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Boltzmann Model of Growth Curve of the β Index for Traffic Networks
CHEN Yanguang
Acta Scientiarum Naturalium Universitatis Pekinensis    2023, 59 (2): 326-330.   DOI: 10.13209/j.0479-8023.2022.118
Abstract331)   HTML    PDF(pc) (449KB)(171)       Save
Based on the verified empirical models of urbanization level and traffic network, a set of mathematical models of traffic network development are proposed. With the help of mathematical deduction, a Boltzmann equation is derived for the β index of traffic networks from the common logistic function of urbanization level growth, and a quadratic Boltzmann equation is derived for the β index from the quadratic logistic function of urbanization curve. The former is applicable to European and American countries and China’s southeast coastal areas, while the latter is applicable to mainland China, especially northern China. The main functions of the models are as follows: the first is to explain and predict the development of traffic networks, and the second is to research the stage division of a growth process or even the spatial dynamics of a traffic network.
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Three Dimensional Fault Enhancement Technique Based on Multi-directional Recognition
AN Shengpei, CHEN Yanyang, LUO Hongmei, YAN Shicui
Acta Scientiarum Naturalium Universitatis Pekinensis    2021, 57 (4): 653-659.   DOI: 10.13209/j.0479-8023.2021.057
Abstract657)   HTML    PDF(pc) (8694KB)(296)       Save
In order to apply the fault enhancement method to improve the accuracy of fault identification, a three-dimensional fault enhancement method based on multi-directional recognition is developed. This method applies directional filtering to enhance the continuity of the seismic events and suppress the background noise, and applies edge-preserving filtering to preserve the fault information in seismic profiles. This method is further improved in two aspects. 1) Multi-directional fault recognition is designed to adapt to the presence of inclined formations. 2) The two-dimensional fault enhancement method is extended to the three-dimensional one which achieves the effect of three-dimensional fault enhancement with a lower amount of calculation. The applications on synthetic data and the three-dimensional post-stacked actual data show that the proposed method can effectively suppress the background noise, enhance the continuity of the seismic events, and improve the resolution of the fault image, which is conducive to the subsequent structural interpretation.
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Study on the Classification of Response Relationship between Total Pollutant Emission Reduction and Water Quality Improvement in China
BAI Hui, CHEN Yan, WANG Dong, WU Shunze, GAO Wei, GUO Huaicheng
Acta Scientiarum Naturalium Universitatis Pekinensis    2020, 56 (4): 765-771.   DOI: 10.13209/j.0479-8023.2020.051
Abstract998)   HTML    PDF(pc) (956KB)(332)       Save
 The response relationship between total pollution emission reduction and water quality improvement from 2011 to 2015 was analyzed by data envelopment analysis (DEA). The results show that the response relationship is different in time and space. The response relationship was further divided into four different models, and suggestions about total pollution emission controlling and water environment prevention were made under different models, in order to make total pollution emission controlling play a better role in water quality improvement. The result should provide scientific basis for precise pollution control in accordance with the water environment quality objectives of the basin.
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Estimating Nitrogen and Phosphorus Pollution Load in Bali Lake Basin of Jiangxi Province Based on SWAT Model
CHEN Yan, ZHAO Yanxin, ZHAO Yue, WANG Dong, BAI Hui, GUO Huaicheng
Acta Scientiarum Naturalium Universitatis Pekinensis    2019, 55 (6): 1112-1118.   DOI: 10.13209/j.0479-8023.2019.086
Abstract1201)   HTML    PDF(pc) (1883KB)(404)       Save
The simulation of nitrogen (N) and phosphorus (P) pollution load structure in Bali Lake basin was performed by SWAT model using the spatial and attribute database acquired through social survey and statistical data. The model was applied and validated based on the data of meteorology, runoff and water quality from 2010 to 2014. The spatial-temporal distribution of N and P in the basin was also studied. The results showed that the urban life was the most important source of N and P load, following by agriculture and livestock breeding pollution source, and the least was industry pollution source. The annual TN and TP loads were mainly concentrated in flood season (from May to September) which took up nearly 55% of the whole year load. As the amount of precipitation increased, TN and TP loads increased during flood period, which was mainly due to the increasing of non-point rural living water and agricultural fertilization pollution source with scouring action of the heavy rainfall during flood season. The spatial distribution of N and P was centered on the Jiujiang county, Xunyang and Lushan district as the urban agglomeration area affected by urban sewage pollution.
