Effective intervals and regular Dirichlet subspaces

It is shown in Li and Ying (2019) that a regular and local Dirichlet form on an interval can be represented by so-called effective intervals with scale functions. This paper focuses on how to operate on effective intervals to obtain regular Dirichlet subspaces. The first result is a complete characterization for a Dirichlet form to be a regular subspace of such a Dirichlet form in terms of effective intervals. Then we give an explicit road map how to obtain all regular Dirichlet subspaces from a local and regular Dirichlet form on an interval, by a series of intuitive operations on the effective intervals in the representation above. Finally applying previous results, we shall prove that every regular and local Dirichlet form has a special standard core generated by a continuous and strictly increasing function.     

Radical polymerization in the presence of peroxide and reducing agent monomer for branched polymers

In this article, we report the radical polymerization in the presence of peroxide and commercially available or designed reducing agent monomer (RAM) for the preparation of branched poly(methyl methacrylate)s (PMMAs). The reaction behavior of the RAM was studied by NMR. Triple‐detection SEC (TD‐SEC) analysis was used to confirm the branching structure of the prepared PMMAs and to investigate the influence of peroxide concentration and RAM concentration on molecular weight and branched structure. The obtained branched PMMAs exhibited high molecular weights and relatively narrow polydispersities at high conversion of MMA. Interestingly, a significant increase in molecular weight and degree of branching of the obtained polymers are observed in higher BPO concentration, these results are quite different from that reported in the literature. The unique radical polymerization mechanism in the RAM/BPO redox‐initiated radical polymerization system resulted in branched PMMAs with high molecular weights at relatively high RAM and BPO concentrations. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 833–840     

One-step mild hydrothermal method to prepare low valent sodium vanadium(III) monohydrogenphosphate: NaV(HPO4)2

Green colored single crystals of a reduced sodium vanadium(III) monohydrogenphosphate, NaV(HPO₄)₂, were grown using a one-step mild hydrothermal method. The in situ reduction of V⁵⁺ to V³⁺ was performed using copper acetate as the reducing agent. The title compound crystalizes in the monoclinic space group Cc and exhibits a three-dimensional crystal structure that consists of distorted VO₆ octahedra connected to PO₃(OH) tetrahedra that are further connected via Na cations. The compound exhibits simple paramagnetic behavior at high temperatures and a discontinuity near 5 K is likely due to the onset of magnetic coupling. The compound was also characterized by TGA, IR and UV–vis spectroscopies.     

Li2B4O7坩埚内预氧化熔融铸片XRF法测定含还原物耐火材料中主量和次量组分

在四硼酸锂坩埚中,以碳酸锂和硝酸铵为氧化剂,在铂金坩埚外对含还原物耐火材料进行预氧化和烧结。在高温氧化过程中,由于样品表面包裹有含氧化剂为主的烧结物,在继续熔融氧化产生的气体浮力作用下,样品在未被氧化前,不与铂金坩埚接触。因此,避免了熔融过程中铂金坩埚腐蚀问题。实验结果表明,氧化温度控制在730℃以下,时间15min内,含还原物耐火材料样品与氧化剂发生氧化烧结反应,四硼酸锂坩埚不会熔穿。确定的预氧化温度为720℃,时间为5~15min。结合现有的报道,确定了熔融铸片所需氧化剂和脱模剂的用量、熔融温度和时间。按拟定的方法,用国家和行业标准样品绘制工作曲线,对含还原物耐火材料样品进行了测定。与湿法分析结果进行比较表明,准确度与湿法分析相当。     

Relationships between the canonical ascending and descending central series of ideals of an associative algebra

We consider the canonical descending and ascending central series of ideals of an associative algebra. In particular, we prove that some ideal in the descending central series is finite-dimensional if and only if some ideal in the ascending central series is finite-codimensional. This result is the associative algebra analogue of results due to Reinhold Baer and Philip Hall in group theory and Ian Stewart in Lie algebra. We also prove various related results.     

Turbulent flow of mildly elastic fluids through rotating straight circular tubes

The turbulent flow of mildly elastic drag reducing fluids through a straight tube rotating around an axis perpendicular to its own is analysed using boundary layer approximations. The momentum integral approach is used and the governing equations have been solved numerically using the Runge-Kutta-Merson method. The influence of the Deborah number on the velocity distribution and the boundary layer thickness has been exemplified through the analysis. NCL Communication No. 3354.     

Trefftz法中的自锁现象及变量减缩法

用Trefftz型边界解法分析了中厚板弯曲问题,发现了一类新的、因Trefftz函数溢机引起的“自锁现象”,并提出了一种消除这类自锁问题的“变量减缩法”。     

High efficiency of Mn–Ce‐modified TiO2 catalysts for the low‐temperature oxidation of Hg0 under a reducing atmosphere

Manganese‐ and cerium oxide‐modified titania catalysts were prepared by the deposition precipitation for the removal of elemental mercury (Hg⁰) from simulated yellow phosphorus off‐gas at low temperature. In addition, these catalysts were characterized by X‐ray diffraction, Brunauer–Emmett–Teller measurements, X‐ray photoelectron spectroscopy and field‐emission scanning electron microscope to determine the surface morphology of the obtained compounds and explore their formation mechanism. The results revealed that a Mn–Ce loading and reaction temperature of 10% and 150 °C, respectively, as well as a Mn/Ce molar ratio of 2:1, led to an optimal efficiency for the oxidation of elemental mercury. Furthermore, the effects of flue gas components were investigated. The presence of O₂ clearly promoted the oxidation of Hg⁰. A CO atmosphere did not affect the Hg⁰ oxidation, when compared with N₂, whereas the presence of H₂S and water vapor inhibited the oxidation process. Furthermore, the X‐ray photoelectron spectroscopy spectra of Hg 4f revealed that the elemental mercury adsorbed by the catalyst is present as HgO. Finally, the Hg⁰ catalytic oxidation mechanism was discussed on the basis of the experimental results and characterization analysis.     

Essential and continuous spectrum of symmetric difference equations

Essential and continuous spectrum of symmetric difference equations have been investigated. It has been shown that the deficiency indices and the existence of these components of the spectrum are determined by the growth conditions of the coefficients. In particular, the deficiency indices are superimposition of those clusters determined by the coefficient growth. Finally, we have proved the neccessary and sufficient conditions for the existence of essential spectrum of selfadjoint subspace extensions using subspace theory and asymtotic summation.