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Chen Prime Liczby Pierwsze Chena
Chen Prime Liczby pierwsze Chena Chen Jingrun • Data urodzenia: 22 maj 1933 • Data śmierci: 19 marzec 1996 Pochodzi z wielodzietnej rodziny z Fuzhou, Fujian, Chiny. W 1953 roku skończył wydział matematyki na Uniwersytecie w Xiamen. Jego prace nad przypuszczeniem o bliźniaczych liczbach pierwszych oraz hipotezą Goldbacha doprowadziły do postępu analitycznej teorii liczb. Największym jego osiągnięciem było tzw. twierdzenie Chena stanowiące słabszą wersję słynnej hipotezy Goldbacha. Nazwiskiem Chen Jingruna została nazwana planetoida 7681 Chenjingrun odkryta w 1996 roku Hipoteza Goldbacha • jeden z najstarszych nierozwiązanych problemów w teorii liczb, liczy sobie ponad 250 lat • W 1742 roku, w liście do Leonharda Eulera, Christian Goldbach postawił hipotezę: każda liczba naturalna większa niż 2 może być przedstawiona w postaci sumy trzech liczb pierwszych (ta sama liczba pierwsza może być użyta dwukrotnie) Euler po otrzymaniu listu stwierdził iż hipotezę Goldbacha można uprościć i przedstawić ją w następujący sposób: każda liczba naturalna parzysta większa od 2 jest sumą dwóch liczb pierwszych Powyższą hipotezę do dzisiaj nazywaną "hipotezą Goldbacha" sformułował w rezultacie Euler, jednak nazwa nie została zmieniona. Oto kilka prostych przykładów: 4=2+2 6=3+3 8=3+5 10=3+7=5+5 … 100=53+47… Dzięki użyciu komputerów udało się pokazać, że hipoteza Goldbacha jest prawdziwa dla liczb naturalnych mniejszych niż 4 × 1017 (przez przedstawienie każdej z tych liczb w postaci sumy dwóch liczb pierwszych). Co więcej, większość współczesnych matematyków -
A 94–10Ka Pollen Record of Vegetation Change in Qaidam Basin
Palaeogeography, Palaeoclimatology, Palaeoecology 431 (2015) 43–52 Contents lists available at ScienceDirect Palaeogeography, Palaeoclimatology, Palaeoecology journal homepage: www.elsevier.com/locate/palaeo A94–10 ka pollen record of vegetation change in Qaidam Basin, northeastern Tibetan Plateau Haicheng Wei a,QishunFana, Yan Zhao b,HaizhouMaa, Fashou Shan a,FuyuanAna,QinYuana a Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, Xining 810008, China b Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China article info abstract Article history: Drill core (ISL1A) was obtained from the Qarhan Salt Lake in central eastern Qaidam Basin, northeastern Tibetan Received 19 May 2014 Plateau (NE TP). Fossil pollen and the lithology of the core sediment were analyzed in conjunction with AMS 14C Received in revised form 27 March 2015 and 230Th dating. The results indicated that Artemisia and Chenopodiaceae dominated the steppe/desert steppe Accepted 24 April 2015 vegetation developed around the lake between 94 and 51.2 ka, corresponding with the organic-rich silty clay de- Available online 4 May 2015 posited in the core sediments. Pediastrum continuously appeared in the core sediments between 94 and 51.2 ka, Keywords: indicating freshwater to oligohaline conditions of the paleo-Qarhan Lake during the late marine isotope stage Pollen record (MIS) 5, MIS 4, and early MIS 3. During the 51.2 to 32.5 ka period, Ephedra dominated shrub-desert vegetation Climate change expanded in the basin, while, Pediastrum disappeared in the core sediments. The core sediments consisted of in- Qaidam Basin terbedded layers of halite silt and clay-rich halite between 51.2 and 32.5 ka, signifying a shift toward drier hydro- Late Pleistocene logic conditions. -
Goldbach, Christian
