In literature:
Did you remember to invite Doctor Rank?
"A Doll's House" by Henrik Ibsen
It is altogether likely that one who pierces the air like an eagle should bear messages between generals of the first rank.
"The Forest of Swords" by Joseph A. Altsheler
Thus far the uniforms were all alike; but there were distinguishing insignia to indicate the rank of each.
"Outward Bound" by Oliver Optic
Fiercely rained the bullets from rank to rank.
"French and English" by Evelyn Everett-Green
In the war of the Revolution, Washington held the rank of General, and in 1798 the rank of Lieutenant-general.
"Elements of Military Art and Science" by Henry Wager Halleck
They vary in form according to the rank of the nobleman.
"The Manual of Heraldry; Fifth Edition" by Anonymous
In the sixteenth century they ranked, as they still rank, among the proudest nobles of the Eternal City.
"Renaissance in Italy, Volumes 1 and 2" by John Addington Symonds
And that was the Boston massacre about which you have heard so much that it would almost seem to rank with that of St. Bartholomew.
"American Men of Action" by Burton E. Stevenson
The news spread rapidly from rank to rank, carrying alarm wherever it came.
"Historical Tales, Vol 5 (of 15)" by Charles Morris
The ranks of the victors were broken up by private dissensions.
"The History of England" by T.F. Tout
Boston was second in rank, with somewhat more than 20,000 people.
"History of the United States" by Charles A. Beard and Mary R. Beard
Bartolommeo Colleoni early distinguished himself among the ranks of the Bracceschi.
"Sketches and Studies in Italy and Greece, Complete" by John Symonds
None of this intermediate art holds much rank by virtue of its inherent worth.
"A Text-Book of the History of Painting" by John C. Van Dyke
John Vaughan was in the ranks of a New York regiment.
"The Southerner" by Thomas Dixon
The twisted spikes of these little orchids are interesting, because their ranks remain so clearly defined as they wind about the stem.
"The Wild Flowers of California: Their Names, Haunts, and Habits" by Mary Elizabeth Parsons
But from eight-thirty to eight-forty-five is known to the rank and file of the organization as its hour for arrival.
"The Romance of a Great Store" by Edward Hungerford
Enthusiasm spread through the ranks.
"Harper's New Monthly Magazine, Vol IV. No. XX. January, 1852." by Various
Initials appertaining to honorary rank should never be written or printed on a card, such as D.L., K.C., M.P., K.C.B., M.D., etc.
"Manners and Rules of Good Society" by Anonymous
He will probably rank in history among the Might-Have-Beens.
"Modern Leaders: Being a Series of Biographical Sketches" by Justin McCarthy
Only from their own ranks must the Wallace and the Bruce rise to free them.
"The Empire Makers" by Hume Nesbit
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In poetry:
And many a bearded Saracen
Went down, both horse and man;
For through their ranks we rode like corn,
So furiously we ran!
"The Heart Of The Bruce" by William Edmondstoune Aytoun
Yet, in thy history I see
Full many a great soul's lot;
Who joins that martyr-army's ranks,
That the world knoweth not; —
"On A Picture Of Harvey Birch" by Anne C Lynch
"He forgets his rank so princely,
To his grievous harm and loss;
A trap for his youth so tender
Is laid by the damsel Fos."
"The Prince Of Anhalt Dessau" by Nora Pembroke
None but he who did create us
Could redeem from sin and hell;
None but he could reinstate us
In the rank from which we fell.
"A Christmas Hymn" by Hannah More
For lo, when through the vapours dank,
Morn shone on Ettrick fair,
A corpse amid the alders rank,
The Palmer welter'd there.
"The Palmer" by Sir Walter Scott
Your serried ranks have never quailed
Before the battle-shock,
Whose maddest fury beats and breaks
Like foam against the rock.
"Beechenbrook - VII" by Margaret Junkin Preston
In news:
Has received high rankings in the US News Media Group and Best Lawyers "Best Law Firms" rankings report.
The Sporting News ranked all the coaches in the NFL from 1-32 and Cowboys boy wonder Jason Garrett ranked 23rd on the list.
The Hawkeyes , ranked No 27 in the Golfweek/Sagarin College Rankings, finished with a tournament-record score of 24-under 840 at Finkbine Golf Course.
But we got this classic recently in our AFC East inbox after ranking the Miami Dolphins second behind the New England Patriots in our division Power Rankings.
