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Bifurcations of travelling wave solutions for two generalized Boussinesq systems

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Science china mathematics 2008年第9期51卷 1577-1592页

作者： LI JiBin1,2.1 department of mathematics, Zhejiang Normal university, Jinhua 32.004,{2. 2.department of mathematics, Kunming university of Science and Technology, Kunming 650093,{2. department of mathematics Zhejiang Normal University Jinhua 321004 China department of mathematics Kunming University of Science and Technology Kunming 650093 China

Using the methods of dynamical systems for two generalized Boussinesq systems, the existence of all possible solitary wave solutions and many uncountably infinite periodic wave solutions is obtained. Exact explicit parametric representations of the travelling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.

关键词： nonlinear wave bifurcation solitary wave exact explicit solution generalized Boussinesq system 34C37 34C2. 74J30 58Z05

The mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate-temporal mode

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Science china(Physics,Mechanics & Astronomy) 2005年第5期48卷 614-625页

作者： HUANG Zhangfeng 1, CAO Wei 1,2.& ZHOU Heng 1,2.1. department of Mechanics, Tianjin university, Tianjin 300072.{2. 2. Liu-Hui Center of Applied mathematics, Nankai university and Tianjin university, Tianjin 300072.{2. 1. department of Mechanics Tianjin University 300072 Tianjin China 2. Liu-Hui Center of Applied mathematics Nankai University and Tianjin University 300072 Tianjin China

Temporal mode direction numerical simulation has been done for the transition of a supersonic boundary layer on a flat plate with Mach number 4.5. Analysis of the result showed that during the breakdown process in laminar-turbulent transition, the mechanism causing the mean flow profile to evolve swiftly from laminar to turbulent was that the modification of mean flow profile by the disturbances,when they became larger,led to a remarkable change of its stability characteristics. Though the most unstable T-S wave was of second mode for laminar flow, the first mode waves played the key role in the breakdown process in laminar-turbulent transition.

关键词： supersonic boundary layer, transition, breakdown.

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L1/2.regularization

Science china(Information Sciences) 2010年第6期53卷 1159-1169页

作者： XU ZongBen 1 , ZHANG Hai 1,2., WANG Yao 1 , CHANG xiangYu 1 & LIANG Yong 3 1 Institute of Information and System Science, xi'an Jiaotong {2., xi'an 710049, china 2.department of mathematics, northwest university, xi'an 710069, china 3 {2. of Science and Technology, Macau 999078, china 1. Institute of Information and System Science Xi’an Jiaotong University Xi’an 710049 China2. Department of Mathematics Northwest University Xi’an 710069 China3. University of Science and Technology Macau 999078 China

In this paper we propose an L1 /2.regularizer which has a nonconvex *** L 1/2.regularizer is shown to have many promising properties such as unbiasedness, sparsity and oracle properties.A reweighed iterative algorithm is proposed so that the solution of the L 1/2.regularizer can be solved through transforming it into the solution of a series of L 1 *** solution of the L 1/2.regularizer is more sparse than that of the L 1 regularizer, while solving the L 1/2.regularizer is much simpler than solving the L 0 *** experiments show that the L 1/2.regularizer is very useful and efficient, and can be taken as a representative of the Lp(0 < p < 1) regularizer.

关键词： machine learning variable selection regularizer compressed sensing

A new method to solve the Reynolds equation including mass-conserving cavitation by physics informed neural networks(PINNs)with both soft and hard constraints

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Friction 2024年第6期12卷 1165-1175页

作者： Yinhu xi Jinhui DENG Yiling LI School of Mechanical Engineering Anhui University of Science and TechnologyHuainan 232001China Ericsson AB Datalinjen 3Linköping 58330Sweden

In this work,a new method to solve the Reynolds equation including mass-conserving cavitation by using the physics informed neural networks(PINNs)is *** complementarity relationship between the pressure and the void fraction is *** are several difficulties in problem solving,and the solutions are ***,the difficulty for considering the pressure inequality constraint by PINNs is solved by transferring it into one equality constraint without introducing *** the void fraction inequality constraint is considered by using the hard constraint with the max-min ***,to avoid the fluctuation of the boundary value problems,the hard constraint method is also utilized to apply the boundary pressure values and the corresponding functions are ***,for avoiding the trivial solution the limitation for the mean value of the void fraction is *** results are validated against existing data,and both the incompressible and compressible lubricant are *** agreement can be found for both the domain and domain boundaries.

