scholarly journals Stability of character sums for positive-depth, supercuspidal representations

2018 ◽  
Vol 2018 (742) ◽  
pp. 47-78 ◽  
Author(s):  
Stephen DeBacker ◽  
Loren Spice
Keyword(s):  
Harmonic Analysis ◽  
Character Sums ◽  
Supercuspidal Representations ◽  
The Stability

Abstract We re-write the character formulae of Adler and the first author in a form amenable to explicit computations in p-adic harmonic analysis, and use them to prove the stability of character sums for a modification of Reeder’s conjectural positive-depth, unramified, toral supercuspidal L-packets.

Characters of Depth-Zero, Supercuspidal Representations of the Rank-2 Symplectic Group

2000 ◽  
Vol 52 (2) ◽  
pp. 306-331 ◽  
Author(s):  
Clifton Cunningham
Keyword(s):  
Lie Algebras ◽  
Symplectic Group ◽  
Orbital Integrals ◽  
Finite Linear Combination ◽  
Supercuspidal Representations ◽  
Rank 2 ◽  
The Fourier Transform ◽  
The Stability ◽  
Springer Correspondence ◽  
Finite Linear

AbstractThis paper expresses the character of certain depth-zero supercuspidal representations of the rank-2 symplectic group as the Fourier transform of a finite linear combination of regular elliptic orbital integrals—an expression which is ideally suited for the study of the stability of those characters. Building on work of F. Murnaghan, our proof involves Lusztig’s Generalised Springer Correspondence in a fundamental way, and also makes use of some results on elliptic orbital integrals proved elsewhere by the author using Moy-Prasad filtrations of p-adic Lie algebras. Two applications of the main result are considered toward the end of the paper.

scholarly journals Harmonic analysis of the stability of reverse routing in channels

2007 ◽  
Vol 11 (1) ◽  
pp. 559-568 ◽  
Author(s):  
M. Bruen ◽  
J. C. I. Dooge
Keyword(s):  
Harmonic Analysis ◽  
High Frequency ◽  
Stable Process ◽  
Linear Solution ◽  
Wave Patterns ◽  
Upstream Direction ◽  
Frequency Components ◽  
The Stability ◽  
Channel Lengths ◽  
Flood Flow

Abstract. Normal downstream routing of a flood flow is a highly stable process for Froude numbers less than 1 and hence the results are reliable. In contrast, reverse routing in an upstream direction, which may be required for flow control, is potentially unstable. This paper reports the results of a study of the practical limits on channel lengths for reverse routing. Harmonic analysis is applied to the full non-linear solution of the St. Venant equations for three different wave patterns and two different wave periods, for a particular channel with a Froude number of 0.5. Reverse routing can be done for prismatic channels longer than 100 km. For long periods (>10 hours) the shape of the upstream hydrograph is recovered well. However, when the wave period is short (<1 hour), the high frequency components of the upstream hydrograph and, thus, its shape, are not recovered. These limits are influenced by the channel morphology and shape of the wave. Further work is needed to determine how these factors interact.

scholarly journals VII. The stability of the pear-shaped figure of equilibrium of a rotating mass of liquid

1903 ◽  
Vol 200 (321-330) ◽  
pp. 251-314
Keyword(s):  
Harmonic Analysis ◽  
Higher Order ◽  
Order Of Accuracy ◽  
Analytical Results ◽  
Arduous Task ◽  
Ellipsoidal Harmonic ◽  
The Subject ◽  
The Stability

By aid of the methods of a paper on “ Ellipsoidal Harmonic Analysis ” (‘ Phil. Trans., A, vol. 197, pp. 461-557), I here resume the subject of a previous paper (‘ Phil. Trans.' A, vol. 198, pp. 301-331). These papers will be referred to hereafter by the abridged titles of " Harmonics ” and " The Pear-shaped Figure.” At the end of the latter of these it was stated that the stability of the figure could not he proved definitely without approximation of a higher order of accuracy. After some correspondence with M. Poincaré during the course of my work, I made an attempt to carry out this further approximation, but found that the expression for a certain portion of the energy entirely foiled me. Meanwhile he had turned his attention to the subject, and he has shown (‘ Phil. Trans.,’A, vol. 198, pp. 333-373) by a method of the greatest ingenuity and skill how the problem may be solved. He has not, however, pursued the arduous task of converting his analytical results into numbers, so that he left the question as to the stability of the pear still unanswered.

scholarly journals V. On the integrals of the squares of ellipsoidal surface harmonic functions

1904 ◽  
Vol 203 (359-371) ◽  
pp. 111-137
Keyword(s):  
Harmonic Analysis ◽  
Harmonic Functions ◽  
Essential Step ◽  
Ellipsoidal Harmonic ◽  
Surface Harmonic ◽  
In Series ◽  
Ellipsoidal Surface ◽  
The Stability

This paper forms a sequel to three others published in Series A of the. ‘ Philosophical Transactions,’ namely, “ On Ellipsoidal Harmonic Analysis,” vol. 197, pp. 461-557, “ On the Pear-shaped Figure of Equilibrium of a Rotating Mass of Liquid,” vol. 198, pp. 301-381, and “ On the Stability of the Pear-shaped Figure of Equilibrium, &c.,” vol. 200, pp. 251-314. 1 shall refer to these three papers as “ Harmonics,” “ The Pear-shaped Figure,” and “ Stability.” In “ Harmonics,” the functions being expressed approximately, approximate formulae are found for the integrals over the surface of the ellipsoid of the squares of all the surface harmonics. These integrals are of course required whenever it is proposed to make practical use of this method of analysis, and the evaluation of them is therefore an absolutely essential step towards any applications.

