bert transform. Section 4 describes the algorithm Narayana, S., Sarkar, T. K., Adve, R., Wicks, M., and Vanused to implement this. In Section 5, a few numerical nicola, V., A Comparison of Two Techniques for the Interexamples are studied and comparisons made. polation/Extrapolation of Frequency Domain Responses, Digital Signal Processing 6 (1996), 51–67. 2. THE CAUCHY METHOD In this paper, a co...

We study the comparison principle and interior Holder continuity of viscosity solutions of F (x; u;Du;D 2 u) +H(x;Du) = f; where F satis es the standard \structure condition" and H has a superlinear growth with respect to Du. Following Ca arelli, Crandall, Kocan and Swi ech [3], we rst present the comparison principle between L p -viscosity subsolutions and L p -strong supersolutions. We next ...

In this paper, we prove a sample-path comparison principle for the nonlinear stochastic fractional heat equation on R with measure-valued initial data. We give quantitative estimates about how close to zero the solution can be. These results extend Mueller’s comparison principle on the stochastic heat equation to allow more general initial data such as the (Dirac) delta measure and measures wit...

We study the dynamics of a one-dimensional non-linear and nonlocal drift-diffusion equation set in the half-line, with the coupling involving the trace value on the boundary. The initial mass M of the density determines the behaviour of the equation: attraction to self similar profile, to a steady state of finite time blow up for supercritical mass. Using the logarithmic Sobolev and the HWI ine...

In this article we consider a lattice system of unbounded continuous spins. Otto and Reznikoff used the two-scale approach to show that exponential decay of correlations yields a logarithmic Sobolev inequality (LSI) with uniform constant in the system size. We improve their statement by weakening the assumptions, for which a more detailed analysis based on two new ingredients is needed. The two...

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The paper deals with the task of polynomial regression, i.e., inducing polynomial that can be used to predict a chosen dependent variable based on the values of independent ones. As in other induction tasks, there is a trade-off between the complexity of the induced polynomial and its predictive error. One of the approaches for searching an optimal trade-off is the Minimal Description Length pr...