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Symmetry theories of Hamiltonian systems with fractional derivatives

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Science China(Physics,Mechanics & Astronomy) 2011年第10期54卷 1847-1853页

作者： ZHOU Sha fu Hao fu JingLi Institute of Mathematical Physics Zhejiang Sci-Tech University Hangzhou 310018 China China Jingye Engineering Corporation Limited Shenzhen Branch Shenzhen 518054 China

The Noether and Lie symmetries as well as the conserved quantities of Hamiltonian system with fractional derivatives are es-tablished. The definitions and criteria for the fractional symmetrical transformations and quasi-symmetrical transformations inthe Noether sense of Hamiltonian system are first discussed. Then, using the invariance of Hamiltonian action under the infini-tesimal transformations with respect to time, generalized coordinates and generalized momentums, the fractional Noethertheorem of the system is obtained. further, the Lie symmetry and conserved quantity of the system are acquired. Two exam-ples are presented to illustrate the application of the results.

关键词： symmetry conserved quantity Hamiltonian system fractional derivative

Effect of geometric parameters and grazing incidence on magnetic polaritons excited in 1D multi-groove gratings

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Science China(Technological Sciences) 2021年第8期64卷 1589-1598页

作者： Su ChengShuai fu CeJi LTCS and Department of Mechanics and Engineering Science College of EngineeringPeking UniversityBeijing100871China

In this paper,effect of geometric parameters and grazing incidence on excitation of magnetic polaritons(MPs)in a 1D multigroove grating with different groove depths made of silver was *** results reveal that when the distance between grooves is sufficiently small,the resonance wavelengths of MPs excited in the grooves of unequal depths exhibit red shift with decrease of the distance,contrary to the case with equal groove *** shift of the MP resonance wavelengths was explained with the LC circuit ***,it was found that the resonance wavelengths of MPs depend linearly on the groove depths except when the difference between the groove depths is *** the grooves have equal depths,a large drop of the absorptance can occur due to the interaction and cancellation of the electric field vectors in the region between the ***,the results show that when a TM wave is at grazing incidence,MPs can be excited simultaneously in the grooves at a blue-shifted wavelength due to reduction of the effective capacitance,resulting in a dramatic enhancement of the ***,the results in this work may provide useful guidance in the design of wavelength-selective absorbers based on MPs.

关键词： multi-groove grating magnetic polaritons absorptance LC circuit model

The Actin Cytoskeleton and Signaling Network during Pollen Tube Tip Growth

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Journal of Integrative Plant Biology 2010年第2期52卷 131-137页

作者： Ying fu State Key Laboratory of Plant Physiology and Biochemistry Department of Plant Sciences College of Biological Sciences ChinaAgricultural University Beijing 100193 China

The organization and dynamics of the actin cytoskeleton play key roles in many aspects of plant cell development. The actin cytoskeleton responds to internal developmental cues and environmental signals and is involved in cell division, subcellular organelle movement, cell polarity and polar cell growth. The tip- growing pollen tubes provide an ideal model system to investigate fundamental mechanisms of underlying polarized cell growth. In this system, most signaling cascades required for tip growth, such as Ca^2＋-, small GTPases- and lipid-mediated signaling have been found to be involved in transmitting signals to a large group of actin-binding proteins. These actin-binding proteins subsequently regulate the structure of the actin network, as well as the rapid turnover of actin filaments （F-actin）, thereby eventually controlling tip growth. The actin cytoskeleton acts as an integrator in which multiple signaling pathways converge, providing a general growth and regulatory mechanism that applies not only for tip growth but also for polarized diffuse growth in plants.

关键词： No English Key Word

Sharp Observability Inequalities for the 1-D Plate Equation with a Potential

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Chinese Annals of Mathematics,Series B 2012年第1期33卷 91-106页

作者： Xiaoyu fu College of Mathematics Sichuan UniversityChengdu 610064China Department of Mathematics Indian Institute of TechnologyBombayMumbai 400076India

This paper deals with the problem of sharp observability inequality for the 1-D plate equation wtt ＋ wxxxx ＋ q（t, x）w = 0 with two types of boundary conditions w = wxx = 0 or w = wx = 0, and q（t, x） being a suitable potential. The author shows that 2 the sharp observability constant is of order exp（C｜｜q｜｜^2/7∞） for ｜｜q｜｜∞〉 1. The main tools to derive the desired observability inequalities are the global Carleman inequalities, based on a new point wise inequality for the fourth order plate operator.

