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Prediction and critical transition mechanism for granite fracture:Insights from critical slowing down theory
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作者 WANG Chun-lai ZHOU Bao-kun +6 位作者 LI Chang-feng WEN Zhi-jie BAI Zhi-an ZHU Chao-yang SUN Liang XUE Xu-hui CAO Peng 《Journal of Central South University》 SCIE EI CAS CSCD 2024年第8期2748-2764,共17页
Rock fracture warning is one of the significant challenges in rock mechanics.Many true triaxial and synchronous acoustic emission(AE)tests were conducted on granite samples.The investigation focused on the characteris... Rock fracture warning is one of the significant challenges in rock mechanics.Many true triaxial and synchronous acoustic emission(AE)tests were conducted on granite samples.The investigation focused on the characteristics of AE signals preceding granite fracture,based on the critical slowing down(CSD)theory.The granite undergoes a transition from the stable phase to the fracture phase and exhibits a clear CSD phenomenon,characterized by a pronounced increase in variance and autocorrelation coefficient.The variance mutation points were found to be more identifiable and suitable as the primary criterion for predicting precursor information related to granite fracture,compared to the autocorrelation coefficient.It is noteworthy to emphasize that the CSD factor holds greater potential in elucidating the underlying mechanisms responsible for the critical transition of granite fracture,in comparison to the AE timing parameters.Furthermore,a novel multi-parameter collaborative prediction method for rock fracture was developed by comprehensively analyzing predictive information,including abnormal variation modes and the CSD factor of AE characteristic parameters.This method enhances the understanding and prediction of rock fracture-related geohazards. 展开更多
关键词 GRANITE triaxial compression acoustic emission rock fracture critical slowing down theory
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Quantitative determination of the critical points of Mott metal–insulator transition in strongly correlated systems
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作者 牛月坤 倪煜 +4 位作者 王建利 陈雷鸣 邢晔 宋筠 冯世平 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第1期647-652,共6页
Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal–insulator transition. We investigate the Mott transiti... Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal–insulator transition. We investigate the Mott transition in a Hubbard model by using the dynamical mean-field theory and introduce the local quantum state fidelity to depict the Mott metal–insulator transition. The local quantum state fidelity provides a convenient approach to determining the critical point of the Mott transition. Additionally, it presents a consistent description of the two distinct forms of the Mott transition points. 展开更多
关键词 critical point metal–insulator transition local quantum state fidelity strongly correlated system quasiparticle coherent weight
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SOLUTIONS TO DISCRETE MULTIPARAMETER PERIODIC BOUNDARY VALUE PROBLEMS INVOLVING THE p-LAPLACIAN VIA CRITICAL POINT THEORY 被引量:8
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作者 高承华 《Acta Mathematica Scientia》 SCIE CSCD 2014年第4期1225-1236,共12页
In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value ... In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88(4) (2009), pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory. 展开更多
关键词 discrete periodic boundary value problem P-LAPLACIAN MULTIPARAMETER three solutions critical point theory
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Stability of the topological quantum critical point between multi-Weyl semimetal and band insulator
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作者 杨兆昆 王景荣 刘国柱 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第5期131-140,共10页
One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the... One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the change of certain topological invariant.A new gapless semimetallic state emerges at each topological quantum critical point.Here we perform a renormalization group analysis to investigate the stability of such critical points against perturbations induced by random scalar potential and random vector potential.We find that the quantum critical point between double-Weyl semimetal and band insulator is unstable and can be easily turned into a compressible diffusive metal by any type of weak disorder.The quantum critical point between triple-Weyl semimetal and band insulator flows to a stable strong-coupling fixed point if the system contains a random vector potential merely along the z-axis,but becomes a compressible diffusive metal when other types of disorders exist. 展开更多
关键词 topological quantum critical points Weyl semimetal DISORDER renormalization group
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Stability Analysis of a Single-Degree-of Freedom Mechanical Model with Distinct Critical Points: I. Bifurcation Theory Approach 被引量:1
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作者 Dimitrios S. Sophianopoulos 《World Journal of Mechanics》 2013年第1期62-81,共20页
