Bahadur representation of nonparametric M-estimators for spatial processes

Under some mild conditions, we establish a strong Bahadur representation of a general class of nonparametric local linear M-estimators for mixing processes on a random field. If the socalled optimal bandwidth hn = O（｜n｜^-1/5）, n ∈ Z^d, is chosen, then the remainder rates in the Bahadur representation for the local M-estimators of the regression function and its derivative are of order O（｜n｜^-4/5 log ｜n｜）. Moreover, we derive some asymptotic properties for the nonparametric local linear M-estimators as applications of our result.     

Laser-induced thermoelastic Leaky Lamb waves at the fluid–solid interface

A model based on the theory of fluid–structure interaction is developed to simulate the laser thermoelastic generation and propagation of Leaky Lamb waves at the water–aluminum interface. Each component of displacement, stress, and temperature are derived in transform domain by the photothermoelastic transfer matrix method. The time domain solutions are obtained by numerically inverting the transforms while the dispersion curves and attenuation curves for the leaky waves are also calculated. Then the propagation characteristics of different modes are analyzed. The model establishes a quantitative relation between the laser parameters, the material parameters, the corresponding waveforms, and the dispersion curves, which provides a useful tool for the Leaky Lamb waves applied to nondestructive evaluation.     

Enantioselective Michael reaction of nitroalkanes onto nitroalkenes catalyzed by cinchona alkaloid derivatives

An effective asymmetric synthesis of optically active 1,3-dinitro compounds via the direct Michael addition of nitroalkanes onto nitroalkenes has been described. In the presence of readily modified cinchona alkaloid derivatives, nitroethane reacted well with a variety of aromatic and heterocyclic aromatic nitroalkenes to afford products with good diastereoselectivities (dr up to 72/28) and enantioselectivities (ee up to 94%). The catalyst loading can be decreased to 2 mol % without compromising the asymmetric induction or the reaction rate.     

Extremality of Graph Entropy Based on Degrees of Uniform Hypergraphs with Few Edges

Let $$\mathcal{H}$$     

A novel approach for synthesis of 3-amino-5-aryl-2,5-dihydropyridazines using onium salt as soluble support

In this work it was presented an application of task specific onium salt as soluble support for the synthesis of 3-amino-5-aryl-2,5- dihydropyridazines.This soluble support is of wide applicability and combines advantages of solid phase synthesis without its limitations with those of solution phase chemistry.After a simple washing step,products were cleaved from the supports and obtained in good yields.     

Chloroferrate(III) Ionic Liquid as Recyclable Catalyst for the Acetylation of Alcohols and Phenols and for 1,1‐Diacylation of Aldehydes

A Lewis acidic ionic liquid, [bmim][FeCl₄], was employed to catalyze acetylation of alcohols and phenols, and the conversion of aldehydes to corresponding 1,1‐diacetates without conventional organic solvents. The catalyst is easily available, water‐tolerant, recoverable and easy to handle.