关键词： Observability inequality Plate equation Point-wise estimate Carlemanestimate

Investigation of the interfacial properties for CO_2-methanol and CO_2-ethanol mixtures

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Science China Chemistry 2011年第5期54卷 856-862页

作者： fu Dong School of Environmental Science and Engineering North China Electric Power UniversityBaoding 071003China

An equation of state (EOS) applicable for the interfacial properties of CO2-methanol and CO2-ethanol mixtures was established by combining the cross-association EOS and the density gradient theory (DGT). The correlated surface tensions of CO2-ethanol mixtures agreed well with the experimental data. The results illustrated the temperature and pressure dependence of the cross-association between CO2 and alcohol hydroxyls in the whole vapor-liquid surface,and the influence of the cross-association on the calculation of the surface tensions of binary mixtures.

关键词： CO2-methanol CO2-ethanol cross-association density gradient theory interfacial properties

Equivalent characterizations of Hardy spaces with variable exponent via wavelets

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Frontiers of Mathematics in China 2019年第4期14卷 737-759页

作者： Xing fu Faculty of Mathematics and Statistics Hubei University Wuhan 430062 China

Via the boundedness of intrinsic g-functions from the Hardy spaces with variable exponent,Hp(·)(Rn),into Lebesgue spaces with variable exponent,Lp(·) (Rn),and establishing some estimates on a discrete Littlewood-Paley g-function and a Peetre-type maximal function,we obtain several equivalent characterizations of Hp(·)(Rn) in terms of wavelets,which extend the wavelet characterizations of the classical Hardy *** main ingredients are that,we overcome the difficulties of the quasi-norms of Hp(·)(Rn) by elaborately using an observation and the Fefferman-Stein vector-valued maximal inequality on Lp(·)(Rn),and also overcome the difficulty of the failure of q =2 in the atomic decomposition of Hp(·) (Rn) by a known idea.

关键词： Hardy space Peetre-type maximal function Littlewood-Paley g-function variable exponent wavelet atom

RELATIVITY AND SUSTAINABLE DEVELOPMENT

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Chinese Geographical Science 2004年第1期14卷 75-81页

作者： YEDai-fu DepartmentofGeography HuizhouUniversityHuizhou516007P.R.China

From the realism of science, and taking the guide of EINSTEIN’s Relativity as guide, this article called in question the present theory of the sustainable development by the rational thinking of philosophy and a close logic inference. It is found that there are many paradoxes to the theory. Through more deepening and meticulous inference, we arrived at philosophic language of science about the sustainable development. The sustainable development is "non-sustainable development", and the non-sustainable development is "the best sustainable development". While carrying out philosophical principle thinking and repeating science demonstration for the sustainable development, this article got further confirmation that the existence of human being at the minimum environment cost may help them obtain motive power of the sustainable development. In fact, this foundation motive power exists in the flow of development in different organization levels, meanwhile it exists in strategy of intuition living of the ancient people. Only in relative lower environment cost to live can we get the support system of science for the sustainable development, and be able really to achieve the basic goal of the sustainable development.

关键词： the Relativity sustainable development existence at minimum environment cost relative development surface

An example of special Lagrangian fibration

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Science China Mathematics 2005年第8期48卷 1027-1032页

作者： fu Jixiang Institute of Mathematics of fudan University Shanghai 200433 China

On the total space of the line bundle π: π*1T*P1(◎)π2*T*P1 → P1× P1, acomplete Ricci-flat Kaehler metric and a smooth special Lagrangian fibration are *** special Lagrangian fibration is smoothly built up of 4 H... 详细信息

关键词： special Lagrangian, special Lagrangian fibration, complete Ricci-flat Kaehler metric.

From Climate to Global Change:Following the Footprint of *** YE's Research

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Advances in Atmospheric Sciences 2017年第10期34卷 1159-1168页

作者： Congbin fu Nanjing University NanjingJiangsu 210023China Institute of Atmospheric Physics Chinese Academy of SciencesBeijing 100029China

To commemorate 100 years since the birth of Professor Duzheng YE, this paper reviews the contribution of Ye and his research team to the development from climate to global change science in the past 30 or so years, including：（1） the role of climate change in global change;（2） the critical time scales and predictability of global change;（3） the sensitive regions of global change—transitional zones of climate and ecosystems; and（4） orderly human activities and adaptation to global change, with a focus on the development of a proactive strategy for adaptation to such change.

关键词： Professor Duzheng YE climate change global change human activity proactive adaptation