关于单位分数问题

设正整数p≥1,a1≥2,利用递推关系,将分数p+1pa1分拆成n个单位分数之和,并且给出分数1a和整数1分拆成n个单位分数之和的几种方法.     

一类分式序列封闭形和式

利用反正切函数关系arctan F（n）-arctan F（n＋1）=arctan （F（n）-F（n＋1））/（1＋F（n）F（n＋1））得到一类反正切序列封闭形和式,利用微分法得到一类分式序列封闭形和式,并给出反正切级数与分式级数恒等式.     

1990-2020年天津市植被覆盖度时空演变特征及影响因素分析

植被覆盖度(FVC)是区域生态环境质量的重要参数,揭示长时序FVC时空分异特征及识别主导影响因子可为评估地表植被状况提供科学参考。以天津市为例,基于Google Earth Engine(GEE)云平台的1990—2020年Landsat遥感影像,结合像元二分模型计算FVC。运用一元线性回归、F检验进行FVC时空演变趋势分析,利用变异系数、Hurst指数分析FVC波动情况及未来变化趋势。在此基础上,应用随机森林(RF)模型的特征重要性排序、偏依赖图技术量化FVC与同期的气候因素(年均气温、年降水量)和人类活动因素(土地利用、人口密度)的非线性响应关系,并进一步分析多因素耦合对FVC空间分布的解释力度。结果表明：(1)在时间上,1990—2020年天津市FVC呈显著下降趋势,变化率为0.001 5(p<0.05),其中1990—2012年FVC显著降低,2012年后变化趋势不显著(p>0.05)。不同等级FVC时序差异明显,低、中低和中植被覆盖比例均呈现显著增加趋势(p<0.05),而中高和高植被覆盖比例一致表现为显著降低(p<0.05)。(2)在空间上,1990...     

Fine earth soil bulk density at 0.2 m depth from Land Use and Coverage Area Frame Survey (LUCAS) soil 2018

Soil Bulk Density (BD) is an extremely important variable because it is an important site characterization parameter, and it is highly relevant for policy development because it is mandatory for calculating soil nutrient stocks. BD can influence soil chemical properties, land-use planning and agronomic management. The 2018 Land Use and Coverage Area Frame Survey (LUCAS) saw the unprecedented collection of BD core analysis in a subset of the locations in Europe and the United Kingdom where soil physical and chemical properties were analysed in the 2009 and the 2015 sampling campaigns. Here, we integrated the LUCAS 2018 BD sampling campaign with the mass fraction of coarse fragments previously determined in LUCAS 2009–2015 in order to provide a dataset of the volume fraction of coarse fragments and the BD of the fine earth and improve soil organic carbon (SOC) stock estimation accuracy for topsoil. BD data sampled at 0–10 and 10–20 cm were averaged to harmonize the BD with the mass fraction of coarse fragments measured in 2009, 2012 and 2015. Samples were from cropland, grassland and woodland soils, which accounted for 41%, 21% and 30%, respectively, of the total number of selected sites (n = 6059); ‘bareland’, and ‘shrubland’ accounted for 3% of the sites each, whereas ‘artificial land’ accounted for <1%. Only six samples were classified as ‘wetland’. The dataset was produced assuming the mass density of the coarse fraction to be constant across all LUCAS soil samples. We also estimated the SOC stocks associated with LUCAS 2018 BD and SOC content measurements and showed that correcting the BD by the coarse mass fraction instead of the coarse volume fraction generates SOC stock underestimation. We found the highest deviations in woodlands and shrublands. We showed that, when SOC stock is computed with coarse mass fraction, the error compared with the computation by volume may vary depending on the SOC and coarse mass fraction. This may imply a SOC stock underestimation for European soils. This dataset fits into the big framework of LUCAS soil properties monitoring and contributes both to soil awareness and soil research and assessments, which are two important objectives of the Soil Strategy and the European Soil Observatory (EUSO).     

