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invariant subspaces for sequentially subdecomposable operators

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Science China Mathematics 2003年第4期46卷 433-439页

作者：刘明学 Institute of Mathematics Changsha UniversityChangsha 410003 China

In this paper, using Brown technique, we prove the Mohebi-Radjabalipour Conjecture by strengthening a slight thickness condition of the spectrum, and obtain some invariant subspace theorems. Our result contains an imp... 详细信息

关键词： Banach space, sequentially subdecomposable operators, invariant subspace.

invariant tori for asymptotically linear impact oscillators

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Science China Mathematics 2006年第5期49卷 669-687页

作者： QIAN Dingbian & SUN Xiying School of Mathematical Sciences, Suzhou University, Suzhou 215006, China Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai 200433, China School of Mathematical Sciences Suzhou University Suzhou 215006 China Laboratory of Mathematics for Nonlinear Sciences Fudan University Shanghai 200433 China

The existence of invariant tori and quasi-periodic solutions for asymptotically linear impact oscillators is proved by using the successor map and some generalized versions of the Moser's twist theorem.

关键词： invariant tori, boundedness of solutions, quasi-periodic solution, impact oscillator.

invariant foliations for parabolic equations

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Science China Mathematics 2000年第4期43卷 357-370页

作者：张伟年 Department of Mathematics Sichuan University Chengdu 610064 China

It is proved for parabolic equations that under certain conditions the weak (un-) stable manifolds possess invariant foliations, called strongly (un-) stable foliations. The relevant results on center manifoids are ge... 详细信息

关键词： parabolic equation invariant foliation weak hyperbolic manifold generalized exponential dichoto-my.

Scale-invariant machine-learning model accelerates the discovery of quaternary chalcogenides with ultralow lattice thermal conductivity

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npj Computational Materials 2022年第1期8卷 455-466页

作者： Koushik Pal Cheol Woo Park Yi Xia Jiahong Shen Chris Wolverton Department of Materials Science and Engineering Northwestern UniversityEvanstonIL60208USA

We design an advanced machine-learning(ML)model based on crystal graph convolutional neural network that is insensitive to volumes(i.e.,scale)of the input crystal structures to discover novel quaternary chalcogenides,AMM′Q3(A/M/M'=alkali,alkaline earth,post-transition metals,lanthanides,and Q=chalcogens).These compounds are shown to possess ultralow lattice thermal conductivity(κ_(l)),a desired requirement for thermal-barrier coatings and *** screening the thermodynamic stability of~1 million compounds using the ML model iteratively and performing density-functional theory(DFT)calculations for a small fraction of compounds,we discover 99 compounds that are validated to be stable in *** several DFT-stable compounds,we calculate theirκl using Peierls–Boltzmann transport equation,which reveals ultralowκ_(l)(invariant ML model in predicting novel compounds and presents experimental-research opportunities with these new compounds.

关键词： ultralow thermal invariant

Constructing Hopf Insulator from Geometric Perspective of Hopf invariant

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Chinese Physics Letters 2024年第3期41卷 121-126页

作者：常治文郝维昌 Miguel Bustamante 刘鑫 Institute of Theoretical Physics School of Physics and Optoelectronic EngineeringBeijing University of TechnologyBeijing 100124China School of Physics Beihang UniversityBeijing 100191China Complex and Adaptive Systems Laboratory School of Mathematics and StatisticsUniversity College DublinBelfield4DublinIreland

We propose a method to construct Hopf insulators based on the study of topological defects from the geometric perspective of Hopf invariant ***,we prove two types of topological defects naturally inhering in the inner... 详细信息

关键词： Hopf topological invariant

ON invariant CHECKING

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Journal of Systems Science & Complexity 2013年第3期26卷 470-482页

作者： ZHANG Zhihai KAPUR Deepak School of Mathematical Sciences Peking University Department of Computer Science University of New Mexico

Checking whether a given formula is an invariant at a given program location(especially,inside a loop) can be quite nontrivial even for simple loop programs,given that it is in general an undecidable *** is especially the case if the given formula is not an inductive loop invariant,as most automated techniques can only check or generate inductive loop *** this paper,conditions are identified on simple loops and formulas when this check can be performed automatically.A general theorem is proved which gives a necessary and sufficient condition for a formula to be an invariant under certain restrictions on a *** a byproduct of this analysis,a new kind of loop invariant inside the loop body,called inside-loop invariant,is *** an invariant is more general than an inductive loop invariant typically used in the Floyd-Hoare axiomatic approach to program *** use of such invariants for program debugging is explored;it is shown that such invariants can be more useful than traditional inductive loop invariants especially when one is interested in checking extreme/side conditions such as underflow,accessing array/collection data structures outside the range,divide by zero,etc.

关键词： Assertion Floyd-Hoare logic invariant invariant generation.

Classification of Four-Qubit States by Means of a Stochastic Local Operation and the Classical Communication invariant

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Chinese Physics Letters 2011年第2期28卷 24-27页

作者： ZHA Xin-Wei MA Gang-Long School of Science Xi’an University of Posts and TelecommunicationsXi’an 710121

It is a recent observation that entanglement classification for qubits is closely related to stochastic local operations and classical communication(SLOCC)*** et al.[***.A 65(2002)052112]showed that for pure states of four qubits there are nine different degenerate SLOCC entanglement *** et al.[***.A 76(2007)052311]showed that there are at least 28 distinct true SLOCC entanglement classes for four qubits by means of the SLOCC invariant and *** give 16 different entanglement classes for four qubits by means of basic SLOCC invariants.

关键词： invariants invariant operations

invariant filtrations of Lie algebras of Cartan type over commutative rings

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Chinese Science Bulletin 1995年第11期40卷 890-893页

作者：金宁沈光宇 Department of Mathematics Nanjing University Nanjing 210008 China Department of East China Normal University Shanghai 200062 China

The work of the classification of the simple Lie algebras over algebraical closed fieldF of prime characteristc p began nearly 50 years ago and the problem has been solved just recentlyunder the condition p>7,and the generalized Kostrikin-Safarevic conjecture that these al-gebras are all of classical or Cartan type is *** the classification of simple Liealgebras over non-closed fields,it is necessary to consider the forms.A central simple

关键词： ring Lie algebra of Cartan type invariant filtration nilpotent.

Computation of invariant Curves and Identifying the Type of Critical Point

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Journal of Systems Science & Complexity 2018年第6期31卷 1698-1708页

作者： ZHI Junhai CHEN Yufu School of Mathematical Sciences University of Chinese Academy of Sciences

This paper considers two dimensional systems which have purely imaginary *** order to obtain more propositions of invariant curves,the authors transform the real systems into complex differential systems by using a suitable linear *** authors also propose an algorithm to compute exponential *** improved method of constructing integrating factor by using all invariant curves is presented and can be used in determining the type of the equilibrium points.

关键词： Complex differential system equilibrium point exponential factor invariant curve