# Diagonal scale

## Definitions

• Diagonal Scale
• Webster's Revised Unabridged Dictionary
• Diagonal scale a scale which consists of a set of parallel lines, with other lines crossing them obliquely, so that their intersections furnish smaller subdivisions of the unit of measure than could be conveniently marked on a plain scale.
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Chambers's Twentieth Century Dictionary
• Diagonal scale a scale for laying down small fractions of the unit of measurement, the parallel lines drawn lengthwise on its surface being divided into sections by lines drawn crosswise, and in one end section being intersected by a series of other parallel lines drawn obliquely at equal distances across them
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## Etymology

Chambers's Twentieth Century Dictionary
Fr.,—L. diagonalis, from Gr. diagōniosdia, through, and gōnia, a corner.

## Usage

### In literature:

On the other side, using the other scales, we have dropped perpendiculars in the same way from the diagonal to 3, 4.
"The Theory and Practice of Perspective" by George Adolphus Storey
This diagonal then represents number 5, and completes the scale or tally of 5.
"Notes and Queries, Vol. IV, Number 89, July 12, 1851" by Various
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### In news:

6 fresh redfish fillets still in their scales, scored diagonally 2 lbs.
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### In science:

We calculate numerically (off-diagonal) spin-operator proﬁles, whose scaling properties are related to (bulk and surface) decay exponents and compare the proﬁles with predictions of conformal invariance.
Random antiferromagnetic quantum spin chains: Exact results from scaling of rare regions
Scale changes with respect to µ2 and M 2 thus nearly cancel again each other along the ﬁrst diagonal but add up in the other case.
The QCD and Standard Model Working Group: Summary Report from Les Houches
For simplicity, we also assume that at high energy scale, the metric is ﬂat and diagonal.
Spontaneous Physical Compactification of the Extra Dimensions
The metrics are block-diagonal and all scale factors, scalar ﬁelds and ﬁelds of forms depend on points of some (mainly Ricci-ﬂat) manifold M0 .
Exact solutions in multidimensional gravity with antisymmetric forms
Without any loss of generality we can always choose the charged lepton Yukawa matrix Ye as well as the quark Yukawa matrices Yu and Yd to be diagonal at the At any energy scale µ, the neutrino mass matrix ν and the charged lepton high scale.
Renormalization group evolution of neutrino masses and mixing in seesaw models: A review
Then from the RG equations in Table 3 we get that they will remain diagonal at all energy scales, and so will P .
Renormalization group evolution of neutrino masses and mixing in seesaw models: A review
Thus between and above the (n)X is diagonal. see-saw scales, the running may become strongly inﬂuenced by the Yukawa couplings of the heavy ﬁelds.
Renormalization group evolution of neutrino masses and mixing in seesaw models: A review
For the intermediate energy scales, ν will receive contributions a number and hence from Eq. (32) we see that Y∆ may be chosen to be diagonal in general.
Renormalization group evolution of neutrino masses and mixing in seesaw models: A review
Hopefully, with appropriate regularization at short scales, the equations will appear to be convenient for future numerical implementation, since all the linear operators (the differentiations and [ˆk coth ˆk ]) are diagonal in Fourier representation.
Nonlinear interfacial waves in a constant-vorticity planar flow over variable depth
Cg to the scale µ, which is readily done by diagonalizing the 3 × 3 matrix ˆγgg, via ˆγ T ggA−1 .
A Motivated Non-Standard Supersymmetric Spectrum
The diagonal entries are displayed in linear scale whereas we adopt a log scale for the off-diagonal elements; for them, we also showed the best ﬁt values with a solid vertical line.
S3 as a flavour symmetry for quarks and leptons after the Daya Bay result on \theta 13
As shown by Paindaveine (2008), this choice indeed is the only one for which the information matrix for scale and shape is block-diagonal, which greatly simpliﬁes inference.
Optimal rank-based testing for principal components
Now, since it is precisely F †F in Eq. (2.4) which affects the ﬂavor diagonal couplings and also induces FCNC, if the mass scale for the exotic fermions is large enough, the suppression of the ordinary–exotic mixings explains in a natural way the non–observations of these effects in the Z0 interactions.
Review of constraints on fermion mixing
The non-zero diagonal entry mR = hvR is set by the breaking scale of the SU (2)R symmetry, which justiﬁes the assumption mD ≪ mR .
Extended Electroweak Models and Their Tests in Future Colliders
This description is based on a semi-classical picture in the diagonal approximation and fails when all energy scales become smaller than the interlevel spacing.
Spectral Fluctuations in Disordered Metals
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