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Inequality Indexes for Measuring Between-Groups Mean Difference of Size and Spatial Distributions
CHEN Yanguang
Acta Scientiarum Naturalium Universitatis Pekinensis    2019, 55 (6): 1097-1102.   DOI: 10.13209/j.0479-8023.2019.107
Abstract2575)   HTML    PDF(pc) (422KB)(380)       Save
A set of new inequality indexes are constructed to measure the relative unbalanced difference between regions or groups of elements in a geographical systems. Firstly, the within-group inequality index, namely, the Gini coefficient based on the Lorenz curve, is transformed into a new mathematical expression. Then, based on the new formula, the within-group index is generalized to between-group inequality index. Technically, the two types of inequality indexes can be integrated into the same logic framework. As an example, the new formulae are applied to three systems of cities in China, including Beijing-Tianjin-Hebei region, Yangtze River Delta, and Pearl River Delta. The results display a spatio-temporal evolution patterns of relative mean differences within and between these urban systems.
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A Word Representation Method Based on Hownet
CHEN Yang, LUO Zhiyong
Acta Scientiarum Naturalium Universitatis Pekinensis    2019, 55 (1): 22-28.   DOI: 10.13209/j.0479-8023.2018.061
Abstract1191)   HTML    PDF(pc) (653KB)(595)       Save

Word embedding method based on pre-training still has some defects in the stability and the quality of low-frequency words. The authors propose a new word embedding method based on Hownet. First, based on the sememe independence assumption, all sememes of Hownet are specified in an Euclidean Space’s standard orthogonal basis to initialize all sememe vectors. Secondly, utilizing the relationship between word and sememe defined in the Hownet, each word vector representation can be regarded as a subspace projection by related sememes. Finally, a deep neural network model is put forward to learn word representations. The experimental results indicate that proposed word embedding method based on Hownet obtained comparable results in the two standard evaluation tasks including the word similarity computation and the word sense disambiguation.

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An Approach Based on Euler’s Formula to Estimating Gini Coefficient of Pareto Distribution
CHEN Yanguang
Acta Scientiarum Naturalium Universitatis Pekinensis    2018, 54 (6): 1283-1289.   DOI: 10.13209/j.0479-8023.2018.052
Abstract741)   HTML    PDF(pc) (1235KB)(290)       Save

A simple approach to estimating Gini coefficient based on Lorenz curve is proposed to solve the problem that the concentration index replacing the Gini coefficient results in deviation from imbalance measurement of spatial distributions and size distributions. In view of the scale-free distribution phenomena in the complex social and economic system, a logarithmic function of convex Lorenz curve is derived from the pure Zipf’s distribution by means of Euler’s formula for the sum of harmonic sequence. Then an approximate formula to estimate Gini coefficient can be constructed by using the parameters of the logarithmic Lorenz curve model. The formula is applied to the cities in Beijing, Tianjin and Hebei (Jing-Jin-Ji) region, and the Gini coefficients of 22 years are evaluated by the night lighting data. The results show that there is a significant difference between the Gini coefficient and the centralization index. A conclusion can be reached that the centralization index is applicable to the distributions with characteristic scales, while the proposed formula are suitable for the scale-free distributions. This work will help researchers to understand the scopes of application of the imbalance measurements and provide a reference for further developing the direct estimation methods of Gini coefficient.

