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Petrology of Metaluminous A-Type Rhyolite Discovered from Hadjer el Hamis Volcanoes (Lake Chad Basin)
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作者 Claudial Amane Lagmet Fadimatou Ngounouno Yamgouot +2 位作者 Mama Ntoumbe Abdou Aziz Youpougam Ismaila Ngounouno 《Open Journal of Geology》 2018年第9期883-895,共13页
Metaluminous (P.I. > 1) rhyolite from Hadjer el Hamis consisted of quartz, alkali feldspar, clinopyroxene (hedenbergite), amphibole (F-arfvedsonite) and oxides-hydroxides (ilmenite, magnetite, limonite) phenocrysts... Metaluminous (P.I. > 1) rhyolite from Hadjer el Hamis consisted of quartz, alkali feldspar, clinopyroxene (hedenbergite), amphibole (F-arfvedsonite) and oxides-hydroxides (ilmenite, magnetite, limonite) phenocrysts is characterized by the negative Eu, Ba, P, Sr and Ti anomalies. This metaluminous rhyolite and the early discovered peralkaline rhyolites in Hadjer el Hamis volcanoes derive likely from the same source, according to their coexistence on the same sector and their similar Zr/Nb ratios. The causes of magma heterogeneity are likely linked to varying amounts of extraction of an earlier melt phase or tectonic juxtaposition or a sudden increasing of fO2 in silicic magmas, triggered from a hydrothermal process, associated with F- and alkali-bearing fluids influx, which promoted the enrichment of Na in the hedenbergite rims and the crystallization of arfvedsonite. 展开更多
关键词 METALUMINOUS RHYOLITES Lake Chad PETROLOGY Hadjer el hamis
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球型模糊Hamacher Hamy集成算子及其决策应用 被引量:1
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作者 杨俊 杨志辉 陈黄山 《江西科学》 2023年第4期621-629,共9页
基于对球型模糊Hamacher运算和Hamy均值算子的研究,将Hamacher运算和HM算子综合应用到信息集成当中,提出了球型模糊Hamacher HM算子,球型模糊Hamacher加权HM算子,分别研究其具有的性质,同时给出属性权重的确定方法。最后基于所提算子提... 基于对球型模糊Hamacher运算和Hamy均值算子的研究,将Hamacher运算和HM算子综合应用到信息集成当中,提出了球型模糊Hamacher HM算子,球型模糊Hamacher加权HM算子,分别研究其具有的性质,同时给出属性权重的确定方法。最后基于所提算子提出决策方法来解决球型模糊环境下的多属性决策问题,并通过示例验证所提出方法的可行性和有效性。 展开更多
关键词 球型模糊数 Hamacher Hamy算子 集成算子 多属性决策
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Effects of Meteorological Conditions on Yield and Quality of Facility Hami Melon
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作者 Lei ZHANG Xuemei LYU Peng LENG 《Agricultural Biotechnology》 CAS 2023年第1期16-18,共3页
With different varieties of facility Hami melon(Cucumis melo var. sacchairinus) as test materials, the effects of meteorological conditions on the yield and quality of different varieties of facility Hami melon were a... With different varieties of facility Hami melon(Cucumis melo var. sacchairinus) as test materials, the effects of meteorological conditions on the yield and quality of different varieties of facility Hami melon were analyzed. The results showed that among the yield and quality traits of melon, the variation degree of average single melon weight was