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Holomorphic invariant forms of a bounded domain

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science china {2. 2008年第11期51卷 1945-1964页

作者： LU QiKeng Institute of mathematics, academy of mathematics and Systems science, chinese academy of sciences, beijing 100190, china Institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Given a complete ortho-normal system ? = (?0,?1,?2.…) of L 2.H( $ \mathcal{D} $ ), the space of holomorphic and absolutely square integrable functions in the bounded domain $ \mathcal{D} $ of ? n , we construct a holomorphic imbedding $ \iota _\phi :\mathcal{D} \to \mathfrak{F}(n,\infty ) $ , the complex infinite dimensional Grassmann manifold of rank n. It is known that in $ \mathfrak{F}(n,\infty ) $ there are n closed (μ, μ)-forms τμ (μ = 1,…,n) which are invariant under the holomorphic isometric automorphism of $ \mathfrak{F}(n,\infty ) $ and generate algebraically all the harmonic differential forms of $ \mathfrak{F}(n,\infty ) $ . So we obtain in $ \mathcal{D} $ a set of (μ, μ)-forms ι ? * τμ (μ = 1,…, n), which are independent of the system ? chosen and are invariant under the bi-holomorphic transformations of $ \mathcal{D} $ . Especially the differential metric ds 2.1 associated to the K?hler form ι ? * τ1 is a K?hler metric which differs from the Bergman metric ds 2.of $ \mathcal{D} $ in general, but in case that the Bergman metric is an Einstein metric, ds 1 2.differs from ds 2.only by a positive constant factor.

关键词： complete ortho-normal system holomorphic invariant forms 32.36 32.65

The reason of Hopf’s and Oleinik’s proofs for countability of shocks being wrong

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science china {2. 2012年第4期55卷 727-729页

作者： LI BangHe academy of mathematics and Systems {2.,chinese academy of sciences,beijing 100190,china academy of mathematics and Systems {2. Chinese Academy of Sciences Beijing China

For the number of complete shock curves of a conservation law with one space variable,Hopf in 1950 for the Burger equation,and Oleinik in 1956 for the general,stated that it is at most *** 1979,the present author published an example to show that the statement of Hopf and Oleinik is *** after so long time,the wrong statement for countability still appeared in some publications,which is at least partly due to that some ones felt difficult to understand Hopf and Oleinik’s proofs being ***,pointing out where they went wrong becomes very necessary.

关键词： countability of shocks uncountability of shocks conservation law

Novel high-safety aeroengine performance predictive control method based on adaptive tracking weight

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chinese Journal of Aeronautics 2024年第7期37卷 352-374页

作者： Qian chen hanlin SHENG Jie ZHANG Jiacheng LI College of Energy and Power Engineering Nanjing University of Aeronautics and AstronauticsNanjing 210016China College of Automation Engineering Nanjing University of Aeronautics and AstronauticsNanjing 210016China

Increasing attention has been attracted to the dynamic performance and safety of advanced performance predictive control systems of the next-generation *** latest research demonstrates that Subspace-based Improved Model Predictive Control(SIMPC)can overcome the difficulty in solving the predictive model in MPC/NMPC ***,applying constant design parameters cannot maintain consistent control effects in all ***,the designed system relies too much on sensor-measured data,and thus it is difficult to thoroughly validate the safety of the system because of its high *** means that any potential hardware/software faults will endanger the ***,this paper first presents a novel nonlinear mapping relationship to adaptively tune the tracking weight online with the change of Power Lever Angle(PLA)and real-time relative tracking ***,without introducing additional design parameters,an Adaptive Tracking Weight-based SIMPC(ATW-SIMPC)controller is designed to improve the control performance in all operating states ***,a Primary/Backup Hybrid Control(PBHC)strategy with the ATW-SIMPC controller as the primary system and the traditional speed(Nf)controller as the backup system is proposed to ensure *** designed affiliated switching controller and the real-time monitor therein can be used to realize reasonable and smooth switching between primary/backup systems,so as to avoid bump *** PBHC system switches to the Nf controller when the ATW-SIMPC controller is wrong because of potential hardware/software faults;otherwise,the ATW-SIMPC controller keeps acting on the *** main results prove that the ATW-SIMPC controller with the optimal nonlinear mapping relationship,compared with the existing SIMPC controller,uplifts the dynamic control performance by 32.and reduces overshoots to an allowable limit,resulting in a better control effect in full *** comparison results consistently i

关键词： Aeroengine Model predictive control Hybrid system Adaptive weight Safety

Poisson kernel and Cauchy formula of a non-symmetric transitive domain

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science china {2. 2010年第7期53卷 1678-1683页

作者： LU Qi-Keng Institute of mathematics, academy of mathematics and System science, chinese academy of sciences, beijing 100190, china Institute of mathematics Academy of Mathematics and System Science Chinese Academy of Sciences Beijing China

In 1965, Lu Yu-Qian discovered that the Poisson kernel of the homogenous domain S m,p,q={Z∈Cm×m, Z1∈Cm×p,Z2.∈Cq×m|2.1( Z-Z+)-Z1Z1′-Z2.Z2.0} does not satisfy the Laplace-Beltrami equation associated with the Be... 详细信息

In 1965, Lu Yu-Qian discovered that the Poisson kernel of the homogenous domain S m,p,q={Z∈Cm×m, Z1∈Cm×p,Z2.∈Cq×m|2.1( Z-Z+)-Z1Z1′-Z2.Z2.gt;0} does not satisfy the Laplace-Beltrami equation associated with the Bergman metric when S m,p,q is not symmetric. However the map T0:Z→Z, Z1→Z1 , Z2.Z2.transforms S m,p,q into a domain S I (m, m + p + q) which can be mapped by the Cayley transformation into the classical domains R I (m, m + p + q). The pull back of the Bergman metric of R I (m, m + p + q) to S m,p,q is a Riemann metric ds 2.which is not a Khler metric and even not a Hermitian metric in general. It is proved that the Laplace-Beltrami operator associated with the metric ds 2.when it acts on the Poisson kernel of S m,p,q equals 0. Consequently, the Cauchy formula of S m,p,q can be obtained from the Poisson formula.