The buckling and post-buckling response of a single-degree-of-freedom mechanical model is re-examined in this work, within the context of nonlinear stability and bifurcation theory. This system has been reported in pi... The buckling and post-buckling response of a single-degree-of-freedom mechanical model is re-examined in this work, within the context of nonlinear stability and bifurcation theory. This system has been reported in pioneer as well as in more recent literature to exhibit all kinds of distinct critical points. Its response is thoroughly discussed, the effect of all parameters involved is extensively examined, including imperfection sensitivity, and the results obtained lead to the important conclusion that the model is possibly associated with the butterfly singularity, a fact which will be validated by the contents of a companion paper, based on catastrophe theory. 展开更多
关键词 Mechanical Models Nonlinear Stability DISTINCT critical pointS BIFURCATION theory SINGULARITIES
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MULTIPLE SOLUTIONS TO CRITICAL MAGNETIC SCHRODINGER EQUATIONS
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作者 Ruijiang WEN Jianfu YANG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1373-1393,共21页
In this paper,we are concerned with the existence of multiple solutions to the critical magnetic Schrödinger equation(-i▽-a(x))^(2)u+⒂λV(x)u=p|u|^(p-2)u+(∫R(n)|u(y)|^(2)_(a)^(*)/|x-y|^(a)dy)|u|2_(a)^(*)-2_(u)... In this paper,we are concerned with the existence of multiple solutions to the critical magnetic Schrödinger equation(-i▽-a(x))^(2)u+⒂λV(x)u=p|u|^(p-2)u+(∫R(n)|u(y)|^(2)_(a)^(*)/|x-y|^(a)dy)|u|2_(a)^(*)-2_(u)in R^(N),(0.1)where N≥4,2≤p<2^(*),2_α^(*)=(2N-α)/(N-2)with 0<α<4,λ>0,μ∈R,A(x)=(A_(1)(x),A_(2)(x),…,A_(N)(x))is a real local Hölder continuous vector function,i is the imaginary unit,and V(x)is a real valued potential function on R^(N).Supposing thatΩ=int V^(-1)(0)■R^(N)is bounded,we show that problem(0.1)possesses at least cat_(Ω)(Ω)nontrivial solutions ifλis large. 展开更多
关键词 critical magnetic Schrödinger equation multiple solutions Ljusternik-Schnirelman theory
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Infinitely Many Solutions and a Ground-State Solution for Klein-Gordon Equation Coupled with Born-Infeld Theory
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作者 Fangfang Huang Qiongfen Zhang 《Journal of Applied Mathematics and Physics》 2024年第4期1441-1458,共18页
In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infin... In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infinitely many high-energy radial solutions and a ground-state solution for this kind of system, which improve and generalize some related results in the literature. 展开更多
关键词 Klein-Gordon Equation Born-Infeld theory Infinitely Many Solutions Ground-State Solution critical point theory
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Stability Analysis of a SDOF Mechanical Model with Distinct Critical Points: II. Catastrophe Theory Approach
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作者 Dimitrios S. Sophianopoulos Vasiliki S. Pantazi 《World Journal of Mechanics》 2015年第12期266-273,共8页
In a recent publication [1], the fully nonlinear stability analysis of a Single-Degree-of Freedom (SDOF) model with distinct critical points was dealt with on the basis of bifurcation theory, and it was demonstrated t... In a recent publication [1], the fully nonlinear stability analysis of a Single-Degree-of Freedom (SDOF) model with distinct critical points was dealt with on the basis of bifurcation theory, and it was demonstrated that this system is associated with the butterfly singularity. The present work is the companion one, tackling the problem via the Theory of Catastrophes. After Taylor expanding the original potential energy function and introducing Padè approximants of the trigonometric expression involved, the resulting truncated potential is a universal unfolding of the original one and an extended canonical form of the butterfly catastrophe potential energy function. Results in terms of equilibrium paths, bifurcation sets and manifold hyper-surface projections fully validate the whole analysis, being in excellent agreement with the findings obtained via bifurcation theory. 展开更多
关键词 Mechanical Models Nonlinear Stability critical pointS CATASTROPHE theory BUTTERFLY SINGULARITY
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On a Heuristic Point of View about the Generalization of Curie Law to Cosmic Higgs Fields with the Casimir Effect
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作者 Hung-Te Henry Su Po-Han Lee 《Journal of Applied Mathematics and Physics》 2024年第9期3135-3147,共13页
