Manifoldness

Definitions

  • Webster's Revised Unabridged Dictionary
    • Manifoldness (Math) A generalized concept of magnitude.
    • Manifoldness Multiplicity.
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Century Dictionary and Cyclopedia
    • n manifoldness The state of being manifold; variety; multiplicity.
    • n manifoldness In mathematics: A manifold or ensemble; especially, a continuous quantity of any number of dimensions.
    • n manifoldness The number of different prime factors of a number.
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Quotations

  • Aldous Huxley
    Aldous%20Huxley
    “A large city cannot be experientially known; its life is too manifold for any individual to be able to participate in it.”

Usage

In literature:

His mind was one of quick perceptions within a wide range, and always alert to grasp an idea in its manifold relations.
"Library Of The World's Best Literature, Ancient And Modern, Vol 3" by Various
He confessed very frankly the manifold crimes and horrid enormities in which he had involved himself.
"Lives Of The Most Remarkable Criminals Who have been Condemned and Executed for Murder, the Highway, Housebreaking, Street Robberies, Coining or other offences" by Arthur L. Hayward
The Keppel Isles, and coast to Cape Manifold.
"A Voyage to Terra Australis Volume 2" by Matthew Flinders
The duties are manifold, and often thankless and unappreciated.
"History of Kershaw's Brigade" by D. Augustus Dickert
Manifold are the ruinous phantasies which lead unhappy mortals to pandemonium.
"International Weekly Miscellany, Vol. 1, No. 5, July 29, 1850" by Various
North-eastwards lie the moorlands, and far off Manifold, the 'metropolis of the moorlands,' as it is called.
"Tales of the Five Towns" by Arnold Bennett
Translations, of course, were manifold.
"McClure's Magazine, Vol. VI., No. 6, May, 1896" by Various
As his duties were consequently manifold some parishes were without his presence on Sunday for a month and sometimes longer.
"The Parish Clerk (1907)" by Peter Hampson Ditchfield
But the midsummer, the gallant midsummer, pranked in manifold splendours, is the true season of poetry for the toilers.
"The Ethics of Drink and Other Social Questions" by James Runciman
See with what manifold uses every accident of human life is crammed!
"Hills and the Sea" by H. Belloc
The practical consequences of all this were both manifold and strongly marked.
"Shakespeare: His Life, Art, And Characters, Volume I." by H. N. Hudson
In the pre-Christian world there were manifold aims and manifold ways and means.
"The Religious Spirit of the Slavs (1916)" by Nikolai Velimirovic
In everything we are sprung Of Earth's best blood, have titles manifold.
"Cambridge Essays on Education" by Various
Therefore Brahman, although one only, is, owing to its manifold powers, able to transform itself into manifold effects; just as milk is.
"The Vedanta-Sutras with the Commentary by Sankaracarya"
All real unity is manifold.
"Sermons Preached at Brighton" by Frederick W. Robertson
I have thee on every side, Jack, and thy sides are manifold; many-folded at any rate.
"Lorna Doone" by R. D. Blackmore
The evidence on this point is manifold and apparently conclusive.
"History and Comprehensive Description of Loudoun County, Virginia" by James W. Head
In viewing the development of artificial light and its manifold effects upon the activities of mankind, it is natural to look into the future.
"Artificial Light" by M. Luckiesh
These men are wont to speak much of a certain secret doctrine of theirs, and of their manifold and sundry readings.
"The Apology of the Church of England" by John Jewel
Hence he regards judgement as the act of unifying a manifold given in perception, directly, or indirectly by means of a conception.
"Kant's Theory of Knowledge" by Harold Arthur Prichard
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In poetry:

But Father, thou hast blessings poured
On all our wayward days
And now thy mercies manifold
Have filled our hearts with praise
"Thanksgiving" by Hanford Lennox Gordon
If only that perfect tale were true
Which ages have not made old,
Which of endless many makes one anew,
And simplicity manifold!
"Come To Me" by George MacDonald
"I would! For if the flesh of me and soul
Are fibred with the ages,
My triumph is of them and manifold
Of all life's mystic stages."
"The Strong Man To His Sires" by Cale Young Rice
Little candles glistening,
Telling those are listening
Legends manifold,
Many a little story,
Tales of blood and glory
Of the days of old.
"The Feast Of Lights" by Morris Rosenfeld
The waves are weary of hiding pearls,
Are aweary of smothering gold,
They would all be air that sweeps and swirls
In the branches manifold.
"The Sea" by Duncan Campbell Scott
And that every yearning within them,
The manifold aim and desire,
Came along that link, as the message
Is spoken in shocks through the wire.
"The Worship of Sorrow" by Alexander Anderson

In news:

