A Note on Purely Imaginary Roots of Generalized Kac–Moody Algebras

Abstract

In this paper, we generalize the concept of purely imaginary roots of Kac–Moody algebras to generalized Kac–Moody algebras. Also we give a complete classification of those generalized Kac–Moody algebras with the purely imaginary property. We also define a new class of indefinite non-hyperbolic generalized Kac–Moody algebras called extended hyperbolic generalized Kac–Moody algebras and find that it does not always possess the purely imaginary property whereas the extended hyperbolic Kac–Moody algebras possess the purely imaginary property.     

Discriminants of polynomials related to Chebyshev polynomials: The “Mutt and Jeff ” syndrome

The discriminants of certain polynomials related to Chebyshev polynomials factor into the product of two polynomials, one of which has coefficients that are much larger than the other?s. Remarkably, these polynomials of dissimilar size have “almost” the same roots, and their discriminants involve exactly the same prime factors.     

Subelliptic estimates on compact semisimple Lie groups

In this paper, we consider a natural subelliptic structure in semisimple, compact and connected Lie groups, and estimate the constant in the so-called subelliptic Friedrichs-Knapp-Stein inequality, which has implications in the regularity theory of p-energy minimizers.     

Characterization of mercury species in soils by HPLC-ICP-MS and measurement of fraction removed by diffusive gradient in thin films

The properties and behaviour of Hg depend on both the oxidation state and the chemical form: the bioavailability, toxicity, persistence and accumulation of mercury in the food web are strongly influenced by chemical speciation. The present work aims to determine the chemical forms of mercury present in soil and to evaluate the fraction of mercury in soil solution available to plants. In order to do this, we analyzed eight samples of contaminated soils with Hg concentrations ranging from 1.31 to 21.7 mg kg⁻¹, collected from different depths (0–10 and 40–50 cm) close to an abandoned industrial site in Val Basento (southern Italy). Two innovative analytical techniques were used: HPLC–ICP-MS and diffusive gradient in thin films (DGT). The analytical procedure was validated using ERM 580-certified sediment and spiked samples in the case of HPLC–ICP-MS, and by a performance test in the case of DGT. In all samples, the only species found in soil and soil solution was MeHg⁺ and Hg²⁺. In soil, the MeHg⁺/Hg_tot ratio ranged from 0.05% to 0.82%; total mercury in soil solution was less than 0.01% of total mercury in soil. The percentage of MeHg⁺ in soil solution varied considerably (from 0% to 50%), with a maximum concentration of 0.02 mg L⁻¹. The root available concentration evaluated by DGT is comparable to the total mercury content of the soil solution measured by HPLC–ICP-MS. The DGT results suggest that all mercury in solution is available for uptake in DGT, and that mercury is supplied from soil to solution. However, for all samples the soluble and root available (DGT-labile) fractions of mercury are generally very low with respect to the total mercury concentration. This study confirmed that both HPLC–ICP-MS and DGT techniques are suitable tools for the estimation of Hg root availability and in assessing the risk from contaminated soils.     

The answer depends on your lecturer

This article is concerned with the approaches to the root concept that lecturers in calculus, linear algebra and complex analysis employ in their instruction. Three highly experienced university lecturers participated in the study. In the individual interviews the participants referred to roots of real numbers, roots of complex numbers, roots as real functions and roots as complex functions. However, participants’ approaches to the root concept were mathematically not equivalent and the lecturers resisted to the approaches of their peers. The choices of approach were shaped by different types of pedagogical considerations, such as the mathematical ideas that appear in the courses that lecturers teach, textbook approaches and lecturers’ interpretations of students’ further academic needs. Several cases were indicated where the participants consciously compromised mathematical rigour and limited the scope of their instruction when teaching general mathematics courses.     

统计方法校正O3LYP方法计算的生成热

由于引入各种内在近似, 密度泛函理论存在固有误差. 本文采用O3LYP/6-311+G(3df, 2p)//O3LYP/6-31G(d)计算了220个中小型有机分子的生成热(Δ_fH_calc^Θ), 随后应用神经网络(ANN)和多元线性回归(MLR)方法对Δ_fH_calc^Θ进行校正. 采用计算得到的生成热、零点能、分子中原子总数、氢原子个数、双中心成键电子数、双中心反键电子数、单中心价层孤对电子数、单中心内层电子数作为ANN和MLR的描述符. 以180个分子作为训练集构造ANN或MLR模型, 并对40 个独立测试集分子的Δ_fH_calc^Θ进行了预测. 结果表明: 经过ANN和MLR校正后,训练集分子生成热的理论计算值和实验值间的均方根偏差(RMSD)从24.7 kJ·mol^-1分别降低到11.8、13.0 kJ·mol^-1; 独立测试集分子的RMSD从21.3 kJ·mol^-1分别降低到10.4、12.1 kJ·mol^-1. 因此ANN模型的拟合和预测能力要明显优于MLR模型.     

复方板蓝根颗粒化学成分的质谱研究

利用电喷雾多级串联质谱(ESI-MSn)和傅里叶变换离子回旋共振质谱(FT-ICR-MS)技术,对复方板蓝根颗粒经溶剂萃取后的95%(体积分数)醇提和水提部位的化学成分进行了系统研究,鉴定出多种氨基酸成分、糖及其衍生物、有机酸、氨基酸和单糖的梅拉德反应初级产物以及含硫化合物表告依春.该方法灵敏快速,适宜于中药提取物的化学成分分析.     

基于主根横断面近红外光谱的西洋参和人参鉴别研究

为了快速准确进行西洋参和人参的品种鉴别,从主根横断面入手,采集其横断面的近红外光谱,分别从物理结构因素和化学因素方面对光谱进行了分析,选定特定波段进行物理因素主导建模、化学因素主导建模、理化因素综合建模,并对三种建模结果进行比较分析,发现三种模型判别率都在96%以上,都能很好的满足批量原材料快速检测的需求。物理因素模型运算简单,但判别率相对低。化学因素判别率较高,但运算量大。理化因素综合模型判别率最高为100%,无需预处理,运算量小,效果最理想,该结果说明近红外定性判别中物理结构因素有时也发挥重要作用。横断面鉴别法准确、便捷,可实际应用于企业原料药材的质量控制,实现对原料药材的快速筛查。     

High quality YBCO superconductive thin films fabricated by laser molecular beam epitaxy

High quality YBa₂.Cu₃O_{6 +x}(YBCO) superconductive thin films have been fabricated on the SrTiO₃(100) substrate using laser molecular beam epitaxy (laser-MBE). The active oxygen source was used, which made the necessary ambient oxygen pressure be 2–3 orders lower than that in pulsed laser deposition (PLD). T_c0 is 85–87 K, and J_c, 1.0 × 10⁶ A/cm². Atomic force microscopy (AFM) measurements show that no obvious particulates can be observed and the root mean square roughness is 7.8 nm. High stability DC superconducting quantum interference devices (DC-SQUID) was fabricated using this YBCO thin film.