最新刊期
      卷 60 ， 期 5 ， 2021

        Invited review

      • WU Jiajing,LIU Jieli,LIN Dan,ZHENG Zibin
        Vol. 60, Issue 5, Pages: 1-12(2021) DOI: 10.13471/j.cnki.acta.snus.2021A007
        摘要：Since the debut of Bitcoin， a blockchain platform， blockchain-based cryptocurrencies have received wide attention and accumulated a wealth of transaction data. These transaction data include rich information and complete traces of financial activities， and therefore provide us an unprecedented opportunity for knowledge discovery. Networks are a universal language for describing interacting real systems， and much work on cryptocurrency transactions is conducted from a network perspective. This survey summarizes the existing work on analyzing and understanding blockchain transactions， aiming to provide a systematic guideline in this area. We first introduce the background of blockchain transaction， and then review existing research in three different aspects， i.e.， transaction network modeling， transaction network analysis， and network-based detection technology， the purpose being to provide a systematic guideline for researchers in this area.  
        关键词：blockchain;cryptocurrency transactions;complex networks;data mining   
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        发布时间：2023-11-01
      • HU Zhijian,LIU Hui
        Vol. 60, Issue 5, Pages: 13-22(2021) DOI: 10.13471/j.cnki.acta.snus.2020B125
        摘要：In view of the anti-explosion ability and safety of bridges, this paper reviews the relevant researches from the aspects of the anti-explosion dynamic response of bridges, the distribution of explosion load and pressure field, and the collapse damage of bridge structures by explosion. The research fields such as load field,dynamic response study of prestressed concrete structure, residual bearing capacity evaluation, explosion test of real bridge and explosion protection of bridge structure are prospected, which can provide reference for further research on anti-explosion of bridge, as well as theoretical reference for design of anti-explosion protection of bridge and condition evaluation of bridge after explosion.  
        关键词：anti-blast for bridges;dynamic response;the pressure field;failure modes   
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        Research articles

      • DENG Jiang,WANG Guorong,XIE Chong,ZHOU Shouwei,ZHONG Lin
        Vol. 60, Issue 5, Pages: 23-31(2021) DOI: 10.13471/j.cnki.acta.snus.2020.01.09.2020B002
        摘要：As a kind of clean energy with abundant reserves， natural gas hydrate has extremely high exploitation value and energy strategic significance. In order to the in-situ natural gas hydrate extraction environment in solid-state fluidized mining and the characteristics and the parameters such as extraction particle size of multiphase flow and the particle size of the multiphase flow during the extraction process， a set of inspection-while-drilling tools based on image technology was designed. In the simulated environment of natural gas hydrate， the strength， pressure resistance， tightness and visibility of the device were verified； the performance of the processing methods between average background and acquisition background was compared； the size distribution of particles was extracted from the flow image through processing techniques such as background subtraction， median filtering， threshold base clipping， Canny processing， morphological processing， etc. The results show that： ① the tool meets the requirements of strength while drilling， pressure resistance， and tightness， and the particle imaging has a good visibility； ② the processing average background is better than the collection background， precenting a good performance of the effect of background subtraction； ③ detected size distribution of particles is generally consistent with the experimental sampling results， which proves the feasibility of the device and lays the research foundation for the general law of multiphase flow detection and exploiting fragmentation in non-diagenetic gas hydrate mining.  
        关键词：natural gas hydrate;detection while drilling;particle size detection;background subtraction;imaging visibility   
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        发布时间：2023-11-01
      • YU Zhi,XU Huanting,HE Zhaocheng
        Vol. 60, Issue 5, Pages: 32-38(2021) DOI: 10.13471/j.cnki.acta.snus.2020.04.09.2020B029
        摘要：Short lanes formed by the widening of an entrance at an intersection may be blocked due to overflows of vehicle queues. In the view of the occurrence probability of short lane effect， this paper studies the traffic capacity calculation model of short lane at signalized intersections. Considering the coupling and continuity of short lane group vehicle movement， this paper uses Markov Chain to describe the state transition relationship between the adjacent phases of short lane vehicle. And the steady-state probability of short lane state is obtained，combined probability theory and queuing theory to construct the probability matrix of short lane state transition. Meanwhile， the steady-state traffic capacity of the short lane is obtained based on the conditional traffic capacity of the one-stage state on the short lane and the probability of the short lane state. Finally， the model is verified by VISSIM simulation software. The results show that the model in this paper is superior to the traditional HCM method in the calculation of short lane traffic capacity and is more accurate than the current mainstream model.  
