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STUDY ON STRUCTURE OF singularpointS OF LAMINAR FLAME SYSTEM

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Applied Mathematics and Mechanics(English Edition) 2005年第5期26卷 679-684页

作者：王秀娥殷先军 Department of Basic Science Beijing Technology and Business UniversityBeijing 100037 P.R.China School of Science Beijing Institute of TechnologyBeijing 100081 P.R.China

Under some certain assumptions, the physical model of the air combustion system was simplified to a laminar flame system. The mathematical model of the laminar flame system, which was built according to thermodynamics theory and the corresponding conservative laws, was studied. With the aid of qualitative theory and method of ordinary differential equations, the location of singular points on the Rayleigh curves is determined, the qualitative structure and the stability of the singular points of the laminar flame system, which are located in the areas of deflagration and detonation, are given for different parameter values and uses of combustion. The phase portraits of the laminar flame system in the reaction-stagnation enthalpy and combustion velocity-stagnation enthalpy planes are shown in the corresponding figures.

关键词： laminar flame system Rayleigh curve singular point orbit phase portrait

TOPOLOGICAL STRUCTURE OF THE singular pointS OF THE THIRD ORDER PHASE LOCKED LOOP EQUATIONS WITH THE CHARACTER OF DETECTED PHASE BEING g(φ)=(1+k)sinφ/(1+kcosφ)

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Applied Mathematics and Mechanics(English Edition) 1992年第9期13卷 883-889页

作者：金均 Shanghai Teachers University Shanghai

In this paper, we study the topological structure of the singular points of the third order phase locked loop equations with the character of detected phase being g(?) =(1+k)sin?/1+kcos?.

关键词： singular point topological structure character of detected phase exponentially asymptotically stable Jordan form

Z2对称非线性方程的X0—分裂双重奇异折叠点附近的奇异点

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Northeastern Mathematical Journal 1994年第3期10卷 385-395页

作者：苏毅吴微

We consider singular points near an X0-breaking double singular fold (DSF) point in Z_2-symmetric nonlinear equations with two parameters, where the linearitazion has a two dimensional null space spanned by a symmetric null vector and an anti-symmetric null vector. In particular, we show that there exist two kinds of singular points passing through the DSF point, a pitchfork point Path and two simple X0-breaking bifurcaiton point paths. Their nondegeneracy is confirmed, which guarantees secondary bifurcations. A numerical example is also given. The main tools for our analysis as well as computation are some extended syStems.

关键词： Double singular fold points Z_2-symmetry singular point X_0-breaking Bifurcation point Ritchfork point Extended System Brusselator

Numerical Investigation of Flow Separation Control on a Highly Loaded Compressor Cascade by Plasma Aerodynamic Actuation

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Chinese Journal of Aeronautics 2012年第3期25卷 349-360页

作者： ZHAO Xiaohu LI Yinghong WU Yun ZHU Tao LI Yiwen Science and Technology on Plasma Dynamics Laboratory Air Force Engineering UniversityXi'an 710038China

To discover the characteristic of separated flows and mechanism of plasma flow control on a highly loaded compressor cascade, numerical investigation is conducted. The simulation method is validated by oil flow visualization and pressure distribution. The loss coefficients, streamline patterns, and topology structure as well as vortex structure are analyzed. Results show that the numbers of singular points increase and three pairs of additional singular points of topology structure on solid surface generate with the increase of angle of attack, and the total pressure loss increases greatly. There are several principal vortices inside the cascade passage. The pressure side leg of horse-shoe vortex coexists within a specific region together with passage vortex, but finally merges into the latter. Corner vortex exists independently and does not evolve from the suction side leg of horse-shoe vortex. One pair of radial coupling-vortex exists near blade trailing edge and becomes the main part of backflow on the suction surface. Passage vortex interacts with the concentrated shedding vortex and they evolve into a large-scale vortex rotating in the direction opposite to passage vortex. The singular points and separation lines represent the basic separation feature of cascade passage. Plasma actuation has better effect at low freestream velocity, and the relative reductions of pitch-averaged total pressure loss coefficient with different actuation layouts of five and two pairs of electrodes are up to 30.8% and 26.7% while the angle of attack is 2~. Plasma actuation changes the local topology structure, but does not change the number relation of singular points. One pair of additional singular point of topology structure generates with plasma actuation and one more reattachment line appears, both of which break the separation line on the suction surface.

