In order to the second order Cauchy problem (CP2): x"(t) Ax(t), z(O) z E D(A"), z"(O) y D(A") on a Banach space, Arendt and Kellermann recently introduced the integrated cosine function. This paper is concerned with its basic theory, which contain some properties, perturbation and approximation theorems, the relationship to analytic integrated semigroups, interpolation and extrapolation theorems.

Exploring the proofs and refutations of an abstract statement, conjecture with aim to give a formal syntactic treatment its proving–refuting process, we introduce notion extrapolation possibly unprovable statement having form if A, then B, propose procedure that should result in new A′, B′, which is similar starting one, but provable. We think this procedure, based on method, can be considered ...

Species distribution models (SDMs) are increasingly applied in conservation management to predict suitable habitat for poorly known populations. High predictive performance of SDMs is evident in validations performed within the model calibration area (interpolation), but few studies have assessed SDM transferability to novel areas (extrapolation), particularly across large spatial scales or pel...

A critical review of experimental technique for measuring high pressures has been made. The broad coverage includes discussions relating to (a) the establishment of a primary pressure scale using the free-piston gage, (b) the selection and precise measurement of identifiable phase changes as fixed pressure points, and (c) the use of interpolation and extrapolation techniques such as resistance ...

Interpolation of signals (arbitrary dimension, here: 2D images) with missing data points is addressed from a statistical point of view. We present a general framework for which a Wiener-style MMSE estimator can be seamlessly adapted to deal with problems such as image interpolation (inpainting), reconstruction from sparse samples, and image extrapolation. The proposed method gives a precise ans...

I critically review recent lattice QCD results relevant for kaon phenomenology, as well as the methods that are used to obtain them. The focus is on calculations with N f = 2 and N f = 2 + 1 flavors of sea quarks. Concerning methodology, the subjects covered include a discussion of how best to extrapolate and/or interpolate results to the physical quark-mass point, a scheme for assessing the ex...