Related papers: Anisotropic interpolation error estimate for arbit…
We examine statistical isotropy of large scale anisotropies of the Internal Linear Combination (ILC) map, based on three year WMAP data. Our study reveals no significant deviation from statistical isotropy on large angular scales of 3-year…
We propose an error analysis in weak norms of a shock capturing finite element method for the Burgers' equation. The estimates can be related to estimates of certain filtered quantities and are robust in the inviscid limit. Using a total…
The statistical expectation values of the temperature fluctuations and polarization of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. We investigate the statistical isotropy (SI) of the CMB maps…
We search for planar deviations of statistical isotropy in the Wilkinson Microwave Anisotropy Probe (WMAP) data by applying a recently introduced angular-planar statistics both to full-sky and to masked temperature maps, including in our…
Recently, the $\vec{H}(\operatorname{div})$-conforming finite element families for second order elliptic problems have come more into focus, since due to hybridization and subsequent advances in computational efficiency their use is no…
A linear modulation of the primordial perturbations is proposed as an explanation for the observed asymmetry between the northern and southern hemispheres of the Wilkinson Microwave Anisotropy Probe (WMAP) data. A cut sky, reduced…
We introduce remarkable upper bounds for the interpolation error constants on triangles, which are sharp and given by simple formulas. These constants are crucial in analyzing interpolation errors, particularly those associated with the…
Large-scale modes in the temperature anisotropy power spectrum C_l measured by the Wilkinson Microwave Anisotropy Probe (WMAP), seem to have lower amplitudes (C_2, C_3 and C_4) than that expected in the so called concordance LCDM model. In…
We test anisotropic dark energy models with the 7-year WMAP temperature observations data. In the presence of imperfect sources, due to large-scale gradients or anisotropies in the dark energy field, the CMB sky will be distorted…
The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants…
The statistical expectation values of the temperature fluctuations of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. We investigate the statistical isotropy of the CMB anisotropy maps recently…
In this paper we use the current and future cosmic microwave background (CMB) experiments to test the Charge-Parity-Time Reversal (CPT) symmetry. We consider a CPT-violating interaction in the photon sector $\mathcal{L}_{\rm cs}\sim p_\mu…
We develop a constructive piecewise polynomial approximation theory in weighted Sobolev spaces with Muckenhoupt weights for any polynomial degree. The main ingredients to derive optimal error estimates for an averaged Taylor polynomial are…
In the present paper, superconvergence of second order, after an appropriate postprocessing, is achieved for both the two and three dimensional first order rectangular Morley elements of biharmonic equations. The analysis is dependent on…
We constrain several models of the early Universe that predict a statistical anisotropy of the cosmic microwave background (CMB) sky. We make use of WMAP9 maps deconvolved with beam asymmetries. As compared to previous releases of WMAP…
For the discretisation of $H_{div}$-functions on rectangular meshes there are at least three families of elements, namely Raviart-Thomas-, Brezzi-Douglas-Marini- and Arnold-Boffi-Falk-elements. In order to prove convergence of a numerical…
We introduce a class of models in which statistical isotropy is broken spontaneously in the CMB by a non-linear response to long-wavelength fluctuations in a mediating field. These fluctuations appear as a gradient locally and pick out a…
We investigate the Statistical Isotropy and Gaussianity of the CMB fluctuations, using a set of multipole vector functions capable of separating these two issues. In general a multipole is broken into a frame and $2\ell-3$ ordered…
We derive an anisotropic a posteriori error estimate for the adaptive conforming Virtual Element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we introduce a quasi-interpolant operator and exploit its…
This article presents novel proof methods for estimating interpolation errors, predicated on the understanding that one has already studied foundational error analysis using the finite element method.