        关键词：short lane;traffic capacity;Markov Chain;simulation   
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        发布时间：2023-11-01
      • CHEN Xinyang,NIE Zisen,JIANG Zichao,YANG Gengchao,YAO Qinghe
        Vol. 60, Issue 5, Pages: 39-49(2021) DOI: 10.13471/j.cnki.acta.snus.2020.07.09.2020B076
        摘要：Compared to the traditional computational fluid dynamics techniques， the Lattice Boltzmann method has the advantages of simple structure of program， strong adaptability to complex boundaries as well as nonlinear problems， and high parallelism. However， since LBM is an explicit algorithm， its calculation usually involves many iteration steps， and thereby consumes a huge amount of computing resources. This study takes advantage of deep learning in prediction and regression to accelerate LBM calculations innovatively. We establish a prediction model （compressed LBM or C-LBM）， which involves an artificial neural network composed of convolution layers and convolution long-term and short-term memory layers. The prediction model is an equivalent substitution of multiple ordinary LBM iterations. For the two dimensional driven cavity circulation problem， the mean square error of C-LBM is less than 5×10-6 for the test set， and is less than 10-5 for the generalized calculation example. The calculation efficiency of C-LBM is about 15 times higher than that of the serial LBM.  
        关键词：Lattice Boltzmann method;Data-driven Model;deep learning;algorithm acceleration   
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      • XU Jun,DENG Feng,SU Tian,LI Gangyan
        Vol. 60, Issue 5, Pages: 50-58(2021) DOI: 10.13471/j.cnki.acta.snus.2020.03.19.2020B024
        摘要：In pure electric vehicle， power battery enclosure generally made of aluminum alloy profile and is a key component of packaging and load bearing of the power battery system. Due to the large structure size and the high thermal expansion coefficient of materials， welding residual stress is easily generated after the inert-gas welding process， which leads to serious shrinkage and deformation of the inner wall. A certain type of power battery enclosure was taken as the research object. Firstly， the typical weld with unique characteristics was extracted， and the optimal solution for welding sequence direction of each typical weld was obtained through numerical simulation of stress deformation by using SYSWELD. Then， the candidate schemes of overall welding sequence direction were proposed based on the distribution characteristics of typical weld and welding process principles， and the optimal scheme was selected based on the principle of minimum mean value of equivalent deformation. Finally， the constraint conditions for welding process in x， y and z directions were determined by adopting the method of rigidity immobility. Field test results have shown that internal shrinkage deformation value of the power battery enclosure’s long and short sides is reduced by 52% and 25% than before， which are decreased to 1.2 mm and 0.9 mm respectively.  
        关键词：power battery enclosure;melt inert-gas welding;welding sequence direction;the method of rigidity immobility   
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        发布时间：2023-11-01
      • JIA Qiwen,ZHANG Guifang,TANG Shilin,ZHANG Haoran
        Vol. 60, Issue 5, Pages: 59-71(2021) DOI: 10.13471/j.cnki.acta.snus.2020D001
        摘要：The Pearl River Estuary is an indispensable region for the economic and social development of the Pearl River delta. The migration law and influencing factors of suspended sediment concentration are the core issues of the estuary research. Remote sensing inversion can realize the dynamic， continuous， and synchronous observation of a large area of water and quickly obtain the spatiotemporal distribution of suspended sediment. In this study， the Landsat 8 OLI data from 2013 to 2018 was used to analyze the correlation between the spectra and the parameters of water quality. By selecting the best band combination and using fitted equations， a remote sensing model of suspended sediment concentration is established to quantitatively invert the suspended sediment in the Lingdingyang waters of the Pearl River Estuary and calculate the dynamic changes of suspended sediment in seasons. The results show that the concentration of suspended sediment in the waters of the Lingdingyang area has clear spatiotemporal patterns， showing temporally higher concentration in summer and lower concentration in winter， and spatially strips of northeast-southwest of decreasing from the coast to the sea， i.e.， high in west and north， low in east and south. The temporal and spatial distribution of suspended sediment concentration is affected by several factors： the westward expansion of the freshwater in the Pearl River is the main factor causing the high value of suspended sediment concentration in the southwest； the underwater terrain and wind direction， have a significant impact on the distribution of suspended sediment concentration； seasonal changes in drainage， sediment discharge， and rainfall directly affect the seasonal changes of suspended sediment concentration； and human activities also have a greater impact on the changes of suspended sediment in the Pearl River Estuary.  
