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The Njiki’s Fundamental Theorem-Definition on Fractions in the Mathematical Set ℚ and by Extension in ℝ and ℂ, for the Purpose of Leading to the Construction of Some Algebraic Structures as Its Theoretical Applications and for the Practical Ones
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作者 Jean Claude Njiki 《American Journal of Computational Mathematics》 2024年第3期358-379,共22页
The purpose of the research in the NJIKI’s fundamental THEOREM-DEFINITION on fractions in the mathematical set ℚand by extension in ℝand ℂand in order to construct some algebraic structures is about the proved EXISTE... The purpose of the research in the NJIKI’s fundamental THEOREM-DEFINITION on fractions in the mathematical set ℚand by extension in ℝand ℂand in order to construct some algebraic structures is about the proved EXISTENCE and the DEFINITION by NJIKI of two INNOVATIVE, IMPORTANT and TEACHABLE operations of addition or additive operations, in ℚ, marked ⊕and +α,β, and taken as VECTORIAL, TRIANGULAR, of THREE or PROPORTIONAL operations and in order to make THEM not be different from the RATIONAL ONE, +, but to bring much more and new information on fractions, and, by extension in ℝand ℂ. And the very NJIKI’s fundamental THEOREM-DEFINITION having many APPLICATIONS in the everyday life of the HUMAN BEINGS and without talking about computer sciences, henceforth being supplied with very interesting new ALGORITHMS. And as for the work done in the research, it will be waiting for its extension to be done after publication and along with the research results concerned. 展开更多
关键词 Operations of Addition Additive Operations in Laws in THEOREM-definition External Multiplication
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Siemens Definition AS128 CT维修5例 被引量:2
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作者 仲建生 刘蕾 +2 位作者 闫瑾 陈奇兵 夏云成 《医疗卫生装备》 CAS 2023年第3期116-120,共5页
介绍了Siemens Definition AS128 CT的硬件构成,分析并总结了该设备在日常使用中出现的检查床水平移动后机架掉电、图像重建系统(image reconstruction system,IRS)计算机硬盘故障、开机时F1开关脱开、“Exam”按钮灰化等故障产生的原... 介绍了Siemens Definition AS128 CT的硬件构成,分析并总结了该设备在日常使用中出现的检查床水平移动后机架掉电、图像重建系统(image reconstruction system,IRS)计算机硬盘故障、开机时F1开关脱开、“Exam”按钮灰化等故障产生的原因及维修思路,为临床工程技术人员排除相似故障提供了参考。 展开更多
关键词 Siemens definition AS128 CT 故障维修 故障排除
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Comparative efficacy and safety between endoscopic submucosal dissection,surgery and definitive chemoradiotherapy in patients with cT1N0M0 esophageal cancer
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作者 Shu-Ai Luo Yu-Ying Sun +1 位作者 Ya-Ting Zeng Chun-Yu Huang 《World Journal of Gastrointestinal Endoscopy》 2024年第2期72-82,共11页
BACKGROUND Endoscopic submucosal dissection(ESD)and surgical resection are the standard of care for cT1N0M0 esophageal cancer(EC),whereas definitive chemoradiotherapy(d-CRT)is a treatment option.Nevertheless,the compa... BACKGROUND Endoscopic submucosal dissection(ESD)and surgical resection are the standard of care for cT1N0M0 esophageal cancer(EC),whereas definitive chemoradiotherapy(d-CRT)is a treatment option.Nevertheless,the comparative efficiency and safety of ESD,surgery and d-CRT for cT1N0M0 EC remain unclear.AIM To compare the efficiency and safety of ESD,surgery and d-CRT for cT1N0M0 EC.METHODS We retrospectively analyzed the hospitalized data of a total of 472 consecutive patients with cT1N0M0 EC treated at Sun Yat-sen University Cancer center between 2017-2019 and followed up until October 30th,2022.We analyzed demographic,medical recorded,histopathologic characteristics,imaging and endoscopic,and follow-up data.The Kaplan-Meier method and Cox proportional hazards modeling were used to analyze the difference of survival outcome by treatments.Inverse probability of treatment weighting(IPTW)was used to minimize potential confounding factors.RESULTS We retrospectively analyzed patients who underwent ESD(n=99)or surgery(n=220)or d-CRT(n=16)at the Sun Yat-sen University Cancer Center from 2017 to 2019.The median follow-up time for the ESD group,the surgery group,and the d-CRT group was 42.0 mo(95%CI:35.0-60.2),45.0 mo(95%CI:34.0-61.75)and 32.5 mo(95%CI:28.3-40.0),respectively.After adjusting for background factors using IPTW,the highest 3-year overall survival(OS)rate and 3-year recurrence-free survival(RFS)rate were observed in the ESD group(3-year OS:99.7% and 94.7% and 79.1%;and 3-year RFS:98.3%,87.4% and 79.1%,in the ESD,surgical,and d-CRT groups,respectively).There was no difference of severe complications occurring between the three groups(P≥0.05).Multivariate analysis showed that treatment method,histology and depth of infiltration were independently associated with OS and RFS.CONCLUSION For cT1N0M0 EC,ESD had better long-term survival and lower hospitalization costs than those who underwent d-CRT and surgery,with a similar rate of severe complications occurring. 展开更多
