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Willmore Surfaces in Spheres via Loop Groups Ⅳ: On Totally Isotropic Willmore Two-Spheres in S^(6)

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Chinese Annals of Mathematics,Series B 2021年第3期42卷 383-408页

作者： peng wang College of Mathematics&Informatics FJKLMAAFujian Normal UniversityQishan CampusFuzhou 350117China

In this paper the author derives a geometric characterization of totally isotropic Willmore two-spheres in S^(6), which also yields to a description of such surfaces in terms of the loop group language. Moreover, applying the loop group method, he also obtains an algorithm to construct totally isotropic Willmore two-spheres in S^(6). This allows him to derive new examples of geometric interests. He first obtains a new, totally isotropic Willmore two-sphere which is not S-Willmore(i.e., has no dual surface) in S^(6). This gives a negative answer to an open problem of Ejiri in 1988. In this way he also derives many new totally isotropic, branched Willmore two-spheres which are not S-Willmore in S^(6).

关键词： Totally isotropic Willmore two-spheres Normalized potential Iwasawa decompositions

An analytical analysis for the mechanical performance of fully-grouted rockbolts based on the exponential softening model

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International Journal of Mining Science and Technology 2022年第5期32卷 981-995页

作者： Zhongwen Yue Akang Li peng wang peng wang Department of Mechanics and Civil Engineering China University of Mining and Technology-BeijingBeijing 100083China Pan-China Construction Group Co. Ltd.Beijing 100070China

This paper presented a novel bond-slip model to better reveal the mechanical behavior of the bolt-grout interface for fully-grouted rockbolts under tensile loads by considering the non-linear response in the softening *** exponential decay function is adopted for describing the non-linear response in the softening *** on the improved bond-slip model,the corresponding analytical solutions for the interfacial shear stress and the axial force of the bolt under different loading stages are ***,the validity of this proposed model was verified by comparing with the experimental *** results show that compared with the linear softening model,the proposed model is more suitable for predicting the mechanical performance of fully-grouted ***,a series of parametric studies are conducted to explore the effect of model parameters on the mechanical properties of fully-grouted *** results indicate that compared with the anchor length,the bolt diameter and the bond strength of the bolt-grout interface have a significance influence on the ultimate load of bolt,especially for the elastic and softening ***,it can be found that using the linear softening model maybe overestimates the supporting performance of grouted bolt,resulting in an unsafe design for bolt.

关键词： Fully-grouted rockbolts Non-linear response Bond-slip model Anchor length Analytical solutions

Perturbation to Noether Symmetry and Noether adiabatic Invariants of Discrete Mechanico-Electrical Systems

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Chinese Physics Letters 2011年第4期28卷 8-11页

作者： wang peng College of Physics and Electronic Engineering Xinjiang Normal UniversityUrumqi 830054 Shanghai Institute of Applied Mathematics and Mechanics Shanghai UniversityShanghai 200072

Perturbation to Noether symmetry of discrete mechanico-electrical systems on an uniform lattice is ***,Noether theorem of a system is ***,the criterion of perturbation to Noether symmetry of the system is *** on the definition of adiabatic invariants,Noether adiabatic invariants of the system are ***,An example is given to support these results.

关键词： adiabatic Noether invariants

A Characterization of the Ejiri Torus in S^5

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Acta Mathematica Sinica,English Series 2016年第9期32卷 1014-1026页

作者： peng wang Department of Mathematics Tongji University Shanghai 200092 P. R. China

We conjecture that a Willmore torus having Willmore functional between 2π2 and 2π2 √3 is either conformally equivalent to the Clifford torus, or conformally equivalent to the Ejiri torus. Ejiri＇s torus in S5 is the first example of Willmore surface which is not conformally equivalent to any minimal surface in any real space form. Li and Vrancken classified all Willmore surfaces of tensor product in S n by reducing them into elastic curves in S3, and the Ejiri torus appeared as a special example. In this paper, we first prove that among all Willmore tori of tensor product, the Willmore functional of the Ejiri torus in S5 attains the minimum 2π2 √3, which indicates our conjecture holds true for Wilhnore surfaces of tensor product. Then we show that all Willmore tori of tensor product are unstable when the co-dimension is big enough. We also show that the Ejiri torus is unstable even in S5. Moreover, similar to Li and Vrancken, we classify all constrained Wilhnore surfaces of tensor product by reducing them with elastic curves in S3. All constrained Willmore tori obtained this way are also shown to bc unstable when the co-dimension is big enough.

