We consider   bivariate  mean-value interpolationproblem, where the integrals over circles are interpolation data. In this case the problem  is described  over   circles of the same radius and with  centers are on astraight line and it is shown that in this case the interpolation is not correct.

The charts of 27 patients with Kawasaki disease (KD) admitted to Nemazee Hospital in Shiraz from January 1991 to October 1998 were reviewed to identify the results of mean peroxidase index (MPXI) values, a measure of neutrophil staining intensity, obtained by the Technicon HI analyzer (Technicon Instruments Corp., Tarrytown, NY) within the first 10 days of the illness 2 separate groups of ...

Abstract: Trivariate barycentric coordinates can be used both to express a point inside a tetrahedron as a convex combination of the four vertices and to linearly interpolate data given at the vertices. In this paper we generalize these coordinates to convex polyhedra and the kernels of star-shaped polyhedra. These coordinates generalize in a natural way a recently constructed set of coordinate...

Evaluating the expectation of a quantum circuit is classically difficult problem known as mean value (QMV). It used to optimize approximate optimization algorithm and other variational eigensolvers. We show that such an can be improved substantially by using approximation rather than exact expectation. Together with efficient classical sampling algorithms, minimal gate count thus improve effici...

We derive several mean value formulae on manifolds, generalizing the classical one for harmonic functions on Euclidean spaces as well as the results of Schoen-Yau, Michael-Simon, etc, on curved Riemannian manifolds. For the heat equation a mean value theorem with respect to ‘heat spheres’ is proved for heat equation with respect to evolving Riemannian metrics via a space-time consideration. Som...