关键词 Retrospective study cT1N0M0 Esophageal squamous cell carcinoma Endoscopic submucosal dissection SURGERY definitive chemoradiotherapy
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西门子Definition双源CT罕见故障维修案例分析 被引量:6
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作者 孙小磊 张晖 汪缨 《医疗卫生装备》 CAS 2020年第11期106-108,共3页
简要介绍了CT稳定运行的重要性,详细分析了西门子Definition双源CT的滤过器运动电动机过流罕见故障并给出了具体的排除方法,保障了机器的正常运行,节省了维修成本,为同行维修类似故障提供了参考。
关键词 西门子definition双源CT 滤过器 运动电动机 故障维修
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西门子64排SOMATOM Definition Flash双源CT机典型故障分析与处理 被引量:7
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作者 韦国文 《医疗卫生装备》 CAS 2017年第9期155-156,共2页
0引言 西门子64排SOMATOM Definition Flash双源CT机(简称"炫速双源CT机")是第二代双源CT,也是目前全球最尖端、最先进的大型医疗设备,它具有不受心率限制的心血管成像,可实现超越探测器宽度的大范围灌注,具备以"炫速扫描、锐影... 0引言 西门子64排SOMATOM Definition Flash双源CT机(简称"炫速双源CT机")是第二代双源CT,也是目前全球最尖端、最先进的大型医疗设备,它具有不受心率限制的心血管成像,可实现超越探测器宽度的大范围灌注,具备以"炫速扫描、锐影技术"为代表的超低剂量成像,负荷条件下的心肌灌注检查等特点。设备平时运行稳定,但由于各种客观因素的存在,各种故障的出现也难以避免。 展开更多
关键词 西门子64排SOMATOM definition Flash双源CT机 故障分析 故障排除
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Mathematical Definitions of Operators for Cartographic Generalization 被引量:2
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作者 王晓妮 张洁 《Geo-Spatial Information Science》 2003年第1期70-73,共4页
This paper puts forword 11 cartographic generalization operator models and introduces their mathematical definitions,and thus a precise mathematical form and quantitative description has been given to these formerly l... This paper puts forword 11 cartographic generalization operator models and introduces their mathematical definitions,and thus a precise mathematical form and quantitative description has been given to these formerly limited qualitative concepts.The meaning of mathematical definition of operators for cartographic generalization and the application prospect in computer_aided cartography (CAC) is stated.ract The Jurassic strata in Jingyan of Sichuan containing the Mamenchinsaurus fauna are dealt with and divided in this paper. The Mamenchisaurus fossils contained there are compared in morphological features and stratigraphically with other types of the genus on by one. The comprehensive analysis show that the Mamenchisaurus fauna of Jingyan appeared in the early Late Jurassic and is primitive in morphology. The results of the morphological identification and stratigraphical study agree with each other. Their evolutionary processes in different apoches of the Late Jurassic also made clear. Key words Jingyan, Sichuan, Mamenchisaurus Fauna, stratigraphy, evolution 展开更多
关键词 operators for cartographic generalization mathematical definition SELECTION SIMPLIFICATION STRESS
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A Feature Definition Hierarchy for Supporting Design Process
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作者 孙正兴 张福炎 蔡士杰 《Journal of Southeast University(English Edition)》 EI CAS 1999年第1期55-62,共8页
The adaptability of features definition to applications is an essential condition for implementing feature based design. This paper makes attempt to present a hierarchical definition structure of features. The propos... The adaptability of features definition to applications is an essential condition for implementing feature based design. This paper makes attempt to present a hierarchical definition structure of features. The proposed scheme divides feature definition into application level, form level and geometric level, and provides links between different levels with feature semantics interpretation and enhanced geometric face adjacent graph. respectively. The results not only enable feature definition to abate from the specific dependence and become more extensive, but also provide a theoretical foundation for establishing the concurrent feature based design process model. 展开更多
关键词 design process feature based modeling feature definition hierarchical construction
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A Definition Formalism of Machining Features for DFM
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作者 孙正兴 张福炎 《Journal of Southeast University(English Edition)》 EI CAS 1999年第1期49-54,共6页