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Effects of Land Use Pattern Change on Regional Scale Habitat Quality Based on InVEST Model—a Case Study in Beijing
CHEN Yan, QIAO Fei, JIANG Lei
Acta Scientiarum Naturalium Universitatis Pekinensis    2016, 52 (3): 553-562.   DOI: 10.13209/j.0479-8023.2016.057
Abstract1280)   HTML    PDF(pc) (10678KB)(1215)       Save

To study the effects of land use pattern change on habitat quality in the background of urbanization, InVEST model was applied to calculate the contributions of habitat threats (urban area, rural construction area, main roads and agriculture land) to habitat degradation, and to assess habitat quality changes between 1990 and 2010 in Beijing. The results showed that the most severe habitat degradation problems occurred in Haidian, Chaoyang, Shijingshan and Fengtai districts, Yongding River, Chaobai River, and the mountain-plain border area (at an elevation about 75-100 m). Agriculture lands had the largest effect on habitat degradation, followed by urban areas, rural construction areas and main roads. During these two decades, the contribution of agriculture lands decreased from 77.79% to 61.15%, but the contribution of urban areas increased from 18.10% to 31.54%. Between 1990 and 2000, habitat quality declined dramatically in Haidian, Chaoyang, Shijingshan and Fengtai districts, which were located at the rim of Dongcheng and Xicheng districts. The total habitat quality value decreased by 2.3%. During 2000 and 2010, the deterioration of habitat quality expanded to most of the plain areas. In the mountain area of Fangshan and the mountain-plain border area (at an elevation about 75-100 m) in Miyun, Huairou, Changping and Fangshan, the value decreased significantly. However, habitat quality had been restored notably in northern and western mountain areas. The total habitat quality value declined by 1.2%, which indicated that habitat deterioration had been mitigated to some extent compared with the last decade. For habitat conservation and urban planning in the future, more attention should be paid to mountain-plain border areas. The current study played an active role in land use policy-making and biodiversity conservation.

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Evolutive Trend of China’s Corn Output and Its Fluctuation Characteristics Based on LMDI Model and EMD Model
LI Yanmei;CHEN Yangfen;LIU Yu;GAO Bingbo
Acta Scientiarum Naturalium Universitatis Pekinensis    2015, 51 (5): 946-954.   DOI: 10.13209/j.0479-8023.2015.103
Abstract1207)      PDF(pc) (780KB)(553)       Save
Based on logarithmic mean weigh division index method (LMDI), empirical mode decomposition method (EMD) and variance decomposition model (VDM), the evolutive trend and fluctuation characteristics of corn production in China during 1978–2012 was analyzed. The contribution difference to corn output fluctuation during eight grain production regions was revealed. The following results were obtained. Corn output increased by 1.50×108 ton from 1978 to 2012, and the corn production advantage in Huang-Huai-Hai region and Northeast Region in China was further highlighted. It was estimated that the accumulated contribution values of corn sowing area and corn yield per hectare at national scale were 0.79×108 ton and 0.71×108 ton respectively, and corn sowing area was the major contributor to the increment of corn output. The residual trend of corn output showed a trend of gradual increase and the grain output has 3-year periodic oscillation. During the eight grain production regions in China, Huang-Huai-Hai Region played the prominent role in the total fluctuation, following by the Northeast Region and Loess Plateau Region. The self-fluctuations in the three regions and their positively mutual affect were the main factors of China’s corn output fluctuation, including Huang-Huai-Hai Region, Northeast Region and Loess Plateau Region in China. For the high contribution ratio and drastic change, more attention should be paid to Huang-Huai-Hai Region and Northeast Region in China.
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A Supervised Dynamic Topic Model
JIANG Zhuoren,CHEN Yan,GAO Liangcai,TANG Zhi,LIU Xiaozhong
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract1254)      PDF(pc) (3346KB)(837)       Save
An innovative Supervised Dynamic Topic Model (S-DTM) is developed for overcoming the limitation of tranditional topic models. S-DTM models the time-varying language dynamics and is combined with supervised learning technology by adding label restriction in topic variational inference. It makes the topic-label mapping and improves the interpret ability of topics. A set of experiments is conducted on a twenty-five-year-spanning Chinese journal paper corpus that is mainly focusing on natural language processing. Experiment results show that compared with static supervised topic model and unsupervised dynamic topic model, S-DTM has a better semantic interpretation performance, reflects the topic structure of a document more accurately, captures the dynamic evolution of the term-distribution of topics more precisely.
