Hopf-algebraic renormalization of QED in the linear covariant gauge

In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green’s functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.     

The role of problem representation and feature knowledge in algebraic equation-solving

Domain experts have two major advantages over novices with regard to problem solving: experts more accurately encode deep problem features (feature encoding) and demonstrate better conceptual understanding of critical problem features (feature knowledge). In the current study, we explore the relative contributions of encoding and knowledge of problem features (e.g., negative signs, the equals sign, variables) when beginning algebra students solve simple algebraic equations. Thirty-two students completed problems designed to measure feature encoding, feature knowledge and equation solving. Results indicate that though both feature encoding and feature knowledge were correlated with equation-solving success, only feature knowledge independently predicted success. These results have implications for the design of instruction in algebra, and suggest that helping students to develop feature knowledge within a meaningful conceptual context may improve both encoding and problem-solving performance.     

透光脉动检测仪研究碱度对絮体形成、破碎及再生的影响

为了解碱度对絮体的形成、破碎及再生过程的影响,采用PDA2000型透光脉动检测仪测定不同碱度下投加硫酸铝时高岭土悬浮液的絮凝指数(FI指数),并以强度因子和再生因子评价絮体的强度和再生能力。结果表明,碱度的高低在很大程度上会影响絮体的形成、破碎及再生过程,所形成絮体的颗粒随碱度的增加而减小。混凝剂投量和碱度高低共同决定了絮体的抗破碎强度,碱度越高,混凝剂投量越大,絮体的强度越高。在电中和作用下形成的絮体在低碱度下经一次破碎后恢复程度接近100%,在网捕卷扫作用下形成的絮体,无论碱度高低,从第2次破碎起,FI指数均以大于10%的幅度逐次下降,絮体不可恢复程度显著增大。     

On-line sample-pre-treatment schemes for trace-level determinations of metals by coupling flow injection or sequential injection with ICP-MS

Within the last decade, the first generation of flow injection (FI) has been supplemented by sequential injection (SI), also termed the second generation, and, recently, by the third generation, i.e., SI-Lab-on-Valve (SI-LOV). As apparent from the literature, FI and/or SI have become dominant as substitutes for labor-intensive, manual, sample-pre-treatment and/or solution-handling procedures prior to analyte detection by inductively coupled plasma mass spectrometry (ICP-MS). The present review presents and discusses the progress of the state of the art in implementing miniaturized FI/SI systems for on-line matrix separation and pre-concentration of trace levels of metals with detection by ICP-MS. It highlights some of the frequently applied on-line, sample-pre-treatment schemes, including solid phase extraction (SPE), on-wall molecular sorption and precipitate/(co)-precipitate retention using a polytetrafluoroethylene (PTFE) knotted reactor (KR), solvent extraction-back extraction and hydride/vapor generation. It also addresses a novel, robust approach, whereby the protocol of SI-LOV-bead injection (BI) on-line separation and pre-concentration of ultra-trace levels of metals by a renewable microcolumn is interfaced to ICP-MS, as conducted in the present authors' group. It discusses the future outlook in this field.     

Ethylene and propylene polymerization behavior of a series of bis(phenoxy–imine)titanium complexes

This contribution reports ethylene and propylene polymerization behavior of a series of Ti complexes bearing a pair of phenoxy–imine chelate ligands. The bis(phenoxy–imine)Ti complexes in conjunction with methylalumoxane (MAO) can be active catalysts for the polymerization of ethylene. Unexpectedly, this C₂ symmetric catalyst produces syndiotactic polypropylene. ¹³C NMR spectroscopy has revealed that the syndiotacticity arises from a chain-end control mechanism. Substitutions on the phenoxy–imine ligands have substantial effects on both ethylene and propylene polymerization behavior of the complexes. In particular, the steric bulk of the substituent ortho to the phenoxy–oxygen is fundamental to obtaining high activity and high molecular weight for ethylene polymerization and high syndioselectivity for the chain-end controlled propylene polymerization. The highest ethylene polymerization activity, 3240 kg/mol-cat h, exhibited by a complex having a t-butyl group ortho to the phenoxy–oxygen, represents one of the highest reported to date for Ti-based non-metallocene catalysts. Additionally, the polypropylene produced exhibits a T_m, 140 °C, and syndioselectivity, rrrr 83.7% (achieved by a complex bearing a trimethylsilyl group ortho to the phenoxy–oxygen) that are among the highest for polypropylenes produced via a chain-end control mechanism. Hence, the bis(phenoxy–imine)Ti complexes are rare examples of non-metallocene catalysts that are useful for the polymerization of not only ethylene but also propylene.     