        关键词：the Pearl River estuary;Landsat 8 OLI;suspended sediment;spatial and temporal distribution;influence factors   
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        发布时间：2023-11-01
      • LIN Lin,WANG Xiner,ZENG Juan
        Vol. 60, Issue 5, Pages: 72-85(2021) DOI: 10.13471/j.cnki.acta.snus.2020D017
        摘要：Based on GIS kernel density estimation methods， combining with the records in local chronicles and villagers' interviews， 2 270 place-name cultural landscapes， including urban and rural settlements， residential areas and plots in Xinhui， were studied. It’s found that the place-names were distributed sparsely in the east and the south， and densely in the north and the east in Xinhui. There are less natural landscape place-names which belted distributing according to the Gudou and Niugu mountains and the tributary of Xi and Tan River. More cultural landscape place-names in Xinhui multi-pointed and beaded distributing in centers of Huicheng， Siqian， Luokeng and three provincial highways. Distribution center swinging migrated by the tributary of upstream of Tan River to both sides of downstream which in eastern part. All kinds of spatial distribution of geographic entities， move and integration of a large population since the Song Dynasty， the oceans piled up into land and the agricultural production proliferated since the Ming Dynasty， the thought about national cultural revival in the republic of China era， the overseas Chinese hometown culture and the rapid rise of commercialization in modern real estate since modern times， all affected the distribution and evolution of place-name. Natural environment constantly and importantly impacting the distribution of place-names which determined by the settlement location. Expression of human characteristics to the connotation of settlements is more and more recognized by residents than natural’s. In recent years， rapid commercialization of real estate resulted in a large number of "big"， "strange" place-names which have a large deviation in the expression of settlement connotation， seriously damaged the inheritance of place-name culture， needed correctly guiding by studying the evolution of place-name culture in Xinhui， strengthening the standardized management， building the positive social atmosphere and guiding the public participation and supervision.  
        关键词：place-name;cultural landscape;Kernel density estimation;spatial distribution;Xinhui   
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        发布时间：2023-11-01
      • HUANG Fenghua,HUANG Bensheng,QIU Jing
        Vol. 60, Issue 5, Pages: 86-93(2021) DOI: 10.13471/j.cnki.acta.snus.2020.06.04.2020D024
        摘要：Based on economic and social indicators and water resources data of Guangdong Province from 2006 to 2018， the Gini coefficient and the equilibrium coefficient of coordinated development are used to research the spatial equilibrium of water resources by constructing a calculation model of water resource load index， matching coefficient of water and soil resources， and water resource benefit index.In 2018， the water resources load index of Guangdong Province was 4.0 in grade Ⅲ， which is a medium level of development and utilization. The water resources load gap was very different from city to city with the highest Gini coefficient of 0.79. It was expressed in areas with large economic aggregates， dense populations， and relatively insufficient water resources， which have a high degree of development and utilization and low potential. The water resources load index shows an increasing trend year by year， with the Gini coefficient between 0.7 and 0.8.The matching coefficient of water and soil resources in Guangdong was 8.3， with the Gini coefficient of 0.69， indicating the spatial distribution of the matching degree in water and soil resources in each city was quite different. The GDP output value per cubic meter of water was 240 Yuan in RMB， with the Gini coefficient of 0.47，which was 22 times higher in the cities with the greatest water efficiency than in those with the smallest. The average value of the spatial equilibrium coefficient of water resources in the province was 0.79 from 2006 to 2018， indicating that the spatial equilibrium level of water resources in Guangdong province was level Ⅳ， which was a moderate imbalance.  