CHRISTIAN GOLDBACH (March 18, 1690 – November 20, 1764) by HEINZ KLAUS STRICK, Germany One of the most famous, still unproven conjectures of number theory is: • Every even number greater than 2 can be represented as the sum of two prime numbers. The scholar CHRISTIAN GOLDBACH made this simple mathematical statement to his pen pal LEONHARD EULER in 1742 as an assumption. (In the original version it said: Every natural number greater than 2 can be represented as the sum of three prime numbers, since at that time the number 1 was still considered a prime number.) All attempts to prove this theorem have so far failed. Even the offer of a prize of one million dollars hardly led to any progress. CHEN JINGRUN (1933-1996, Chinese stamp on the left), student of HUA LUOGENG (1910-1985, stamp on the right), the most important Chinese mathematician of the 20th century, succeeded in 1966 in making the "best approximation" to GOLDBACH's conjecture. CHEN JINGRUN was able to prove that any sufficiently large even number can be represented as the sum of a prime number and another number that has at most two prime factors. Among the first even numbers are those that have only one GOLDBACH decomposition: 4 = 2 + 2; 6 = 3 + 3; 8 = 3 + 5; 12 = 5 + 7. For larger even numbers one finds a "tendency" to increase the number of possibilities, but even then there is always a number that has only a few decompositions, such as 98 = 19 + 79 = 31 + 67 = 37 + 61. See the graph below and The On-Line Encyclopedia of Integer Sequences A045917. -
Conjecture of Twin Primes (Still Unsolved Problem in Number Theory) an Expository Essay
Surveys in Mathematics and its Applications ISSN 1842-6298 (electronic), 1843-7265 (print) Volume 12 (2017), 229 { 252 CONJECTURE OF TWIN PRIMES (STILL UNSOLVED PROBLEM IN NUMBER THEORY) AN EXPOSITORY ESSAY Hayat Rezgui Abstract. The purpose of this paper is to gather as much results of advances, recent and previous works as possible concerning the oldest outstanding still unsolved problem in Number Theory (and the most elusive open problem in prime numbers) called "Twin primes conjecture" (8th problem of David Hilbert, stated in 1900) which has eluded many gifted mathematicians. This conjecture has been circulating for decades, even with the progress of contemporary technology that puts the whole world within our reach. So, simple to state, yet so hard to prove. Basic Concepts, many and varied topics regarding the Twin prime conjecture will be cover. Petronas towers (Twin towers) Kuala Lumpur, Malaysia 2010 Mathematics Subject Classification: 11A41; 97Fxx; 11Yxx. Keywords: Twin primes; Brun's constant; Zhang's discovery; Polymath project. ****************************************************************************** http://www.utgjiu.ro/math/sma 230 H. Rezgui Contents 1 Introduction 230 2 History and some interesting deep results 231 2.1 Yitang Zhang's discovery (April 17, 2013)............... 236 2.2 "Polymath project"........................... 236 2.2.1 Computational successes (June 4, July 27, 2013)....... 237 2.2.2 Spectacular progress (November 19, 2013)........... 237 3 Some of largest (titanic & gigantic) known twin primes 238 4 Properties 240 5 First twin primes less than 3002 241 6 Rarefaction of twin prime numbers 244 7 Conclusion 246 1 Introduction The prime numbers's study is the foundation and basic part of the oldest branches of mathematics so called "Arithmetic" which supposes the establishment of theorems. -
Research on the Relationship Between Transportation Industry and Economic Growth
E3S Web of Conferences 257, 03055 (2021) https://doi.org/10.1051/e3sconf/202125703055 AESEE 2021 Research on the Relationship between Transportation Industry and Economic Growth Jiaxin Wu1,a*, Yi Peng2,b, Xubing Zhou3,c 1School of Economics and Management, Beijing Jiaotong University, Beijing, China 2School of Economics and Management, Beijing Jiaotong University, Beijing, China 3School of Economics and Management, Beijing Jiaotong University, Beijing, China Abstract—Transportation industry is the leading capital of social and economic development, which plays an important role in regional economic development. Based on the data of Tibet Autonomous Region in the past 15 years, this paper makes further grey relation analysis and elastic analysis on the basis of analyzing the current situation of its transportation industry and economic development, obtains the conclusion about the development relationship between them. The empirical results show that there is a close relationship