相关论文: Anisotropic interpolation error estimate for arbit…

This paper contains a survey of results obtained by the authors mostly during the past few years and published by 2021. In particular, we present the best of known estimates of numerical characteristics related to the research theme.…

Anisotropic mesh quality measures and anisotropic mesh adaptation are studied for polygonal meshes. Three sets of alignment and equidistribution measures are developed, one based on least squares fitting, one based on generalized…

Analyses of recent cosmic microwave background (CMB) observations have provided increasing indications for the existence of large scale anisotropy in the universe. Given the far reaching consequences of such an anisotropy for our…

Several anomalies appear to be present in the large-angle cosmic microwave background (CMB) anisotropy maps of WMAP. One of these is a lack of large-scale power. Because the data otherwise match standard models extremely well, it is natural…

Recent high precision cosmological observations have revealed several anomalies in the Cosmic Microwave Background (CMB), indicating possible violations of statistical isotropy (nSI). Typically, nSI in the CMB sky is studied in the harmonic…

Several accurate analyses of the CMB temperature maps from the Wilkinson Microwave Anisotropy Probe (WMAP) have revealed a set of anomalous results, at large angular scales, that appears inconsistent with the statistical isotropy expected…

This paper presents an a posteriori error analysis for a coupled continuum pipe-flow/Darcy model in karst aquifers. We consider a unified anisotropic finite element discretization (i.e. elements with very large aspect ratio). Our analysis…

This paper introduces a quasi-interpolation operator for scalar- and vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces.This operator gives optimal estimates of the…

The divergence of the momentum density field of the large scale structure generates a secondary anisotropy contribution to the Cosmic Microwave Background (CMB). While the effect is best described as a non-linear extension to the well-known…

We present the analysis on the quadrupole phases of the Internal Linear Combination map, ILC(I) and (III) derived by the WMAP team (1 and 3-year data release). This approach allows us to see the global trend of non-Gaussianity of the…

We propose a parallel version of the cross interpolation algorithm and apply it to calculate high-dimensional integrals motivated by Ising model in quantum physics. In contrast to mainstream approaches, such as Monte Carlo and quasi Monte…

Measurements of the cosmic microwave background (CMB) spectral $y$-distortion anisotropy offer a test for the statistical isotropy of the primordial density perturbations on $0.01\lesssim k{\rm Mpc}\lesssim 1$. We compute the 1-point…

We compute the two-, three- and four-point correlation functions from the Wilkinson Microwave Anisotropy Probe (WMAP) first-year data, and compare these to a Monte Carlo ensemble of 5000 realizations, based on the best-fit WMAP…

The confrontation of the Cosmic Microwave Background (CMB) theoretical angular power spectrum with available data often requires the calculation of large numbers of power spectra. The standard practice is to use a fast code to compute the…

This work is devoted to the study of integration with respect to binomial measures. We develop interpolatory quadrature rules and study their properties. Local error estimates for these rules are derived in a general framework.

The low quadrupole of the cosmic microwave background (CMB), measured by COBE and confirmed by WMAP, has generated much discussion recently. We point out that the well-known correlation between temperature and polarization anisotropies of…

We study the problem $-\Delta u = \gamma$, where $\gamma$ is a singular measure, with support on a curve or a point. We prove that optimal rates of convergence for the finite element method can be obtained using properly graded meshes. In…

We present an expression for the leading-color (planar) four-loop four-point amplitude of N=4 supersymmetric Yang-Mills theory in 4-2 e dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity…

Optically isotropic metamaterials (MMs) are required for the implementation of subwavelength imaging systems. At first glance one would expect that their design should be based on unit cells exhibiting a cubic symmetry being the highest…

In this paper we give a geometric condition which ensures that $(q,p)$-Poincar\'e-Sobolev inequalities are implied from generalized $(1,1)$-Poincar\'e inequalities related to $L^1$ norms in the context of product spaces. The concept of…