Condensed state physics demonstrates that the Curie temperature is the point at which spontaneous magnetization drops to zero, marking the critical transition where ferromagnetic or ferrimagnetic materials transform i... Condensed state physics demonstrates that the Curie temperature is the point at which spontaneous magnetization drops to zero, marking the critical transition where ferromagnetic or ferrimagnetic materials transform into paramagnetic substances. Below the Curie temperature, a material remains ferromagnetic;above it, the material becomes paramagnetic, with its magnetic field easily influenced by external magnetic fileds. For example, the Curie temperature of iron (Fe) is 1043 K, while that of neodymium magnets ranges from 583 to 673 K. From both physics and mathematics perspectives, examining the temperature properties of materials is essential, as it provides valuable insights into their electromagnetic and thermodynamic behaviors. This paper makes a bold assumption and, for the first time, carefully verifies the existence of a Casimir temperature at 0.00206 K under conditions of one-atomic spacing. 展开更多
关键词 Curie Temperature Curie point Casimir Temperature critical point Fields Materials One-Atomic Spacing
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Innovative Teaching Research on Literary Theory and Criticism
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作者 HOU Xia 《Sino-US English Teaching》 2024年第7期309-313,共5页
As a core compulsory course for English majors majoring in teacher education,Literary Theory and Criticism plays an important role in enhancing text understanding,cultivating critical thinking,and shaping correct valu... As a core compulsory course for English majors majoring in teacher education,Literary Theory and Criticism plays an important role in enhancing text understanding,cultivating critical thinking,and shaping correct values in the future development of students.Influenced by traditional teaching ideas,students have many difficulties when learning this course,such as insufficient theoretical understanding,inadequate ability improvement,and not enough investment in course learning.In response to the above issues,this course focuses closely on the fundamental task of“cultivating virtue and nurturing people”,relying on modern information technology and introducing research methods of digital humanities.This course uses“7C”teaching mode under the“three-level integration”,in which“teaching”and“education”are carried out synchronously,and“teacher”and“student”are developed together,in order to greatly enhance students’learning participation and course satisfaction. 展开更多
关键词 literary theory and criticism double helix 7C teaching mode three-level integration participation rate satisfaction level
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On Ethical Literary Criticism and Game Theory--An Interview with Professor Nie Zhenzhao
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作者 HUANG Kai-hong NIE Zhen-zhao HE Qiong(Translator) 《Journal of Literature and Art Studies》 2024年第3期207-214,共8页
In 2014,Huang Kaihong,a professor at School of Foreign Languages and Cultures,Southwest University of Science and Technology,interviewed the Doctoral advisor Professor Nie Zhenzhao during the period of his academic vi... In 2014,Huang Kaihong,a professor at School of Foreign Languages and Cultures,Southwest University of Science and Technology,interviewed the Doctoral advisor Professor Nie Zhenzhao during the period of his academic visiting to Central China Normal University.As early as in 2005,Huang Kaihong conducted an interview with Professor Nie Zhenzhao on the topic of the general introduction of ethical literary criticism.So around 11 years later,the second interview mainly covers not only the ethical literary criticism theory,but the game theory and the relationship between them as well.Professor Nie thinks whether the game theory can be applied to literature research is still under discussion.The theory of ethical literary criticism is a kind of methodology based on science and it can get the attention of literary critics at home and abroad,which is because it fits the practical needs of literary criticism,draws the literary criticism away from only emphasizing criticism genres and the research of criticism terms,and pays attention to the true nature of the literary text in literature research.After consulting Professor Nie Zhenzhao about some related questions from the perspective of game theory.Huang Kaihong gets some significant information concerning literature research and understands the latest core terms and the concrete application method of ethical literary criticism,especially the relationship between the instructing and aesthetic functions of literature. 展开更多
关键词 ethical literary criticism game theory relationship methodology application
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Linear numerical calculation method for obtaining critical point,pore fluid,and framework parameters of gas-bearing media 被引量:3
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作者 牛滨华 孙春岩 +2 位作者 闫国英 杨维 刘畅 《Applied Geophysics》 SCIE CSCD 2009年第4期319-326,393,共9页