Hopping Kovach Grinnel Design Consultants State: Canada Rank 2012: 155 Rank 2011: 176.
Rank in Internet Services and Retailing: 4 (Previous rank: N.A.
7.25 Top 50 rank: 37** Rank in Soaps and Cosmetics*: 2.
Country Rank Company Global 500 rank City Revenues ($ millions).
The UCLA Bruins were 3-0, ranked in the top 20 and already had a signature win over a ranked Nebraska squad.
1 Alabama Crimson Tide, who are coming off a home win against a Top-20 opponent Mississippi State, have a tough test Saturday against another highly-ranked opponent in the fifth-ranked LSU Tigers at Tiger Stadium.
Maryland will play its first game of the season against a ranked opponent on Saturday when it travels to face interstate rival West Virginia, which is ranked No.
Pioneers Conf Rank CBK Rank.
Bearkats Conf Rank CBK Rank.
Scarlet Knights Conf Rank CBK Rank.
Lumberjacks Conf Rank CBK Rank.
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In science:
Hk (S ) ≤ rank Hk (T ). (ii) In the constructible case, for (4.5.1) and for every 1 ≤ k ≤ m − 1, ψk and φk are isomorphisms, in particular rank Hk (S ) = rank Hk (T ).
Bounding Betti Numbers of Sets Definable in O-Minimal Structures Over the Reals
Simplify T using Algorithm 2.5. (2) Compute the ﬁrst homology of T , and let r, t2 and t3 denote the rank, Z2 rank and Z3 rank respectively. (3) Create an input list L of triangulations to process, initial ly containing just T , and an output list O of prime summands, initial ly empty.
Computational topology with Regina: Algorithms, heuristics and implementations
However, if rank(A) = rank(B ) = 2 then rank(CAdA ◦Φ◦AdB ) ≥ 2, so AdA ◦ Φ ◦ AdB 6= id in this case as well.
Generation of Mapping Cones from Small Sets
Remark that the G-co-rank of H is inferior or equal to n, since if the co-rank is superior to n the ﬁrst stage of the proof shows that we can construct a chain of G-free prime ideals of length strictly greater than n and whose G-co-rank is strictly decreasing.
Some properties of schemes in group theory and Top couples
Suppose that the G-rank of G/P0 is strictly inferior to n; this implies that there exists, i ≤ n such that co-rank(Pi) =co-rank(Pi+1).
Some properties of schemes in group theory and Top couples
A-bimodules that is closed under ﬁnite direct sums and direct summands and contains A and al l ΩnA and has the property that rank M = rank ¯M and rank (M ⊕ N ) = rank M + rank N .
Noncommutative complex differential geometry
The connection is that the crossed product of a simple unital C*-algebra with tracial rank zero by an action with the tracial Rokhlin property necessarily has real rank zero (this follows from Theorem 4.5 of ), and often has tracial rank zero (combine Theorems 2.9 and 3.4 of ).
The tracial Rokhlin property is generic
The deﬁnition of the generator rank is analogous to that of the real rank, and we show that the latter always dominates the generator rank.
The generator rank for C*-algebras
This shows that the generator rank has many properties which are also satisﬁed by other “dimension theories” for C ∗ -algebras, such as the real and stable rank, the nuclear dimension, and the decomposition rank.
The generator rank for C*-algebras
We use the same index shift in Deﬁnition 2.2 since the generator rank is more closely connected to the real rank than to the stable rank, as we will see now.
The generator rank for C*-algebras
Since the generator rank gr(A) is deﬁned in analogy to the real rank (using tuples of self-adjoint elements), one might expect that the invariant gr′ (using tuples of not necessarily self-adjoint elements) has a closer connection to the stable rank.
The generator rank for C*-algebras
Thus, if A is a separable, unital, real rank zero, stable rank one C ∗-algebra with ﬁnite generator rank, then gr(A ⊗ B ) = 1 for any inﬁnite UHF-algebra B .
The generator rank for C*-algebras
Since rank(Vr ) = kr a.s., for a.e. t, and since rank((Vr )tr Vr ) = rank(Vr ), we have that the dimension of ~W r is kr .
Dimension for Martingales
If a well conditioned m × n matrix A has a rank ρ < l = min{m, n}, then almost all its close neighbours have full rank l (see Section 3.2), and all of them have numerical rank ρ.
Randomized Matrix Computations
If also σn > 0, then rank(GΣ) = rank(G), rank(ΣH ) = rank(H ).
Randomized Matrix Computations
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