Single rows in STIS rectified spectral images are being analyzed in science programs where the highest obtainable spatial resolution is needed. Here we discuss two problems that have limited the accuracy of the rectified spectral images produced by the STScI pipeline: (1) the changing tilts of the spectral traces across the detector have not been taken into account, and (2) interpolation betwee...

This article is devoted to the construction of a Hermite-type regularization operator transforming functions that are not necessarily C1 into globally C1 finite-element functions that are piecewise polynomials. This regularization operator is a projection, it preserves appropriate first and second order polynomial traces, and it has approximation properties of optimal order. As an illustration,...

Abstract We prove several trace inequalities that extend the Golden-Thompson and the Araki-LiebThirring inequality to arbitrarily many matrices. In particular, we strengthen Lieb’s triple matrix inequality. As an example application of our four matrix extension of the Golden-Thompson inequality, we prove remainder terms for the monotonicity of the quantum relative entropy and strong sub-additiv...

Many applications in vehicular communications require the collection of vehicular position traces. So far this has been done by recording and transmitting unencoded position samples. Depending on the frequency and resolution of these samples, the resulting data may be very large, consuming significant resources for storage and transmission. In this paper, we propose a method based on two-dimens...

We develop algorithms for computing Craig interpolants for first-order formulas over real numbers with a wide range of nonlinear functions, including transcendental functions and differential equations. We transform proof traces from δ-complete decision procedures into interpolants that consist of Boolean combinations of linear constraints. The algorithms are guaranteed to find the interpolants...

Interpolation-based model-checking and acceleration techniques have been widely proved successful and efficient for reachability checking. Surprisingly, these two techniques have never been combined to strengthen each other. Intuitively, acceleration provides under-approximation of the reachability set by computing the exact effect of some control-flow cycles and combining them with other trans...

Prediction error filters can be used in a variety of ways to interpolate missing data. One of the main problems with inverse interpolation is its speed. Filters tend to be small, and thus take a long time to propagate information into unknown portions of the much larger model. One answer to this problem is a change of variables, to something closely related to the model but which has the proper...

Several abstract model problems of elliptic and parabolic type with inhomogeneous initial and boundary data are discussed. By means of a variant of the Dore-Venni theorem, real and complex interpolation, and trace theorems, optimal Lp-regularity is shown. By means of this purely operator theoretic approach, classical results on Lp-regularity of the diffusion equation with inhomogeneous Dirichle...