Benefiting from advances in feature technology for design and manufacture can not be expected before a formal methodology is established. This paper makes attempt to establish a definition formalism of machining featu... Benefiting from advances in feature technology for design and manufacture can not be expected before a formal methodology is established. This paper makes attempt to establish a definition formalism of machining features in design for manufacturability from two aspects: formal definition and manufacturability analysis. Some definitions for machining feature based upon the selection and sequencing of material removal operations for component in accordance with the design geometry are presented and a framework of feature based design for manufacturability is outlined correspondingly. The proposed scheme contributes to several aspects of feature based CAD/CAM integration, especially to encourage potentially a more generic approach to the automation of design. 展开更多
关键词 design for manufacturability(DFM) feature technology machining feature definition formalism process planning
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一种基于内容模型图的XML Schema Definition的提取方法 被引量:3
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作者 宁静 刘杰 叶丹 《计算机科学》 CSCD 北大核心 2010年第6期179-185,共7页
使用XML Schema能够对XML文档进行有效性验证以及对查询、转换等操作进行优化,但是实际应用中大量XML文档缺失关联的Schema。提出了一种根据XML文档自动提取对应的XML Schema Definition(XSD)的方法XSDInfer,先根据合并规则将XML解析过... 使用XML Schema能够对XML文档进行有效性验证以及对查询、转换等操作进行优化,但是实际应用中大量XML文档缺失关联的Schema。提出了一种根据XML文档自动提取对应的XML Schema Definition(XSD)的方法XSDInfer,先根据合并规则将XML解析过程中分析得到的模式信息记录在内容模型图中,再根据生成规则将其转化为内容模型表达式,进而得到XSD。XSDInfer能够在内存消耗比较少的情况下快速地处理超大规模、深度嵌套的XML文档,同时支持XSD的上下文相关的内容模型,提取出的XSD也具有更好的可读性。实验表明,与同类方法相比,XSDInfer具有更好的可扩展性和表达能力。 展开更多
关键词 XML XML SCHEMA definition 模式提取 内容模型
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西门子Definition AS 128层螺旋CT故障维修3例 被引量:8
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作者 肖吴进 孙小磊 +1 位作者 汪缨 张晖 《医疗卫生装备》 CAS 2022年第3期106-108,共3页
分析了西门子Definition AS 128层螺旋CT出现的检查床升降偶发中断、主机无法上传患者数据至工作站、检查床无法正常移动等故障原因,并给出了科学有效的解决方法,为工程技术人员维修此类故障提供了参考。
关键词 西门子definition AS 128层螺旋CT 网络通信 故障维修
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西门子Definition AS术中CT两例硬件故障维修分析 被引量:2
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作者 孔康辉 赵东升 张龙 《中国医疗设备》 2022年第11期176-179,共4页
本文介绍了西门子Definition AS术中CT两例典型硬件故障。一例故障现象为停电导致扫描机架不上电,F1开关跳闸,复位后设备重启正常,随着停电次数的增多,F1开关复位困难。故障排除方法是更换工业继电器SIEMENS SIRIUS 3RS1800-2BP00。另... 本文介绍了西门子Definition AS术中CT两例典型硬件故障。一例故障现象为停电导致扫描机架不上电,F1开关跳闸,复位后设备重启正常,随着停电次数的增多,F1开关复位困难。故障排除方法是更换工业继电器SIEMENS SIRIUS 3RS1800-2BP00。另一例故障现象为扫描架显示屏呈灰色条纹状,进入故障日志查到216故障代码,故障现象描述故障点存在于XDC模块。故障排除方法是更换品牌为TDK-Lambda、型号为PH50S280-5的DC-DC模块。基于CT电路板的故障维修方法及其技术规律对两例硬件典型故障排查和修复、医疗电子设备维修技术水平有效提升提供借鉴价值。 展开更多
关键词 西门子definition AS XDC模块 DC-DC模块 反求电路原理图
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西门子CT Definition AS中CAN通信原理及故障分析 被引量:3
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作者 袁保锋 李郑 张振东 《中国医疗设备》 2019年第2期165-167,176,共4页
目的本文主要介绍CAN通信在西门子CT Definition AS中的应用原理、CAN通信常见故障及其排查方法。方法以我院西门子CT Definition AS为研究对象,对实际应用中发生的2例CAN通信故障案例进行深入分析,查找故障原因,根据分析的结果制定相... 目的本文主要介绍CAN通信在西门子CT Definition AS中的应用原理、CAN通信常见故障及其排查方法。方法以我院西门子CT Definition AS为研究对象,对实际应用中发生的2例CAN通信故障案例进行深入分析,查找故障原因,根据分析的结果制定相应的解决方案。结果通过对CAN通信故障现象及设备错误信息进行分析,故障得以排除,为设备的维修提供了借鉴。结论了解和掌握大型医疗设备中CAN通信的原理,对设备的使用、维修有着重要意义。 展开更多
关键词 CAN通信 definition AS CT 故障排查 故障分析
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The International Study Group of Pancreatic Surgery definition of delayed gastric emptying and the effects of various surgical modifications on the occurrence of delayed gastric emptying after pancreatoduodenectomy 被引量:16
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作者 Rajesh Panwar Sujoy Pal 《Hepatobiliary & Pancreatic Diseases International》 SCIE CAS CSCD 2017年第4期353-363,共11页
