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Sharp Upper Bounds for λ_1^(L_r) of Immersed Hypersurfaces and Their Stability in Space Forms

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Acta Mathematica Sinica,English Series 2008年第5期24卷 749-760页

作者： ru Shan wang College of Mathematics and Computer Science Anhui Normal University Wuhu 241000 P. R. China School of Mathematical Sciences Fudan University Shanghai 200433 P. R. China

In this paper we derive new sharp upper bounds for the first positive eigenvalue λ1^Lr of the linearized operator of the higher order mean curvature of a closed hypersurface immersed into a Riemannian space form R^（n＋l）（c）（c 〉 0）. Our bounds are extrinsic in the sense that they are given in terms of the higher order mean curvatures. Under the assumption Hr＋2 〉 0, by establishing two valuable integral formulas, we obtain unified sharp upper bounds of λ1^Lr. We also give an estimation of the upper bounds of the first eigenvalue of a SchrSdinger-type operator, by which we prove those hypersurfaces with positive constant Hr＋l in any space forms are stable if and only if they are geodesic spheres, thus generalizing the previous result obtained only in the case c≤0.

关键词： r-mean curvature Schrodinger-type operator stability geodesic hypersphere

Uniform Convergence of Wavelet Solution to the Sideways Heat Equation

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Acta Mathematica Sinica,English Series 2010年第10期26卷 1981-1992页

作者： Jin ru wang Department of Applied Mathematics Beijing University of Technology Beijing 100124 P. R. China

We consider the problem uxx（x, t） = ut（x, t）, 0 ≤ x 〈 1, t ≥ 0, where the Cauchy data g（t） is given at x = 1. This is an ill-posed problem in the sense that a small disturbance on the boundary g（t） can produce a big alteration on its solution （if it exists）. We shall define a wavelet solution to obtain the well-posed approximating problem in the scaling space Vj. In the previous papers, the theoretical results concerning the error estimate are L2-norm and the solutions aren＇t stable at x = 0. However, in practice, the solution is usually required to be stable at the boundary. In this paper we shall give uniform convergence on interval x ∈ [0, 1].

关键词： Sideways heat equation multi-resolution analysis Meyer wavelet solution

Nonlinear Wavelet Methods for High-dimensional Backward Heat Equation

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Acta Mathematica Sinica,English Series 2013年第5期29卷 913-922页

作者： rui LI Jin ru wang Department of Applied Mathematics Beijing University of Technology

The backward heat equation is a typical ill-posed problem. In this paper, we shall apply a dual least squares method connecting Shannon wavelet to the following equation Motivated by Reginska＇s work, we shall give two nonlinear approximate methods to regularize the approximate solutions for high-dimensional backward heat equation, and prove that our methods are convergent.

关键词： Backward heat equation nonlinear wavelet method convergence

Improved multipath routing with WNN for the open networks

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The Journal of China Universities of Posts and Telecommunications 2008年第2期15卷 107-113页

作者： wang Yang wang ru-chuan CHENG Xi Depamnent of Computer Science and Technology Nanjing University ofPosts and Telecommunications Nanjing 210003 China College of Mathematics and Computer Science Anhui Normal UniversityWuhu 241000 China College of Computer Science Soochow University Suzhou 215006 China

Multipath routing mechanism is vital for reliable packet delivery, load balance, and flexibility in the open network because its topology is dynamic and the nodes have limited capability. This article proposes a new multipath switch approach based on traffic prediction according to some characteristics of open networks. We use wavelet neural network （WNN） to predict the node traffic because the method has not only good approximation property of wavelet, but also self-learning adaptive quality of neural network. When the traffic prediction indicates that the primary path is a failure, the alternate path will be occupied promptly according to the switch strategy, which can save time for the switch in advance The simulation results show that the presented traffic prediction model has better prediction accuracy; and the approach based on the above model can balance network load, prolong network lifetime, and decrease the overall energy consumption of the network.

关键词： open network multipath routing traffic prediction,WNN

Multiple Positive Solutions for One Dimensional Third Order p-Laplacian Equations with Integral Boundary Conditions

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Acta Mathematicae Applicatae Sinica 2022年第1期38卷 116-127页

作者： You-yuan YANG Qi-ru wang School of Financial Mathematics and Statistics Guangdong University of Finance School of Mathematics Sun Yat-Sen UniversityGuangzhou 510275China

In this paper,we consider the one dimensional third order p-Laplacian equation(Фp(u″))′+h(t)f(t,u(t))=0 with integral boundary conditions u(0)-αu′(0)=∫_(0)^(1) g1(s)u(s)ds,u(1)+βu′(1)=∫_(0)^(1)g2(s)u(s)ds,u″(0)=*** using kernel functions and the Avery-Peterson fixed point theorem,we establish the existence of at least three positive solutions.