        关键词：Guangdong province;water load index;matching soil and water resources;water efficiency;Gini coefficient;equilibrium coefficient   
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        发布时间：2023-11-01
      • MA Yingping,LI Yanhong,YAN Jingjie
        Vol. 60, Issue 5, Pages: 94-102(2021) DOI: 10.13471/j.cnki.acta.snus.2020.08.02.2020D033
        摘要：In order to study the pollution status of NO2 and SO2 in Karamay city， Xinjiang， and understand their spatial and temporal distribution characteristics and influencing factors， multi-axis differential absorption spectrometer （MAX-DOAS） was used to conduct fixed-point monitoring and vehicle-mounted mobile round-town monitoring in Karamay City to obtain the concentration data of NO2 and SO2 vertical columns in 2018. The daily variation of NO2 and SO2 shows a U-shaped characteristic. The concentration of NO2 vertical column is generally higher during 9：00 - 11：00， 17：00 - 19：00， and lower during 11：00 - 17：00. The vertical column concentration of SO2 is generally higher during 11：00 - 13：00， 15：00 - 17：00， and lower during 13：00 - 15：00， namely high in the morning and evening low at noon. The seasonal variation of NO2 and SO2 shows a characteristics of winter ＞ autumn ＞ spring and summer. On the whole， the concentration of NO2 vertical column is higher than that of SO2 vertical column.The concentration of NO2 vertical column and SO2 vertical column is closely related to wind direction and wind speed， showing that the higher the wind speed is， the greater the pollution range is. And because of the special geographical conditions and meteorological factors， the pollutants are difficult to disperse in time.Backward trajectory analysis shows that the pollutants mainly come from other places. Among the influences of air mass transmission from the external regions， Karamay city is mainly affected by the long-distance transmission of air mass from the northwest （accounting for 51.12%～75.83%） and the short-distance transmission of air mass from the east （accounting for 14.0%～26.37%）.  
        关键词：Karamay city;vertical column concentration of NO2;vertical column concentration of SO2   
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        发布时间：2023-11-01
      • SUN Tingzhe,CUI Jun
        Vol. 60, Issue 5, Pages: 103-110(2021) DOI: 10.13471/j.cnki.acta.snus.2021E003
        摘要：The pandemic of emerging coronavirus disease 2019 （COVID-19） has been a serious threat to public health. Specifically， the asymptomatic patients are not easily identified but contribute significantly to coronavirus transmission. We used a previously developed SCIRA model with asymptomatic populations， fitted the model to the epidemic data and performed stochastic simulations. The results showed that complete recovery of asymptomatic patients usually showed remarkable delays compared to that of diagnosed cases. The mutual contacts among populations can be significantly lowered under strictly controlled measures to impede COVID-19 transmission. If strict interventions are only maintained for short durations after curation of all diagnosed patients， there might be potentially a second outbreak owing to asymptomatic patients. Therefore， strict interventions should be continuously implemented to impede potential COVID-19 transmission even after diagnosed patients are all cured.  
        关键词：COVID-19;strict intervention;asymptomatic patient;delayed recovery   
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        发布时间：2023-11-01
      • DAI Qiaokun,HUA Hong,REN Jinjie,CUI Zaihang,LUO Jinzhou,PAN Xiaoqiang
        Vol. 60, Issue 5, Pages: 111-118(2021) DOI: 10.13471/j.cnki.acta.snus.2020.06.30.2020E026
        摘要：A small sea tank with a volume of 45 cm × 40 cm × 40 cm was set up to simulate the establishment of a simple marine ecosystem in mid-May， 2019. Three living corals were added and cultured in tank with artificial ratio water for observation and research. From the middle of May to the middle of November， this sea tank has gone through three stages： “appropriate environment establishment and bloom of algae” “adding of new organisms and colonization” and “the stabilization of seawater tank”. It was found that the succession of community followed a certain niche substitution rule. Many species have appeared in the process of coral growth and marine environment evolution， and the growth stage patterns of Caulerpa and tubeworms have been summarized in corresponding to the colonization of the corals and a large number of other new species. The record of this tank can reconstruct the formation process of a small stable marine ecosystem， which not only provides some references for the observation experiment of sea tanks and culturists， but also for palaeoecology.  
        关键词：seawater tank;community succession;coral;tube worms;Caulerpa   
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        发布时间：2023-11-01
      • WANG Xue,FU Xue,SAI Xuqi,WANG Jiajia,YU Huiling,YE Lefu
        Vol. 60, Issue 5, Pages: 119-125(2021) DOI: 10.13471/j.cnki.acta.snus.2020E052
        摘要：Under various adversity factors， male and female multicolored lady beetles individuals show different tolerances， resulting in imbalance of sex ratio. Understanding the species to respond differently from other species and maintain high fecundity and adaptability can explain why this predatory natural enemy breaks out in the world. In this experiment， 5 SR （female∶male=1∶9， 3∶7， 5∶5， 7∶3， 9∶1） treatments were set up， and oviposition， hatching rate， development duration， and other traits were observed. The results showed that： ① Populations with a 1∶1 SR had the highest oviposition number and reproductive rate per female， and shorter larvae & pupae developmental time. ② The populations with more females laid more eggs. ③ The female lifespan was longer when there were fewer males. It can be inferred that the optimal sex ratio of multicolored lady beetles is 1∶1. When the population is affected by environmental factors that are obviously unfavorable or favorable to the specific sex， the species will respond to the sex ratio to a certain extent， and can always recover to the optimal sex ratio through one generation reproduction after the stress factor is removed. While on the optimal sex ratio， the fecundity of multicolored lady beetles is the strongest； the natural population's sex ratio can always be balanced at the best value， that is， it has outstanding self-regulation ability of sex ratio， which may be one of the important reasons for the outbreak of multicolored lady beetles.  