Autologous point‐of‐care cellular therapies variably induce equine mesenchymal stem cell migration,proliferation and cytokine expression

Reasons for performing study: Autologous cellular therapy products including adipose‐derived stromal vascular fraction (SVF), bone marrow mononuclear cells (BMMNs), cord blood mononuclear cells (CBMNs) and platelet rich plasma are options for treatment of acute orthopaedic lesions while mesenchymal stem cells (MSCs) are culture expanded. These products may contribute to healing by secreting matrix proteins or growth factors, but they may also act on endogenous MSCs to facilitate healing. Objectives: To determine the effects of cell therapy products on MSCs function in vitro. The hypothesis was that cell therapy products promote MSCs functions including proliferation, migration and mediator release. Methods: Fat, bone marrow (BM), cord blood and platelets were obtained from 6 Quarter Horses. The BM‐MSCs and their autologous cell therapy products were co‐incubated in transwells. Mesenchymal stem cells proliferation, migration, gene expression and cytokine concentrations were determined. Results: All cell therapy products increased MSCs proliferation, but SVF induced significantly more proliferation than any other product. Also SVF elicited more MSCs chemotaxis and, along with BMMNs, significantly more MSCs chemoinvasion. Cord blood mononuclear cells stimulated MSCs to produce high concentrations of interleukin‐6 (IL‐6), transforming growth factor‐β1 (TGF‐β1), and prostaglandin E₂ (PGE₂). Stromal vascular fraction and platelet lysate did not stimulate MSCs but SVF and platelet lysate themselves contained high concentrations of PGE₂ and IL‐6 (SVF) and TGF‐β1 (platelet lysate). Conclusions: Autologous cell products variably stimulate MSCs functions with 2 primary patterns apparent. Products either contained preformed mediators that may have intrinsic healing function, or products stimulated MSCs to secrete mediators. Potential relevance: The specific clinical indications for these products may differ to include administration as a sole treatment modality prior to MSCs injection for intrinsic cell and cytokine activity (i.e. SVF) or administration concurrently with MSCs to activate MSCs for treatment of chronic lesions (i.e. CBMNs).     

Characterization of the perylenequinone pigments in Japanese Andosols and Cambisol

The green fraction of humic acid (Pg) and the chloroform-extractable green fraction (CEGF) are characteristic soil organic matter (SOM) components. These alkaline solutions are green-colored due to the presence of 4,9-dihydroxyperylene-3,10-quinone (DHPQ) chromophore. While both of which are potential indicators for the effect of land use and paleoclimatic environment in the fields of soil science as well as geochemistry, CEGF as well as its relationship with Pg in soils are not yet fully documented. In this study, we firstly investigated the chemical properties of soil CEGF fractions by ultraviolet–visible (UV–Vis) and infrared (IR) method. Two CEGF components were separated by sequential liquid-liquid extraction using aqueous ammonium hydroxide (NH₄OH) followed by aqueous sodium hydroxide (NaOH). Results showed that the UV–Vis spectral shape of NH₄OH-extractable component is very similar to that of DHPQ, except that it is red-shifted. The solubility and UV–Vis spectrum of the NaOH-extractable fraction were completely identical with those of synthesized DHPQ. Their IR spectral shapes were also almost the same. Subsequently, the distribution of CEGF in humic acid (HA), fulvic acid (FA) and humin (HN) from Japanese Andosols and Cambisol was quantitatively evaluated by sequential extraction. Most of CEGF was detected in the HA (60–78%) and HN (22–40%), but not in the FA. While the UV–Vis spectral shape of CEGF extracted from Andosols HAs showed a relatively higher proportion of DHPQ than its derivative, the opposite was observed in Cambisol HA, whose CEGF is similar to that of sclerotium grain (one of the possible origin of CEGF). These results suggest the diversity of CEGF-producing soil fungi. Quantitative data also indicated that 35–49% of Pg consisted of a chloroform-soluble fraction (i.e., CEGF) and the remaining 51–65% of Pg was chloroform-insoluble. Based on these results, we propose that CEGF is composed of DHPQ and DHPQ-derivatives and that CEGF is one of the major fractions of Pg.     

