相关论文: Anisotropic interpolation error estimate for arbit…

In this paper, we present some extensions of interpolation between the arithmetic-geometric means inequality. Among other inequalities, it is shown that if $A, B, X$ are $n\times n$ matrices, then \begin{align*}…

Cosmology and other scientific results from the WMAP mission require an accurate knowledge of the beam patterns in flight. While the degree of beam knowledge for the WMAP one-year and three-year results was unprecedented for a CMB…

Error estimates of cubic interpolated pseudo-particle scheme (CIP scheme) for the one-dimensional advection equation with periodic boundary conditions are presented. The CIP scheme is a semi-Lagrangian method involving the piecewise cubic…

Common model selection criteria, such as $AIC$ and its variants, are based on in-sample prediction error estimators. However, in many applications involving predicting at interpolation and extrapolation points, in-sample error cannot be…

To reliably detect the cosmic microwave background (CMB) anisotropy is of great importance in understanding the birth and evolution of the Universe. One of the difficulties in CMB experiments is the domination of measured CMB anisotropy…

In this paper we suggest two modified one-point Gauss integration rules for the Q1 bi- or trilinear element. The modifications both stabilize the hourglass modes of the one-point rule, and one of them is accurate also on severely distorted…

A new error bound which is better than the current exponential-type error bound is presented in this paper.

While isotropic in-plane swelling problems for thin elastic sheets have been studied extensively in recent years, many shape-programmable materials, including nematic solids and 3D-printed structures, are anisotropic, as are most industrial…

Several accurate analyses have revealed a statistically significant North-South ecliptic asymmetry in the large-angle correlations strength of the Cosmic Microwave Background (CMB) radiation temperature field data from the Wilkinson…

We cross-correlate the cosmic microwave background temperature anisotropy maps from the WMAP, MAXIMA-I, and MAXIMA-II experiments. We use the cross-spectrum, which is the spherical harmonic transform of the angular two-point correlation…

Layer potentials represent solutions to partial differential equations in an integral equation formulation. When numerically evaluating layer potentials at evaluation points close to the domain boundary, specialized quadrature techniques…

We discuss the problem of the bias of the Internal Linear Combination (ILC) CMB map and show that it is closely related to the coefficient of cross-correlation K(l) of the true CMB and the foreground for each multipole l. We present…

This paper reviews the application of a novel methodology for analysing the isotropy of the universe by probing the alignment of local structures in the CMB. The strength of the proposed methodology relies on the steerable wavelet filtering…

We present local extrema studies of two models that introduce a preferred direction into the observed cosmic microwave background (CMB) temperature field. In particular, we make a frequentist comparison of the one- and two-point statistics…

We test the hemispherical power asymmetry of the WMAP 7-year low-resolution temperature and polarization maps. We consider two natural estimators for such an asymmetry and exploit our implementation of an optimal angular power spectrum…

An adaptive interpolation scheme is proposed to accurately calculate the wideband responses in electromagnetic simulations. In the proposed scheme, the sampling points are first carefully divided into several groups based on their responses…

Quadrilaterals in the complex plane play a significant part in the theory of planar quasiconformal mappings. Motivated by the geometric definition of quasiconformality, we prove that every quadrilateral with modulus in an interval $[1/K,…

Most of the analysis of the Cosmic Microwave Background relies on the assumption of statistical isotropy. However, given some recent evidence pointing against isotropy, as for instance the observed alignment of different multipoles on large…

We investigate {\bf explicit} universal estimate of finite Morse index solutions to polyharmonic equations. \,Differently to previous works \cite{BL2, DDF, fa, H1}, propose here a direct proof using a new interpolation inequality and a…

We consider quasi-interpolation with a main application in radial basis function approximations and compression in this article. Constructing and using these quasi-interpolants, we consider wavelet and compression-type approximations from…