressed through non-forward nucleon structure functions and provide a new tool to access hadron structure information.
Two-Photon Physics in Hadronic Processes
Similar expressions containing bilinear products of the imaginary and real parts of the quark-hadron amplitudes, A, can be written for the other contributions. A formal proof of factorization was given only in the case of longitudinally polarized virtual photons producing longitudinally polarized vector mesons .
Chiral-Odd Generalized Parton Distributions from Exclusive pi^o Electroproduction
It then follows from (the imaginary part of ) this expression that the function f (r) in Eq. (8.19) obeys f (r) ∝ M log r .
Primordial Fluctuations in String Cosmology
IV A — only on the imaginary part of ˜RM (ω ); its real part can be obtained from the Kramers-Kronig relation , as discussed in App. B 2.] These expressions allow us to determine the effective temperature T M eff (ω ) on the basis of the FDR in Eq. (19).
Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain
We note that the last term of the latter expression is an anti-hermitean operator and therefore its expectation value is imaginary, contributing only with a subleading, O(t2 ) term to the response function ∝ Im C x , which receives a contribution O(t) from the first commutator calculated above.
Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain
A path integral expression for the partition function may be easily found by noting that e−βH is nothing but the time-evolution operator for an imaginary amount of time t = iβ .
The Electroweak Phase Transition, Part 1: Review of Perturbative Methods
The complex fermion d has been expressed in terms of its real and imaginary (i.e.
Bosonization in the two-channel Kondo model
In partial waves this imaginary part is given by the square of the phase-shift calculated from one-pion exchange, eq.(11); in the case of the mixing triplet states with L = J ± 1 it is actually a quadratic expression in these phase shifts and the mixing angle.
Peripheral Nucleon-Nucleon Phase Shifts and Chiral Symmetry
Therefore the imaginary part of iterated one-pion exchange allows for a numerical check of unitarity, which actually serves as a check of both, the analytical expressions for iterated one-pion exchange, eqs.(31-34) and the pro jection formulas, eqs.(6-9).
Peripheral Nucleon-Nucleon Phase Shifts and Chiral Symmetry
The Roy equations express the real part of tI ℓ (q) in terms of the imaginary part.
Probing the quark condensate by means of pi-pi scattering
Note that, since ξ− = ξ ∗+ , the last factors in the two expressions above are respectively purely real and purely imaginary.
Factorisation in Higher-Twist Single-Spin Amplitudes
The important point to note is that in the expression for the amplitudes only the s-channel resonance contributes an imaginary part whereas the others are completely real.
A note on low scale unification and gamma-gamma scattering
In brief, we have used the general expression of the likelihood function, assuming that the statistics of the real and imaginary parts of the Fourier transform follows a multi-normal distribution, described by a covariance matrix (Schou, 1992; Appourchaux et al., 1998).
The solar tachocline and its variation (?)
However, we wish to retain both n1 and n2 to show the cancellation of their product in the final expression for the imaginary part.
Spectral representation and QCD sum rules for nucleon at finite temperature
W 2 (1 + |i − j |) The covariance B has the same expression as C , but with an imaginary term in the mass.
Density of states for Random Band Matrix
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