the highest, and the coefficient of variation was 33.05%. The variation degree of leaf area index was the lowest, and the coefficient of variation was 11.00%. Through the correlation analysis of meteorological factors with the yield and quality of facility Hami melon, it was found that the quality traits of facility Hami melon were significantly positively correlated with maximum temperature and sunshine duration, and significantly negatively correlated with precipitation. The yield traits were positively correlated with maximum temperature, sunshine duration and precipitation. 展开更多
关键词 Meteorological conditions Facility Hami melon(Cucumis melo var.sacchairinus) YIELD QUALITY
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基于语言图犹豫模糊Hamy平均算子的多属性决策方法
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作者 俞弋峰 杨志辉 《江西科学》 2023年第1期19-27,共9页
将图犹豫模糊集与语言术语集结合,定义了语言图犹豫模糊集和语言图犹豫模糊数的运算,为比较语言图犹豫模糊数的大小,考虑了语言图犹豫模糊数中元素的离散程度对评估结果的影响,定义了得分函数和精确函数,提高了得分函数对语言图犹豫模... 将图犹豫模糊集与语言术语集结合,定义了语言图犹豫模糊集和语言图犹豫模糊数的运算,为比较语言图犹豫模糊数的大小,考虑了语言图犹豫模糊数中元素的离散程度对评估结果的影响,定义了得分函数和精确函数,提高了得分函数对语言图犹豫模糊数的区分能力。结合Hamy平均算子,定义了语言图犹豫模糊Hamy平均算子,研究了语言图犹豫模糊Hamy平均算子的性质,并提出了语言图犹豫模糊Hamy平均算子的多属性决策方法。最后,将其应用于建筑公司原料供应商的选择中,并与现有方法进行对比分析,验证了所提方法的有效性和可行性。 展开更多
关键词 语言图犹豫模糊集 Hamy平均算子 多属性决策 得分函数
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半胱氨酰白三烯受体拮抗剂通过下调自噬减轻长爪沙鼠的全脑缺血再灌注损伤 被引量:6
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作者 石巧娟 郭红刚 +5 位作者 楼琦 卢领群 潘若真 应华忠 周文伟 褚晓峰 《中国实验动物学报》 CAS CSCD 北大核心 2018年第1期57-64,共8页
目的探讨半胱氨酰白三烯受体拮抗剂(普鲁司特、HAMI 3379)对长爪沙鼠全脑缺血再灌注损伤的保护作用及其作用机制。方法采用结扎双侧颈总动脉缺血10 min再灌注24 h,建立长爪沙鼠全脑缺血再灌注损伤模型,随机分为假手术组、模型组、普鲁... 目的探讨半胱氨酰白三烯受体拮抗剂(普鲁司特、HAMI 3379)对长爪沙鼠全脑缺血再灌注损伤的保护作用及其作用机制。方法采用结扎双侧颈总动脉缺血10 min再灌注24 h,建立长爪沙鼠全脑缺血再灌注损伤模型,随机分为假手术组、模型组、普鲁司特、HAMI 3379组,每组20只,术前3 d开始腹腔注射给药,1次/日,术前30 min给药1次。观察再灌注24 h神经症状及功能;尼氏染色法观察皮层及海马区神经元;免疫印迹法检测皮层、海马中自噬相关蛋白beclin-1及LC3的表达情况;电镜观察海马区自噬小体。结果与模型组比较,普鲁司特、HAMI 3379组可提高神经症状评分,减少神经功能损伤,减轻皮层及海马区神经元损伤及丢失,减少自噬相关蛋白beclin-1及LC3的表达及海马区自噬小体的数量。结论半胱氨酰白三烯受体拮抗剂通过下调大脑皮层、海马区的自噬减轻长爪沙鼠全脑缺血再灌注损伤。 展开更多
关键词 长爪沙鼠 全脑缺血 普鲁司特 HAMI 3379 自噬
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考虑多元关联关系和语义变换的直觉不确定语言多属性决策方法 被引量:2
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作者 刘政敏 徐洪雪 +1 位作者 刘培德 梁霞 《运筹与管理》 CSSCI CSCD 北大核心 2021年第2期45-52,共8页
针对属性值为直觉不确定语言变量的多属性决策问题,提出一种不仅可以捕获属性间的多元关联关系并且能够满足决策者不同语义转换需求的多属性决策方法。首先,考虑已有运算法则缺少封闭性和灵活性,结合语言刻度函数,提出一种新的直觉不确... 针对属性值为直觉不确定语言变量的多属性决策问题,提出一种不仅可以捕获属性间的多元关联关系并且能够满足决策者不同语义转换需求的多属性决策方法。首先,考虑已有运算法则缺少封闭性和灵活性,结合语言刻度函数,提出一种新的直觉不确定语言变量运算法则和排序方法。其次,根据新的运算法则,提出可以捕获属性间多元关联关系的直觉不确定语言Hamy平均及其加权形式,并对新算子的优良性质和特例进行了探讨和分析。进而,提出一种新的多属性决策方法。最后,通过算例和对比分析验证了该方法的有效性和优越性。 展开更多
关键词 直觉不确定语言变量 Hamy平均算子 语言刻度函数 多属性决策方法
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关于Hardy平均的一个不等式及其应用 被引量:2
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作者 何晓红 《浙江大学学报(理学版)》 CAS CSCD 北大核心 2015年第2期133-135,141,共4页
根据最值压缩定理,建立了n个正数的Hardy平均、算术平均和几何平均之间的一个不等式.作为应用,得到了关于Hamy平均和k次初等对称函数的2个不等式.