关键词： Willmore functional Ejiri's Willmore torus surfaces of tensor product elastic curves,constrained Willmore surfaces

Response surface method using grey relational analysis for decision making in weapon system selection

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Journal of Systems Engineering and Electronics 2014年第2期25卷 265-272页

作者： peng wang peng Meng Baowei Song School of Marine Science and Technology Northwestern Polytechnical University

A proper weapon system is very important for a na- tional defense system. Generally, it means selecting the optimal weapon system among many alternatives, which is a multiple- attribute decision making （MADM） problem. This paper proposes a new mathematical model based on the response surface method （RSM） and the grey relational analysis （GRA）. RSM is used to obtain the experimental points and analyze the factors that have a significant impact on the selection results. GRA is used to an- alyze the trend relationship between alternatives and reference series. And then an RSM model is obtained, which can be used to calculate all alternatives and obtain ranking results. A real world application is introduced to illustrate the utilization of the model for the weapon selection problem. The results show that this model can be used to help decision-makers to make a quick comparison of alternatives and select a proper weapon system from multiple alternatives, which is an effective and adaptable method for solving the weapon system selection problem.

关键词： weapon system multiple-attribute decision making(MADM) response surface method (RSM) grey relational analysis(GRA).

Partial Correlation Analysis Based Identification of Distribution Network Topology

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CSEE Journal of Power and Energy Systems 2023年第4期9卷 1493-1504页

作者： Yanli Liu peng wang School of electrical and information engineering Tianjin UniversityTianjin300072China

Accurately identifying distribution network topol-ogy,which tends to be a mesh configuration with increasing penetration rate of distributed energy resources(DERs),is critical for reliable operation of a smart distribution *** among node voltages makes existing topology identification methods unstable and *** partial correlation analysis can reveal the intrinsic correlation of two variables by eliminating the influence of other variables,this paper develops a novel data-driven method based on partial correlation analysis to identify distribution network topology(radial,mesh,or including DERs)using only historical voltage amplitude ***,maximum spanning tree of network is generated through Prim ***,the loops of network are identified by taking tree neighbors as controlling variables in partial correlation ***,a new topology verification mechanism based on partial correlation analysis is developed to correct wrong connections caused by *** results on IEEE 33-node system,IEEE 123-node system and practical distribution network demonstrate that our method outperforms common data-driven methods,and can robustly identify both radial and mesh distribution network with ***-Data-driven,linear correlation,partial correlation,smart meter,topology identification.

关键词： Data-driven linear correlation partial correlation smart meter topology identification.

Research on optimal guaranteed cost control of flexible spacecraft

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Journal of Systems Engineering and Electronics 2008年第5期19卷 988-995页

作者： wang Qingchao Cai peng School of Astronautics Harbin Inst. of Technology Harbin 150001 P. R. China

This article is concerned with the modeling and control problems of the flexible spacecraft. First, the state observer is designed to estimate the vibration mode on the basis of free vibration models, Then, an optimal guaranteed cost controller is proposed to stabilize system attitude and damp the vibration of the flexible beam at the same time. Numerical simulation examples show the feasibility and validity of the proposed method.

关键词： spacecraft attitude control Euler-Bernoulli beam optimal guaranteed cost control.

Accelerated water harvesting from vapor via a bio-inspired hydrogel pattern

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National Science Review 2024年第3期11卷 48-49页

作者： Lianbin Zhang peng wang State Key Laboratory of Material Processing and Die&Mould Technology Key Laboratory of Materials Chemistry for Energy Conversion and Storage of Ministry of Education School of Chemistry and Chemical Engineering Huazhong University of Science and Technology(HUST) School of Environmental Science and Engineering Sun Yat-sen University

Water and energy sustainability are integral parts of resource sustainability of the world. Due to water molecules' superior capability of serving as both hydrogenbond donor and acceptor, phase change of water, especially between liquid and vapor, underpins global water cycles,facilitates energy transformation and transfer, and thus helps shape the unique local weather and global climate patterns.

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The Morse index of minimal products of minimal submanifolds in spheres

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Science China Mathematics 2023年第4期66卷 799-818页

作者： Changping wang peng wang School of Mathematics and Statistics Fujian Key Laboratory of Mathematical Analysis and ApplicationsFujian Normal UniversityFuzhou 350117China

Tang and Zhang(2020)and Choe and Hoppe(2018)showed independently that one can produce minimal submanifolds in spheres via the Clifford type minimal product of minimal *** this paper,we show that the minimal product is immersed by its first eigenfunctions(of its Laplacian)if and only if the two beginning minimal submanifolds are immersed by their first ***,we give the estimates of the Morse index and the nullity of the minimal *** particular,we show that the Clifford minimal submanifold(√n1/nS^(n1).....,√nk/nS^(nk)■S^(n+k-1))has the index(k-1)(n+k+1)and the nullity(k-1)∑_(1≤i

关键词： minimal product index nullity Clifford minimal submanifold

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