BACKGROUND:A number of definitions have been used for delayed gastric emptying(DGE) after pancreatoduodenectomy and the reported rates varied widely.The International Study Group of Pancreatic Surgery(ISGPS) definitio... BACKGROUND:A number of definitions have been used for delayed gastric emptying(DGE) after pancreatoduodenectomy and the reported rates varied widely.The International Study Group of Pancreatic Surgery(ISGPS) definition is the current standard but it is not used universally.In this comprehensive review,we aimed to determine the acceptance rate of ISGPS definition of DGE,the incidence of DGE after pancreatoduodenectomy and the effect of various technical modifications on its incidence.DATA SOURCE:We searched PubM ed for studies regarding DGE after pancreatoduodenectomy that were published from 1 January 1980 to 1 July 2015 and extracted data on DGE definition,DGE rates and comparison of DGE rates among different technical modifications from all of the relevant articles.RESULTS:Out of 435 search results,178 were selected for data extraction.The ISGPS definition was used in 80% of the studies published since 2010 and the average rates of DGE and clinically relevant DGE were 27.7%(range:0-100%;median:18.7%) and 14.3%(range:1.8%-58.2%;median:13.6%),respectively.Pylorus preservation or retrocolic reconstruction were not associated with increased DGE rates.Although pyloric dilatation,Braun’s entero-enterostomy and Billroth Ⅱ reconstruction were associated with significantly lower DGE rates,pyloric ring resection appears to be most promising with favorable results in 7 out of 10 studies.CONCLUSIONS:ISGPS definition of DGE has been used in majority of studies published after 2010.Clinically relevant DGE rates remain high at 14.3% despite a number of proposed surgical modifications.Pyloric ring resection seems to offer the most promising solution to reduce the occurrence of DGE. 展开更多
关键词 PANCREATODUODENECTOMY delayed gastric emptying ISGPS definition pyloric ring resection
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Spatial Boundary Definition of Urban-rural Fringe in Beijing City
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作者 许新国 陈佑启 +3 位作者 姚艳敏 何英彬 李志斌 余强毅 《Journal of Landscape Research》 2009年第10期23-28,66,共7页
Through reviewing domestic and overseas literatures about the definition of urban-rural fringe,it can be found that the combination of qualitative and quantitative definition methods has become a dominant one.This pap... Through reviewing domestic and overseas literatures about the definition of urban-rural fringe,it can be found that the combination of qualitative and quantitative definition methods has become a dominant one.This paper makes out the principle and basis,uses the data of villages and towns,and establishes an index system from three angles:population,land use and landscape.And then the gravitational model is applied to define the urban-rural fringe with Beijing as an example. 展开更多
关键词 Urban-rural FRINGE definition GRAVITATIONAL MODEL BEIJING
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Gait Definition and Successive Gait-transition Method Based on Energy Consumption for a Quadruped 被引量:6
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作者 ZHAO Danpu XU Jing +2 位作者 WU Dan CHEN Ken LI Chengrong 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2012年第1期29-37,共9页
In nature, to realize the smooth motion for different speeds, the continuous gait transition is usually required for the quadrupeds. Thus, the gait simulation of quadrupeds is a requisite step to obtain the stable and... In nature, to realize the smooth motion for different speeds, the continuous gait transition is usually required for the quadrupeds. Thus, the gait simulation of quadrupeds is a requisite step to obtain the stable and energy-efficient gait for the walking machines. In this paper, the definitions of the two gait parameters, phasic difference and duty factor are presented, which can determine the gait of the quadrupeds. Then, several typical gaits of the quadrupeds are analyzed such that the seven standard gaits and corresponding parameters are summarized. Additionally, the variance law of the two parameters, which determine the relationship of gait transition, is analyzed. Furthermore, the quadruped gait derivative spectrum (QGDS) is proposed and the gait definition of the quadrupeds is presented. To minimize the power consumption, the choice criterion of gait, the optimal gait in terms of the motion speed, duty factory, and power consumption for the walking machines, is developed. Last, the continuous variance of the gait is implemented by the simulation of the gait transition from walk to trot, which evaluate the choice criterion and transition of gait. 展开更多
关键词 gait definition standard gaits QUADRUPED gait-transition
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Definition of a plant-based diet and overview of this special issue 被引量:4
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作者 Robert J Ostfeld 《Journal of Geriatric Cardiology》 SCIE CAS CSCD 2017年第5期315-315,共1页