Up to now, the primary method for studying critical porosity and porous media are experimental measurements and data analysis. There are few references on how to numerically calculate porosity at the critical point, p... Up to now, the primary method for studying critical porosity and porous media are experimental measurements and data analysis. There are few references on how to numerically calculate porosity at the critical point, pore fluid-related parameters, or framework-related parameters. So in this article, we provide a method for calculating these elastic parameters and use this method to analyze gas-bearing samples. We first derive three linear equations for numerical calculations. They are the equation of density p versus porosity Ф, density times the square of compressional wave velocity p Vp^2 versus porosity, and density times the square of shear wave velocity pVs^2 versus porosity. Here porosity is viewed as an independent variable and the other parameters are dependent variables. We elaborate on the calculation steps and provide some notes. Then we use our method to analyze gas-bearing sandstone samples. In the calculations, density and P- and S-velocities are input data and we calculate eleven relative parameters for porous fluid, framework, and critical point. In the end, by comparing our results with experiment measurements, we prove the viability of the method. 展开更多
关键词 linear equation numerical calculation gas-bearing media critical point pore fluid and framework elastic parameters
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NONSMOOTH CRITICAL POINT THEOREMS AND ITS APPLICATIONS TO QUASILINEAR SCHRDINGER EQUATIONS 被引量:5
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作者 李周欣 沈尧天 《Acta Mathematica Scientia》 SCIE CSCD 2016年第1期73-86,共14页
In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear SchrSdinger equatio... In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear SchrSdinger equations with negative parameter which arose from the study of self-channeling of high-power ultrashort laser in matter. 展开更多
关键词 nonsmooth critical point theorems quasilinear elliptic equations SchrSdingerequation
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ASYMPTOTIC EXPANSION OF DIRAC-TYPE DISTRIBUTION ASSOCIATED WITH A CLASS OF HYPERSURFACES WITH DEGENERATED CRITICAL POINTS 被引量:1
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作者 齐民友 张果平 《Acta Mathematica Scientia》 SCIE CSCD 1999年第2期127-137,共11页
In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE, this paper studies the asymptotic expansion of Dirac-type distribution associated with a class of hypers... In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE, this paper studies the asymptotic expansion of Dirac-type distribution associated with a class of hypersurfaces F(x) with degenerate critical points and proves that [F(x)](+)(lambda) is a distribution-valued meromorphic of lambda is an element of C under some assumptions on F(x). Next, the authors use the Normal form theory of Arnold and prove that for a hypersurface F(x) = 0 with A(mu) type degenerate critical point at x = 0, F-+(lambda) is a distribution-valued meromorphic function of lambda. 展开更多
关键词 asymptotic expansion degenerate critical point HYPERSURFACE distribution-valued meromorphic function analytic extension
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Search for the QCD critical point with fluctuations of conserved quantities in relativistic heavy-ion collisions at RHIC: an overview 被引量:25
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作者 Xiaofeng Luo Nu XU 《Nuclear Science and Techniques》 SCIE CAS CSCD 2017年第8期1-40,共40页
Fluctuations of conserved quantities, such as baryon, electric charge, and strangeness number, are sensitive observables in relativistic heavy-ion collisions to probe the QCD phase transition and search for the QCD cr... Fluctuations of conserved quantities, such as baryon, electric charge, and strangeness number, are sensitive observables in relativistic heavy-ion collisions to probe the QCD phase transition and search for the QCD critical point. In this paper, we review the experimental measurements of the cumulants(up to fourth order) of event-byevent net-proton(proxy for net-baryon), net-charge and netkaon(proxy for net-strangeness) multiplicity distributions Au+Au collisions at sNN^(1/2) 7:7; 11:5; 14:5; 19:6; 27;39; 62:4; 200 Ge V from the first phase of beam energy scan program at the relativistic heavy-ion collider(RHIC). We also summarize the data analysis methods of suppressing the volume fluctuations, auto-correlations, and the unified description of efficiency correction and error estimation.Based on theoretical and model calculations, we will discuss the characteristic signatures of critical point as well as backgrounds for the fluctuation observables in heavy-ion collisions. The physics implications and the future secondphase of the beam energy scan(2019–2020) at RHIC will also be discussed. 展开更多
关键词 高能重离子碰撞 QCD相变 RHIC 临界点 守恒量 波动 搜索 相对论重离子碰撞
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Determination of Weak Points Based on Risk Theory and Application to Transmission Network Planning 被引量:1
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作者 LIU Zhe JIA Hongjie +1 位作者 ZENG Yuan QIN Chao 《Transactions of Tianjin University》 EI CAS 2012年第1期38-45,共8页