关键词 Hardy平均 Hamy平均 初等对称函数 最值压缩定理
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HAMI 3379抑制自噬减轻BV2细胞缺氧缺糖损伤的机制 被引量:1
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作者 汤利荣 田晔 +5 位作者 齐倩倩 高莉洁 陈建华 王康军 石巧娟 史文珍 《临床医学研究与实践》 2019年第7期1-3,11,共4页
目的探讨HAMI 3379抑制自噬减轻BV2细胞缺氧缺糖损伤的机制。方法随机将对数生长期BV2细胞分为正常对照组、氧糖剥夺(OGD)组和1、10、100 nM HAMI 3379组,然后采用OGD处理对细胞进行造模,培养48 h,采用MTT检测、LDH释放检测及蛋白印记... 目的探讨HAMI 3379抑制自噬减轻BV2细胞缺氧缺糖损伤的机制。方法随机将对数生长期BV2细胞分为正常对照组、氧糖剥夺(OGD)组和1、10、100 nM HAMI 3379组,然后采用OGD处理对细胞进行造模,培养48 h,采用MTT检测、LDH释放检测及蛋白印记检测观察HAMI 3379对OGD处理后BV2细胞活性及自噬的影响。结果与正常对照组比较,1、10、100 nMHAMI 3379组细胞均有明显损伤,且LDH释放增加(P<0.05);而与OGD组比较,给予1 nM HAMI 3379有改善细胞活性趋势,但差异无统计学意义(P>0.05);10、100 nM HAMI 3379可明显增加细胞存活率,减少LDH的释放(P<0.05)。与正常对照组比较,OGD组和10、100 n M HAMI 3379组Beclin-1表达量显著升高(P<0.05);而与OGD组比较,10、100 nM HAMI 3379组的BV2细胞Beclin-1表达量明显降低(P<0.05)。与正常对照组比较,OGD组和10、100 nM HAMI 3379组LC3Ⅱ/Ⅰ表达量显著升高,差异具有统计学意义(P<0.05);与OGD组比较,10、100 nM HAMI 3379组BV2细胞LC3Ⅱ/Ⅰ表达量明显降低(P<0.05)。结论HAMI 3379可改善OGD处理后BV2细胞活性,减少LDH释放,也可降低OGD处理激活的自噬信号分子Beclin-1和LC3的表达,说明HAMI 3379可通过调节自噬信号通路分子部分逆转OGD处理后BV2细胞的损伤。 展开更多
关键词 HAMI3379 缺氧缺糖损伤 自噬 BV2细胞
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关于Hamy平均的一个优化不等式
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作者 何晓红 《安徽大学学报(自然科学版)》 CAS 北大核心 2018年第4期56-60,共5页
关于n个正数的k次Hamy平均σ_n(a,k)=1/C_n^k sum from 1≤i1<…<ik≤n(multiply from j=1 to k a_(ij))^(1/k),利用最值压缩定理,证明了与Hamy平均、算术平均和几何平均有关的一个双向不等式(A_n(a^(1/k)))^(kp)·(G_n(a^(1/... 关于n个正数的k次Hamy平均σ_n(a,k)=1/C_n^k sum from 1≤i1<…<ik≤n(multiply from j=1 to k a_(ij))^(1/k),利用最值压缩定理,证明了与Hamy平均、算术平均和几何平均有关的一个双向不等式(A_n(a^(1/k)))^(kp)·(G_n(a^(1/k)))^(k(1-p))≤σ_n(a,k)≤qA_n(a)+(1-q)G_n(a),其中q=n-k/n-1和p=n-k/kn-k为最佳,从而得到一个较理想的优化不等式. 展开更多
关键词 Hamy平均 优化不等式 最值压缩定理
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Hamy对称函数及其一类不等式
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作者 关开中 《贵州师范大学学报(自然科学版)》 CAS 2001年第1期48-50,共3页
证明了Hamy对称函数是Schur凹函数 ,利用控制不等式理论建立了Hamy对称函数的一类不等式。
关键词 HAMY对称函数 SCHUR凹函 控制不等式理论 SCHUR凸函数 几何-算术不等式 NEWMAM不等式 KLAMKIN不等式
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一类Hamy型对称函数的Schur凸性质 被引量:2
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作者 张涛 白瑞芳 宝音特古斯 《内蒙古民族大学学报(自然科学版)》 2010年第2期133-135,共3页
对称函数的Schur凸性理论的研究是相当活跃的研究课题,有关文献研究了一些对称函数的Schur凸性问题.本文定义了一类新的Hamy对称函数,并研究了该类Hamy对称函数的Schur凸性、Schur几何凸性及Schur调和凸性,得到几个不等式.
