We show that the lower-order terms in the ANOVA decomposition of a function f(x) := max(φ(x), 0) for x ∈ [0, 1], with φ a smooth function, may be smoother than f itself. Specifically, f in general belongs only toW d,∞, i.e., f has one essentially bounded derivative with respect to any component of x, whereas, for each u ⊆ {1, . . . , d}, the ANOVA term fu (which depends only on the variables xj...

Mixed-effect models are widely used for the analysis of correlated data such as longitudinal data and repeated measures. In this article, we study an approach to the nonparametric estimation of mixed-effect models. We consider models with parametric random effects and flexible fixed effects, and employ the penalized least squares method to estimate the models. The issue to be addressed is the s...

We show the necessity of the non trapping condition for the plain smoothing effect (H) for Schrödinger equation with Dirichlet boundary conditions in exterior problems. We also give a class of trapped obstacles (Ikawa’s example) for which we can prove a weak (H) smoothing effect Résumé. On démontre que l’hypothèse de non capture est nécessaire pour l’effet régularisant (H) pour l’équation de Sc...

— We prove the equivalence between the smoothing effect for a Schrödinger operator and the decay of the associate spectral projectors. We give two applications to the Schrödinger operator in dimension one. Résumé. — On donne une caractérisation de l’effet régularisant pour un opérateur de Schrödinger par la décroissance de ses projecteurs spectraux. On en déduit deux applications à l’opérateur ...

A generalized model is developed to quantitatively describe the smoothing effects from different polishing tools used for optical surfaces. The smoothing effect naturally corrects mid-to-high spatial frequency errors that have features small compared to the size of the polishing lap. The original parametric smoothing model provided a convenient way to compare smoothing efficiency of different p...

Implosion process in laser fusion can be divided into three phases: start-up, acceleration and stagnation phases and various hydrodynamic instabilities appear in each phase. Analytical models are developed to study nonlinear evolutions of the hydrodynamic instabilities in these phases, and compared with multi-dimensional simulations. We mainly discuss the formation of double spiral structures c...

405 Abstract— Image processing operations like smoothing and edge detection, and many more are very widely used in areas like Computer Vision. We classify the image processing domain as seven branches-image acquirement and output, image coding and compression, image enhancement and restoration, image transformation, image segmentation, image description, and image recognition and description. W...

Direction of arrival estimation in coherent multipath environment by using the superresolution technique often requires decorrelation techniques. Spatial smoothing preprocessings are the most popular scheme as the techniques. In mobile environment, position change of the target/transmitter often brings us decorrelation effect. Multiple transmitting signals by an antenna array like a MIMO transm...