And the other was a frivolous system of pick-pocketing the Kansasters that had the department stores reduced to a decimal fraction.
"Rolling Stones" by O. Henry
He also worked with numbers that had exponents that were fractions, unending decimals, or negative numbers.
"Our Legal Heritage, 5th Ed." by S. A. Reilly
Common fractions may often be changed to decimals very readily, and the calculations thereby made much easier.
"Burroughs' Encyclopaedia of Astounding Facts and Useful Information, 1889" by Barkham Burroughs
Ether is so rare that its density, compared with water, is represented by a decimal fraction with twenty-seven ciphers before it.
"Among the Forces" by Henry White Warren
He had also worked at fractions and decimals, and tried a little algebra; but he was, and had been as a boy, a poor hand at figures.
"Little Classics, Volume 8 (of 18)" by Various
Complex and improper fractions and recurring decimals are not allowed.
"Amusements in Mathematics" by Henry Ernest Dudeney
He was a mathematician as far as long division and decimal fractions.
"Oomphel in the Sky" by Henry Beam Piper
Will decimal fractions support his back or strengthen his lumbar vertebrae?
"Cornelius O'Dowd Upon Men And Women And Other Things In General Originally Published In Blackwood's Magazine - 1864" by Charles Lever
These are made in different patterns, having either decimal divisions or the vulgar fractions.
"Mechanical Drawing Self-Taught" by Joshua Rose
HOW TO DEAL WITH DECIMAL FRACTIONS.
"Assimilative Memory" by Marcus Dwight Larrowe (AKA Prof. A. Loisette)
Expressed as a vulgar fraction it is 2/3; but as a decimal fraction it is .6666 ad infinitum.
"The Hidden Power" by Thomas Troward
Fractions and decimals were unsolvable mysteries to him.
"The Grain Ship" by Morgan Robertson
With every respect in a two hours' speech on for decimal fractions, of moving that 100000l.
"A Budget of Paradoxes, Volume II (of II)" by Augustus de Morgan
A man who would involve the monastery in a fraction of fifty-eight decimals deserved severe punishment.
"The Canterbury Puzzles" by Henry Ernest Dudeney
If the old weight has fractions these should first be changed to decimals for convenience.
"A Text-Book of Precious Stones for Jewelers and the Gem-Loving Public" by Frank Bertram Wade
The bulk was overwhelming, but the figures were only decimal points, and the worth of the whole was a fraction above zero.
"Library of the World's Best Literature, Ancient and Modern, Vol. 15" by Various
A period placed to the left of a series of figures indicates that they are decimal fractions.
"The New Gresham Encyclopedia. Vol. 1 Part 2" by Various
I've ciphered up to decimal fractions, an' begun grammar.
"The Girl From Tim's Place" by Charles Clark Munn
Fractions of ounces of butter, and incomplete periods of less than ten days, to be worked out in decimals and added to the total points.
"Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 9" by Various
The names 'decimal fractions or decimals,' and 'decimal mixed numbers or decimals.
"The Psychology of Arithmetic" by Edward L. Thorndike
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If Γ is increased by dΓ, a fraction dnΓ = (2p + q) nΓρ(0; Γ)dΓ of active spin clusters is decimated.
Random Antiferromagnetic SU(N) Spin Chains
Fig. 1, we show the fraction of ﬁrst order decimation steps as a function of the energy scale Ω, for the symmetry groups SU (3) and SU (4).
Random Antiferromagnetic SU(N) Spin Chains
Figure 1: The fractions of ﬁrst order decimation steps, of sp ins in the fundamental (Q = 1), and in the self-conjugate (Q = 2, only for SU (4)) representations, all as a function of Ω.
Random Antiferromagnetic SU(N) Spin Chains
The numerical procedure consists in completely decimating a chain, and counting the fraction of spin pairs that become strongly correlated at the distance |i − j | .
Random Antiferromagnetic SU(N) Spin Chains
However, this does not necessarily mean that we can do all the decimation process eﬃciently at the initial y∗ , after decimation of a c-dependent fraction of the graph SP starts to diverge even for large c.
Message passing for vertex covers
At this point the fraction φ(θ) of decimated and logically implied variables has a ﬁnite discontinuity (see right panel of Fig. 2), which means that the assignment of a few new variables triggers an avalanche of implications of extensive size.
On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms
Finally the average fraction of either decimated or directly implied variables can be obtained as φ(θ) = E[(1 − tanh h)eh− ] .
On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms
As a ﬁrst result, we show in Fig. 10 the success probability for the BP guided decimation algorithm, i.e. the fraction of formulas which have been solved by this algorithm.
On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms
FIG. 13: Residual entropy as a function of the fraction θ of decimated variables for α = 7 (upper curves) and α = 8.4 (lower curves).
On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms
We also keep track of the fraction of logically implied variables in the partially decimated formulas, measuring it with the WP algorithm (equivalent to UCP as explained in Sec.
On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms
What is more interesting is that the fraction of extremely biased variables (BP prob< 10−10) does not show any sign of hysteresis: the same smooth curve is followed by the decimation algorithm as well as by the backward algorithm.
On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms
Consider now the fraction of decimated or implied variables φ(θ), computed for the satisﬁability ensemble according to Eqs. (51,52).
On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms
TABLE I: Values of the thresholds α∗ and α′ ∗ , and the associated fraction of decimated variables θ∗ and θ ′ ∗ , for random k-satisﬁability formulas, k = 4, 5.
On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms
Two successive steps will be performed : the logical implications of the decimation of a fraction θ of the variables are ﬁrst drawn with Unit Propagation.
On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms
Deﬁning ﬁnally φ = θ + t∗ , one realizes that φ is the smallest solution of Eq. (32): this quantity gives the fraction of variables that are either ﬁxed by the decimation or by the propagation of logical implications.
On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms
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