Kinetics of Ligand-Controlled Release of Zinc in Acid Sulfate Paddy Soils

The elevated solubility of zinc(Zn) in acid sulfate paddy soils can limit rice production and pose a risk of environmental pollution.However, little attention has been paid to the ligand-controlled release of Zn in these soils. Here we quantified the rate of ligandcontrolled Zn release in Thai acid sulfate paddy soils, using ethylenediaminetetraacetic acid as the extractant. Sequential extractions were performed to obtain quantitative information on Zn fractions contributing to the ligand-controlled mechanisms. The amount of Zn released within 192 h varied significantly(8–43 mg kg~(-1)), which corresponded to 12%–40% of the total soil Zn, indicating that Zn solubility in most soils was relatively low and that Zn mainly occurred as residual phases. The kinetics of Zn release was well described by the power function model(r = 0.65–0.99, median = 0.87). The magnitude of initial Zn release(coefficient a) was significantly(P 0.05) related to the aqua regia-soluble Zn. Easily mobile Zn, organically bound Zn, and Zn associated with Fe and Mn oxides also contributed to the ligand-controlled release mechanisms to various degrees. Our results provide a systematic understanding of Zn fractions and release from acid sulfate paddy soils, the dynamics of which have a significant influence on the availability, phytoextraction, and mobility of Zn in terrestrial and engineered environments.     

离心泵作透平固液两相流动及磨损的数值模拟

为研究离心泵作透平内部固液两相流动特性,基于Euler-Lagrange模型,应用ANSYS CFX软件对一比转数为82的离心泵作透平进行数值计算,分别模拟颗粒直径为0.1,0.3,0.5 mm及初始体积分数为5%,10%,15%的9组不同工况,以揭示介质中固体颗粒对离心泵作透平运行的影响.计算结果表明:固体颗粒主要分布在叶片吸力面头部、前盖板壁面附近以及蜗壳尾部区域;当固体颗粒质量分数不变时,随着粒径的增大,叶片表面固相体积分数增大,叶片吸力面轮缘处出现了大量颗粒堆积,透平的扬程和功率上升,效率有所下降;当颗粒直径不变时,随着固体颗粒质量分数的增大,固体颗粒在叶轮流道内的分布出现向轮毂处延伸的趋势,堆积区域面积增大,透平的扬程和功率上升,效率变化不大.该研究扩展了液力透平设计方法,可为离心泵作透平设计提供一定的参考.     

Estimation of soil texture from permanent wilting point measured with a chilled‐mirror dewpoint technique

Soil texture is an important factor governing a range of physical properties and processes in soil. The clay and fine fractions of soil are particularly important in controlling soil water retention, hydraulic properties, water flow and transport. Modern soil texture analysis techniques (x‐ray attenuation, laser diffraction and particle counting) are very laborious with expensive instrumentation. Chilled‐mirror dewpoint potentiameters allows for the rapid measurement of the permanent wilting point (PWP) of soil. As the PWP is strongly dictated by soil texture, we tested the applicability of PWP measured by a dewpoint potentiameter in predicting the clay, silt and sand content of humid tropical soils. The clay, silt, and sand content, organic matter and PWP were determined for 21 soils. Three regression models were developed to estimate the fine fractions and validated using independent soil data. While the first model showed reasonable accuracy (RMSE 16.4%; MAE 13.5%) in estimating the clay, incorporating the organic matter into the equation improved the predictions of the second model (RMSE 17.3%; MAE 10.9%). When used on all soil data, the accuracy of the third model in predicting the fine fraction was poor (RMSE 31.9%; MAE 24.5%). However, for soils with silt content greater than 30%, the model prediction was quite accurate (RMSE 7–12%; MAE 7–9%). The models were used to estimate the sand content and soil textures of soils, which proved relatively accurate. The dewpoint potentiometer can serve a dual purpose of rapidly estimating the PWP and the clay, fine fraction, and soil texture of soils in a cost efficient way.