In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,...In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.展开更多
The study integrates both the geological and geophysical mapping techniques for groundwater potential studies at Ekwegbe-Agu and the environs, Enugu state, Nigeria for optimal citing of borehole. Located in the Anambr...The study integrates both the geological and geophysical mapping techniques for groundwater potential studies at Ekwegbe-Agu and the environs, Enugu state, Nigeria for optimal citing of borehole. Located in the Anambra Basin between latitudes 6˚43'N and 6˚47'N and longitudes 7˚28'E and 7˚32'E, it is stratigraphycally underlain by, from bottom to top, the Enugu/Nkporo, Mamu and Ajali Formation respectively, a complex geology that make citing of productive borehole in the area problematic leading to borehole failure and dry holes due to inadequate sampling. The study adopted a field and analytic sampling approach, integrating field geological, electrical resistivity and self-potential methods. The software, SedLog v3.1, InterpexIx1Dv.3, and Surfer v10 were employed for the data integration and interpretation. The result of the geological field and borehole data shows 11 sedimentary facies consisting of sandstone, shales and heterolith of sandstone/shale, with the aquifer zone mostly prevalent in the more porous sand-dominated horizons. Mostly the AK and HK were the dominant curve types. An average of 6 geo-electric layers were delineated across all transects with resistivity values ranging from 25.42 - 105.85 Ωm, 186.38 - 3383.3 Ωm, and 2992 - 6286.4 Ωm in the Enugu, Mamu and Ajali Formations respectively. The resistivity of the main aquifer layer ranges from 1 to 500 Ωm. The aquifer thickness within the study area varies between 95 and 140 m. The western and northwestern part of the study area which is underlain mainly by the Ajali Formation showed the highest groundwater potential in the area and suitable for citing productive boreholes.展开更多
文摘背景:腰椎小关节炎是引起下腰痛的一个主要原因,目前主要依靠MRI进行初步定性诊断,但仍有一定漏诊、误诊的概率发生,因此MR T2^(*)mapping成像技术有望成为定量检查腰椎小关节炎软骨损伤的重要检测手段。目的:探讨MR T2^(*)mapping成像技术在定量分析腰椎小关节炎软骨损伤退变中的应用价值。方法:收集南京医科大学第四附属医院2020年4月至2022年3月门诊或住院合并下腰痛共110例患者,设为病例组;同时招募无症状志愿者80例,设为对照组。对所有纳入对象L1-S1的小关节行3.0 T MR扫描,获取T2^(*)mapping横断位图像和T2WI图像,分别对所有小关节软骨进行Weishaupt分级及T2^(*)值测量,收集数据并行统计学分析。不同小关节Weishaupt分级之间小关节软骨T2^(*)值比较采用单因素方差分析。结果与结论:①经统计分析发现,病例组腰椎小关节软骨T2^(*)值(17.6±1.5)ms明显较对照组(21.4±1.3)ms降低,差异有显著性意义(P<0.05);②在病例组中,随着腰椎小关节Weishaupt分级增加,小关节软骨T2^(*)值也呈逐渐下降趋势,且这种差异有显著性意义(P<0.05);③提示T2^(*)mapping能够较好地显示腰椎小关节软骨损伤的早期病理变化,腰椎小关节软骨的T2^(*)值能够定量评估腰椎小关节的软骨损伤程度;T2^(*)mapping成像技术能为影像学诊断腰椎小关节炎软骨早期损伤提供很好的理论依据,具有重要的临床应用价值。
基金supported by the Natural Science Foundation of Guangdong Province(2021A1515010058)。
文摘In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.
文摘The study integrates both the geological and geophysical mapping techniques for groundwater potential studies at Ekwegbe-Agu and the environs, Enugu state, Nigeria for optimal citing of borehole. Located in the Anambra Basin between latitudes 6˚43'N and 6˚47'N and longitudes 7˚28'E and 7˚32'E, it is stratigraphycally underlain by, from bottom to top, the Enugu/Nkporo, Mamu and Ajali Formation respectively, a complex geology that make citing of productive borehole in the area problematic leading to borehole failure and dry holes due to inadequate sampling. The study adopted a field and analytic sampling approach, integrating field geological, electrical resistivity and self-potential methods. The software, SedLog v3.1, InterpexIx1Dv.3, and Surfer v10 were employed for the data integration and interpretation. The result of the geological field and borehole data shows 11 sedimentary facies consisting of sandstone, shales and heterolith of sandstone/shale, with the aquifer zone mostly prevalent in the more porous sand-dominated horizons. Mostly the AK and HK were the dominant curve types. An average of 6 geo-electric layers were delineated across all transects with resistivity values ranging from 25.42 - 105.85 Ωm, 186.38 - 3383.3 Ωm, and 2992 - 6286.4 Ωm in the Enugu, Mamu and Ajali Formations respectively. The resistivity of the main aquifer layer ranges from 1 to 500 Ωm. The aquifer thickness within the study area varies between 95 and 140 m. The western and northwestern part of the study area which is underlain mainly by the Ajali Formation showed the highest groundwater potential in the area and suitable for citing productive boreholes.
