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Memory Function and Fractional Intergral Associated to the Random self-similar Fractal

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Chinese Quarterly Journal of Mathematics 2003年第2期18卷 186-191页

作者： LIANG Hong-liang,liu Xiao-shu(department of Mathematics, shangqiu teacher’s college, shangqiu 476000, china) department of Mathematics Shangqiu Teacher's College Shangqiu 476000

For a physics system which exhibits memory,if memory is preserved only at points of random self-similar fractals,we define random memory functions and give the connection between the expectation of flux and the fractional *** particular,when memory sets degenerate to Cantor type fractals or non-random self-similar fractals our results coincide with that of Nigmatullin and Ren et al.

关键词： random self-similar fractals memory functions memory measures Laplace transform

The spaces bp with 0 < p < 1

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Chinese Quarterly Journal of Mathematics 2004年第4期19卷 331-337页

作者： HU Zhang-jian, liu Tai-shun(1.department of Mathematics, University of science and Technology of china, Hefei 230026, china 2.department of Mathematics, Huzhou teacher's college, Huzhou 313000, china ) department of Mathematics University of Science and Technology of China Hefei 230026China department of Mathematics Huzhou Teacher's College Huzhou 313000China department of Mathematics University of Science and Technology of China Hefei 230026China

Let 0 < p < 1. In this paper we prove that the Bergman norm on the p-th Bergman space bp(H) is equivalent to certain "normal direction norm" as well as certain "tangential direction norm", where H = Rn-1 × R+ is the ... 详细信息

Let 0 s paper we prove that the Bergman norm on the p-th Bergman space bp(H) is equivalent to certain "normal direction norm" as well as certain "tangential direction norm", where H = Rn-1 × R+ is the upper half space. As an application, we get the boundedness of harmonic conjugation operators on bp(H).

关键词： Bergman space upper half space harmonic conjugation

WEAK TYPE INEQUALITIEs FOR FRACTIONAL MAXIMAL OPERATOR ON WEIGHTED ORLICZ sPACEs

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Analysis in Theory and Applications 1999年第4期15卷 64-70页

作者： liu Zongguang (Huaihua teacher’s college, china).

The fractional maximal operator on homogeneous space (X, d, μ) is de fined as

关键词： oscillatory integral operator multiplier singularity

Regulation of the pore structure of carbon nanosheets based electrocatalyst for efficient polysulfides phase conversions

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Journal of Materials science & Technology 2024年第4期171卷 37-46页

作者： Xiaoyang liu Jingbo Zhang Kangli liu shijie Zhang Rouhan Hou Xiaoyi Hu Peng Zhang Guosheng shao state Center for International Cooperation on Designer Low-Carbon&Environmental Materials(CDLCEM) School of Materials Science and EngineeringZhengzhou UniversityZhengzhou 450001China Zhengzhou Materials Genome Institute(ZMGI) Xingyang 450100China

The practical applications of lithium-sulfur(Li-s)batteries are hampered by the sluggish redox kinetics and polysulfides shuttle in the cyclic process,which leads to a series of problems including the loss of active materials and poor cycling *** this paper,the pore structures of carbon nanosheets based electrocatalysts were precisely controlled by regulating the content of water-soluble KCl *** relationship between pore structures and Li-s electrochemical behavior was studied,which demonstrates a key influence of pore structure in polysulfides phase *** the liquid-sloid redox reaction of polysulfides,the micropores and small mesopores(dso-pores(d>20 nm)and macropores played a decisive *** a typical exhibition,the nickel-embedded carbon nanosheets(Ni-CNs)with a high content of large mesopores and macropores can aid Li-s batteries in exhibiting stable cycling performance(760.1 mAh g^(-1)at 1 C after 300 cycles)and superior rate capac-ity(847.8 mAh g^(-1)at 2 C).Furthermore,even with high sulfur loading(8 mg cm^(−2))and low electrolyte(E/s is around 6μL mg^(-1)),the high area capacity of 7.7 mAh cm^(−2)at 0.05 C could be *** work can provide a guideline for the design of the pore structure of carbon-based electrocatalysts toward high-efficiency sulfur species redox reactions,and afford a general,controllable,and simple approach to constructing high performance Li-s batteries.