关键词 Hamy对称函数 SCHUR凸性 不等式
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OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT FOR A CONSTANT ELASTICITY OF VARIANCE MODEL UNDER VARIANCE PRINCIPLE 被引量:5
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作者 周杰明 邓迎春 +1 位作者 黄娅 杨向群 《Acta Mathematica Scientia》 SCIE CSCD 2015年第2期303-312,共10页
This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance (CEV) model. Assume that the insurer's surplus process follows a jump-diffusion process, the ... This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance (CEV) model. Assume that the insurer's surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer via the variance principle and invest in a risk-free asset and a risky asset whose price is modeled by a CEV model. The diffusion term can explain the uncertainty associated with the surplus of the insurer or the additional small claims. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. This optimization problem is studied in two cases depending on the diffusion term's explanation. In all cases, by using techniques of stochastic control theory, closed-form expressions for the value functions and optimal strategies are obtained. 展开更多
关键词 Constant elasticity of variance Hami!ton-Jacobi-Bellman equation jump-diffusion process exponential utility REINSURANCE
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CysLT2受体拮抗剂HAMI3379抑制LPS诱导小鼠小胶质瘤细胞系的炎性反应
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作者 顾胜龙 李明星 +3 位作者 应苗法 方三华 饶跃峰 赵蕊 《基础医学与临床》 CSCD 2020年第2期145-150,共6页
目的探究半胱氨酰白三烯2(CysLT2)受体拮抗剂HAMI3379对LPS诱导小鼠小胶质细胞(BV-2)炎性反应的调控作用及其可能的作用机制。方法体外培养BV-2,将BV-2分为对照组、LPS(100 ng/mL)组、HAMI3379(0.01、0.1和1μmol/mL)组和LPS+HAMI3379组... 目的探究半胱氨酰白三烯2(CysLT2)受体拮抗剂HAMI3379对LPS诱导小鼠小胶质细胞(BV-2)炎性反应的调控作用及其可能的作用机制。方法体外培养BV-2,将BV-2分为对照组、LPS(100 ng/mL)组、HAMI3379(0.01、0.1和1μmol/mL)组和LPS+HAMI3379组。CCK-8法检测BV-2细胞的增殖;ELISA检测细胞上清液中炎性因子IL-1β、TNF-α、IL-10的含量;Western-blot检测PKCα、IKBα、NF-κB p50和p65蛋白的表达。结果LPS能够激活BV-2细胞,促进其细胞的增殖(P<0.05);显著增加细胞上清液中炎性因子IL-1β、TNF-α的分泌,减少IL-10的分泌(P<0.05);且显著上调PKCα、IKBα、p65蛋白的表达水平(P<0.05)。CysLT2受体拮抗剂HAMI3379能够显著减轻上述变化(P<0.05)。结论CysLT2受体拮抗剂HAMI3379能够抑制LPS激活BV-2细胞,抑制炎性反应,其作用机制可能与抑制PKCα/NF-κB信号通路有关。 展开更多
关键词 CysLT2受体 HAMI3379 炎性反应 PKCα/NF-κB信号通路
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Pythagorean Uncertain Linguistic Variable Hamy Mean Operator and Its Application to Multi-attribute Group Decision Making 被引量:2
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作者 Huidong Wang Shifan He +1 位作者 Chengdong Li Xiaohong Pan 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2019年第2期527-539,共13页
Pythagorean fuzzy set(PFS) can provide more flexibility than intuitionistic fuzzy set(IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper... Pythagorean fuzzy set(PFS) can provide more flexibility than intuitionistic fuzzy set(IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper proposes a new multiattribute group decision making method based on Pythagorean uncertain linguistic variable Hamy mean(PULVHM) operator and VIKOR method. Firstly, we define operation rules and a new aggregation operator of Pythagorean uncertain linguistic variable(PULV) and explore some properties of the operator.Secondly, taking the decision makers' hesitation degree into account, a new score function is defined, and we further develop a new group decision making approach integrated with VIKOR method. Finally, an investment example is demonstrated to elaborate the validity of the proposed method. Sensibility analysis and comprehensive comparisons with another two methods are performed to show the stability and advantage of our method. 展开更多
关键词 Hamy mean(HM) OPERATOR MULTI-ATTRIBUTE group decision making(MAGDM) PYTHAGOREAN fuzzy set PYTHAGOREAN UNCERTAIN LINGUISTIC variable
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Influence of Climatic Conditions on Planting of Hami Melon 被引量:2
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作者 Jiangang WANG Min JIANG +1 位作者 Yuchao LI Guangjun LI 《Asian Agricultural Research》 2018年第2期82-86,共5页