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Geochronology, Geochemistry and Geological Significance of the Permian Bimodal Volcanic Rocks in Xi Ujimqin Banner, Inner Mongolia
CHEN Yan,ZHANG Zhicheng,LI Ke,LUO Zhiwen,TANG Wenhao,LI Qiugen
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract649)      PDF(pc) (3574KB)(662)       Save
In order to understand the Late Paleozoic tectonic setting of eastern part of Central Asian Orogenic Belt more deeply, the Permian volcanic rocks from Xi Ujimqin Banner, Inner Mongolia were selected to study their geochronology and geochemistry. The contents of major elements, the age, the contents of trace elements and REEs and the Sr-Nd isotopes of the volcanic rocks were measured by X-ray fluorescence spectrometry (XRF), SHRIMP zircon U-Pb, ICP-MS and ISOPROBE-T, respectively, and the results are as follows. The volcanic rocks consist of subordinate basaltic andesites and dominant rhyolites, with the SiO2 content ranges of 53.54%?54.71% and 72.61%?80.81%, respectively. The SHRIMP zircon U-Pb age of one rhyolite specimen is about 279 ± 4.3 Ma, indicating that the rhyolites erupted in Early Permian. The basaltic andesites are characterized by slightly enriched LREE, depleted HREE, slightly negative Eu, Nb, Ta and Sr anomalies, and high abundances of LILE and HFSE, with the (La/Yb)N ratios of 2.06 to 2.34. The mafic rocks may be inferred to generate from deep non-primitive mantle largely mixed by crustal source according to these features above. The rhyolites are characterized by slightly enriched LREE, depleted HREE, intensively negative Eu, Sr, P and Ti anomalies, slightly depleted Nb and Ta, and high abundances in K, Zr and Hf, with the (La/Yb)N ratios ranging from 1.70 to 3.81, relatively high positive εNd(t) values (+3.98?+5.62) and relatively young TDM (490?690 Ma). The felsic rocks show an A-type affinity and may be inferred to come from a juvenile crustal source. According to their geochemistry, regional geology and previous studies, these bimodal volcanic rocks were generated by intra-plate volcanism and formed in a post-collisional extensional setting.
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In vitro Degradation Performance of Nano-Hydroxyapatite/Bacterial Cellulose for Bone Tissue Engineering
CHEN Yanmei,XI Tingfei,ZHENG Yudong,ZHENG Yufeng,WAN Yizao
Acta Scientiarum Naturalium Universitatis Pekinensis   
Verifiable Multi-secret Sharing Scheme Based on Homogeneous Linear Recursion
CHEN Yangkui,YU Jia,CHENG Xiangguo,HAO Rong,LIU Hongyan,LI Xin
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract643)            Save
A new multi-secret sharing scheme based on homogeneous linear recursion is proposed, and then it is converted into a verifiable scheme. In the distribution phase, very few of public values are needed to publish. In the recovery phase, each participant only needs to submit a pseudo shadow instead of his secret shadow, and his secret shadow cannot be disclosed. When secrets are changed, secret shadows don?t need to be redistributed, which makes secret shadow able to be used multiple times. The proposed scheme has many advantages, for example, the secret shares can be used multiple times and the scheme publishes very few parameters as well as the reconstructed polynomial has a low degree. This makes the proposed scheme more efficient. Therefore, it better satisfies demands of various applications.
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Provenance Analysis of the Member 2 and 3 of the Upper Cretaceous Nenjiang Formation in Northern Songliao Basin
PENG Guoliang,WU Chaodong,ZHANG Shun,CHEN Yang
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract607)            Save
Based on the core observation and analytical data, the provenance of the Member 2 and 3 of the Upper Cretaceous Nenjiang Formation in Northern Songliao Basin was estimated according to the mineral content of sedimentary rocks, planar distributing of sandstone, ZTR index of heavy mineral and mudstone color distribution. The results show that the provenance of the Member 2 and 3 of Nenjiang Formation changes with time, but the change is small. The sediments of the Member 2 of Nenjiang Formation are mainly derived from the eastern provenance, whereas the sediments of the Member 3 of the Nenjiang Formation are derived from the eastern and northeastern provenances. Such a provenancial change might be aroused by the uplift of strata in the north area. During the deposition of the Member 2 and 3 of the Nenj iang Formation, three main provenances exist in Northern Songliao Basin: the northeastern source area, the eastern one and the western one. The eastern provenance dominates the sediments of the Member 2 and 3, while the latter Member 3 is dominated by both the eastern and the northeastern provenance. And the western provenance exists during the latter Member 3, but its incidence is small.