        关键词：lady beetles;sex ratio;fecundity;outbreak   
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        发布时间：2023-11-01
      • SUN Yani,WU Shuhong
        Vol. 60, Issue 5, Pages: 126-135(2021) DOI: 10.13471/j.cnki.acta.snus.2020.05.29.2020C013
        摘要：Environmental education is one of the main functions of nature reserves， and the standardization of management measures， educational contents， educational methods and other elements is the prerequisite to ensure the best order of environmental education in nature reserves in China. This study designed a total of 58 elements of environmental education in nature reserves in four categories： basic management， staffing， educational methods， and facility systems. The PCI values and the average agreement of the four types of factors were compared by distributing questionnaires to the environmental education expert group and processing the results of the questionnaire using the potential conflict indicators （PCI） method. The research results showed that： 1） A total of 51 elements of the four types of elements have been generally recognized by the industry，only 1 item needs to be modified， which is of reference significance in the development of environmental education in nature reserves； 2） The basic management elements have the highest average degree of agreement， which is the core component of environmental education in nature reserves. The second is the facility system， staffing and educational means， which are an indispensable part of the environmental education of nature reserves；3） It is necessary to start from management elements such as rules and regulations， work plans， funding and policy guarantees， safety supervision and training， explainers， experts， cooperative institutions and other personnel elements， various types of educational methods and complete educational facilities， to strengthen environmental education in nature reserves. Finally， based on the research results， it is recommended to speed up the standardization of environmental education and integrate environmental education with the internet and technology.  
        关键词：environmental education;potential conflict indicator （PCI）;nature reserve   
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        发布时间：2023-11-01
      • DING Weijia,YE Juntao,SHE Zhigang,ZHONG Aiqing,LI Ziyang,LIN Longsheng,XIONG Yahong,LI Chunyuan
        Vol. 60, Issue 5, Pages: 136-140(2021) DOI: 10.13471/j.cnki.acta.snus.2020C020
        摘要：The study investigated the metabolites by solid fermentation of the endophytic fungus Fusarium sp. R5 from the semi-mangrove plant Myoporum bontioides A. Gray . The metabolites were isolated from the ethanol extract by the chromatography technology. Their structures were elucidated by spectral methods. The antifungal activities were evaluated using the dilution method. Ten compounds， ZSU-H85 A （1）， 7-acetyl-1， 3， 6-trihydroxyanthracene-9， 10- dione （2）， 6-［（7S， 8R）-8-propyloxiran-1-yl］-4-methoxy-pyran-2-one （3）， 6-pentyl-4-methoxy-pyran-2-one （4）， xylapyrone C （5）， simplicilopyrone （6）， 2-（Hydroxymethyl）-3-propylphenol （7）， （-）-brassicadiol （8）， ergosterol and ergosterol peroxide were isolated. Among them， compounds 3-8 were obtained from Fusarium sp. for the first time. Compound 6 exhibited a high inhibitory activity against Colletotrichum musae （Berk. And M. A. Curtis） Arx. and Fusarium oxysporum Schlecht. f. sp. lycopersici （Sacc.） W. C. Snyder et H. N. Hansen. Compounds 6，7 and 8 showed moderate inhibitory activities against O1 and O2 serotypes of avian pathogenic Escherichia coli.  