A plant-based diet consists of all minimally processedfruits, vegetables, whole grains, legumes, nuts and seeds,herbs, and spices and excludes all animal products, includ-ing red meat, poultry, fish, eggs, and dairy p... A plant-based diet consists of all minimally processedfruits, vegetables, whole grains, legumes, nuts and seeds,herbs, and spices and excludes all animal products, includ-ing red meat, poultry, fish, eggs, and dairy products. 展开更多
关键词 definition OVERVIEW Plant-based DIET
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Definition of colorectal anastomotic leakage: A consensus survey among Dutch and Chinese colorectal surgeons 被引量:5
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作者 Stefanus J van Rooijen Audrey CHM Jongen +4 位作者 Zhou-qiao Wu Jia-fu Ji Gerrit D Slooter Rudi MH Roumen Nicole D Bouvy 《World Journal of Gastroenterology》 SCIE CAS 2017年第33期6172-6180,共9页
AIM To determine the level of consensus on the definition of colorectal anastomotic leakage(CAL) among Dutch and Chinese colorectal surgeons.METHODS Dutch and Chinese colorectal surgeons were asked to partake in an on... AIM To determine the level of consensus on the definition of colorectal anastomotic leakage(CAL) among Dutch and Chinese colorectal surgeons.METHODS Dutch and Chinese colorectal surgeons were asked to partake in an online questionnaire. Consensus in the online questionnaire was defined as > 80% agreement between respondents on various statements regarding a general definition of CAL,and regarding clinical and radiological diagnosis of the complication.RESULTS Fifty-nine Dutch and 202 Chinese dedicated colorectal surgeons participated in the online survey. Consensus was found on only one of the proposed elements of a general definition of CAL in both countries: ‘extravasation of contrast medium after rectal enema on a CT scan'. Another two were found relevant according to Dutch surgeons: ‘necrosis of the anastomosis found during reoperation',and ‘a radiological collection treated with percutaneous drainage'. No consensus was found for all other proposed elements that may be included in a general definition.CONCLUSION There is no universally accepted definition of CAL in the Netherlands and China. Diagnosis of CAL based on clinical manifestations remains a point of discussion in both countries. Dutch surgeons are more likely to report ‘subclinical' leaks as CAL,which partly explains the higher reported Dutch CAL rates. 展开更多
关键词 Colorectal anastomotic leakage Colorectal surgery definition COMPLICATION
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Wetland Definitions:Creation,Evolution and Application 被引量:4
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作者 CHEN Hongjun WANG Guoping LU Xianguo 《湿地科学》 CSCD 2010年第3期299-304,共6页
In this paper,we review the creation,evolution and application of wetland definitions.Varying wetlands are found from the tundra to the tropics and on every continent except Antarctica in the planet.Wetlands have many... In this paper,we review the creation,evolution and application of wetland definitions.Varying wetlands are found from the tundra to the tropics and on every continent except Antarctica in the planet.Wetlands have many distinguishing features,the most notable of which are water presence,unique soil conditions,and biota that are adapted to or tolerant of saturated soils.Many wetland definitions have been developed by scientists,U.S.federal agencies,and the Ramsar Convention for both scientific and regulatory purposes.Wetlands are not easily defined but a well-conceived,science-based definition of wetlands is important for scientists and resource managers to understand the nature of wetlands and/or to use and protect wetlands.A scientific definition is the basis for wetland classification.Developing an effective wetland classification system requires a well-conceived,science-based definition and clearly explicit guidance on the appropriate use of various wetland indicators to verify the presence of wetlands on the ground.Based on a well-accepted wetland definition,both wetland classification and inventory further provide needed information and a working frame for wise use and management of wetlands. 展开更多
关键词 wetland definition EVOLUTION APPLICATION
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Circulation Indices of the Aleutian Low Pressure System:Definitions and Relationships to Climate Anomalies in the Northern Hemisphere 被引量:3
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作者 王盘兴 汪学良 +2 位作者 智海 王玉坤 孙晓娟 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2012年第5期1111-1118,共8页
