32,557 research outputs found
On the Fourier transform of the characteristic functions of domains with -smooth boundary
We consider domains with -smooth boundary and
study the following question: when the Fourier transform of the
characteristic function belongs to ?Comment: added two references; added footnotes on pages 6 and 1
Estimating Third-Order Moments for an Absorber Catalog
Thanks to the recent availability of large surveys, there has been renewed
interest in third-order correlation statistics. Measures of third-order
clustering are sensitive to the structure of filaments and voids in the
universe and are useful for studying large-scale structure. Thus, statistics of
these third-order measures can be used to test and constrain parameters in
cosmological models. Third-order measures such as the three-point correlation
function are now commonly estimated for galaxy surveys. Studies of third-order
clustering of absorption systems will complement these analyses. We define a
statistic, which we denote K, that measures third-order clustering of a data
set of point observations and focus on estimating this statistic for an
absorber catalog. The statistic K can be considered a third-order version of
the second-order Ripley K-function and allows one to study the abundance of
various configurations of point triplets. In particular, configurations
consisting of point triplets that lie close to a straight line can be examined.
Studying third-order clustering of absorbers requires consideration of the
absorbers as a three-dimensional process, observed on QSO lines of sight that
extend radially in three-dimensional space from Earth. Since most of this
three-dimensional space is not probed by the lines of sight, edge corrections
become important. We use an analytical form of edge correction weights and
construct an estimator of the statistic K for use with an absorber catalog. We
show that with these weights, ratio-unbiased estimates of K can be obtained.
Results from a simulation study also verify unbiasedness and provide
information on the decrease of standard errors with increasing number of lines
of sight.Comment: 19 pages, 4 figure
OPE analysis of the nucleon scattering tensor including weak interaction and finite mass effects
We perform a systematic operator product expansion of the most general form
of the nucleon scattering tensor including electro-magnetic and
weak interaction processes. Finite quark masses are taken into account and a
number of higher-twist corrections are included. In this way we derive
relations between the lowest moments of all 14 structure functions and matrix
elements of local operators. Besides reproducing well-known results, new sum
rules for parity-violating polarized structure functions and new mass
correction terms are obtained.Comment: 50 pages, additional references adde
An approximate buckling analysis for rectangular orthotropic plates with centrally located cutouts
An approximate analysis for predicting buckling of rectangular orthotropic composite plates with centrally located cutouts is presented. In this analysis, prebuckling and buckling problems are converted from a two-dimensional to a one-dimensional system of linear differential equations with variable coefficients. The conversion is accomplished by expressing the displacements as series with each element containing a trigonometric function of one coordinate and a coefficient that is an arbitrary function of the other coordinate. Ordinary differential equations are then obtained from a variational principle. Analytical results obtained from the approximate analysis are compared with finite element analyses for isotropic plates and for specially orthotropic plates with central circular cutouts of various sizes. Experimental results for the specially orthotropic plates are also presented. In nearly all cases, the approximate analysis predicts the buckling mode shapes correctly and predicts the buckling loads to within a few percent of the finite element and experimental results
On a fourth order nonlinear Helmholtz equation
In this paper, we study the mixed dispersion fourth order nonlinear Helmholtz
equation in for positive, bounded and -periodic functions . Using
the dual method of Evequoz and Weth, we find solutions to this equation and
establish some of their qualitative properties
- âŠ