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Derivation of the 2n Rulefromthe Rank-Size Rule of City-Size Distribution
CHEN Yanguang,HU Yuwang
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract888)            Save
This paper demonstrates the equivalent relation between the 2n rule of hierarchy of cities and the rank-size rule of city size distribution. According as the rank-size rule, if the largest city P1 = 1 , then the size of the kth city by rank Pk will be 1?k. Thus city sizes can be abstracted as a harmonic sequences, {1 k}. Grouping the harmonic sequences into many classes in atop-n down way according to the 2 principle yields a hierarchy of fractions with cascade structure . In this instance , the interclass number ratio is rf = 2. Thetotal population of the first classis 1, second class, 1 2 + 1 3 ≈0. 8333, thethird class, 1 4 + 1 5 + 1 6 + 1 7 ≈0. 7595 , and so on. If the sequence number of a classis large enough, it will have total population approaching to ln2 ≈0. 6931 in theory . By limit analysis, the mean size ratio of two immediate classes is close to rp = 2. Accordingly, the fractal dimension of the cascade structure is D= lnrf lnrp →1. However, the first several classes depart fromthe scaling range to some extent theoretically. As for the empirical data, the last class always goes beyondthe scalingrange because of undergrowth of small cities andtowns. Therefore, the exponential laws andthe power laws of hierarchy of cities are al ways invalid at the extreme scales, i .e . the very large and small scales. Key words 2 n rule ; rank-size rule ; Zipf’s law; fractal ; hierarchy of cities ; cascade structure ; symmetry
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On the Mathematical Form, Dimension, and Locality of the Spatial Interaction Model
CHEN Yanguang
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract883)            Save
The spatial interaction models (SIMs) in geography are developed by using the ideas from fractals and spatial complexity, and three pending questions are answered. Firstly, based on the supposition that the distance cost exhibits a logarithmic growth instead of a linear growth, the impedance function of Wilson's spatial interaction model is converted from a negative exponential expression into an inverse power law. The contradiction of locality to action at a distance of SIM is thus avoided through this revision. Secondly, the inverse power law based gravity model is gotten out of the dimensional dilemma with the concept of fractal dimension. Geographical gravity measure is consequently made more understandable. Thirdly, the notion from symmetry based on the nonlinear dual programming of spatial interaction is employed to reveal the essence of entropy maximizing process of human geographical systems. The relationship between entropy maximization and structural optimization is brought to light for geographical analysis. The distinction and connection between the gravity model originating from the analogy with the law of universal gravitation and Wilson's spatial interaction model is discussed, and the similarities and differences are compared between the exponential function based and the power law based SIMs.
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The Construction of 4-Band Symmetric Biorthogonal Wavelets
CHEN Yanna,LIU Yu,SHEN Yanan
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract630)            Save
The symmetric biorthogonal low-pass filters of 4-band and the corresponding scaling functions are constructed by using the sum rules. Also, the symmetric or anti-symmetric biorthogonal wavelet filters of 4-band with high order vanishing moment and short support are obtained. Especially, the coefficients of filter constructed are all rational numbers and their denominators are all binary. Therefore, it is very convenient for these filters to be applied. At last, the smoothness index of the scaling functions constructed can be estimated by the method of Hanbin.
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The Revision of the Personal Need for Structure Scale in Chinese
CHEN Yang,HUANG Yunhui,WANG Lei,SHI Junqi
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract840)            Save
The purpose was to revise the Chinese version of the Personal Need for Structure (PNS) Scale. The questionnaire was administered to 1042 participants. The item analysis showed that all of the 11 items met the psychometric criteria. The confirmatory factor analysis indicated that the Chinese version of PNS containing 11 items was composed of two dimensions, which remained the same structure as the original version. These two dimensions were desire for structure and response to lack of structure. The internal consistency reliability and the split-half reliability were all above 0.80. The test-retest reliability was 0.79. The results indicated that the scale has acceptable discriminant validity and convergent validity.
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Modeling the Urbanization Process of China by Using Nonlinear Dynamic Equations
CHEN Yanguang,ZHOU Yixing
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract791)            Save
A model based on nonlinear dynamics is proposed to characterize the urbanization process of China. Then a universal model of urbanization process is presented by combining the above mentioned model with the United Notions' model, which can be used to describe the United States' urbanization process. The time series data of urbanization level in China from 1949 to 2000 is employed to verify the new model, and the result is satisfying. The model bears an analogy with the Lotka-Volterra model of predator prey ecological interaction, one of the most widely discussed examples of a non linear system in two dimensions. The difference lies in that one of the parameters is zero. Extensions of such models should help us understand Holland's question: why predator prey ecological interaction exhibit strong oscillations, whereas the interactions that form a city are typically more stable.