关键词： Poisson kernel Cauchy formula

Remarks on Hard Lefschetz conjectures on Chow groups Dedicated in celebration of science china on the occasion of its 60th birthday

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science china {2. 2010年第1期53卷 105-114页

作者： FU BaoHua Institute of mathematics, academy of Mathematic and Systems {2., chinese academy of sciences, beijing 100190, china Institute of mathematics Academy of Mathematic and Systems Science Chinese Academy of Sciences Beijing China

We propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we show that they are equivalent to the well-known conjectures of Beauville and Murre.

关键词： Chow groups abelian varieties Bloch-Beilinson conjectures Beauville conjecture Murre conjecture

On the ratio of different norms of caloric functions and related eigenfunctions of an integral operator

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science china {2. 2012年第8期55卷 1597-1612页

作者： DING YuTao 1,2.& ZHANG LiQun 1,2.1 Institute of mathematics,academy of mathematics and Systems science,chinese academy of sciences,beijing 100190,china 2.Hua Loo-Keng Key Laboratory of mathematics,chinese academy of sciences,beijing 100190,china Institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Hua Loo-Keng Key Laboratory of mathematics Chinese Academy of Sciences Beijing China

We investigate the ratio of L 1 and L 2.norms of the Cauchy problem solutions of heat equations with compact support initial *** related asymptotic behavior of the eigenvalues and eigenfunctions of certain integral op... 详细信息

关键词： integral operators eigenvalues heat equation

Direct Optimization of Low-thrust Many-revolution Earth-orbit Transfers

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chinese Journal of Aeronautics 2009年第4期22卷 426-433页

作者： Gao Yang academy of Opto-Electronics,chinese academy of sciences,{2.,china academy of Opto-Electronics Chinese Academy of Sciences Beijing 100190 China

Low-thrust Earth-orbit transfers with 10^- 5-order thrust-to-weight ratios involve a large number of orbital revolutions which poses a real challenge to trajectory optimization. This article develops a direct method to optimize minimum-time low-thrust many-revolution Earth-orbit transfers. A parameterized control law in each orbit, in the form of the true optimal control, is proposed, and the time history of the parameters governing the control law is interpolated through a finite number of nodal values. The orbital averaging method is used to significantly reduce the computational workload and the trajectory optimization is conducted based on the orbital averaging dynamics expressed by nonsingular equinoctial elements. Furthermore, Earth＇s shadowing and perturbation effects are taken into account. The optimal transfer problem is thus converted to the parameter optimization problem that can be solved by nonlinear programming. Taking advantage of the mapping between the parameterized control law and the Lyapunov control law, a technique is proposed to acquire good initial guesses for optimization variables, which results in enlarged convergence domain of the direct optimization method. Numerical examples of optimal Earth-orbit transfers are presented.

关键词： low thrust orbital transfer optimization direct method orbital averaging Lyapunov method

NONPARAMETRIC APPROACH TO IDENTIFYING NARX SYSTEMS

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Journal of Systems science & Complexity 2010年第1期23卷 3-21页

作者： Qijiang SONG·Han-Pu chen Key Laboratory of Systems and Control,Institute of Systems science,{2. of mathematics and Systems science,chinese academy of sciences,beijing 100190,china Key Laboratory of Systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

This paper considers identification of the nonlinear autoregression with exogenous inputs(NARX system).The growth rate of the nonlinear function is required be not faster than linear withslope less than *** value of f(·) at any fixed point is recursively estimated by the stochasticapproximation (SA) algorithm with the help of kernel *** consistency of the estimatesis established under reasonable conditions,which,in particular,imply stability of the *** simulation is consistent with the theoretical analysis.

关键词： α-mixing geometrically ergodic Markov chains NARX nonparametric recursive estimate stochastic approximation strongly consistent.

MODELLING AND NUMERICAL SOLUTIONS OF A GAUGE PERIODIC TIME DEPENDENT GINZBURG-LANDAU MODEL FOR TYPE-Ⅱ SUPERCONDUCTORS

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Journal of Computational mathematics 1997年第4期15卷 365-384页

作者： Zhi-ming chen (Institute of mathematics, {2., beijing, china) 中科院数学所北京

In this paper we seek the solutions of the time dependent Ginzburg-Landau model for type-Ⅱ superconductors such that the associated physical observables are spatially periodic with respect to some lattice whose basic lattice cell is not necessarily rectangular. After appropriately foring the gange, the model can be formulated as a system of nonlinear parabolic partial differential equations with quasi-periodic boundary conditions. We first give some results concerning the existence, uniqueness and regularity of solutions and then we propose a semiimplicit finite element scheme solving the system of nonlinear partial dmerential equations and show the optimal error estimates both in the L2.and energy *** also report on some numerical results at the end of the paper.

关键词： Math QT MODELLING AND NUMERICAL SOLUTIONS OF A GAUGE PERIODIC TIME DEPENDENT GINZBURG-LANDAU MODEL FOR TYPE SUPERCONDUCTORS