We develop a solver for nonseparable, self adjoint elliptic equations with a variable coefficient. If the coefficient is the square of a harmonic function,a transformation of the dependent variable, results in a constant coefficient Poisson equation. A highly accurate, fast, Fourier-spectral algorithm can solve this equation. When the square root of the coefficient is not harmonic, we approxima...

The transient flow analyzing by the frequency domain method (FDM) is computationally much faster than the method of characteristic (MOC) in the time domain. FDM needs no discretization in time and space, but requires the linearization of governing equations and boundary conditions. Hence, the FDM is only valid for small perturbations in which the system’s hydraulics is almost linear. In this st...

Some statistics in common use take a form of a ratio of two statistics such as sample correlation coefficient, Pearson’s coefficient of variation and so on. In this paper, obtaining an asymptotic representation of the ratio statistic until the third order term, we will discuss asymptotic mean squared errors of the ratio statistics. We will also discuss bias correction of the sample correlation ...

Background: Accurate data on dietary habits are crucial for understanding impacts on disease and informing policy priorities. Nationspecific food balance sheets from the United Nations FAO provided the only available global dietary estimates but with uncertain validity. Objectives: We investigated how FAO estimates compared with nationally representative, individual-based dietary surveys from t...

We consider the large-scale regularity of solutions to second-order linear elliptic equations with random coefficient fields. In contrast to previous works on regularity theory for random elliptic operators, our interest is in the regularity at the boundary: We consider problems posed on the halfspace with homogeneous Dirichlet boundary conditions and derive an associated C1,α-type large-scale ...

We virtually restore faded black and white photographic prints by the method of decomposing the image into a smooth component that contains edges and smoothed homogeneous regions, and a rough component that may include grain noise but also fine detail. The decomposition into smooth and rough components is achieved using a rational filter. Two approaches are considered; in one, the smooth compon...