On actions of Drinfel'd doubles on finite dimensional algebras

Let q be an nth root of unity for $n>2$ and let $T_n(q)$ be the Taft (Hopf) algebra of dimension $n^2$. In 2001, Susan Montgomery and Hans-Jürgen Schneider classified all non-trivial $T_n(q)$-module algebra structures on an n-dimensional associative algebra A. They further showed that each such module structure extends uniquely to make A a module algebra over the Drinfel'd double of $T_n(q)$. We explore what it is about the Taft algebras that leads to this uniqueness, by examining actions of (the Drinfel'd double of) Hopf algebras H “close” to the Taft algebras on finite-dimensional algebras analogous to A above. Such Hopf algebras H include the Sweedler (Hopf) algebra of dimension 4, bosonizations of quantum linear spaces, and the Frobenius–Lusztig kernel $u_q({\mathfrak{sl}}_2)$.     

Mixing time of an unaligned Gibbs sampler on the square

The paper concerns a particular example of the Gibbs sampler and its mixing efficiency. Coordinates of a point are rerandomized in the unit square ${[0,1]}^2$ to approach a stationary distribution with density proportional to $exp(?A^2{(u?v)}^2)$ for $(u,v)\in {[0,1]}^2$ with some large parameter $A$.Diaconis conjectured the mixing time of this process to be $O\left(A^2\right)$ which we confirm in this paper. This improves on the currently known $O(exp\left(A^2\right))$ estimate.     

Heinz type inequalities for mappings satisfying Poisson’s equation

In this paper, we study the Heinz type inequalities for mappings satisfying Poisson’s equation. Some results generalize the ones obtained by Partyka and Sakan.     

Application of a sensitive and specific LC‐MS/MS method for determination of eriodictyol‐8‐C‐β‐d‐glucopyranoside in rat plasma for a bioavailability study

This study is the first to detail the development and validation of a rapid, sensitive and specific LC‐ESI‐MS/MS method for the determination of eriodictyol‐8‐C‐β‐d ‐glucopyranoside (EG) in rat plasma. A simple protein precipitation method was used for plasma sample preparation. Chromatographic separation was successfully achieved on an Agilent Zorbax XDB C₁₈ column (2.1 × 50 mm, 3.5 µm) using a step gradient program with the mobile phase of 0.1% formic acid aqueous solution and acetonitrile with 0.1% formic acid. EG and the internal standard (IS) were detected using an electrospray negative ionization mass spectrometry in the multiple reaction monitoring mode. This method demonstrated good linearity and did not show any endogenous interference with the active compound and IS peaks. The lower limit of quantification of EG was 0.20 ng/mL in 50 μL rat plasma. The average recoveries of EG and IS from rat plasma were both above 80%. The inter‐day precisions (relative standard deviation) of EG determined over 5 days were all within 15%. The present method was successfully applied to a quantification and bioavailability study of EG in rats after intravenous and oral administration. The oral absolute bioavailability of EG in rats was estimated to be 7.71 ± 1.52%. Copyright © 2014 John Wiley & Sons, Ltd.     

Modified two-grid method for solving coupled Navier-Stokes/Darcy model based on Newton iteration

A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the err...     

On the complexity of extending the convergence ball of Wang’s method for finding a zero of a derivative

Ball convergence results are very important, since they demonstrate the complexity in choosing initial points for iterative methods. One of the most important problems in the study of iterative methods is to determine the convergence ball. This ball is small in general restricting the choice of initial points. We address this problem in the case of Wang’s method utilized to determine a zero of a derivative. Finding such a zero has many applications in computational fields, especially in function optimization. In particular, we find the convergence ball of Wang’s method using hypotheses up to the second derivative in contrast to earlier studies using hypotheses up to the fourth derivative. This way, we also extend the applicability of Wang’s method. Numerical experiments used to test the convergence criteria complete this study.     

Malliavin and Dirichlet structures for independent random variables

On any denumerable product of probability spaces, we construct a Malliavin gradient and then a divergence and a number operator. This yields a Dirichlet structure which can be shown to approach the usual structures for Poisson and Brownian processes. We obtain versions of almost all the classical functional inequalities in discrete settings which show that the Efron–Stein inequality can be interpreted as a Poincaré inequality or that the Hoeffding decomposition of $U$-statistics can be interpreted as an avatar of the Clark representation formula. Thanks to our framework, we obtain a bound for the distance between the distribution of any functional of independent variables and the Gaussian and Gamma distributions.