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A large fraction of the previously estimated WMAP CMB quadrupole signal would be an artefact of incorrect Doppler dipole subtraction if the hypothesis of a small timing interpolation error were correct. Observations of bright foreground…
In this paper we introduce a class of BMO spaces which interpolate with $L_p$ and are sufficiently large to serve as endpoints for new singular integral operators. More precisely, let $(\Omega, \Sigma, \mu)$ be a $\sigma$-finite measure…
We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.
The atomic-level structure of bulk metallic glasses is a key determinant of their properties. An accurate representation of amorphous systems in computational studies has traditionally required large supercells that are unfortunately…
We find sufficient conditions for a discrete sequence to be interpolating or sampling for certain generalized Bergman spaces on open Riemann surfaces. As in previous work of Bendtsson, Ortega-Cerda, Seip, Wallsten and others, our conditions…
The maximum entropy principle (MEP) is one of the most prominent methods to investigate and model complex systems. Despite its popularity, the standard form of the MEP can only generate Boltzmann-Gibbs distributions, which are ill-suited…
We prove optimal order error estimates for the Raviart-Thomas interpolation of arbitrary order under the maximum angle condition for triangles and under two generalizations of this condition, namely, the so-called three dimensional maximum…
In this paper we shed more light on determinants of interval matrices. Computing the exact bounds on a determinant of an interval matrix is an NP-hard problem. Therefore, attention is first paid to approximations. NP-hardness of both…
Zernike polynomials are widely used in optics and ophthalmology due to their direct connection to classical optical aberrations. While orthogonal on the unit disk, their application to discrete data or non-circular domains--such as…
The Maxwell equations have a fairly simple form. However, finding solutions of Maxwell's equations is an extremely difficult task. Therefore, various simplifying approaches are often used in optics. One such simplifying approach is to use…
Quadratically constrained quadratic programs (QCQPs) are a highly expressive class of nonconvex optimization problems. While QCQPs are NP-hard in general, they admit a natural convex relaxation via the standard semidefinite program (SDP)…
We investigate the combinatorial discrepancy of geometric set systems having bounded shallow cell complexity in the \emph{Beck-Fiala} setting, where each point belongs to at most $t$ ranges. For set systems with shallow cell complexity…
This paper establishes a necessary and sufficient condition for $L^p$-boundedness of a class of multilinear functionals which includes both the Brascamp-Lieb inequalities and generalized Radon transforms associated to algebraic incidence…
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…
For the quadratic Lagrange interpolation function, an algorithm is proposed to provide explicit and verified bound for the interpolation error constant that appears in the interpolation error estimation. The upper bound for the…
Very recently, Bai [Linear Algebra Appl., 681:150-186, 2024 \& Appl. Math. Lett., 166:109510, 2025] studied some concrete structures, and obtained essential algebraic and computational properties of the one-dimensional, two-dimensional and…
Suppose that $1<p\leq\infty$ and $\varphi\in L^{p}(\mathbb{B}^{n},\mathbb{R}^{n}).$ In this note, we use H\"{o}lder inequality and some basic properties of hypergeometric functions to establish the sharp constant $C_{p}$ and function…
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…
Quadratically constrained quadratic programs (QCQPs) are a highly expressive class of nonconvex optimization problems. While QCQPs are NP-hard in general, they admit a natural convex relaxation via the standard (Shor) semidefinite program…
We show that measures with finite support on the real line are the unique solution to an algorithm, named generalized minimal extrapolation, involving only a finite number of generalized moments (which encompass the standard moments, the…