In the traditional power transmission network planning,deterministic analysis methods are widely used.In such methods,all contingencies are deemed to have the same occurrence probability,which is not reasonable.In thi... In the traditional power transmission network planning,deterministic analysis methods are widely used.In such methods,all contingencies are deemed to have the same occurrence probability,which is not reasonable.In this paper,risk assessment is introduced to the process of transmission network planning considering the probabilistic characteristics of contingencies.Risk indices are given to determine the weak points of the transmission network based on local information,such as bus risk,line overload risk,contingency severity.The indices are calculated by the optimal cost control method based on risk theory,which can help planners to quickly determine weak points in the planning and find solution to them.For simplification,only line overload violation is considered.Finally,the proposed method is validated by an IEEE-RTS test system and a real power system in China from two aspects.In the first case,the original system is evaluated by the proposed method to find the weak points,and then four planning schemes are established,among which the best scheme is selected.In the second case,four initial planning schemes are established by combining the experiences of planners,and after the evaluation by using the proposed method,the best planning scheme is improved based on the information of weak points in the initial schemes,and the risk of improved scheme is reduced from 42 531.86 MW·h per year to 4 431.26 MW·h per year. 展开更多
关键词 risk assessment weak point transmission network planning risk theory
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Self-Organized Criticality Theory Model of Thermal Sandpile 被引量:1
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作者 彭晓东 曲洪鹏 +1 位作者 许健强 韩最蛟 《Chinese Physics Letters》 SCIE CAS CSCD 2015年第9期79-83,共5页
A self-organized criticality model of a thermal sandpile is formulated for the first time to simulate the dynamic process with interaction between avalanche events on the fast time scale and diffusive transports on th... A self-organized criticality model of a thermal sandpile is formulated for the first time to simulate the dynamic process with interaction between avalanche events on the fast time scale and diffusive transports on the slow time scale. The main characteristics of the model are that both particle and energy avalanches of sand grains are considered simultaneously. Properties of intermittent transport and improved confinement are analyzed in detail. The results imply that the intermittent phenomenon such as blobs in the low confinement mode as well as edge localized modes in the high confinement mode observed in tokamak experiments are not only determined by the edge plasma physics, but also affected by the core plasma dynamics. 展开更多
关键词 Self-Organized criticality theory Model of Thermal Sandpile
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Limit Cycle Containing Nine Critical Points in its Interior for a Class of Cubic Systems
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作者 Liu Yi-rong Xiao Ping 《Journal of Central South University》 SCIE EI CAS 2000年第2期111-112,共2页
Discuss a class of real planar cubic systems with a critical point O (0,0) of nine orders and obtain the conditions for its limit cycle surrounding the origin, and prove that when small pertubations of coefficients ar... Discuss a class of real planar cubic systems with a critical point O (0,0) of nine orders and obtain the conditions for its limit cycle surrounding the origin, and prove that when small pertubations of coefficients are made, the critical point O (0,0) of nine orders is split into nine real simple critical points and the limit cycle surrounding the origin becomes the limit cycle containing nine critical points in its interior. 展开更多
关键词 CUBIC SYSTEMS critical point of NINE ORDERS limit cycle
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BIFURCATION PROBLEM OF CRITICAL POINTSFOR QUADRATIC DIFFERENTIAL SYSTEMS
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作者 张祥 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1997年第12期0-0,0-0+0-0+0-0+0-0+0-0+0-0,共14页
In this paper foe bifurcation of critical points for the quadratic systems of type(II)and (III) is investigated. and an answer to the problem given in[1] is given.
关键词 quadratic system DIVERGENCE critical point
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ON THE CRITICAL POINTS OF THE MAP F_p:X→‖AXB-C‖_p^p
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作者 杨长森 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第4期485-488,共4页
Suppose A,B and C are the bounded linear operators on a Hilbert space H, when A has a generalized inverse A - such that (AA -) *=AA - and B has a generalized inverse B - such that (B -B) *=B -B,the general cha... Suppose A,B and C are the bounded linear operators on a Hilbert space H, when A has a generalized inverse A - such that (AA -) *=AA - and B has a generalized inverse B - such that (B -B) *=B -B,the general characteristic forms for the critical points of the map F p:X→‖ A X B-C ‖ p p (1<p<∞), have been obtained, it is a generalization for P J Maher's result about p=2. Similarly, the same question has been discussed for several operators. 展开更多
关键词 generalized inverse critical point polar decomposition
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