关键词： Hierarchical porous carbon network Electrocatalyst Molten salt templating method Modified separators Li-s batteries

Resonant Interaction between Atom and Large Period Quantized standingLight Wave in a Quantized Trap

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Chinese Journal of Lasers 1997年第1期B6卷 39-42页

作者： WANG Xiaoguang Xie Chengjun liu Xiuhuan liu Xiaohua(department of Computer, Changchun University, Changchun,130022 Changchun Institute of Physics, Chinese Academy of scieces, Changchun, 130021 department of Physics,Jilin teacher's college, Jilin, 132011 Chungchun Univ Changchun China

A two-level atom in a quantized trap interacting with a large period quantized standing light wave is considered, an exactly solvable model is obtained. The coupling coeffiecients between the atom and the field are ti... 详细信息

关键词： quantized trap coherent state collapse and revival phenomenon

Wetland changes in Jianghan Plain and simulation with GIs

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Journal of Geographical sciences 1998年第3期8卷 116-121页

作者： ZHANG Huanhai department of Geography, Daqing teacher’s college, Daqing 163716 china liu Haiyan Commission for Integrated survey of Natural Resources, Chinese Academy of sciences Beijing 100101 china

Wetland plays an important role in the tempo spatial evolution of climate, biogeochemistry and biodiversity of the terrestrial ecosystems of the earth. To trace the patterns of wetland changes in the past and predict the changing trends in the future in the dimension of human activities is an arduous task for geographers and ecologists. The paper describes how to combine GIs with geo informatics and geography to simulate the wetland changes happened in Jianghan Plain in the middle reaches of the Yantze River in the last 40 years, and presents the results. The environmental implications of the wetland changes are discussed.

关键词： wetland ecosystems biodiversity GIs remote sensing Jianghan Plain.

α-Oxoketene Cyclic s, s-cetals Chemistry-substitution Reaction of α,α'-Dicinnamoyl Ketene Cyclic s, s-Acetals with Ethylenediamine

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Chinese Chemical Letters 1998年第3期9卷 231-232页

作者： Mei Xin ZHAO Qun liu Fu shun LIANG Jing Fu liu Bao Zhong ZHAO LianZhong LI (department of Chemistry, Northeast Normal University, Changchun, 130024)(department of Chemistry, Jilin teacher college, Jilin, 131000) department of Chemistry Northeast Normal University Changchun 130024 China

α,α'-Dicinnamoyl ketene cyclic s, s-acetals 4 were reacted with ethylenediamine to afford α,α'-dicinnamoyl ketene cyclic N,N-acetals 5. This process provides a new method for thesynthesis of 5 in high yield under ... 详细信息

关键词： α,α'-dicinnamoyl ketene cyclic s,s-acetals ethylenediamine substitution reaction,α,α'-dicinnamoyl ketene cyclic N,N-acetals

sTUDY ON HARVEsTED POPULATION WITH DIFFUsIONAL MIGRATION

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Journal of systems science & Complexity 2001年第2期14卷 139-148页

作者： FAN Meng WANG Ke (Deportment of Mathematics, Northeast Normal University, Changchun 130024, china) ZHANG Yujuan ZHANG shuwen liu Huimin (department of Mathematics, Anshan teacher’s college, Anshan 114005, china) 东北师范大学吉林长春 130024 鞍山师范学院辽宁鞍山 114005

This paper is devoted to the study of the dynamical behavior and harvesting problem of an exploited population with diffusional migration, for which a protective patch is established. We examine the effects of protective patch and harvest on the population resources and conclude that the protective patch is effective for the conservation of population resources and ecological environment, though in some cases the extinction can not be eliminated. The dangerous region, the parameters domains and the typical bifurcation curves of stability of steady states for the considered system are determined. The optimal harvest policy for the considered population is made also. The explicit expressions are obtained for the optimal harvesting effort, the maximum sustainable yield and the corre- sponding population density. Our results provide a theoretical evidence for the practical management of biological resources.

关键词： Protective patch diffusional migration harvest.

Persistence and Global stability for Two-species Predator-Prey system With Diffusion

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systems science and systems Engineering 1999年第4期9卷 108-115页

作者： liu He\|long,\ WU Jin\|gang Dept. of Math., Xinyang teacher′s college, Xinyang 464000, china

In this paper, a predator\|prey model with diffusion is studied. The system, which is composed of two Lotka\|Volterra patches, has two species: one can diffuse between two patches, while the other is confined to one patch and can not diffuse. It is proved that the system can be made persistent. Further more, sufficient conditions are established for the global stability of the system.

关键词： diffusion persistent periodic orbit global asymptotic stability