        关键词：mangrove endophytic fungus;Fusarium sp.;metabolites;antimicrobial activity   
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        发布时间：2023-11-01
      • ZHAO Yu,LIU Fang,KE Zhuofeng,LIU Jun,GAO Feng,MA Hongyuan,WANG Zuocheng
        Vol. 60, Issue 5, Pages: 141-151(2021) DOI: 10.13471/j.cnki.acta.snus.2020C017
        摘要：The optical isomerization of amphoteric S-α-Ala·Na+ in water-liquid phase environment was investigated by using the M06-2X method based on density functional theory and the SMD model method based on self consistent reaction field （SCRF） theory. The results showed that the optical isomerization of S-α-Ala·Na+ has three channels a，b and c. In channel a， the proton transfers with amino nitrogen as a bridge after the isomerization of amphoteric S-α-Ala·Na+ to neutral S-α-Ala·Na+. And the proton is transferred merely using carbonyl oxygen as a bridge in channel b. In channel c， the proton transfers to α-C from protonation amino after α-H is transferred to carbonyl oxygen. The potential energy surface showed that the channel a has the most advantage under the effect of recessive solvent and the energy barrier of the rate-determining step is 234.8 kJ·mol-1； While channel b and c had a disadvantage， they both have the common energy barrier of the rate-determining step about 267.9 kJ·mol-1. Under the effect of explicit solvent， channel a turned to an inferior channel， and its energy barrier of the rate-determining step is between 155.9 and 156.5 kJ·mol-1； channel b and c have a slight advantage and the energy barrier of the rate-determining step is between 132.2 and 138.6 kJ·mol-1. The results showed that α-alanineNa（I） complex could only racemize at an extremely slow speed in the water-liquid environment.  
        关键词：α-alanine（α-Ala）;sodium ion （Na+）;optical isomerization;density functional theory;self consistent reaction field theory;transition state;energy barrier   
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        发布时间：2023-11-01
      • SUN Meng
        Vol. 60, Issue 5, Pages: 152-165(2021) DOI: 10.13471/j.cnki.acta.snus.2020.04.30.2020B047
        摘要：Let (X,d,μ) be a metric measure space with non-negative Ricci curvature. This paper is focuses on the Cauchy problem for the heat equation on the upper half-space X×R+.The heat equation is∂xu(x,t)-Δxu(x,t)=0,   x∈X,   t>0u(x,0)=f(x),   x∈X,where Δx is the Laplace operator on X. We derive that a function f of bounded mean oscillation BMO is the trace of solution u(x,t) of heat equation above （called Caloric function）， u(x,0)=f(x)， whenever u satisfies the following Carleson measure condition（*） supxB,rB1μ(B(xB,rB))∫0rB2∫B(xB,rB)|t∂tu|+|t∇xu|2dμdtt≤C ，Conversely， the condition (*) characterizes all the Caloric functions whose traces are in BMO space.  
        关键词：Caloric function;metric measure space;BMO;Carleson measure   
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        发布时间：2023-11-01
      • LIU Lindong,WU Yilin
        Vol. 60, Issue 5, Pages: 166-174(2021) DOI: 10.13471/j.cnki.acta.snus.2020.04.21.2020A014
        摘要：In the heterogeneous and distributed computing environment of fog computing， in order to improve the efficiency of fog computing and allocate appropriate resources to corresponding tasks， task scheduling problem needs to be studied. The scheduling of pipeline independent tasks is studied. Firstly， based on the traditional Apriori algorithm， a task classification algorithm I-Apriori algorithm in fog computing environment is proposed. Association rules generated by I-Apriori algorithm are combined with the weighted earliest completion time of tasks in the task set. Tasks appear in the association rules are selected to schedule first， other fog nodes are scheduled according to the earliest completion time and the number of weighted links. The performance of ITPS algorithm is evaluated by simulation experiments. The results show that ITPS algorithm has a good performance in makespan and AWT.  
        关键词：fog computing;task scheduling;association rule;fog computing node   
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        发布时间：2023-11-01
      • DU Zhenye,LAN Shiyi
        Vol. 60, Issue 5, Pages: 175-184(2021) DOI: 10.13471/j.cnki.acta.snus.2020.06.18.2020A027
        摘要：The Loewner differential equation is a partial differential equation that generates a Loewner chain. An estimation of the solution of the dipolar Loewner differential equation for time-direction is first derived by using Bieberbach theorem.Based on the reverse-time Loewner equation the difference of two solutions to the dipolar Loewner equation with two different deriving functions is estimated in terms of the supremum norm of the difference of the two driving functions. This generalizes some related results for the chordal and radial Loewner equations to the dipolar setting.  
        关键词：Loewner differential equation;driving function;stochastic Loewner evolution （SLE）   
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        发布时间：2023-11-01
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