Climate warming has made the planting area of Hami melon expand northward to Barry Bakai Town,Altay City,near 47° N. Climate events often induce the occurrence of pests and diseases in crops,affecting the steady ... Climate warming has made the planting area of Hami melon expand northward to Barry Bakai Town,Altay City,near 47° N. Climate events often induce the occurrence of pests and diseases in crops,affecting the steady production of Hami melon. In 2013,pests and diseases occurred seriously,resulting in low yield and poor quality of Hami melon. Based on the production survey data of Hami melon in recent20 years,the interaction of various meteorological factors in different time and different intervals of various factors was analyzed in this paper to explore the characteristics of the meteorological factors that cause diseases and influence the quality of Hami melon. 展开更多
关键词 Climatic conditions Hami melon PLANTING Impact analysis
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Effect of Different Pretreatments on Explosion Puffing Drying of Hami Melon at Modified Temperature and Pressure in Xinjiang 被引量:2
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作者 Wenting JIA Hui YANG +2 位作者 Hongbin WU Hong WU Xinwen JIN 《Asian Agricultural Research》 2016年第9期64-66,70,共4页
This paper studies the influence of three different pretreatments( blanching,citric acid soaking,and Na Cl soaking) on the moisture content,degree of puffing,color,hardness and crispness of Hami melon under explosion ... This paper studies the influence of three different pretreatments( blanching,citric acid soaking,and Na Cl soaking) on the moisture content,degree of puffing,color,hardness and crispness of Hami melon under explosion puffing drying at modified temperature and pressure in Xinjiang. The results show that using 60 s blanching pretreatment can help to reduce the moisture content of puffed product while maintaining product color; 2. 5% citric acid pretreatment can make products maintain high degree of puffing and crispness,but reduce product color; 2%Na Cl penetrating fluid plays a significant role in maintaining product color,while maintaining crispness. 展开更多
关键词 PRETREATMENT XINJIANG Hami melon Modified temperature and pressure
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The World's Largest Soda-Niter Ore Intensive Region Found in the Turpan–Hami Basin 被引量:1
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作者 Hao Ziguo,Fei Hongcai, Liu Lian 《Acta Geologica Sinica(English Edition)》 SCIE CAS CSCD 2012年第3期789-789,共1页
The Xinjiang Geology and Mineral Resources Exploration and Development Bureau have conducted a detailed investigation project of the Xigobi soda-niter deposit in Hami, Xinjiang Province, which was completed at the end... The Xinjiang Geology and Mineral Resources Exploration and Development Bureau have conducted a detailed investigation project of the Xigobi soda-niter deposit in Hami, Xinjiang Province, which was completed at the end of 2011. The project put much emphasis on research of soda-niter mineralization rules, stratum classification, ore-forming 展开更多
关键词 Hami Basin World The World’s Largest Soda-Niter Ore Intensive Region Found in the Turpan
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Evaluation and analysis on the tourism resources in Hami Region based on GIS mapping technology 被引量:1
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作者 FENG Xian-hua JU Chun-yan 《Ecological Economy》 2010年第4期457-462,共6页
According to the data from the national standard classification and investigation of tourism resources(GB/T 18972-2003) in Hami region,the abundance,quality and dimensional distribution of the tourism resources in Ham... According to the data from the national standard classification and investigation of tourism resources(GB/T 18972-2003) in Hami region,the abundance,quality and dimensional distribution of the tourism resources in Hami region were evaluated based on GIS mapping technology.The evaluation results on the tourism resources in Hami region are described as follows:there are rich tourism resources categories;the quality of tourism resources is ordinary;the resources distribute equably;the number of the historical resources is much more than the natural resources,but the 1atter still has great potential for developing.All the results of the evaluation can provide important references for strategic decision making of Hami region. 展开更多
