This inscription was merely placed here for the ornament of the Grotto, and the sentiments and the Hermit are equally imaginary.
"The Monk; a romance" by M. G. Lewis
The place where any two of these imaginary lines, crossing at right angles, meet may be exactly determined by the science of navigation.
"Tom Swift and his Undersea Search" by Victor Appleton
In the morning he said that they were on the way from some imaginary place, and would arrive in the course of the day.
"Personal Memoirs of U. S. Grant, Complete" by Ulysses S. Grant
In the morning he said that they were on the way from some imaginary place, and would arrive in the course of the day.
"Memoirs of Three Civil War Generals, Complete" by U. S. Grant, W. T. Sherman, P. H. Sheridan
Among those who cherished this imaginary privilege with undoubting faith was an old clergyman with whom Mannering was placed during his youth.
"Guy Mannering, or The Astrologer, Complete, Illustrated" by Sir Walter Scott
Imaginary devils, and imaginary places of punishment, are coming near to our revolutionary France!
"The Wing-and-Wing" by J. Fenimore Cooper
He positively pervaded the place, nervously changing the napkin from arm to arm, and frantically flicking off imaginary crumbs.
"Faces and Places" by Henry William Lucy
In the young man's nature, Gloria had taken the place of all other divinities, real and imaginary.
"Casa Braccio, Volumes 1 and 2 (of 2)" by F. Marion Crawford
But imaginary dangers soon gave place to present interests.
"In the Musgrave Ranges" by Jim Bushman
They are family names and titles, not of certain places, but of districts with imaginary boundaries.
"With the French in France and Salonika" by Richard Harding Davis
Our failure to identify Cloisterham Weir exhibits another instance where, for the purposes of the story, an imaginary place is introduced.
"A Week's Tramp in Dickens-Land" by William R. Hughes
It was soon learned that the place had been surveyed, imaginary streets provided for, and town lots duly awarded.
"The Land of Nome" by Lanier McKee
It's just an imaginary place, you know.
"The Children of the Top Floor" by Nina Rhoades
Jenkins followed meekly, placing his chair at what would have been the tail of Martha's imaginary retinue.
"Through the Postern Gate" by Florence L. Barclay
Gerald made up his mind to have his teeth seen to at one place, and to attend at the other with some imaginary complaint.
"'£19,000'" by Burford Delannoy
Placing an imaginary character at the side does not make words necessarily dramatic.
"Browning and the Dramatic Monologue" by S. S. Curry
The imaginary tree was well enough in play, but it could not take the place of the real one.
"If Any Man Sin" by H. A. Cody
At the extremities of the earth were placed imaginary regions and fortunate isles, inhabited by giants or pigmies.
"Astronomical Myths" by John F. Blake
Joe picked them up, took his place again in the imaginary box, and repeated the performance.
"Baseball Joe of the Silver Stars" by Lester Chadwick
Irene thought the Manor a fine old place, but she preferred to see its rooms filled with scarlet coats to imaginary monkish habits.
"The Runaways" by Nat Gould
***
Then all places of E lying above a place b ∈ B are imaginary.
Generators for Arithmetic Groups
Therefore, for each archimedean (necessarily real) place a of F , we have y (a) = 1 and d = 2y (a) = 2, that is there is only one place of E lying above the place a of F and is a complex place, whence E /F is a quadratic extension, which is totally imaginary.
Generators for Arithmetic Groups
In addition, this is meant to parallel the fact that these two states are incompatible states of consciousness; namely when the solution is an imaginary number it cannot be placed on the real axis at the same time.
Founding quantum theory on the basis of consciousness
In Eq. (1.1.6), however, we introduced quantities Lp which determine the side of the real axis where the imaginary increment is placed.
Supersymmetry in Random Matrix Theory
The discussion in [7, Subsection 5.2] is not modiﬁed by the previously discussed changes: in fact, it deals only the reduction algebra placed on the positive imaginary axis, which is left untouched by the changes occurring in biquantization.
Biquantization of symmetric pairs and the quantum shift
With , race calculations can involve up to 41 Dirichlet characters, but results to 6 decimal places, as set out below Figure (row “E act”) can be obtained with K = 3 by explicitly representing only the 7 first zeros with imaginary parts of magnitude less than 1 (the smallest being about 0.138) .
Application of an accurate remainder term in the calculation of Residue Class Distributions
Thus, if the effective action possesses an imaginary part the right hand side of the above equation shows that the probability that the system remains in the vacuum is less than unity and that pair production may take place.
On Effective Field Theories at Finite Temperature
Leading coeﬃcients of the difference equation could a priori be vanishing in different places with the new term, but this does not happen since the new contribution is imaginary (the additional sine implies an additional factor of i in a difference operator from (8)).
Degenerate Configurations, Singularities and the Non-Abelian Nature of Loop Quantum Gravity
One can easily check that conjugation of elements of Q[√d ] has many of the same properties as complex conjugation, and indeed Q[√d ] behaves in many respects like C, with √d taking the place of the imaginary unit i = √−1.
Quantum algorithms for algebraic problems
Schwinger interpreted this imaginary part as an indication that the QED vacuum in a background electric ﬁeld is unstable and in strong enough ﬁelds a kind of vacuum electrical breakdown due to spontaneous electron-positron pair production takes place .
LHC card games: bringing about retrocausality?
We assume that this contour is made of a large semicircle (with radius tending to inﬁnity) centered at the origin and placed to its right, plus a straight part overlapping the imaginary axis.
Casimir energy in the Fulling--Rindler vacuum
The same conclusion holds with noncompact imaginary in place of real.
Duality for nonlinear simply laced groups
N random numbers are placed in N/2 real and N/2 imaginary parts of the positive and negative frequency spectrum.
Discrete simulation of power law noise
First, the metric γ on S 2 is written in terms of the coordinates (z , ¯z ) in place of the real and imaginary parts of z .
Conformal immersions of prescribed mean curvature in R^3
We also give an alternate proof which holds only when the group of S -units in K is inﬁnite (thus, this alternate proof only fails to apply when K is either Q or a quadratic imaginary extension of Q, and S consists of the sole Archimedean place of K ).
On quadratic rational maps with prescribed good reduction
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