Manifold writing

Definitions

  • Webster's Revised Unabridged Dictionary
    • Manifold writing a process or method by which several copies, as of a letter, are simultaneously made, sheets of coloring paper being infolded with thin sheets of plain paper upon which the marks made by a stylus or a type-writer are transferred; writing several copies of a document at once by use of carbon paper or the like.
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Usage

In literature:

You and I write our lives as if on one of those manifold writers which you use.
"Expositions of Holy Scripture: Romans Corinthians (To II Corinthians, Chap. V)" by Alexander Maclaren
Such is the general outline which we shall fill up and color from allusions throughout his varied and manifold writings.
"Great Men and Famous Women. Vol. 5 of 8" by Various
Although she died at the age of fifty-seven, she found time during her manifold cares to write thirty-eight volumes.
"Woman's Work in English Fiction" by Clara Helen Whitmore
In all their manifold writings it does not occur a single time, though they make frequent reference to the past.
"Creed And Deed" by Felix Adler
Had my skill in writing and drawing on stone been greater at that time, Herr Steiner would have given me opportunity enough and manifold.
"The Invention of Lithography" by Alois Senefelder
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In news:

One of the savviest points I've seen raised in our manifold discussions of gaming journalism is that many video game writers are not really journalists at all—they're bloggers writing about games that interest them.
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In science:

This means that we can write ωn = dωn−1 over the entire manifold - there is no point where it fails to hold.
A Simple Introduction to Particle Physics Part II
For any manifold N that you can write as a submanifold of another M, you can easily find the metric on N that is induced by the metric on M by simply using the pullback.
A Simple Introduction to Particle Physics Part II
The essential idea of that section was to introduce a vielbein, or basis at each point that was unrelated to the coordinates of the spacetime manifold, and by writing quantities in terms of the vielbein, we were working with an internal space.
A Simple Introduction to Particle Physics Part II
We will write (Y , ξ ) = ∂ (X , ω , Z ) and call it the ideal contact boundary of the Liouville manifold (X , ω , Z ) with cylindrical end.
Effect of Legendrian Surgery
When X is a Riemannian manifold and dx is the volume form on X , we write Lp (X ) ≡ Lp (X, dx).
Measure Theory in Noncommutative Spaces
We write also F instead of F(M ) if it is clear from the context which quasitoric manifold is meant.
Non-abelian symmetries of quasitoric manifolds
Write C∞Ringsop for the opposite category of C∞Rings, with directions of morphisms reversed, and Man for the category of manifolds without boundary.
D-manifolds, d-orbifolds and derived differential geometry: a detailed summary
Write dMan for the full 2-subcategory of d-manifolds in dSpa.
D-manifolds, d-orbifolds and derived differential geometry: a detailed summary
We will write down an explicit principal d-manifold S = (S , O ′ S , ES , ıS , S ) which is equivalent to V ×s,E ,0 V in Proposition 4.2(c).
D-manifolds, d-orbifolds and derived differential geometry: a detailed summary
Similarly, if W is a manifold and f , g : V → W are smooth then we write f = g + O(s) if c ◦ f − c ◦ g = O(s) for all smooth c : W → R, and f = g + O(s2 ) if c ◦ f − c ◦ g = O(s2 ) for all c.
D-manifolds, d-orbifolds and derived differential geometry: a detailed summary
Write X = S V ,E ,s , Y = SW,F,t for the ‘standard model’ principal d-manifolds from Example 4.4.
D-manifolds, d-orbifolds and derived differential geometry: a detailed summary
If a d-manifold X can be embedded into a manifold Y , we show in [35, §4.4] that we can write X as the zeroes of a section of a vector bundle over Y near its image.
D-manifolds, d-orbifolds and derived differential geometry: a detailed summary
We write Manc for the category of manifolds with corners, with morphisms smooth maps, and Manb for the full subcategory of manifolds with boundary.
D-manifolds, d-orbifolds and derived differential geometry: a detailed summary
Let g : X → Z, h : Y → Z be strongly transverse smooth maps of manifolds with corners, and write W for the fibre product X ×g,Z,h Y given by Theorem 5.13.
D-manifolds, d-orbifolds and derived differential geometry: a detailed summary
When X is an oriented manifold, we write −X for X with the opposite orientation.
D-manifolds, d-orbifolds and derived differential geometry: a detailed summary
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