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Product of Uniform Distribution and Stirling Numbers of the First Kind

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Acta Mathematica Sinica,English Series 2005年第6期21卷 1435-1442页

作者： ping sun Department of Mathematics Northeastern University Shenyang 110004 P. R. China

Let Vk=u1u2……uk, ui＇s be i.i.d - U（0, 1）, the p.d.f of 1 - Vk＋l be the GF of the unsigned Stirling numbers of the first kind s（n, k）. This paper discusses the applications of uniform distribution to combinatorial analysis and Riemann zeta function; several identities of Stifling series are established, and the Euler＇s result for ∑ Hn/n^k-l, k ≥ 3 is given a new probabilistic proof.

关键词： Stirling numbers generating function uniform distribution moment Riemann zeta function

Tracking Control for a Cushion Robot Based on Fuzzy Path Planning With Safe Angular Velocity

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IEEE/CAA Journal of Automatica Sinica 2017年第4期4卷 610-619页

作者： ping sun Zhuang Yu School of Information Science and Engineering Shenyang University of TechnologyShenyang 110870China

This study proposes a new nonlinear tracking control method with safe angular velocity constraints for a cushion robot. A fuzzy path planning algorithm is investigated and a realtime desired motion path of obstacle avoidance is obtained. The angular velocity is constrained by the controller, so the planned path guarantees the safety of users. According to Lyapunov theory, the controller is designed to maintain stability in terms of solutions of linear matrix inequalities and the controller's performance with safe angular velocity constraints is *** simulation and experiment results confirm the effectiveness of the proposed method and verify that the angular velocity of the cushion robot provided safe motion with obstacle avoidance.

关键词： Cushion robot path planning safe angular velocity tracking control

Three Symmetric Positive Solutions for Second-order Nonlocal Boundary Value Problems

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Acta Mathematicae Applicatae Sinica 2011年第2期27卷 233-242页

作者： Yong-ping sun College of Electron and Information Zhejiang University of Media and Communications Hangzhou 310018China

Using the Leggett-Williams fixed point theorem, we will obtain at least three symmetric positive solutions to the second-order nonlocal boundary value problem of the form u″（t）＋g（t）f（t,u（t））=0,0〈t〈1,u（0）=u（1）=∫01m（s）u（s）ds. where m ∈ L1[0 1], g ：（0, 1）→ [0, ∞） is continuous, symmetric on （0, 1） and maybe singular at t = 0 and t = 1, f： [0, 1] × [0, ∞） → [0, ∞） is continuous and f（-, x） is symmetric on [0, 1] for all x∈ [0, ∞）.

关键词： symmetric positive solution nonlocal boundary value problem fixed point theorem

Existence and multiplicity of positive solutions for an elastic beam equation

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Applied Mathematics(A Journal of Chinese Universities) 2011年第3期26卷 253-264页

作者： sun Yong-ping College of Electron and Information Zhejiang University of Media and Communications Hangzhou310018 China.

This paper investigates the boundary value problem for elastic beam equation of the formu″″（t） q（t）f（t, u（t）,u′（t）,u″（t）,u′″（t））, 0〈t〈1,with the boundary conditionsu=（0）=u′（1）=u″（0）=u′″（1）=0.The boundary conditions describe the deformation of an elastic beam simply supported at left and clamped at right by sliding clamps. By using Leray-Schauder nonlinear alternate, Leray-Schauder fixed point theorem and a fixed point theorem due to Avery and Peterson, we establish some results on the existence and multiplicity of positive solutions to the boundary value problem. Our results extend and improve some recent work in the literature.

关键词： Positive solution existence and multiplicity elastic beam equation fixed point theorem nonlinear alternate.

Monotone positive solution for three-point boundary value problem

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Applied Mathematics(A Journal of Chinese Universities) 2008年第3期23卷 279-285页

作者： sun Yong-ping College of Electronics and Information Zhejiang University of Media and Communications Hangzhou310018 China

In this paper, the existence of monotone positive solution for the following secondorder three-point boundary value problem is studied：x″（t）＋f（t,x（t））=0,0〈t〈1,x′（0）=0,x（1）＋δx′（η）=0,where η ∈ （0, 1）, δ∈ [0, ∞）, f ∈ C（[0, 1] × [0, ∞）, [0, ∞））. Under certain growth conditions on the nonlinear term f and by using a fixed point theorem of cone expansion and compression of functional type due to Avery, Anderson and Krueger, sufficient conditions for the existence of monotone positive solution are obtained and the bounds of solution are given. At last, an example is given to illustrate the result of the paper.

