Periods of generalized Fermat curves

Let $k,n\ge 2$ be integers. A generalized Fermat curve of type $(k,n)$ is a compact Riemann surface S that admits a subgroup of conformal automorphisms $H\le \text{Aut}(S)$ isomorphic to ${\mathbb{Z}}_k^n$, such that the quotient surface $S/H$ is biholomorphic to the Riemann sphere $\stackrel{?}{\mathbb{C}}$ and has $n+1$ branch points, each one of order k. There exists a good algebraic model for these objects, which makes them easier to study. Using tools from algebraic topology and integration theory on Riemann surfaces, we find a set of generators for the first homology group of a generalized Fermat curve. Finally, with this information, we find a set of generators for the period lattice of the associated Jacobian variety.     

Lamb波频域逆散射全聚焦成像方法研究

Lamb波因其传播距离远、衰减小常被用于板状结构的无损检测中,在基于Lamb波损伤检测的诸多成像技术中,全聚焦方法(Total Focus Method,TFM)方法因其成像分辨率高、信噪比高而受青睐。然而Lamb波的频散效应导致时域延时量不能被准确计算,进而影响传统TFM方法对损伤定位及成像的精度;此外,既有的TFM方法仅以回波幅值作为成像指标,忽略了Lamb波与损伤的相互作用,故而不能通过损伤表面的物理参数增强成像质量。针对这两个问题,本文首先在时域TFM基础上发展了频域TFM,在计算中纳入频散关系以规避频散的影响;其次以包含明确的损伤特征参数--反射率为成像指标,结合频域TFM方法建立损伤逆散射模型,以实现对损伤的准确成像。仿真和实验结果表明:频域逆散射TFM成像方法能够实现对铝板结构中的损伤检测,在工程实践中具有应用价值。     

Parabolic subgroups in FC-type Artin groups

Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results of Cumplido, Gebhardt, Gonzales-Meneses and Wiest, known only for parabolic subgroups of finite type Artin groups, to parabolic subgroups of FC-type Artin groups. We show that the class of finite type parabolic subgroups is closed under intersection. We also study an analog of the curve complex for mapping class group constructed by Cumplido et al. using parabolic subgroups. We extend the construction of this complex, called the complex of parabolic subgroups, to FC-type Artin groups. We show that this simplicial complex is, in most cases, infinite diameter and conjecture that it is δ-hyperbolic.     

Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

Salt Metathesis: Tetrafluoroborate Anion Rapidly Fluoridates Organoboronic Acids to give Organotrifluoroborates

Tetrafluoroborate (BF₄⁻) has long been used as a spectator counter anion. Herein, we report an unprecedented salt metathesis between a variety of BF₄⁻ salts and a series of organoboronic acids yielding the corresponding organotrifluoroborates. We identified conditions for fast and efficient fluoridation (<1 h) with minimal workup. Fundamentally, this work discloses the proclivity of BF₄⁻ to exchange fluoride atoms with organoboronates, highlighting the lability of BF₄⁻.     

Dopant-free NiOx Nanocrystals: A Low-cost and Stable Hole Transport Material for Commercializing Perovskite Optoelectronics

Advancing inverted (p-i-n) perovskite solar cells (PSCs) is critical for commercial applications given their compatibility with different bottom cells for tandem photovoltaics, low-temperature processability (≤100 °C), and promising operational stability. Although inverted PSCs have achieved an efficiency of over 25 % using doped or expensive organic hole transport materials (HTMs), their synthesis cost and stability still cannot meet the requirements for their commercialization. Recently, dopant-free and low-cost non-stoichiometric nickel oxide nanocrystals (NiO_x NCs) have been extensively studied as a low-cost and effective HTM in perovskite optoelectronics. In this minireview, we summarize the synthesis and surface-functionalization methods of NiO_x NCs. Then, the applications of NiO_x NCs in other perovskite optoelectronics beyond photovoltaics are discussed. Finally, we provide a perspective for the future development of NiO_x NCs for the commercialization of perovskite optoelectronics.     

Self-Accelerating Diels–Alder Reaction for Preparing Polymers of Intrinsic Microporosity

It is a formidable challenge in polycondensation to simultaneously construct multiple covalent bonds to prepare double-stranded polymers of intrinsic microporosity (PIMs) with fused multicyclic linkages. To the best of our knowledge, this is the first study to develop a self-accelerating Diels–Alder reaction for successfully preparing double-stranded PIMs with fused multicyclic backbone structures. A self-accelerating Diels–Alder reaction was developed based on the [4+2] cycloaddition of sym-dibenzo-1,5-cyclooctadiene-3,7-diyne (DIBOD) and ortho-quinone compounds. In this reaction, the cycloaddition of ortho-quinone with the first alkyne of DIBOD activates the second alkyne, which reacts with ortho-quinone at a rate constant 192 times larger than that of the original alkyne. Using this self-accelerating reaction to polymerize DIBOD and spirocyclic/cyclic difunctional ortho-quinone monomers, a novel stoichiometric imbalance-promoted step-growth polymerization method was developed to prepare PIMs. The resultant PIMs possess intrinsic ultramicropores with pore sizes between 0.45 to 0.7 nm, high specific surface areas above 646 m² g⁻¹, and good H₂ separation performance.     

