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RADIAL DENSITY IN APOLLONIAN PACKINGS
"... Abstract. Given P, an Apollonian Circle Packing, and a circle C0 = ∂B(z0, r0) in P, color the set of disks in P tangent to C0 red. What proportion of the concentric circle C = ∂B(z0, r0 + ) is red, and what is the behavior of this quantity as → 0? Using equidistribution of closed horocycles on t ..."
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on the modular surface H2/SL(2,Z), we show that the answer is 3 pi = 0.9549... We also describe an observation due to Alex Kontorovich connecting the rate of this convergence in the FareyFord packing to the Riemann Hypothesis. For the analogous problem for Soddy Sphere packings, we find that the limiting radial
BEAM WITH A ROUNDED RADIAL DENSITY PROFILE
, 1982
"... 19. KEY WORDS (Continue on reverse aide it neceeary end identi.y by block nmber) Selfpinched Beam Radial Density Profile 20. AESTRACT (Continue an reverse aide If neceeeary and Identity by block number) The axisymmetric perturbations (sausage and hollowing modes) of an intense relativistic selfpin ..."
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19. KEY WORDS (Continue on reverse aide it neceeary end identi.y by block nmber) Selfpinched Beam Radial Density Profile 20. AESTRACT (Continue an reverse aide If neceeeary and Identity by block number) The axisymmetric perturbations (sausage and hollowing modes) of an intense relativistic self
Radial density profiles of timedelay lensing galaxies
, 704
"... We present nonparametric radial mass profiles for ten QSO strong lensing galaxies. Five of the galaxies have profiles close to ρ(r) ∝ r−2, while the rest are closer to r−1, consistent with an NFW profile. The former are all relatively isolated earlytypes and dominated by their stellar light. The ..."
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We present nonparametric radial mass profiles for ten QSO strong lensing galaxies. Five of the galaxies have profiles close to ρ(r) ∝ r−2, while the rest are closer to r−1, consistent with an NFW profile. The former are all relatively isolated earlytypes and dominated by their stellar light
RADIAL DENSITY STATISTICS OF THE GALAXY DISTRIBUTION AND THE LUMINOSITY FUNCTION
, 2014
"... ar ..."
On the Four Vertex Theorem on planes with radial density e ϕ(r)
, 2008
"... It is showed that on a plane with a radial density the Four Vertex Theorem holds for the class of all simple closed curves if and only if the density is constant. But for the class of simple closed curves that are invariant under a rotation about the origin, the Four Vertex Theorem holds for every r ..."
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It is showed that on a plane with a radial density the Four Vertex Theorem holds for the class of all simple closed curves if and only if the density is constant. But for the class of simple closed curves that are invariant under a rotation about the origin, the Four Vertex Theorem holds for every
The effect of radiative cooling on the radial density and temperature profiles of galaxy clusters.
, 1999
"... Clusters of galaxies are the largest virialised structures in the Universe, evolving rapidly at recent times because in most cosmologies big objects form last. Even at moderate ..."
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Clusters of galaxies are the largest virialised structures in the Universe, evolving rapidly at recent times because in most cosmologies big objects form last. Even at moderate
Radial Density Profiles of Fluorine Negative Ions and Electrons around a Magnetized String Plasma in CF4 Gas
"... Radial density profiles of electrons and fluorine negative ions around a stringtype CF4 plasma across a magnetic field are measured using a wiretype Langmuir probe. Modified Bohm theory is applied to evaluate negativeion density, and it is confirmed that negative ions are well confined between tw ..."
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Radial density profiles of electrons and fluorine negative ions around a stringtype CF4 plasma across a magnetic field are measured using a wiretype Langmuir probe. Modified Bohm theory is applied to evaluate negativeion density, and it is confirmed that negative ions are well confined between
NorthHolland Use of radial density plots to calibrate image magnification for frozenhydrated specimens
, 1992
"... Accurate magnification calibration for transmission electron microscopy is best achieved with the use of appropriate standards and an objective calibration technique. We have developed a reliable method for calibrating the magnification of images from frozenhydrated specimens. Invariant features in ..."
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in radial density plots of a standard are compared with the corresponding features in a “defocused ” Xray model of the same standard. Defocused Xray models were generated to mimic the conditions of cryoelectron microscopy. The technique is demonstrated with polyoma virus, which was used as an internal
Maximumentropy technique with logarithmic constraints: Estimation of atomic radial densities, European Phys
 J. D
, 1999
"... Abstract. Maximumentropy (ME) approximations to density functions involving logarithmic constraints are studied. It is proved the existence and uniqueness of the ME approximation constrained by the normalization, the geometric mean and (i) a moment of arbitrary order, or (ii) the logarithmic uncer ..."
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uncertainty. A numerical analysis of the accuracy of these ME approximations is carried out for the radial electron densities of neutral atoms in both position and momentum spaces. PACS
Results 1  10
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3,558