关键词： plasma aerodynamic actuation cascade oil flow visualization topology structure vortex singular point

Remark on Gauss curvature equations on punctured disk

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Frontiers of Mathematics in China 2020年第4期15卷 701-707页

作者： Yuxiang LI Hongyan TANG Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China

We give a new argument on the classification of solutions of Gauss curvature equation on R2,which was first proved by *** and ***[Duke Math.J.,1991,63(3):615-622].Our argument bases on the decomposition properties of ... 详细信息

关键词： Gauss curvature equation singular point

Planar Lyapunov Algebras

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Algebra Colloquium 2020年第3期27卷 433-446页

作者： Matej Mencinger Borut Zalar Faculty of Civil Engineering Transportation Engineering and Architecture University of MariborSmetanova 172000 MariborSlovenia Institute of MathematicsPhysics and Mechanics Jadranska 191000 LjubljanaSlovenia Center for Applied Mathematics and Theoretical Physics University of MariborMladinska 32000 MariborSlovenia Faculty of Civil Engineering Transportation Engineering and Architecture University of MariborSmetanova 172000MariborSlovenia

We study complex involutive algebras generated by a single nonselfadjoint idempotent and use them to construct a family of algebras,which we call planar Lyapunov *** our main result,we prove that every 2-dimensional commutative real algebra whose homogeneous Riccati differential equation is stable at the origin must be isomorphic either to an algebra with zero multiplication or to some planar Lyapunov algebra.

关键词： quadratic differential system commutative algebra singular point stability

TRACING A PLANAR ALGEBRAIC CURVE

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Applied Mathematics(A Journal of Chinese Universities) 1997年第1期12卷 15-24页

作者： EllENFALAI FENGYUYU JERENJKOZAK SupportedbyNSFandSFofNatlonaiEducationalCommitteeofChina. SuppotredinpartbyICTP andinpartbyNSFandSFofNationalEducationalCommitteeofChina SupportedbytheMinistryofScienceandTechnologyofSlovenia.

In this paper, an algorithm that determines a real algebraic curve is outlined. Its basicstep is to divide the plane into subdomain1s that include only simple branches of the algebraic curvewithout singular points. Each of the branches is then stably and efficiently traced in the particularsubdomain. Except for tracing, the algorithm requires only a couple of simple operations on poly-nomials that ran be carried out exacrly if the coefficients are rational, and the determination of the real roots of several univariate polynomials.

关键词： Algebraic curve singular point asymptotic line resultant MR Subject Classification 68V05 86U07 65D17

QUALITATIVE ANALYSIS OF BIOECOLOGY DIFFERENTIAL SYSTEM

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生物数学学报 1993年第2期8卷 1-8页

作者： Gu Daoxiu (Hunan Educational Institute, Changsha 410012, China) 湖南教育所湖南长沙

In this paper, the author studies the quartic bioecology differential system:Here n and q are positive constants, l、m and p are constants. The author also proves some theorems of existence and uniqueness of limit cyc... 详细信息

关键词： Bioecology system singular point characteristic equations limit cycle.

EXISTENCE AND UNIQUENESS OF LIMIT CYCLE OF A MULTIMOLECULE-BIOCHEMICAL SYSTEM

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生物数学学报 1996年第1期 5-8页

作者： Gu Daoxiu(Hunan Educational Institute,Changsha,410012 China)

In this paper the author proves some theorems of the existence and uniqueness of the limit cycles of a multimolecule-biochemical system under some *** global structure of the trajectories of the system and the cause o... 详细信息

关键词： Biochemical system singular point limit cycle