关键词： one dimensional third order p-Laplacian equations integral boundary conditions positive solutions the Avery-Peterson fixed point theorem kernel functions

Influence of aeration and initial water thickness on axial velocity attenuation of jet flows

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2013年第5期14卷 362-370页

作者： wang-ru WEI Jun DENG Bin LIU State Key Laboratory of Hydraulics and Mountain River Engineering Sichuan University Hydro-China Kunming Engineering Corporation

With the development of ski-jump energy dissipation for high and large discharge among the hydraulic projects,the effects of characteristics of water flow on energy dissipation are increasingly *** the present study,the effects of aeration and the initial water thickness on axial velocity attenuation of jet flow were analyzed,using variance analysis and numerical calculated *** the analysis of test data,both of the air concentration and initial water thickness are sensitive factors for the axial velocity attenuation of jet flow along the axial way,and there is no significant interaction effect between the aeration and initial water *** has a more significant effect on the axial velocity attenuation of jet *** the initial water thickness of jet flow can reduce the length of jet core,and make the initial position of axial velocity attenuation closer to the nozzle *** numerical calculation results show that aeration can contribute to the enhancement of entrainment ability of jet flow,which may improve the interaction between jet flow and *** ski-jump energy dissipation among the hydraulic projects,combining aeration with decreasing initial water thickness of jet flow is an effective way to enhance the rate of axial velocity attenuation.

关键词： Velocity Aeration Initial water thickness Jet flows

Limits on sequential sharing of nonlocal advantage of quantum coherence

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Science China(Physics,Mechanics & Astronomy) 2022年第6期65卷 26-35页

作者： Ming-Liang Hu Jia-ru wang Heng Fan School of Science Xi’an University of Posts and TelecommunicationsXi’an 710121China Institute of Physics Chinese Academy of SciencesBeijing 100190China CAS Center for Excellence in Topological Quantum Computation University of Chinese Academy of SciencesBeijing 100190China Songshan Lake Materials Laboratory Dongguan 523808China

Sequential sharing of nonlocal correlation is inherently related to its *** address the question as to how many observers can share the nonlocal advantage of quantum coherence(NAQC)in a(d×d)-dimensional state,where d is a prime or a power of a *** first analyze the trade-off between disturbance and information gain of the general d-dimensional unsharp *** in a scenario where multiple Alices perform unsharp measurements on one party of the state sequentially and independently and a single Bob measures coherence of the conditional states on the other party,we show that at most one Alice can demonstrate NAQC with *** limit holds even when considering the weak measurements with optimal pointer *** results may shed light on the interplay between nonlocal correlations and quantum measurements on high-dimensional systems and the hierarchy of different quantum correlations.

关键词： quantum coherence quantum correlation unsharp measurement

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Energy-efficient node deployment strategy for wireless sensor networks

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The Journal of China Universities of Posts and Telecommunications 2013年第1期20卷 54-57页

作者： SHA Chao wang ru-chuan College of Computer Science and Technology Nanjing University of Posts and Telecommunications Jiangsu Provincial Key Laboratory of Wireless Sensor Networks Institute of Computer Technology Nanjing University of Posts and Telecommunications

To balancing energy consumption in wireless sensor networks, we proposed a fixed time interval node broadcasting scheme under variational acceleration straight-line movement model. Simulation results show that the approach proposed in this paper has a superior performance on energy consumption balance compared to uniform broadcasting methods.

关键词： wireless sensor networks energy balance variational acceleration movement

DDoS detection based on wavelet kernel support vector machine

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The Journal of China Universities of Posts and Telecommunications 2008年第3期15卷 59-63,94页

作者： YANG Ming-hui wang ru-chuan College of Computer Nanjing University of Posts and Telecommunications Nanjing 210003 China

To enhance the detection accuracy and deduce false positive rate of distributed denial of service （DDoS） attack detection, a new machine learning method was proposed. With the analysis of support vector machine （SVM） and the wavelet kernel function theory, an admissive support vector kernel, which is a wavelet kernel constructed in this article, implements the combination of the wavelet technique with SVM. Then, wavelet support vector machine （WSVM） is applied to DDoS attack detections and as a classifying means to test the validity of the wavelet kernel function. Simulation experiments show that under the same conditions, the predictive ability of WSVM is improved and the computation burden is alleviated. The detection accuracy of WSVM is higher than the traditional SVM by about 4%, while its false positive is lower than the traditional SVM. Thus, for DDoS detections, WSVM shows better detection performance and is more adaptive to the changing network environment.

关键词： wavelet kernel function wavelet supporting vector machine DDoS detection