关于多线性振荡奇异积分在加权Hardy-型空间上的一致估计

本文对一类具有光滑位相函数的多线性振荡奇异积分算子建立了一致的加权（H^1(R^n),L^1(R^n))估计及一致的加权（HKp(R^n),Kp(R^n)估计。     

探究Cu/ZnO相互作用对CO2加氢制甲醇反应性能的影响

Using renewable green hydrogen and carbon dioxide (CO₂) to produce methanol is one of the fundamental ways to reduce CO₂ emissions in the future, and research and development related to catalysts for efficient and stable methanol synthesis is one of the key factors in determining the entire synthesis process. Metal nanoparticles stabilized on a support are frequently employed to catalyze the methanol synthesis reaction. Metal-support interactions (MSIs) in these supported catalysts can play a significant role in catalysis. Tuning the MSI is an effective strategy to modulate the activity, selectivity, and stability of heterogeneous catalysts. Numerous studies have been conducted on this topic; however, a systematic understanding of the role of various strengths of MSI is lacking. Herein, three Cu/ZnO-SiO₂ catalysts with different strengths of MSI, namely, normal precipitation Cu/ZnO-SiO₂ (Nor-CZS), co-precipitation Cu/ZnO-SiO₂ (Co-CZS), and reverse precipitation Cu/ZnO-SiO₂ (Re-CZS), were successfully prepared to determine the role of such interactions in the hydrogenation of CO₂ to methanol. The results of temperature-programmed reduction (H₂-TPR) and X-ray photoelectron spectroscopy (XPS) characterization illustrated that the MSI of the catalysts was considerably affected by the precipitation sequence. Fourier transform infrared reflection spectroscopy (FT-IR) results indicated that the Cu species existed as CuO in all cases and that copper phyllosilicate was absent (except for strong Cu-SiO₂ interaction). Transmission electron microscopy (TEM), X-ray diffraction (XRD), and N₂O chemical titration results revealed that strong interactions between the Cu and Zn species would promote the dispersion of Cu species, thereby leading to a higher CO₂ conversion rate and improved catalytic stability. As expected, the Re-CZS catalyst exhibited the highest activity with 12.4% CO₂ conversion, followed by the Co-CZS catalyst (12.1%), and the Nor-CZS catalyst (9.8%). After the same reaction time, the normalized CO₂ conversion of the three catalysts decreased in the following order: Re-CZS (75%) > Co-CZS (70%) > Nor-CZS (65%). Notably, the methanol selectivity of the Re-CZS catalyst was found to level off after a prolonged period, in contrast to that of Co-CZS and Nor-CZS. Investigation of the structural evolution of the catalyst with time on stream revealed that the high methanol selectivity of the catalyst was caused by the reconstruction of the catalyst, which was induced by the strong MSI between the Cu and Zn species, and the migration of ZnO onto Cu species, which caused an enlargement of the Cu/ZnO interface. This work offers an alternative strategy for the rational and optimized design of efficient catalysts.     

Hydrothermal synthesis and electrochemical performance of Fe-doped Co hydroxide electrode materials

Journal of Solid State Electrochemistry - In order to meet the growing energy demand, it is of great significance to develop high-performance electrochemical energy storage materials. In this...     

Gaussian curvature in the negative case

In this paper, we reinvestigate an old problem of prescribing Gaussian curvature in the negative case.

In 1974, Kazdan and Warner considered the equation

on any compact two dimensional manifold with . They showed that there exists a number , such that the equation is solvable for every \alpha > \alpha_o$"> and it is not solvable for .

Then one may naturally ask:

Is the equation solvable for ?

In this paper, we answer the question affirmatively. We show that there exists at least one solution for .

     

Determination of Six Resorcylic Acid Lactones in Feed by GC–MS

A method was developed to simultaneously detect six resorcylic acid lactones in feed by GC–MS. Samples were extracted with methanol followed by a two step liquid–liquid extraction and an HLB SPE clean-up. The samples were derivatized with BSTFA + TMCS (99/1; v/v) and determined by GC–MS. For all analytes, the ranges of recoveries were 81.2–98.2%, with RSDs of 3.2–15.2%, and the LODs were 0.2–0.6 μg kg⁻¹.

     

AN EXTENSION OF THE HARDY-LITTLEWOOD-PóLYA INEQUALITY

The Hardy-Littlewood-Pólya (HLP) inequality [1] states that if a∈l~p,b∈l~q and p>1,q>1,1/p + 1/q>1, λ=2-(1/p+1/q),then Σ[(a_rb_s)/︱r-s︱~λ](r≠s)≤C‖a‖_P‖b‖_q.In this article, we prove the HLP inequality in the case where λ= 1, p = q = 2 with a logarithm correction, as conjectured by Ding [2]:Σ[(a_rb_s)/︱r-s︱~λ](r≠s,1≤r,s≤N)≤(2㏑N+1)‖a‖_2‖b‖_2.In addition, we derive an accurate estimate for the best constant for this inequality.     

Radial symmetry for systems of fractional Laplacian

In this paper, we consider systems of fractional Laplacian equations in Rnwith nonlinear terms satisfying some quite general structural conditions. These systems were categorized critical and subcritical cases. We show that there is no positive solution in the subcritical cases, and we classify all positive solutions ui in the critical cases by using a direct method of moving planes introduced in Chen-Li-Li [11] and some new maximum principles in Li-Wu-Xu [27].     

Classification of solutions for an integral equation

Let n be a positive integer and let 0 < α < n. Consider the integral equation We prove that every positive regular solution u(x) is radially symmetric and monotone about some point and therefore assumes the form with some constant c = c(n, α) and for some t > 0 and x₀ ? ?ⁿ. This solves an open problem posed by Lieb 12 . The technique we use is the method of moving planes in an integral form, which is quite different from those for differential equations. From the point of view of general methodology, this is another interesting part of the paper. Moreover, we show that the family of well‐known semilinear partial differential equations is equivalent to our integral equation (0.1), and we thus classify all the solutions of the PDEs. © 2005 Wiley Periodicals, Inc.