between the transportation industry and economic growth in Tibet Autonomous Region, and the development of them is in a state of coordination on the whole. Among them, the promotion effect of freight transport on the economic growth of Tibet is greater than that of passenger transport, and the belt action of economic growth on railway transport is much greater than that on highway transport. of industrial structure, and significantly improved the 1 Introduction investability of Tibet. The second is quantitative analysis method. Pan (2005) investigated the relationship between As a basic industry to promote economic development, the development of transportation and GDP in Tibet and transportation industry plays an increasingly significant believed that the transportation industry had a great role in promoting regional economic development. -
A Tibetan Perspective on Development and Globalization
HIMALAYA, the Journal of the Association for Nepal and Himalayan Studies Volume 24 Number 1 Himalaya; The Journal of the Association for Nepal and Himalayan Studies Article 13 No. 1 & 2 2004 A Tibetan Perspective on Development and Globalization Tashi Tsering University of British Columbia Follow this and additional works at: https://digitalcommons.macalester.edu/himalaya Recommended Citation Tsering, Tashi. 2004. A Tibetan Perspective on Development and Globalization. HIMALAYA 24(1). Available at: https://digitalcommons.macalester.edu/himalaya/vol24/iss1/13 This Research Article is brought to you for free and open access by the DigitalCommons@Macalester College at DigitalCommons@Macalester College. It has been accepted for inclusion in HIMALAYA, the Journal of the Association for Nepal and Himalayan Studies by an authorized administrator of DigitalCommons@Macalester College. For more information, please contact [email protected]. TASHI TSERING, UNIVERSITY OF BRITISH COLUMBIA A TIBETAN PERSPECTIVE ON DEVELOPMENT AND GLOBALIZATION The Chinese word for Tibet, Xizang, means the “western treasure house.” “…the trends in re- cent decades show that the Chinese government may now be success- ful in what it has always wanted to do—to put Tibet on the escalator to be- coming a profitable resource colony. Consumer goods on a Lhasa sidewalk PHOTO: TASHI TSERING INTRODUCTION ovember 30, 1999 marked a turning point in tribute to the scant literature by providing a Tibetan global history. Tens of thousands of ordinary perspective on this complex and relevant subject. The peopleN took to the streets of Seattle to stop the second purpose of this paper is a simple one: to articulate ” round of the World Trade Organization (WTO) what globalization (and thus development) means to Ministerial Conference. -
Elliot Sperling, Professor, Department of Central Eurasian Studies, Indiana University
Demographic Changes on the Sino-Tibetan Frontier in the 15th Century and their Implications Speaker: Elliot Sperling, Professor, Department of Central Eurasian Studies, Indiana University Chair: Patricia Uberoi, Chairperson, Institute of Chinese Studies 9 April 2015 Institute of Chinese Studies Delhi Elliot Sperling’s presentation provided a brief background to the social, economic and cultural situation of Tibet in the 15th century, as well as, the demographic changes which took place in Tibet during this period. These include the deterioration of the position of Buddhism in India, consequent decline of pilgrimage and reduction of trade with India. These demographic changes in the 15th century, along with its implications on the economy of Tibet, played an important role in Sino-Tibetan relations in the later centuries. It gave an increased level of importance to the Tibetan economy, especially Kham. The demographic changes that took place in Tibet were reflected in the massive migration of Tibetan population into eastern Tibet, making it the most populous part of the Plateau and the influx of Chinese into the province of Sichuan making it the most populous province of China. While pointing towards the implications of the demographic changes that took place in Tibet during 15th century, the speaker argued that the fact that the majority, albeit a slim majority, of the Tibetan population in China resides outside the territory that constitutes present-day Tibet Autonomous Region (TAR), has its roots in the changes that took place in the 15th century. He started his presentation by raising an important question i.e., what Tibet is and what the boundaries of Tibet are. -