Open discussion

1982 ◽  
Vol 99 ◽  
pp. 605-613
Author(s):  
P. S. Conti
Keyword(s):  
Buenos Aires ◽  
Large Mass ◽  
List Type ◽  
Common Phenomenon ◽  
Open Discussion ◽  
The Stability ◽  
Ring Nebulae

Conti: One of the main conclusions of the Wolf-Rayet symposium in Buenos Aires was that Wolf-Rayet stars are evolutionary products of massive objects. Some questions:–Do hot helium-rich stars, that are not Wolf-Rayet stars, exist?–What about the stability of helium rich stars of large mass? We know a helium rich star of ∼40 MO. Has the stability something to do with the wind?–Ring nebulae and bubbles : this seems to be a much more common phenomenon than we thought of some years age.–What is the origin of the subtypes? This is important to find a possible matching of scenarios to subtypes.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

Uniformity of Magnification from Different Electron Microscopes

1967 ◽  
Vol 25 ◽  
pp. 32-33
Author(s):  
Godfrey C. Hoskins ◽  
V. Williams ◽  
V. Allison
Keyword(s):  
Diffraction Grating ◽  
The Other ◽  
Carbon Replica ◽  
Electron Microscopes ◽  
The Stability

The method demonstrated is an adaptation of a proven procedure for accurately determining the magnification of light photomicrographs. Because of the stability of modern electrical lenses, the method is shown to be directly applicable for providing precise reproducibility of magnification in various models of electron microscopes.A readily recognizable area of a carbon replica of a crossed-line diffraction grating is used as a standard. The same area of the standard was photographed in Phillips EM 200, Hitachi HU-11B2, and RCA EMU 3F electron microscopes at taps representative of the range of magnification of each. Negatives from one microscope were selected as guides and printed at convenient magnifications; then negatives from each of the other microscopes were projected to register with these prints. By deferring measurement to the print rather than comparing negatives, correspondence of magnification of the specimen in the three microscopes could be brought to within 2%.

Effect of Improved ThO2 Particle Dispersion in Nickel on High-Temperature Strength

1970 ◽  
Vol 28 ◽  
pp. 444-445
Author(s):  
E. R. Kimmel ◽  
H. L. Anthony ◽  
W. Scheithauer
Keyword(s):  
High Temperature ◽  
Metal Matrix ◽  
Oxide Particle ◽  
Oxide Phase ◽  
Dislocation Motion ◽  
Particle Dispersion ◽  
High Temperature Strength ◽  
Strengthening Effect ◽  
Oxide Particles ◽  
The Stability

The strengthening effect at high temperature produced by a dispersed oxide phase in a metal matrix is seemingly dependent on at least two major contributors: oxide particle size and spatial distribution, and stability of the worked microstructure. These two are strongly interrelated. The stability of the microstructure is produced by polygonization of the worked structure forming low angle cell boundaries which become anchored by the dispersed oxide particles. The effect of the particles on strength is therefore twofold, in that they stabilize the worked microstructure and also hinder dislocation motion during loading.

An Analysis of Dissociation of Molecules in a High Resolution Electron Microscope

1973 ◽  
Vol 31 ◽  
pp. 486-487
Author(s):  
Mihir Parikh
Keyword(s):  
Electron Microscope ◽  
High Resolution ◽  
Cross Sections ◽  
Resolving Power ◽  
Peak Intensity ◽  
Molecular Film ◽  
Resolution Electron ◽  
Dissociation Cross Section ◽  
High Resolution Electron Microscope ◽  
The Stability

It is well known that the resolution of bio-molecules in a high resolution electron microscope depends not just on the physical resolving power of the instrument, but also on the stability of these molecules under the electron beam. Experimentally, the damage to the bio-molecules is commo ly monitored by the decrease in the intensity of the diffraction pattern, or more quantitatively by the decrease in the peaks of an energy loss spectrum. In the latter case the exposure, EC, to decrease the peak intensity from IO to I’O can be related to the molecular dissociation cross-section, σD, by EC = ℓn(IO /I’O) /ℓD. Qu ntitative data on damage cross-sections are just being reported, However, the microscopist needs to know the explicit dependence of damage on: (1) the molecular properties, (2) the density and characteristics of the molecular film and that of the support film, if any, (3) the temperature of the molecular film and (4) certain characteristics of the electron microscope used

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