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...

This article introduces a bivariate shape-preserving interpolation algorithm to approximate the value function of a dynamic program. First, we present a savings allocation problem between a pension account and another non-pension one. With the objective of maximizing the present value of utility over a life cycle, the investor can distribute his or her savings, in each account, between stocks a...

This paper presents two algorithms used to derive Aerosol Optical Depth (AOD) from a synergy of satellite and ground-based observations, as well as aerosol transport model output. The Spinning Enhanced Visible Infrared Radiometer (SEVIRI) instrument on board Meteosat Second Generation (MSG) allows us to monitor aerosol loading over land at high temporal and spatial resolution. We present the al...

A mesoscale objective analysis scheme for producing daily rainfall analysis on a regular latitude/longitude grid over the Indian monsoon region is described. The Barnes scheme is applied to interpolate irregularly distributed daily rainfall data on to a regular grid. The spatial resolution of the interpolated arrays is 0.25 degrees of latitude by 0.25 degrees of longitude. Daily rainfall derive...

This paper presents a comparison of modern time and frequency domain coding of ElectroCardioGram (ECG) signals. A set of diierent subband decompositions are compared for coding purposes. These results are then compared with a time domain linear interpolation technique which is optimal with respect to reconstruction error given the number of retained samples. Comparing the optimized time domain ...

Linear interpolation is the computationally simplest of all possible interpolation techniques. Interestingly, it works reasonably well in many practical situations, even in situations when the corresponding computational models are rather complex. In this paper, we explain this empirical fact by showing that linear interpolation is the only interpolation procedure that satisfies several reasona...

We consider the spline approximation of a continuous (continuously diierentiable) random process with nite second moments based on n observations of the process (and its derivatives). The performance of the approximation is measured by mean errors (e.g., integrated or maximal quadratic mean errors). For Hermite interpolation splines, an optimal rule sets n observation locations (i.e., a design,...

Spatial and temporal sampling errors inherent in large-scale, weather-station (raingauge) climatologies of precipitation are evaluated. A primary goal is to assess whether more representative large-scale precipitation climatologies emerge when (i) more station means are included, even when they are based on unequal periods of record, or (ii) fewer station means are included but all are derived ...