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Economic Value of Urban Ecosystem Services: A Case Study in Shenzhen
PENG Jian,WANG Yanglin,CHEN Yanfei,LI Weifeng,JIANG Yiyi
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract1010)            Save
Based on research progress on economic value of ecosystem services, taking Shenzhen for instance, the authors analyze the functions of ecosystem services such as conditioning climate, fixing carbon and releasing oxygen, preserving soil, keeping waterhead, purifying environment, and restraining noises. Economic values of all the six kinds of ecological service functions are calculated. The results show that ecosystems in Shenzhen provide enormous ecological economic benefits with the total value of RMB 126292000000, which corresponds with the RMB 166524000000 of GDP of Shenzhen in 2000. Meanwhile, the importance of different ecosystem services in urban areas is different. The function of fixing carbon and releasing oxygen is the most important, the function of conditioning climate is the second, and the functions of keeping waterhead, preserving soil, purifying environment, and restraining noises are the last important. As for the case study in Shenzhen, the functions of purifying environment and restraining noises are in great need of protection in urban landscape management and ecological construction.
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Modeling Self-Organized Network of Cities Based on the Urban Triangular Lattice Model
CHEN Yanguang,HOU Yixing
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract600)            Save
An exclusively mathematical approach is proposed to address the scale-free property of selforganized networks of cities. Defining a spatial correlation function based on the triangular lattice model of cities stemming from central place networks, a scaling relationship is established between yardstick (r) and city-city correlation density (C(r)) such as C(r)∝rD, where D is the scaling factor. The scaling factor is in fact the spatial correlation dimension if only 1≤D≤2. A self-organized network of cities is regarded as scale-free system provided there exists a linear range on the logr-logC(r) plot. The Henan cities of China are taken as an example to show how to fit the observed data to the correlation function for calculating the scaling factor, and to illustrate the process of spatial complication of urban evolution. The results indicate that urban systems and the traffic networks based on urban systems are scale-free networks, and the network of cities can be characterized with the power-law of yardstick and correlation density relation.
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Development of Gene Theory
CHEN Yanhui,YANG Xiaoyuan,QU Lijia
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract775)            Save
The discovery of DNA double helix structure is one of the most important discoveries in the last century. The core rule and the technology of gene cloning provide us powerful tools to elucidate the nature of human beings. In the history of molecular biology, the importance of DNA, which is the carrier of genetic information, and its double helix structure, is clearly recognized. The completion of the human genome project opens up a broad field, and makes it possible for us to study the biological processes at the whole-genome level, and the biology is going into post-genome era.
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Derivations and Empirical Analysis of the Allometric Equation and C-D-type Function on Geographical Systems of Cities
CHEN Yanguang
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract775)            Save
A Cobb-Douglas-function-type model on cities as systems is derived from general expressions on urban dynamic systems, y=kfi(x1, x2,..., xn), the model can be named C-D function of cities and written as y=μxii^σi,where xi(i=1, 2,..., n) represents some kind of measure on cities, y is output in some sense, k and μ both proportionality coefficients. Throught the allometric relationship between two elements of cities, xixj^αij, the C-D function can be transformed into the two-variable expression, y=η(xi^bi) (xj^bj). A number of equations of fractal dimension are deduced out such as αij=Di/Dj=σj/σi=bj/bi, σiDi=σjDj. It is proved that the equation. σi/(wixi)=σj/(wjxj), should be met in order to optimize urban structure and function. Taking the city of Zhengzhou as example, the models presented and advanced are verified and vindicated.