Multidisciplinary green approaches (ultrasonic,co-precipitation,hydrothermal, and microwave) for fabrication and characterization of Erbium-promoted Ni-Al2O3 catalyst for CO2 methanation

The dispersion of nickel catalysts is crucial for the catalytic ability of CO₂ methanation, which can be influenced by the fabrication method and the operation process of the catalysts. Therefore, a series of fabrication methods, including ultrasonic, hydrothermal, microwave, and co-precipitation, have been applied to prepare 25Ni-5Er-Al₂O₃ catalysts. The fabrication method can partially influence the structural and catalytic activity of the nickel aluminate catalysts. Among the catalysts modified by Erbium prepared with various methods, the catalyst fabricated by ultrasonic pathway exhibited better catalytic performance and CH₄ selectivity especially, at a temperature (400 ℃). The impact of the temperature of the reaction (200–500 °C) was examined under a stoichiometric precursor ratio of (H₂:CO₂) = 4: 1, atmospheric pressure, and space velocity (GHSV) of 25000 mL/gcath. The results demonstrate that the ultrasonic method is strongly efficient for fabricating Ni-based catalysts with a high BET surface area of about 190.33 m²g^?1. The catalyst composed via the ultrasonic technique has 69.38 % carbon dioxide conversion and 100 % methane selectivity at 400 °C for excellent catalytic performance in CO₂ methanation reactions. The fabrication effect can be associated with its high surface area, which is achieved via the hot spot mechanism. Besides, the addition of Erbium promotes the Ni dispersion on the supports and stimulates the positive reaction because of the erbium oxygen vacancies.     

涡旋提取-改进BCR法测定土壤中重金属的化学形态

土壤中重金属的化学形态更能表明其迁移性和生物毒性。传统的重金属化学形态检测方法BCR法由于其提取时间长,影响检测效率。采用涡旋提取对传统BCR法进行方法优化,对土壤中Cu、Zn、Pb、Cd、Ni、Cr等6种重金属元素化学形态进行了实验分析。研究了涡旋转速、涡旋时间以及涡旋提取的方法精密度与准确度。结果表明,当涡旋转速为2500rpm,酸可交换态涡旋10min,可还原态涡旋10min,可氧化态涡旋5min时,涡旋提取效果良好。采用土壤标准物质对方法的适用性进行了验证,6种元素的检出限在0.4?32μg/kg,测定值均在标准值范围内,相对标准偏差在0.3%?5.5%之间。涡旋提取-改进BCR法分析速度快,灵敏度高,能满足同时测定土壤中多种金属元素化学形态的检测要求。     

重量法测定土壤水溶性盐总量的优化

土壤水溶性盐是表征土壤盐碱化程度的重要指标,也是评价耕地地力的重要参数,被纳入第三次全国土壤普查（“三普”）监测指标体系中。重量法是测定土壤水溶性盐总量的最常用方法,其测定过程易受多种因素影响,导致其测定结果不准。鉴于此,本文设计试验分别验证了水溶性盐浸提和浸提液固液分离这两个过程对测定结果的影响,结果表明浸提液固液分离是影响土壤水溶性盐总量测定准确度和精密度的主要因素。基于此进一步探究4种不同固液分离方式（布氏漏斗过滤、滤膜真空抽滤、离心、滤纸组合过滤）对测定结果的影响,结果表明相较于其它方式,滤纸组合过滤测定结果准确度高,适用于土壤水溶性盐总量的测定。对改进后的重量法测定土壤水溶性盐总量进行方法学确认,结果表明其检出限为0.01 g/kg,测定下限为0.04 g/kg;方法的准确度和精密度、适用范围等均符合相关要求。本文推荐的土壤水溶性盐总量测定方法为：土壤样品采用1:5土水比浸提,180 r/min振荡3 min,浸提液采用滤纸组合自然过滤;其测定结果的准确度和精密度符合相关要求。本文旨在为“三普”内业检测提供参考和借鉴,为全面摸清不同区域土壤水溶性盐含量水平及土壤盐渍化程度提供技术支撑。