252 research outputs found
High Order Riesz Transforms and Mean Value Formula for Generalized Translate Operator
In this paper, the mean value formula depends on the Bessel generalized shift
operator corresponding to the solutions of the boundary value problem related
to the Bessel operator are studied. In addition to, Riesz Bessel transforms
related to the Bessel operators are studied. Since Bessel generalized shift
operator is translation operator corresponding to the Bessel operator, we
construct a family of RBxj by using Bessel generalized shift operator. Finally,
we analysis weighted inequalities involving Riesz Bessel transforms
A new Tolman test of a cosmic distance duality relation at 21 cm
Under certain general conditions in an expanding universe, the luminosity
distance (d_L) and angular diameter distance (d_A) are connected by the
Etherington relation as d_L = d_A (1 + z)^2. The Tolman test suggests the use
of objects of known surface brightness, to test this relation. In this letter,
we propose the use of redshifted 21 cm signal from disk galaxies, where neutral
hydrogen (HI) masses are seen to be almost linearly correlated with surface
area, to conduct a new Tolman test. We construct simulated catalogs of
galaxies, with the observed size-luminosity relation and realistic redshift
evolution of HI mass functions, likely to be detected with the planned Square
Kilometer Array (SKA). We demonstrate that these observations may soon provide
the best implementation of the Tolman test to detect any violation of the
Etherington relation.Comment: 4 pages, 2 figures, 1 table, v2: published versio
Asymptotics of Bayesian Uncertainty Estimation in Random Features Regression
In this paper we compare and contrast the behavior of the posterior
predictive distribution to the risk of the maximum a posteriori estimator for
the random features regression model in the overparameterized regime. We will
focus on the variance of the posterior predictive distribution (Bayesian model
average) and compare its asymptotics to that of the risk of the MAP estimator.
In the regime where the model dimensions grow faster than any constant multiple
of the number of samples, asymptotic agreement between these two quantities is
governed by the phase transition in the signal-to-noise ratio. They also
asymptotically agree with each other when the number of samples grow faster
than any constant multiple of model dimensions. Numerical simulations
illustrate finer distributional properties of the two quantities for finite
dimensions. We conjecture they have Gaussian fluctuations and exhibit similar
properties as found by previous authors in a Gaussian sequence model, which is
of independent theoretical interest.Comment: 11 pages, 3 figure
Proton-electron mass ratio from HD revisited
We present a new derivation of the proton-electron mass ratio from the
hydrogen molecular ion, HD. The derivation entails the adjustment of the
mass ratio in highly precise theory so as to reproduce accurately measured
ro-vibrational frequencies. This work is motivated by recent improvements of
the theory, as well as the more accurate value of the electron mass in the
recently published CODATA-14 set of fundamental constants, which justifies
using it as input data in the adjustment, rather than the proton mass value as
done in previous works. This leads to significantly different sensitivity
coefficients and, consequently, a different value and larger uncertainty margin
of the proton-electron mass ratio as obtained from HD
Planetoid strings : solutions and perturbations
A novel ansatz for solving the string equations of motion and constraints in
generic curved backgrounds, namely the planetoid ansatz, was proposed recently
by some authors. We construct several specific examples of planetoid strings in
curved backgrounds which include Lorentzian wormholes, spherical Rindler
spacetime and the 2+1 dimensional black hole. A semiclassical quantisation is
performed and the Regge relations for the planetoids are obtained. The general
equations for the study of small perturbations about these solutions are
written down using the standard, manifestly covariant formalism. Applications
to special cases such as those of planetoid strings in Minkowski and spherical
Rindler spacetimes are also presented.Comment: 24 pages (including two figures), RevTex, expanded and figures adde
Probing liquid surface waves, liquid properties and liquid films with light diffraction
Surface waves on liquids act as a dynamical phase grating for incident light.
In this article, we revisit the classical method of probing such waves
(wavelengths of the order of mm) as well as inherent properties of liquids and
liquid films on liquids, using optical diffraction. A combination of simulation
and experiment is proposed to trace out the surface wave profiles in various
situations (\emph{eg.} for one or more vertical, slightly immersed,
electrically driven exciters). Subsequently, the surface tension and the
spatial damping coefficient (related to viscosity) of a variety of liquids are
measured carefully in order to gauge the efficiency of measuring liquid
properties using this optical probe. The final set of results deal with liquid
films where dispersion relations, surface and interface modes, interfacial
tension and related issues are investigated in some detail, both theoretically
and experimentally. On the whole, our observations and analyses seem to support
the claim that this simple, low--cost apparatus is capable of providing a
wealth of information on liquids and liquid surface waves in a non--destructive
way.Comment: 25 pages, 12 figures, to appear in Measurement Science and Technology
(IOP
Schild's Null Strings in Flat and Curved Backgrounds
Schild's null (tensionless) strings are discussed in certain flat and curved
backgrounds. We find closed, stationary, null strings as natural configurations
existing on the horizons of spacetimes which possess such null hypersurfaces.
Examples of these are obtained in Schwarzschild and Rindler spacetimes. A
dynamic null string is also identified in Rindler spacetime. Furthermore, a
general prescription (with explicit examples) is outlined by means of which
null string configurations can be obtained in a large class of cosmological
backgrounds.Comment: RevTex 3.0, 14 Pages, no figure
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