In this study, a group of indices were defined regarding intensity (P), area (S) and central position (λc, Фc) of the Aleutian low (AL) in the Northern Hemisphere in winter, using seasonal and monthly mean h... In this study, a group of indices were defined regarding intensity (P), area (S) and central position (λc, Фc) of the Aleutian low (AL) in the Northern Hemisphere in winter, using seasonal and monthly mean height field at 1000-hPa. These indices were calculated over 60 winter seasons from 1948/1949 to 2007/2008 using reanalysis data. Climatic and anomalous characteristics of the AL were analyzed based on these indices and relationships between the AL, and general circulations were explored using correlations between indicesP, λc, and Pacific SST, as well as Northern Hemisphere temperature and precipitation. The main results are these: (1) AL is the strongest in January, when the center shifts to the south and west of its climatological position, and it is the weakest in December when the center shifts to the north and east. (2) AL intensity (P) is negatively correlated with its longitude (λc): a deeper low occurs toward the east and a shallower low occurs toward the west. On a decadal scale, the AL has been persistently strong and has shifted eastward since the 1970s, but reversal signs have been observed in recent years. (3) The AL is stronger and is located toward the east during strong E1 Nifio winters and vice versa during strong La Nifia years; this tendency is particularly evident after 1975. The AL is also strongly correlated with SST in the North Pacific. It intensifies and moves eastward with negative SST anomalies, and it weakens and moves westward with positive SST anomalies. (4) Maps of significance correlation between AL intensity and Northern Hemisphere temperature and rainfall resemble the PNA teleconnection pattern in mid-latitudes in the North Pacific and across North America. The AL and the Mongolian High are two permanent atmospheric pressure systems adjacent to each other during boreal winter over the middle and high latitudes in the Northern Hemisphere, but their relationships with the E1 Nifio/La Nifia events and with temperature and precipitation in the Northern Hemisphere are significantly different. 展开更多
关键词 circulation indices the Aleutian Low definitions and relationships climate anomalies
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A note on the definition of fractional derivatives applied in rheology 被引量:1
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作者 Fan Yang Ke-Qin Zhu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2011年第6期866-876,共11页
It is known that there exist obivious differences between the two most commonly used definitions of fractional derivatives-Riemann-Liouville (R-L) definition and Caputo definition. The multiple definitions of fracti... It is known that there exist obivious differences between the two most commonly used definitions of fractional derivatives-Riemann-Liouville (R-L) definition and Caputo definition. The multiple definitions of fractional derivatives in fractional calculus have hindered the application of fractional calculus in rheology. In this paper, we clarify that the R-L definition and Caputo definition are both rheologically imperfect with the help of mechanical analogues of the fractional element model (Scott-Blair model). We also clarify that to make them perfect rheologically, the lower terminals of both definitions should be put to ∞. We further prove that the R-L definition with lower terminal a →∞ and the Caputo definition with lower terminal a →∞ are equivalent in the differentiation of functions that are smooth enough and functions that have finite number of singular points. Thus we can define the fractional derivatives in rheology as the R-L derivatives with lower terminal a →∞ (or, equivalently, the Caputo derivatives with lower terminal a →∞) not only for steady-state processes, but also for transient processes. Based on the above definition, the problems of composition rules of fractional operators and the initial conditions for fractional differential equations are discussed, respectively. As an example we study a fractional oscillator with Scott-Blair model and give an exact solution of this equation under given initial conditions. 展开更多
关键词 Fractional derivatives RHEOLOGY Riemann-Liouville definition Caputo definition
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