Chalcogenide based all-solid-state thin electroplated ion-selective membrane for Hg(II) flow-injection determinations

The response to Hg(II) of a thin all-solid-state Te-doped silver chalcogenide membrane, described by the general formula Ag₂ + δSe_{1 − x}Te_x, which has been electrochemically prepared following a previously proposed approach, has been investigated. The kinetics of formation of the membrane's secondary dynamic response to Hg(II) has been successfully combined with the precise timing and transient signal, typical for flow-injection (FI) measurements, in developing a sensitive and reliable mercury FI detector. Under optimized stream conditions it exhibits a linear Nernstian response, with a double slope of the calibration graph of 59 mV dec⁻¹, over the mercury(II) concentration range 10⁻⁶ − 10⁻³ M, the typical sample throughput amounting to about 70 samples per hour. The observed chemical amplification of the signal is due to the specificity of the processes dominating the initial step in formation of the steady-state signal of the membrane to mercury. The analytical performance of the Hg(II) FI detector, as regards sensitivity, reproducibility, selectivity and long-term stability has been thoroughly investigated. The exact procedure for membrane electrodeposition is given and the potential of the proposed approach as a cost-effective way for preparing chalcogenides of unique structure and properties has been outlined in the above context.     

Cobalt Determination by Means of Flow Injection On-line Sorbent Preconcentration-Flame Atomic Absorption Spectrometry with 1-Nitroso-2-naphthol as a Complexing Reagent

The suitability of 1-nitroso-2-naphthol(NN) as a complexing agent for on-line preconcentration of cobalt eluted on the C_(18) microcolumn by means of the FI-FAAS system was tested. Various parameters affecting the complex formation and its elution were optimized. A 2.3×10~(-3) mol/L reagent solution and the aqueous sample solution acidified with 0.1％ (volume fraction) nitric acid were on-line mixed (6.4 mL/min) on a reaction coil set at (65±1)℃ and flowed through the microcolumn for 30 s. The pH of the mixed solution was adjusted to 3—4 with HNO_3(1 mol/L) or NaOH(1 mol/L). The adsorbed complexes in the microcolumn were eluted into the nebulizer of FAAS in 10 s with ethanol acidified with 1％ HNO_3(3.0 mL/min). A good precision(1.6％ for 100μg/L Co(Ⅱ), n=10), a high enrichment factor 17.2, with detection limit (3σ) 3.2μg/L, and sample throughput (90 h~(-1)) were obtained. The method was applied to the certified reference materials(CRMs), NBS-362 and NBS-364, for the determination of cobalt and the results were in good agreement with the certified values.     

N(2,2,0)代数的(∈,∈Vq_(λ,μ))-模糊关联理想若干性质

对N(2,2,0)代数(∈,∈∨q_((λ,μ)))-模糊关联理想若干性质进行了详细的研究.首先,运用点态化的方法证明了(∈,∈∨q_((λ,μ)))-模糊关联理想的同态像与同态原像的基本性质;其次,研究了(∈,∈∨q_((λ,μ)))-模糊关联理想的直积;最后,讨论了(∈,∈∨q_((λ,μ)))-模糊关联理想的直积的投影子集.     

良序套张量积的代数中的强不可约算子

设Ｈ为复的可分无限维Ｈｉｌｂｅｒｔ空间，称有界线性算子Ｔ为强不可约的，如果与Ｔ可交换的幂等算子只有０和Ｉ．王宗尧、蒋春澜、纪有清等人证明了在任何一个套的套代数中都存在大量的强不可约算子，并且找到了它们的酉轨道闭包．本文考虑有限个套的张量积的代数中强不可约算子的存在性问题。证明了：对复平面上任何一个连通完备集σ、总存在一个对角算子Ｎ和它的一个范数可以任意小的紧摄动Ｔ＝Ｘ＋Ｋ，使得Ｔ是一个强不可约算子、Ｔ在有限个良序套的张量积的代数中，并且σ（Ｔ）＝σｌｒｅ（Ｔ）＝σ（Ｎ）＝σｌｒｅ（Ｎ）＝σ进一步，文章还对具有单点谱的算子和良序套与正交补为良序套的张量积的代数进行了讨论，得到了一些结果．     

剩余格与正则剩余格的特征定理

本文进一步研究了具有广泛应用的一类模糊逻辑代数系统——剩余格，并引入了正则剩余格的概念，对剩余格与正则剩余格的定义进行了讨论，给出了剩余格与正则剩余格的特征定理，其中包含剩余格与正则剩余格的等式特征，从而这两个格类都构成簇．本文还讨论了剩余格与正则剩余格公理系统的独立性，以及它们与相近代数结构的关系．