The length and depth of algebraic groups

Mathematische Zeitschrift - Let G be a connected algebraic group. An unrefinable chain of G is a chain of subgroups $$G = G_0> G_1> \cdots > G_t = 1$$ , where each $$G_i$$ is a...     

Weighted estimates for the multilinear maximal function on the upper half‐spaces

For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates.     

An Inexact Modified Newton Method for Viscc and Application in Grasping Force

Acta Mathematicae Applicatae Sinica, English Series - For the variational inequality with symmetric cone constraints problem, we consider using the inexact modified Newton method to efficiently...     

On concentration of solution to a Schrödinger logarithmic equation with deepening potential well

In this work, we prove the existence of positive solution for the following class of problems where λ>0 and is a potential satisfying some conditions. Using the variational method developed by Szulkin for functionals, which are the sum of a C¹ functional with a convex lower semicontinuous functional, we prove that for each large enough λ>0, there exists a positive solution for the problem, and that, as λ→+∞, such solutions converge to a positive solution of the limit problem defined on the domain Ω=int(V^?1({0})).     

Polystyrene-supported phosphine oxide-catalysed Beckmann rearrangement of ketoximes in 1,1,1,3,3,3-hexafluoro-2-propanol

A polystyrene-supported phosphine oxide-catalysed Beckmann rearrangement of ketoximes in 1,1,1,3,3,3-hexafluoro-2-propanol (HFIP) has been developed. Good substrate compatibility, mild reaction conditions, good yields as well as the reusability of the catalyst/solvent made this procedure more environmentally benign.     

Poisson discretizations of Wiener functionals and Malliavin operators with Wasserstein estimates

This article proposes a global, chaos-based procedure for the discretization of functionals of Brownian motion into functionals of a Poisson process with intensity $\lambda >0$. Under this discretization we study the weak convergence, as the intensity of the underlying Poisson process goes to infinity, of Poisson functionals and their corresponding Malliavin-type derivatives to their Wiener counterparts. In addition, we derive a convergence rate of $O\left({\lambda }^{?1∕4}\right)$ for the Poisson discretization of Wiener functionals by combining the multivariate Chen–Stein method with the Malliavin calculus. Our proposed sufficient condition for establishing the mentioned convergence rate involves the kernel functions in the Wiener chaos, yet we provide examples, especially the discretization of some common path dependent Wiener functionals, to which our results apply without committing the explicit computations of such kernels. To the best our knowledge, these are the first results in the literature on the universal convergence rate of a global discretization of general Wiener functionals.     

Inhibition effect of butan-1-ol on the corrosion behavior of austenitic stainless steel (Type 304) in dilute sulfuric acid

The electrochemical behavior of austenitic stainless steel (Type 304) in 3 M sulfuric acid with 3.5% recrystallized sodium chloride at specific concentrations of butan-1-ol was investigated with the aid of potentiodynamic polarization, open circuit measurement and weight loss technique. Butan-1-ol effectively inhibited the steel corrosion with a maximum inhibition efficiency of 78.7% from weight-loss analysis and 80.9% from potentiodynamic polarization test at highest concentration studied. Adsorption of the compound obeyed the Freundlich isotherm. Thermodynamic calculations reveal physiochemical interactions and spontaneous adsorption mechanism. Surface characterizations showed the absence of corrosion products and topographic modifications of the steel. Statistical analysis depicts the overwhelming influence and statistical significance of inhibitor concentration on the inhibition performance.     

Nukiangendines A and B,two novel 13,14-seco-abietanes from Abies nukiangensis

From Abies nukiangensis, two novel 13,14-seco-abietane diterpenes, nukiangendines A (1) and B (2) were isolated. Their relative structures were determined by extensive NMR and HRMS spectroscopic analysis. The absolute configuration of 1 was established by ECD calculations. Compound 1 showed significant anti-hepatitis C virus (HCV) effects.     

Polysilsesquioxanes Containing Superparamagnetic Nanoclusters of Cobalt or Nickel

Theoretical and Experimental Chemistry - A method was developed for the synthesis of ion-coordinated polysilsesquioxanes (OSS-M) by reaction of amphiphilic carboxyl-containing oligosilsesquioxanes...