关键词： three-point boundary value problem fixed point theorem monotone positive solution

Existence and iteration of monotone positive solutions for a third-order two-point boundary value problem

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Applied Mathematics(A Journal of Chinese Universities) 2008年第4期23卷 413-419页

作者： sun Yong-ping School of Electronics and Information Zhejiang University of Media and Communications Hangzhou 310018 China

The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t）＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied.... 详细信息

关键词： third-order two-point boundary value problem monotone iterative method positive solution,existence iterative scheme

Strong Subgame Consistency of the Core in Stochastic Network Formation Games

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Journal of the Operations Research Society of China 2024年第1期12卷 189-213页

作者： ping sun Elena Parilina Faculty of Applied Mathematics and Control Processes Saint Petersburg State UniversitySaint Petersburg199034Russia

We consider a model of network formation as a stochastic game with random duration proposed initially in sun and Parilina(Autom Remote Control 82(6):1065–1082,2021).In the model,the leader first suggests a joint project to other players,i.e.,the network connecting ***,the players are allowed to form fresh links with each other updating the initially proposed *** stage payoff of any player is defined depending on the network *** are two types of randomness in the network formation process:(i)links may fail to be formed with different probabilities although players intend to establish them,(ii)the game process may terminate at any stage or transit to the next stage with a certain probability ***,a network is formed as a result of players’decisions and realization of random *** cooperative version of the stochastic game is *** particular,we examine the properties of subgame consistency as well as strong subgame consistency of the *** provide a payment mechanism or regularization of the core elements to sustain its subgame consistency and avoid the player’s deviations from the cooperative *** addition,the distribution procedure of the core elements is regularized in case there are negative payments to achieve only nonnegative payments to the players at any *** sufficient condition of a strongly subgame consistent core is also *** illustrate our theoretical results with a numerical example.

关键词： Stochastic game Network formation Core Strong subgame consistency

On stability of elastic domain during isothermal solid-solid phase transformationin a tube configuration

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Acta Mechanica Sinica 2012年第3期28卷 683-694页

作者： Liang Dong Qing-ping sun Department of Mechanical Engineering The Hong Kong University of Science and TechnologyClear Water Bay Hong Kong China

Under isothermal quasi-static stretching the phase transition of a superelastic NiTi tube involves the formation （during loading） and vanishing （in unloading） of a high strain （martensite） domain. The two events are accompanied by a rapid stress drop/rise due to the formation/vanishing of do- main fronts. From a thermodynamic point of view, both are instability phenomena that occur once the system reaches its critical state. This paper investigates the stability of a shrink- ing cylindrical domain in a tube configuration during unload- ing. The energetics and thermodynamic driving force of the cylindrical domain are quantified by using an elastic inclu- sion model. It is demonstrated that the two domain fronts ex- hibit strong interaction when they come close to each other, which brings a peak in the total energy and a sign change in the thermodynamic driving force. It is proved that such domain front interaction plays an important role in control- ling the stability of the domain and in the occurrence of stress jumps during domain vanishing. It is also shown that the pro- cess is governed by two nondimensional length scales （the normalized tube length and normalized wall-thickness） and that the length scale dependence of the critical domain length and stress jump for the domain vanishing can be quantified by the elastic inclusion model.

关键词： Cylindrical elastic domain Stability of domain Domain front Critical domain length Stress jump ~ Ther-modynamic driving force

Compositional metric learning for multi-label classification

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Frontiers of Computer Science 2021年第5期15卷 1-12页

作者： Yan-ping sun Min-Ling ZHANG School of Computer Science and Engineering Southeast UniversityNanjing 210096China Key Laboratory of Computer Network and Information Integration(Southeast University) Ministry of EducationChina Collaborative Innovation Center for Wireless Communications Technology Nanjing 211100China

Multi-label classification aims to assign a set of proper labels for each instance,where distance metric learning can help improve the generalization ability of instance-based multi-label classification *** multi-label metric learning techniques work by utilizing pairwise constraints to enforce that examples with similar label assignments should have close distance in the embedded feature *** this paper,a novel distance metric learning approach for multi-label classification is proposed by modeling structural interactions between instance space and label *** one hand,compositional distance metric is employed which adopts the representation of a weighted sum of rank-1 PSD matrices based on com-ponent *** the other hand,compositional weights are optimized by exploiting triplet similarity constraints derived from both instance and label *** to the compositional nature of employed distance metric,the resulting problem admits quadratic programming formulation with linear optimization complexity *** number of training *** also derive the generalization bound for the proposed approach based on algorithmic robustness analysis of the compositional *** experiments on sixteen benchmark data sets clearly validate the usefulness of compositional metric in yielding effective distance metric for multi-label classification.

关键词： machine learning multi-label learning metric learning compositional metric positive semidefinite matrix decomposition