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第 6 卷 第 4 期 地球环境学报 Vol.6 No.4 2015 年 8 月 Journal of Earth Environment Aug. 2015 doi:10.7515/JEE201504001 柴达木盆地西台吉乃尔盐湖区域晚更新世环境变化 曾方明 1,张 萍 2 (1. 中国科学院青海盐湖研究所,西宁 810008;2. 中国地质大学图书馆,武汉 430074) 摘 要:本文对柴达木盆地西台吉乃尔盐湖剖面沉积物(XT 剖面,240 cm 厚)的粒度、磁化率、 色度和总有机碳(TOC)等指标记录的晚更新世环境变化进行了研究。结果表明:(1)XT 剖面 沉积物的粒度总体较细(中值粒径变化范围为 3.4 ~ 10.0 μm),但是 25 ~ 47 cm 深和 185 ~ 199 cm 深的粒度明显变粗(中值粒径变化范围为 15.7 ~ 59.0 μm)。(2)XT 剖面沉积物的中值粒径与低 频磁化率(χlf)呈正相关关系;红度(a*)与低频磁化率呈负相关关系。(3)XT 剖面低频磁化 率与全球深海 δ18O 记录试探性的对比表明西台吉乃尔盐湖区域晚更新世的气候变化可能受全球 气候影响。 关键词:环境变化;更新世;柴达木盆地;西台吉乃尔盐湖 中图分类号:P534.631 文献标志码:A 文章编号:1674-9901(2015)04-0201-07 Late Pleistocene environmental change in the Xitaijinair salt lake region, Qaidam Basin ZENG Fang-ming1, ZHANG Ping2 (1. Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, Xining 810008, China; 2. Library, China University of Geosciences, Wuhan 430074, China) Abstract: This study investigated late Pleistocene environmental change indicated by proxies (grain size, magnetic susceptibility, color reflectance, and total organic carbon) of the 240 cm-deep XT section in the Xitaijinair salt lake region. The results suggest that: (1) Sediments in the XT section are generally fine (median grain size ranging from 3.4 μm to 10.0 μm), but are coarse at the depth of 25 ~ 47 cm and 185 ~ 199 cm (median grain size varying from 15.7 μm to 59.0 μm). (2) Median grain size is positively correlated with low-frequency magnetic susceptibility (χlf). Redness a* is negatively correlated with χlf . 18 (3) Tentative comparison with χlf records in the XT section and δ O records in the global deep oceans shows that the Pleistocene climate change in the Xitaijinair salt lake region is possibly influenced by global climate. -
Report on China's Development Policy in Tibet
China’s Development Policy in Tibet A Report Tibet Policy Institute 2017 Contents Preface .......................................................................................i Understanding China’s Economic Development Policies in Tibet: From Mao Zedong to Jiang Zemin Period .................................1 Dolma Tsering Ph.D Candidate , Jawaharlal Nehru University The Riddle of Tibet’s Economy ..................................................20 Dr Tenzin Desal Research Fellow, Tibet Policy Institute Saving Tibetans from Tibet: Poverty Alleviation with Chinese Char- acteristics ...................................................................................26 Gabriel Lafitte China’s Model of Economic Development of Tibet: From Darkness to Light, From Feudal Serfdom to Modernity, Thanks To the Gift of Development ........................................................................38 Gabriel Lafitte Outcomes of China’s Development Strategy in Tibet, As Experi- enced by Tibetans ......................................................................54 Gabriel Lafitte Tibet’s Traditional Economy: Comparative Advantage, Value Add- ing and Linkages .......................................................................61 Gabriel Lafitte 13th Five-Year Plan: China’s New National Parks in Tibet .....................................................................................69 Gabriel Lafitte Economy of Tibet Preface Economists who are reliant on GDP growth figures to read the pulse for the state of the economy, it is easy to be -
N N Ln N N Ln N N Ln N N Ln
