Non-perturbative positive Lyapunov exponent of Schrödinger equations and its applications to skew-shift mapping

We first study the discrete Schrödinger equations with analytic potentials given by a class of transformations. It is shown that if the coupling number is large, then the Lyapunov exponent equals approximately to the logarithm of this coupling number. When the transformation becomes the skew-shift mapping, we prove that the Lyapunov exponent is weak Hölder continuous, and the spectrum satisfies Anderson Localization and contains large intervals. Moreover, all of these conclusions are non-perturbative.     

Liouville theorem for weighted p-Lichnerowicz equation on smooth metric measure space

In this paper, let $(M^n,g,d\mu )$ be n-dimensional noncompact metric measure space which satisfies Poincaré inequality with some Ricci curvature condition. We obtain a Liouville theorem for positive weak solutions to weighted p-Lichnerowicz equation

${△}_{p,f}v+c{v}^{\sigma }=0,$

where $c\le 0,m>n\ge 1,1<p<\frac{m?1+\sqrt{(m?1)(m+3)}}{2},\sigma \le p?1$ are real constants.     

Contractivity results in ordered spaces. Applications to relative operator bounds and projections with norm one

This paper provides various “contractivity” results for linear operators of the form where C are positive contractions on real ordered Banach spaces X . If A generates a positive contraction semigroup in Lebesgue spaces , we show (M. Pierre's result) that is a “contraction on the positive cone ”, i.e. for all provided that .  We show also that this result is not true for 1 ⩽ . We give an extension of M. Pierre's result to general ordered Banach spaces X under a suitable uniform monotony assumption on the duality map on the positive cone . We deduce from this result that, in such spaces, is a contraction on for any positive projection C with norm 1. We give also a direct proof (by E. Ricard) of this last result if additionally the norm is smooth on the positive cone. For any positive contraction C on base‐norm spaces X (e.g. in real spaces or in preduals of hermitian part of von Neumann algebras), we show that for all where N is the canonical half‐norm in X . For any positive contraction C on order‐unit spaces X (e.g. on the hermitian part of a algebra), we show that is a contraction on . Applications to relative operator bounds, ergodic projections and conditional expectations are given.     

How do the positive embeddings of Banach lattices depend on the αth derivatives of K?

Let K and S be locally compact Hausdorff spaces and X be an abstract space. Suppose that T is a positive Banach lattice isomorphism from into . Then for each ordinal α the cardinalities of the αth derivatives and satisfy the following inequality Moreover, if then is a continuous image of a subset of which can be taken closed when K is compact. The first statement of this result for is a vector‐valued extension of a Cengiz's theorem and the second one is vector‐valued version of a Holsztyński's theorem. A simple example shows that the number is sharp in these vector‐valued theorems.     

Determination of macrolides in livestock excreta by syringe purification coupled with liquid chromatography tandem mass spectrometryEI北大核心CSCD

A method of syringe-dispersive solid-phase extraction combined with ultrahigh performance liquid chromatography with tandem mass spectrometry for the simultanous determination of 10 macrolides in manurebased fertilizers was developed. After extraction with methanol and acetonitrile,the extracts were purified by insyringe dispersion solid-phase extraction in syringes pre-filled with 60 mg PSA and 30 mg C18. The resulted extracts were further separated by a BEH C18 column,detected by multiple reaction monitoring in electrospray positive ion mode,and quantified by matrix-matched external standard method. The results showed that the recoveries of the target compounds ranged from 70% to 110% at three spiked levels（10,30,and 50 μµg/kg）with the relative standard deviations ranged from 1.4% to 12%. The limits of detection and quantification were 0.57 1.75 and 2.77-5.40 μµg/kg,respectively. This method was suitable for the simultaneous determination of residual macrolides in organic fertilizers. © 2023, Youke Publishing Co.,Ltd. All rights reserved.     

Enhanced Reproducibility of Positive Temperature Coefficient Effect of CB/HDPE/PVDF Composites with the Addition of Ionic Liquid

Developing an effective method for improving the reproducibility of positive temperature coefficient(PTC) effect is of great significance for large-scale application of polymer based PTC composites, owing to its contribution to the security and reliability. Herein, we developed a carbon black(CB)/high density polyethylene(HDPE)/poly(vinylidene fluoride)(PVDF) composite with outstanding PTC reproducibility, by incorporating 1-octyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide([OMIm][NTf_2]) into the composite. After multiple repeated temperature cycles, the PTC performance of as-prepared material keeps almost unchanged and the varition of resistance at room temperature is less than 7%. Our studies revealed that [OMIm][NTf2] contributes to the improvement of PTC reproducibility in two ways:(i)it acts as an efficient plasticizer for refining the co-continuous phase morphology of HDPE/PVDE blends;(ii) it inhibits the crystallization of PVDF through the dilution effect, leading to more overlaps of the volume shrinkage process of HDPE and PVDF melt which results in the decrease of interface gap between HDPE and PVDF. This study demonstrated that ionic liquids as the multifunctional agents have great potential for improving the reproducibility in the application of the binary polymer based PTC composites.     

Ideal and non-ideal behaviour of {1-butyl-1-methylpyrrolydinium bis(trifluoromethylsulfonyl)imide + γ-butyrolactone} binary mixtures

Density, electrical conductivity and viscosity of binary liquid mixtures of 1-butyl-1-methylpyrrolydinium bis(trifluoromethylsulfonyl)imide, [bmpyrr][NTf₂], with γ-butyrolactone (GBL) were measured at temperatures from (293.15 to 323.15) K and at atmospheric pressure over the whole composition range. Excess molar volumes have been calculated from the experimental densities and fitted with the Redlich–Kister polynomial equation. These values are positive over the whole range of ionic liquid mole fraction and at all temperatures. In the range between 0.55 and 0.6 [bmpyrr][NTf₂] mole fraction, an ideal behaviour of the ionic liquid mixture with molecular solvent was observed for the first time. Other volumetric properties, such as isobaric thermal expansion coefficients, partial molar volumes and partial molar volumes at infinite dilution have been also calculated, in order to obtain information about interactions between GBL and selected ionic liquid. Positive values of these properties for both components also indicate weaker interactions between GBL and IL compared to the pure components. From the viscosity results, the Angell strength parameter was calculated and found to be 3.24 indicating that [bmpyrr][NTf₂] is a “fragile” liquid. From the volumetric and transport properties obtained, formation of the [bmpyrr]⁺ micellar structures was also discussed. All the results are compared to those obtained for imidazolium-based ionic liquid with GBL.