关键词 Hami region evaluation of tourism resource GIS mapping technology
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Analysis on Hydrological Regimes of the Medium and Small Rivers in Hami of Xinjiang——Take Toudaogou Basin as an Example
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作者 Ruozihan Tayier Guangxiao Luo 《Meteorological and Environmental Research》 CAS 2013年第10期37-40,44,共5页
[ Objective] The research aimed to analyze hydrological regimes of the medium and small rivers in Hami of Xinjiang. [ Method] According to actual observation data at Toudaogou hydrological station during 1956 -2010, c... [ Objective] The research aimed to analyze hydrological regimes of the medium and small rivers in Hami of Xinjiang. [ Method] According to actual observation data at Toudaogou hydrological station during 1956 -2010, climate, runoff, flood, sediment and water quality in the basin were analyzed. [ Result] Runoff in Toudaogou River was mainly from bedrock fissure water and rainfall, and depended on temperature and precipi- tation in the catchment zone. Runoff in Toudaogou River had very big change during the year. Runoff in whole year mainly concentrated during April -June, which occupied 57.9% of annual runoff. Flood in Toudaogou basin was divided into spring and summer flood from time, and snowmelt and rainstorm flood from type. Sediment load was related to terrain, gradient, runoff, precipitation, flood and process. Suspended sediment load at Toudaogou hydrological station had close relationship with the annual maximum flow capacity of flood peak, and related coefficient was 0.917. [ Conclusion] Hydrological regime in Toudaogou basin basically represented corresponding hydrological information of rivers without glacier water supply in Hami even whole western arid zone of China. The research could provide theoretical basis for scientifically using water resources of the medium and small rivers in the zone. 展开更多
关键词 Hydrological regime Medium and small dvers Toudaogou basin Hami of Xinjiang China
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Diagnosis and Analysis of a Rainstorm Process in Summer in Hami,Xinjiang
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作者 Yi erpanjiang·YASHENG Ruqi LI 《Meteorological and Environmental Research》 CAS 2022年第5期9-13,共5页
Based on conventional meteorological detection data and NCEP global reanalysis data,a rainstorm process in Hami,Xinjiang at the end of July 2018 was diagnosed and analyzed.The results show that this rare rainstorm occ... Based on conventional meteorological detection data and NCEP global reanalysis data,a rainstorm process in Hami,Xinjiang at the end of July 2018 was diagnosed and analyzed.The results show that this rare rainstorm occurred in the large-scale circulation situation of South Asia high,two ridges and one trough.The heavy precipitation area appeared on the right side of the southeasterly wind convergence area at 700 hPa,southerly flow at 500 hPa and the inlet area of southwest jet core at 200 hPa.The structure of high-level divergence and low-and middle-level convergence and strong vertical speed were important dynamic conditions for the occurrence and development of this rare rainstorm.The warm and moist air from the southern Sea of Japan and the Bay of Bengal was transported through different routes,providing a constant supply of water vapor and energy to the rainstorm area.Both EC and NCEP models have good predictive significance for this rainstorm,and the former is slightly better than the latter in terms of prediction effect. 展开更多
关键词 Hami XINJIANG RAINSTORM Circulation situation Physical quantities
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