Strike out sections 2, 3, and 5 and renumber section 4 as 2.
"Compilation of the Messages and Papers of the Presidents" by Grover Cleveland
Do you renumber your oath?
"Fardorougha, The Miser The Works of William Carleton, Volume One" by William Carleton
Jimmy is warm-hearted afther all, an' will be sorry for it when he cools, an' renumbers that you wor only doin' your duty.
"Phelim O'toole's Courtship and Other Stories Traits And Stories Of The Irish Peasantry, The Works of William Carleton, Volume Three" by William Carleton
All subsequent Fragments have accordingly been renumbered.
"Pascal's Pensées" by Blaise Pascal
The houses have since been renumbered.
"Mayfair, Belgravia, and Bayswater" by Geraldine Edith Mitton
All that day and for several following, official and guards were busy numbering and renumbering us and assigning us to our companies.
"The Escape of a Princess Pat" by George Pearson
I want you to renumber that.
"Nine Little Goslings" by Susan Coolidge
Pepys' books were numbered consecutively throughout the library, and therefore, when rearranged, they needed to be all renumbered.
"The Private Library" by Arthur L. Humphreys
But half, at least, of these dull people, he renumbered, were birds of passage only; to-morrow or the next day they would take the train.
"The Wave" by Algernon Blackwood
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If the negative trivial loop does not interfere with the moves leading from Ki+1 to Km , just renumber terms so that the negative destabilization becomes Km and every other Kj , j > i becomes Kj−1 .
On transversally simple knots
So after renumbering the spins (27) can be used without further changes.
Dynamical temperature study for classical planar spin systems
After renumbering, we may assume may assume that (li , r0 ), (li , r1 ) lie on P , and we may select i′ 6= 0, i so that (li′ , r2 ) lies on P .
The maximum number of points on a curve of genus 4 over F_8 is 25
For the minimal oracle, one may renumber the eigenvectors identifying the index (ℓ, sℓ) with f sℓ (xℓ ) and observe it is not basic because the knowledge of f (x) is not suﬃcient to determine the length of the orbit containing x and any other renumbering would suffer from a similar problem.
Comparative Computational Strength of Quantum Oracles
The determinant of the matrix does not change while renumbering crossings and long arcs correspondingly.
Virtual Biquandles
In order to determine the true combination of the photons in the detached region as well, we renumber the events in this region as follows: we ascribe number two to the third photon and number three to the second one.
New result on the measurement of the direct photon emission in K+ --> pi^+ pi^0 gamma decay
Such simple cross-renumbering of events allowed us to enhance the pairing eﬃciency of the IB component up to 93%, although the DE component was reduced down to 81%.
New result on the measurement of the direct photon emission in K+ --> pi^+ pi^0 gamma decay
The ﬁrst idea was to study matrix E(Φ) by renumbering the triples of PD-s from 1 to M 3 .
On LAO Testing of Multiple Hypotheses for Many Independent Objects
Let bk be a renumbering of the points in |D | such that |bk+1 − z | ≥ |bk − z | for all k .
On Meromorphic Functions which are Brody Curves
We remove such pairs of carets, renumber the leaves and check this condition again, repeating until there are no more pairs of exposed carets with identical leaf numbers.
Convexity properties of Thompson's group F
Let S = {i ∈ [n] | Vrp (i) ≤ t} and renumber the coordinates such that S = [k ′ ].
Efficiently Testing Sparse GF(2) Polynomials
Then we introduce an operator δ on G 0 E that acts by contracting a regular edge one at a time in Γ, followed by a consistent renumbering of edges and vertices.
Integral Invariants of 3-Manifolds. II
Note that we have assumed n 6= N , N − 1 in the ﬁrst manipulation, which is no loss of generality, since we can always achieve this by renumbering the propagators.
Separation of soft and collinear singularities from one-loop N-point integrals
Reorder and renumbering the vertices and cost matrix for the solution.
The Complexity Of The NP-Class
Proof of Proposition 5 First, we note that by renumbering it suﬃces to show the result for i = 1.
Conditional Sampling for Max-Stable Processes with a Mixed Moving Maxima Representation
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