65,390 research outputs found
Tests for covariance matrices, particularly for high dimensional data
Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can be larger than the sample size, n. The statistics, derived under very general conditions, follow an approximate normal distribution for large p, also when p >> n. Simulation results, particularly emphasizing the case when p can be much larger than n, show that the proposed statistics are accurate for both size control and power. A discussion of the commonly used assumptions for high dimensional set up is also given, with the conclusions applicable in general as well as in the special case of high dimensional covariance testing
Optical phonons in new ordered perovskite Sr2Cu(Re0.69Ca0.31) Oy system observed by infrared reflectance spectroscopy
We report infrared reflectivity spectra for a new correlated cupric oxide
system Sr2Cu(Re0.69Ca0.31)Oy with y ~ 0.6 at several temperatures ranging
between 8 and 380 K. The reflectivity spectrum at 300 K comprises of several
optical phonons. A couple of residual bands located around 315 and 653 cm-1
exhibit exceptionally large intensity as compared to the other ones. The
overall reflectivity spectrum lifts up slightly with increasing temperature.
The energy and damping factor of transverse-optical phonons are determined by
fitting the imaginary dielectric constant by Lorentz oscillator model and
discussed as a function of temperature in terms of lattice anharmonicity.Comment: 9 pages, 3 figures, presented at ISS2005, to appear in Physica
More on Five Dimensional EVH Black Rings
In this paper we continue our analysis of arXiv:1308.1478[hep-th] and study
in detail the parameter space of three families of doubly spinning black ring
solutions: balanced black ring, unbalanced ring and dipole-charged balanced
black rings. In all these three families the Extremal Vanishing Horizon (EVH)
ring appears in the vanishing limit of the dimensionful parameter of the
solution which measures the ring size. We study the near horizon limit of the
EVH black rings and for all three cases we find a (pinching orbifold) AdS
throat with the AdS radius where is the ring
mass and is the 5d Newton constant. We also discuss the near horizon
limit of near-EVH black rings and show that the AdS factor is replaced with
a generic BTZ black hole. We use these results to extend the EVH/CFT
correspondence for black rings, a 2d CFT dual to near-EVH black rings.Comment: 30 page
R^4 Corrections to D1D5p Black Hole Entropy from Entropy Function Formalism
We show that in IIB string theory and for D1D5p black holes in ten dimensions
the method of entropy function works. Despite the more complicated Wald formula
for the entropy of D1D5p black holes in ten dimensions, their entropy is given
by entropy function at its extremum point. We use this method for computing the
entropy of the system both at the level of supergravity and for its higher
order alpha'^3R^4 corrections.Comment: 15 pages, minor corrections, typos correcte
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Dispersion-engineered silicon nitride waveguides for mid-infrared supercontinuum generation covering the wavelength range 0.8-6.5 mu m
We numerically demonstrate the generation of a mid-infrared supercontinuum (SC) through the design of an on-chip complementary metal oxide semiconductor (CMOS) compatible 10-mm-long air-clad rectangular waveguide made using stoichiometric silicon nitride (Si 3 N 4 ) as the core and MgF 2 glass as its lower cladding. The proposed waveguide is optimized for pumping in both the anomalous and all-normal dispersion regimes. A number of waveguide geometries are optimized for pumping at 1.55 μ m with ultrashort pulses of 50-fs duration and a peak power of 5 kW. By initially keeping the thickness constant at 0.8 μ m, four different structures are engineered with varying widths between 3 μ m and 6 μ m. The largest SC spectral evolution covering a region of 0.8 μ m to beyond 6.5 μ m could be realized by a waveguide geometry with a width of 3 μ m. Numerical analysis shows that increasing width beyond 3 μ m by fixing thickness at 0.8 μ m results in a reduction of the SC extension in the long wavelength side. However, the SC spectrum can be enhanced beyond 6.5 μ m by increasing the waveguide thickness beyond 0.9 μ m with the same peak power and pump source. To the best of our knowledge, this is first time report of a broad SC spectral evolution through numerical demonstration in the mid-infrared region by the silicon nitride waveguide. In the case of all-normal dispersion pumping, a flatter SC spectra can be predicted with the same power and pump pulse but with a reduced bandwidth spanning 950–2100 nm
A Closer Look at the Elementary Fermions
Although there have been many experimental and theoretical efforts to measure
and interpret small deviations from the standard model of particle physics, the
gap that the model leaves in understanding why there are only three generations
of elementary fermions, with hierarchical masses, has not received the
attention it deserves. I present here an attempt to fill this gap. Although our
findings are mostly only qualitative, they nevertheless may be of heuristic
value. Rules concerning the elementary fermions, some previously known and some
new, lead to a number of conclusions and questions that seem worth pursuing.
Some clarify the standard model, and others suggest possible modifications, the
implications of which are discussed.Comment: 8 page
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