关键词： Reynolds equation mass-conserving cavitation physics informed neural networks hard constraints trivial solution

The generalized Roper-Suffridge extension operator in Banach spaces (Ⅲ)

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Science china mathematics 2009年第11期52卷 2432-2446页

作者： ZHU YuCan1 & LIU MingSheng2.1 department of mathematics,Fuzhou university,Fuzhou 350002.{2. 2.department of mathematics,South china Normal university,Guangzhou 510631,{2. 1. department of mathematics Fuzhou University Fuzhou 350002 China 2. department of mathematics South China Normal University Guangzhou 510631 China

Suppose that X is a complex Banach space with the norm ||·|| and n is a positive integer with dim X ≥n≥ 2. In this paper,we consider the generalized Roper-Suffridge extension operator Φn,β2.γ2....,βn+1,γn+1(f)... 详细信息

关键词： Roper-Suffridge extension operator biholomorphic starlike mapping almost spirallike mapping of type β and order α spirallike mapping of type β and order α

Boundary element-free method for elastodynamics

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Science china(Physics,Mechanics & Astronomy) 2005年第6期48卷 641-657页

作者： CHENG Yumin1 & PENG Miaojuan2.1. Shanghai Institute of Applied mathematics and Mechanics, Shanghai university, Shanghai 2.0072.{2. 2. department of Civil Engineering, Shanghai university, Shanghai 2.0072.{2. 1. Shanghai Institute of Applied mathematics and Mechanics Shanghai University 200072 Shanghai China 2. department of Civil Engineering Shanghai University 200072 Shanghai China

The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.

关键词： moving least-square approximation, improved moving least-square approximation, elastodynamics, boundary integral equation, meshless method, boundary element-free method, Fourier eigen transform.

Gorenstein projective modules over rings of Morita contexts

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Science china mathematics 2024年第11期67卷 2453-2484页

作者： Qianqian Guo Changchang xi School of Mathematical Sciences Capital Normal University School of Mathematical Sciences Laboratory of Mathematics and Complex Systems(Ministry of Education of China)Beijing Normal University School of mathematics and Statistics Shaanxi Normal University

Under semi-weak and weak compatibility conditions of bimodules,we establish necessary and sufficient conditions of Gorenstein-projective modules over rings of Morita contexts with one bimodule homomorphism *** extends greatly the results on triangular matrix Artin algebras and on Artin algebras of Morita contexts with two bimodule homomorphisms zero in the literature,where only sufficient conditions are given under a strong assumption of compatibility of *** application is provided to describe Gorenstein-projective modules over noncommutative tensor products arising from Morita *** results are proved under a general setting of noetherian rings and modules instead of Artin algebras and modules.

关键词： Gorenstein-projective module noetherian ring noncommutative tensor product totally exact complex weakly compatible bimodule

Role of biochar in raising blue carbon stock capacity of salt marshes

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Pedosphere 2024年第1期34卷 19-22页

作者： Yuzhou HUANG xi xiAO Ocean College Zhejiang UniversityZhoushan 316021China Key Laboratory of Marine Ecological Monitoring and Restoration Technologies of the Ministry of Natural Resources of china Shanghai 201306China Donghai Laboratory Zhoushan 316021China Ocean Academy Zhejiang UniversityZhoushan 316021China Key Laboratory of Watershed Non-point Source Pollution Control and Water Eco-security of Ministry of Water Resources College of Environmental and Resources SciencesZhejiang UniversityHangzhou 310058China

Salt marshes are an important blue carbon ecosystem, with surprisingly fast carbon accumulation rates that are 40 times higher than those of terrestrial forests. In recent decades, salt marshes have suffered great degradation and loss all over the world. The idea to enhance carbon stock in salt marshes(so-called blue carbon) using biochar (so-called black carbon) has recently been proposed. Although experiments and observations remain limited, significant enhancements in soil organic carbon and plant growth have been documented in most case studies. However, due to the limited number of observations and their relatively short time window ranging from months to less than one year, there still exists a knowledge gap regarding the process, mechanism, and effect of biochar in enhancing carbon stock in salt marshes. Future research is urgently needed in the following perspectives:1) exploring the relationship between carbon stock enhancement efficiency and biochar properties, 2. optimizing the physical and chemical properties of biochar to boost its efficiency, and 3)studying the in-situ responses of complex carbon pools to biochar addition, especially under tidal conditions and over a longer period of time.

关键词： soil stock char

L-R smash products for bimodule algebras

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Progress in Natural Science:Materials International 2006年第6期16卷 580-587页

作者： ZHANG Liangyun (department of mathematics, Nanjing Agricultural university, Nanjing 2.0095,{2. department of mathematics, Nanjing university, Nanjing 2.0008,{2.) [a] department of mathematics Nanjing Agricultural University Nanjing China [b] department of mathematics Nanjing University Nanjing China

In this paper, we prove that the L-R smash product A(?)H is exactly the twisted smash product A * H if H is a finite dimensional cocommutative Hopf algebra, and give a sufficient and necessary condition for L-R smash products to be bialgebras (Hopf algebras) . For any finite dimensional coquasitriangular Hopf algebra (H,σ), we prove that the L-R smash product H(?)H is semisimple Artinian if H is semisimple and H * is unimodular. In particular, the L-R smash product D(H)* (?)D(H)* semisimple Artinian if the Drin-fel'd double D(H) is semisimple.

关键词： bimodule algebras L-R smash products coquasitriangular Hopf algebras Long bialgebras.