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Multifractal Measures of City-size Distributions Based on the Three-Parameter Zipf Law: Mathematical Frameworks and Empirical Evidence
CHEN Yanguang,ZHOU Yixing
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract900)            Save
Urban hierarchy as a result of some fractal recursion is generalized to the binomia l multiplicative process and accordingly city-size distributions can be describ ed by multifractal measures. Based on the generalized Beckmann-Davis model advan ced by the authors Pm=P1rp1-mfm=f1fm-1,where rf=fm+1/fm denotes number ratio of cities in the mth and (m+1)th level of central-place hierarchies, the spectrum of fractal dimensions Dq as a function of the moment order q of city class-size relationships is expressed asDq=pq+(1-p)q]/[(1-q)lnrf],where p=P(2)/[P(2)+P(3)],(P(2) is the population of rank 2,etc.), thus the mass exponent can be given by the formula, τ(q)=(1-q)Dq. By means of the Legendre transformation, the Lipschitz-Holder exponent α(q) for the mass can be derived as α(q)=[pqlnp+(1-p)qln(1-p)]/{[pq+(1-p)q]ln(1/rf)}, correspondingly, the fractal dimension of the set supporting this exponent will yield through the equation f(α)=(q)+τ(q). An empirical analysis is made with the population data of the US cities to verify the theory and models developed in this paper, which will contribute to reconcile the apparent difference between the hierarchical step-like frequency distribution of city sizes suggested by central place theory and the smooth curve reflected by the work on the rank-size rule.
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A Review on Petrologic Evidences for Mesozoic Lithosphere Delamination in East Qinling-Dabie Mountains
LI Chao,CHEN Yanjing
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract719)            Save
Lithosphere delamination is an important way for compositional and structural evolution of collisional orogens. Geotectonic research, geophysical survey and geochemical analysis have revealed that the lithosphere of East Qinling-Dabie Mountains had delaminated intensively in Mesozoic. However, the extensive Mesozoic metamorphism and magmatism have been weakly related to lithosphere delamination. Based on a comprehensive review on research results of metamorphic rocks, the authors argue that the formation and exhumation of UHPM (ultra-high pressure metamorphite) experienced two stages, i.e., cold slab subduction and exhumation during 240~200Ma, and lithosphere delamination and thermal exhumation during 196~163Ma. The rapid thermal exhumation, co-occurred with extensive regional metamorphism and intermediate-acidic magmatism, implied that the subducted slabs had broken off and delaminated. The p-T-t path of UHPM consists of two curves, i.e., a barrette-like curve reflecting the process of cold slab subduction and exhumation (cold overthrusting), and a crescent curve representing the thermal exhumation after slab breakoff. By statistically analyzing of isotopic ages for granitoids and commenting on previous studies, the authors preliminarily determine that a large volume of granitoids developed during 200~100Ma, predominately formed in the period of 150~100Ma, with the peak age at about 130Ma. The inferred lithosphere delamination from the development of granitoids occurred slightly later than that deduced from researches on metamorphic rocks. Distant effect of Jurassic collisions of Qiangtang terrane, Lasa terrane and Paleo-Pacific land onto the Eurasian land made East Qinling-Dabie Mountains in a compressional circumstance for a long time, and suppressed its orogenic extension; whereas, Cretaceous late-collisional extension and appearance of West Pacific trench-arc-basin system relieved East Qinling-Dabie Mountains of external compression, instantly result in violent orogenic lithosphere delamination-extension and depressurized-calefactive melting, and consequently, led to the formation of large scale Early Cretaceous granitoids and intermediate-acidic volcanic rocks. In conclusion the magmatism caused by lithosphere delamination in East Qinling-Dabie Mountains occurred in the transition from compression to extension in the period of J3-K2.
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The Preliminary Study of Laumontitization of Axi Gold Deposit and Paleogeothermal Minerogenetic Fluid System in West Tianshan
BAO Jingxin,CHEN Yanjing,ZHANG Zengjie,CHEN Huayong,LIU Yulin
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract719)            Save
Through field investigation, microscopic study, X-ray phase analysis and mineral infrared spectrum analysis, the authors determine the laumontitization had occurred widely in the Axi gold field. According to the development of laumontitization and its relationship to mineralization, authors reveal that the laumontitization appeared mainly at the top and periphery to ore-bodies. It befallen at the edge of the geothermal fluid system or happened in the late stage of geothermal fluid system evolution, hence can be assigned as an indicator to prospect for epithermal gold deposit. The fluid causing laumontitization in the Axi gold deposit is similar to those causing hot spring type gold deposit or in modern geothermal field.The fluidization of the Axi gold deposit happened in Carboniferous, showing the West Tianshan is a good district for epithermal gold mineralization and preservation. So west Tianshan is prospecting for exploring epithermal gold deposit.