Practice and Understanding of the Goldbach Problem (A) Tong Xinping (童 信 平) [email protected] Abstract Practice shows: Without enough parameters, 1+2 cannot estimate 1+1 and 1+1×1. At the same time, it is pointed out that among the prime numbers not greater than N, the prime number 6t-1 is more than the prime number 6t+1, (this is the "detail" that Hardy and the others did not notice.) "detail" (= "remainder") affects Represents the negligible oscillation in the accuracy curve of the number r2(N) of Hardy-Litttlewood conjecture (A) in 1921. (In 1989, Hua Luogeng (华罗庚) confirmed that conjecture (A) is the "main term" of even Goldbach's problem.) [Tong Xinping(童信平)Practice and Understanding of theGoldbachProblem(A)AcademArena2021;13(4):71-75]. ISSN1553-992X(print);ISSN2158-771X(online).http://www.sciencepub.net/academia. 7. doi:10.7537/marsaaj130421. 07. Keywords: Practice; Understanding; Goldbach; Problem In 1977, from a logical and philosophical point of view, I thought that "1+2" could not reach "1+1" (short The c(N) in the formula is represented c in the other for even Goldbach conjecture). Starting from interest, I book. am determined to find mathematical evidence that "1+2" Wang Yuan said that to prove "1+1" is to prove cannot reach "1+1" under the guidance of philosophical (1+O(1))→1, which is the "remainder" O(1)→0. The viewpoints. Seeing Xu Chi's article, I dare not act. -0.665 here is a definite value, not →0, and it cannot be However, the passion in my heart cannot be extinguished. -
The Mineral Industry of China in 2012
2012 Minerals Yearbook CHINA U.S. Department of the Interior February 2015 U.S. Geological Survey THE MINERAL INDUSTRY OF CHINA By Pui-Kwan Tse China ranked second behind the United States as the world’s social welfare costs. The working-age population decreased by leading economic power; it was also one of the world’s 3.5 million in 2012. The labor force in the mining sector was leading mineral producing and consuming countries. In 2012, 6.11 million, or 4.2% of the country’s total workforce in 2011. China’s economy remained strong compared with most of the In the manufacturing sector, rising production and developed countries in the West. During the past two decades, environmental costs, overcapacity, and uncertain external China’s economic growth was the result of a combination demand were likely to affect the sector’s profit margin. of trade and investment, and this growth greatly affected the Month-on-month production growth in the ferrous metals sector global commodity market. The country’s demand for energy, decreased significantly to 19.1% in November from 23.2% metals, and minerals was particularly strong. China imported in August, and the trend toward decreased production was significant amounts of raw materials and transformed the mirrored in the cement sector as well. During the past decade, materials into products for export. During the 1980s and the Chinese Government has tried to restrict the expansion 1990s, China’s commodity exports went primarily to Europe capacity in such energy-intensive sectors as aluminum, cement, and the United States; however, during the past several years, and iron and steel. -
The Evolution and Preservation of the Old City of Lhasa the Evolution and Preservation of the Old City of Lhasa Qing Li
Qing Li The Evolution and Preservation of the Old City of Lhasa The Evolution and Preservation of the Old City of Lhasa Qing Li The Evolution and Preservation of the Old City of Lhasa 123 Qing Li Institute of Quantitative and Technical Economics Chinese Academy of Social Sciences Beijing China ISBN 978-981-10-6733-4 ISBN 978-981-10-6735-8 (eBook) https://doi.org/10.1007/978-981-10-6735-8 Jointly published with Social Sciences Academic Press The printed edition is not for sale in China Mainland. Customers from China Mainland please order the print book from Social Sciences Academic Press. Library of Congress Control Number: 2017956325 © Springer Nature Singapore Pte Ltd. and Social Sciences Academic Press 2018 This work is subject to copyright. All rights are reserved by the Publishers, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication.