We examine the effect of errors in covariates in nonparametric function estimation. These functions include densities, regressions and conditional quantiles. To estimate these functions, we use the idea of deconvoluting kernels in conjunction with the ordinary kernel methods. We also discuss a new class of function estimators based on local polynomials.

The formation and propagation of thermal fronts in a cylindrical medium that is undergoing microwave heating is studied in detail. The model consists of Maxwell's wave equation coupled to a temperature diffusion equation containing a bistable nonlinear term.

For the symmetric cone complementarity problem, we show that each stationary point of the unconstrained minimization reformulation based on the FischerBurmeister merit function is a solution to the problem, provided that the gradient operators of the mappings involved in the problem satisfy column monotonicity or have the Cartesian P 0-property. These results answer the open question proposed in the article that appeared in Journal of Mathematical Analysis and Applications 355 (2009) 195215.

We briefly survey our recent results about the Mumford goodness of several canonical metrics on the moduli spaces of Riemann surfaces, including the Weil-Petersson metric, the Ricci metric, the Perturbed Ricci metric and the Kahler-Einstein metric. We prove the dual Nakano negativity of the Weil-Petersson metric. As applications of these results we deduce certain important results about the <i>L</i> ²-cohomology groups of the logarithmic tangent bundle over the compactified moduli spaces.

We present a novel modification to the well-known infomax algorithm of blind source separation. Under natural gradient descent, the infomax algorithm converges to a stationary point of a limiting ordinary differential equation. However, due to the presence of saddle points or local minima of the corresponding likelihood function, the algorithm may be trapped around these bad stationary points for a long time, especially if the initial data are near them. To speed up convergence, we propose to add a sequence of random perturbations to the infomax algorithm to shake the iterating sequence so that it is captured by a path descending to a more stable stationary point. We analyze the convergence of the randomly perturbed algorithm, and illustrate its fast convergence through numerical examples on blind demixing of stochastic signals. The examples have analytical structures so that saddle points or local minima of