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Researches in Models of Allometric Analysis of Urban Systems and Forecast of Urbanization Level Based on RS Data of Urban Area
CHEN Yanguang,ZHOU Yixing
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract743)            Save
The model of allometric growth relationships between urban area and population, A=aPb, can be rewrited as A(t)=a1P(t)b1 for cities as systems, or as A(k)=a2P(k)b2for systems of cities, where A is the land area, P is the population size, a is the proportionality coefficient, b is the scaling factor, t is the time (year), and k is the rank of city k. It was proved that the parameter b has fractal dimension nature and can be expressed as b=Da/Dp, where Da is the generalized dimension of urban area,and Dp,the dimension of urban population. With fractal theory related the hierarchical structure of urban systems and the dynamics of urbanization can be analysed. On the other hand,by defining As=∑A(k),Ps=∑P(k), it is easy to have a new model As(t)=a3Ps(t)b3, so once obtaining RS data of A(k), the value of Ps in year t can be calculated. Going a step further, it is possible to analyse cities and systems of cities and predict the course of regional urbanization by means of integrating the allometric growth models and the RS data into geographical information systems. Allometric analyses of the urban system of Henan, China, are made as examples to show how to use the models advanced in the paper.
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A Study of Multifractal Measures of the Spatial Structure of the Urban System in Central Plains
CHEN Yanguang,ZHOU Yixing
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract618)            Save
The study is made of the spatial structure of the systems of cities and towns in Central Plains, mainly including North Henan, China, using the theory of multifractals. By means of the box counting method and μ-weight formulae, we calculate the values of the Lipschitz-Hölder exponent α(q), the fractal dimension of the support of singularities f(α), the sequence of mass exponent τ(q), and the dimensions of fractal measures Dq of the urban systems in the studied area. The resultant values show that there is a scaling breakdown in the f(α) curve as well as the spectrum of fractal dimensions Dq when the moment order q≈-1, where qc=-1 perhaps is a critical value for q, i.e., the multifractals come on well when q∈[0, ∞], as for q≤-1, the multifractal measures are abnormal (dysplasia or hypolasia): the f(α) curve and the Dq function cannot converge, which maybe implies a sort of phase transition from a rural to urban settlement system during the course of regional urbanization. This research demonstrates that the spatial structure of urban systems can be characterized with multifractal geometry, and moreover, wavelet transformation can be used to analyse the multifractal structure of urban systems.
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Formation of the p-Toluenesulphinyl Anion from the Diester of N-Tosyl Alanine with 2, 6-Bis(hydroxylmethyl) pyridine and Its Nucleophilic Addition Product with 2, 6-Bis(chloromethyl) pyridine
CHEN Yantao,HUA Wenting
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract623)            Save
The mechanism of the formation of 2, 6-bis(hydroxymethyl) pyridine di-p -toluenesulphinate(3) and its mass spectrum were studied in detail.
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Study on the Electrochemical Behaviors of Artemisinin(Qinghaosu) and Its Derivatives Ⅱ
Reduction Mechanism of Artemisinin in the Presence of Hemin
CHEN Yang,ZHU Shimin,CHEN Hongyuan
Acta Scientiarum Naturalium Universitatis Pekinensis   
Abstract767)            Save
The interaction between artemisinin and hemin was investigated by electrochemical methods. Artemisinin was irreversibly reduced at -1.08V via a two-electron transfer at the glassy carbon electrode. In the presence of concentration of hemin as low as 4.0×10-8mol/L, artemisinin can be reduced via the hemin-catalysis and its original cathodic peak at -1.08V completely disappeared. The cathodic overpotential of artemisinin is decreased ca.600mV. This process is verified by the fact that complex EDTA-Fe(Ⅲ) can also promote the artemisinin reduction with decreasing the cathodic overpotential of artemisinin for 590mV. These results show that the reduction of artemisinin at the glassy carbon electrode is a catalytic process with the aids of hemin. Hemin can greatly decrease the cathodic activation energy of the reduction of artemisinin and promote the decomposition of artemisinin.
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