The first time I visited his Northern California garage and saw those manifolds mounted like so many silver trophies on his garage walls, I was hooked.
This new heat pump manifold from YELLOW JACKET has 3-1/8-inch high- and low-side gauges with 1 percent accuracy that are designed to handle heat pump pressures and transitions in heating or cooling mode.
Hauck's Regulator Gas Manifold (RGM) is a factory assembled and prepiped gas train designed to provide overpressure protection and precise outlet pressure control.
Brochure Details Nitrogen Manifold Systems.
Uponor is introducing its Engineered Plastic (EP) Heating Manifold for radiant applications.
This manufacturer achieved greater programming efficiency for large manifolds used deep underwater.
R-and PR-6000 pressure regulators mount directly on pneumatic circuit boards or manifold subplates.
A new Filter-Regulator- Manifold (FRM) assembly kit from Nordson Corp.
HPM's hydraulic manifolds are processed through five stainless steel tanks, each holding 800 gallons of solution.
Blackening HPM's manifolds takes 15 to 20 minutes from start to completion.
After your rod sits overnight, is there any visible fuel puddling above the carb's throttle blades and/or in the intake manifold 's plenum floor.
A fit clenches him whole, strains his red-combed head into one shrill remonstrance that scythes clean through night's manifold silence.
Three Point Manifold, 2008, watercolor on Dura-Lar, 60" x 36".
Next Holley Stealth Ram Efi Kit Manifold.
The manifold valves would clamp the plate and retract several large cylinders to stretch it.
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In science:

This figure shows the pro jection on (x, y ) coordinates of: (a) the critical manifold (solid) (b) the critical manifold (solid), and the slow manifold (dotted) (c) the critical manifold (solid), the slow manifold (dotted), and the two enclosing surfaces (dashed).
Rigorous Enclosures of a Slow Manifold
Note that the vertices of all 4 triangulations: the critical manifold, the approximate slow manifold, and the two perturbed manifolds, all have the same (y , z) components.
Rigorous Enclosures of a Slow Manifold
Informally, a computable slow manifold is a manifold close to the critical manifold where the flow is slow.
Rigorous Enclosures of a Slow Manifold
Definition 3.1. A computable slow manifold is a C 1 local ly invariant, normal ly hyperbolic manifold, of the same dimension as the critical manifold, which projects injectively along the fast variable to the critical manifold, such that the its relative slope satisfies s(ε) ≤ 1√ε .
Rigorous Enclosures of a Slow Manifold
However, computable slow manifolds are often the ob jects that are identified in applications: a locally invariant manifold at a fixed value of epsilon that follows the critical manifold closely, and on which the flow is slow [6, 10, 14].
Rigorous Enclosures of a Slow Manifold
A repelling sheet of the slow manifold is plotted in dark blue, an attracting sheet in cyan. A selection of tra jectories in the unstable manifold of the equilibrium near the origin are plotted in red, a strip of unstable manifold that escapes from the fold region is shaded in magenta.
Rigorous Enclosures of a Slow Manifold
In the following, we refer to such a tangential intersection of the equilibrium’s unstable manifold with the repelling slow manifold as a tangency or tangency of invariant manifolds.
Rigorous Enclosures of a Slow Manifold
Note that since slow manifolds are not unique, there is some ambiguity in what it means for a slow manifold to intersect another manifold.
Rigorous Enclosures of a Slow Manifold
The natural setting is therefore to define when a one parameter family of slow manifolds is tangential to another manifold or family of manifolds.
Rigorous Enclosures of a Slow Manifold
To compute normally hyperbolic manifolds of saddle type, see e.g. , one usually first computes the manifold’s stable and unstable manifolds, and then intersects them.
Rigorous Enclosures of a Slow Manifold
Manifolds with vanishing Ricci tensor are called Ricci-flat manifolds while manifolds with a Ricci tensor proportional to the metric are known as Einstein manifolds (see [23, p.
Backreaction and the Covariant Formalism of General Relativity
Vector fields formulation Let (M, g) be an n-dimensional manifold, TpM (cid:39) Rn the tangent space to the manifold at the point p,5 and T M . = {∪p∈MTpM} the tangent space to the manifold.
Backreaction and the Covariant Formalism of General Relativity
For odd dimensional manifolds, and in particular for three-dimensional manifolds, there is no analogue of these theorems.5 For a two-dimensional manifold, i.e. a surface, the Ricci scalar assumes a particularly interesting form.
Backreaction and the Covariant Formalism of General Relativity
These should not be confused with open and closed manifolds. A closed manifold is a compact manifold without boundaries; an open manifold is one that is not compact and without boundary.
Backreaction and the Covariant Formalism of General Relativity
Next, we show that there exists a random invariant manifold M 0 (ω ), which is called a random slow manifold for system (5.3)-(5.4), will be the asymptotic limit of the manifold ˘M ǫ (ω ) as ǫ → 0.
Slow Manifolds for Multi-Time-Scale Stochastic Evolutionary Systems
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