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Science China mathematics 2024年第11期67卷 2433-2452页

作者： Feng Shao institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical sciences University of Chinese Academy of Sciences

Let X be an irreducible Hermitian symmetric space of compact type(iHSS for short).in this paper,we give the irreducible decomposition of *** a by-product,we give a cohomological characterization of the rank of ***,we introduce pseudoeffective thresholds to measure the bigness of tangent bundles of smooth complex projective varieties precisely and calculate them for irreducible Hermitian symmetric spaces of compact type.

关键词： tangent bundle pseudoeffective threshold irreducible Hermitian symmetric space of compact type (iHSS) multiplicity free action

2-local unstable homotopy groups of indecomposable A3～2-complexes

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Science China mathematics 2024年第3期67卷 607-626页

作者： Zhongjian Zhu Jianzhong Pan College of mathematics and Physics Wenzhou University Hua Loo-Keng Key Laboratory of mathematics Institute of MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical sciences University of Chinese Academy of Sciences

in this paper,we calculate the 2-local unstable homotopy groups of indecomposable A3～*** main technique used is analysing the homotopy property of J（A,X）,defined by Gray（1973） for a CW-pair（X,A）,which is homoto... 详细信息

关键词： homotopy groups A 2 n -complexes fibration sequence relative James construction 55P15

Density peak clustering using tensor network

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Science China(information sciences) 2024年第3期67卷 321-322页

作者： Xiao SHi Yun SHANG institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical sciences University of Chinese Academy of Sciences National Center for mathematics and interdisciplinary sciences Key Laboratory of ManagementDecision and Information SystemsAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

Tensor networks have been a powerful tool in simulating many-body physics and have recently gained recognition in the machine learning community due to their remarkable representation capabilities. However, using tens... 详细信息

关键词： Tensors

A Deep Learning Method for Computing Eigenvalues of the Fractional Schrödinger Operator

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Journal of Systems Science & Complexity 2024年第2期37卷 391-412页

作者： GUO Yixiao MiNG Pingbing LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger *** proposed approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior knowledge of the *** improvements enable the proposed method to handle both high-dimensional problems and problems posed on irregular bounded *** authors successfully compute up to the first 30 eigenvalues for various fractional Schrödinger *** an application,the authors share a conjecture to the fractional order isospectral problem that has not yet been studied.

关键词： Eigenvalue problem deep learning fractional Schrödinger operator isospectral problem

Recursive Projected Filter Algorithm with Binary-valued Observations

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Journal of Systems Science & Complexity 2024年第5期37卷 1832-1860页

作者： ZHANG Xiaoyan WANG Ying XUE Wenchao ZHAO Yanlong Key Laboratory of Systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical sciences University of Chinese Academy of Sciences

This paper focuses on the state estimate for a class of systems with both process noise and measurement noise under binary-valued observations, in which the Gaussian assumption on the predicted density of the state is not required. A recursive projected filter algorithm with time-varying thresholds is constructed to estimate the state under binary-valued observations. The time-varying thresholds are designed as the prediction value of the measurement, which can provide more information about the system state. The convergence property is established with some suitable stability,boundedness and observability conditions. in particular, the estimation error between state and estimate is proved to be asymptotically bounded in the mean-square sense, whose upper bound is related to the variance of process noise. Finally, the theoretical results are demonstrated via numerical examples of first-order and high-order systems.

关键词： Binary-valued observations convergence recursive filter time-varying thresholds

Central Asia revealed as a key area in evolution of Eremurus (Asphodelaceae)

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Plant Diversity 2024年第3期46卷 333-343页

作者： Dilmurod Makhmudjanov Sergei volis Ziyoviddin Yusupov inom Juramurodov Komiljon Tojibaev Tao Deng Hang Sun CAS Key Laboratory for Plant Diversity and Biogeography of East Asia Kunming Institute of BotanyChinese Academy of SciencesKunming 650201YunnanChina Yunnan international Joint Laboratory for Biodiversity of Central Asia Kunming Institute of BotanyChinese Academy of SciencesKunming 650201YunnanChina institute of Botany Academy Sciences of UzbekistanTashkent 100125Uzbekistan University of Chinese academy of sciences Beijing 100864China

Eremurus was described at the beginning of the 19th ***,due to limited sampling and the small number of gene markers to date,its phylogeny and evolution are largely *** this study,we analyzed plastomes from 27 species belonging to 2 subgenera and 3 sections of Eremurus,which are found in Central Asia(its center of diversity)and *** also analyzed nuclear DNA iTS of 33 species,encompassing all subgenera and sections of the genus in Central Asia,southwest Asia and *** findings revealed that the genus was monophyletic,although both subgenera Eremurus and Henningia were found to be *** plastome and nrDNA-based phylogenetic trees had three clades that did not reflect the current taxonomy of the *** biogeographical and time-calibrated trees suggest that Eremurus originated in the ancient Tethyan area in the second half of the *** of Eremurus occurred from the early Oligocene to the late *** Sea retreat and several orogenetic events,such as the progressive uplift of the Qinghai-Tibet Plateau and surrounding mountain belts(Altai,Pamir,Tian Shan),caused serious topographic and climate(aridification)changes in Central Asia that may have triggered a split of clades and *** this transformed Central Asia,speciation proceeded rapidly driven mainly by vicariance caused by numerous mountain chains and specialization to a variety of climatic,topographic and soil conditions that exist in this region.

关键词： Asphodelaceae Asphodeloideae Plastome Central Asia Qinghai-Tibet Plateau

C^(α)regularity of weak solutions of non-homogeneous ultraparabolic equations with drift terms

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Science China mathematics 2024年第1期67卷 23-44页

作者： Wendong Wang Liqun Zhang School of Mathematical sciences Dalian University of TechnologyDalian 116024China institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

We consider a class of non-homogeneous ultraparabolic differential equations with singular drift terms arising from some physical models,and prove that weak solutions are H?lder continuous,which are sharp in some sense and also generalize the well-known De Giorgi-Nash-Moser theory to degenerate parabolic equations satisfying the H?rmander hypoellipticity *** new ingredients are manifested in two aspects:on the one hand,for lower-order terms,we exploit a new Sobolev inequality suitable for the Moser iteration by improving the result of Pascucci and Polidoro(2004);on the other hand,we explore the G-function from an early idea of Kruzhkov(1964)and an approximate weak Poincaréinequality for non-negative weak sub-solutions to prove the H?lder regularity.

关键词： ultraparabolic equations Moser iteration Poincare inequality C^a regularity

New black-to-white hole solutions with improved geometry and energy conditions

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Science China(Physics,Mechanics & Astronomy) 2024年第7期67卷 30-43页

作者： Zhongwen Feng Yi Ling Xiaoning Wu Qingquan Jiang School of Physics and Astronomy China West Normal UniversityNanchong 637009China institute of High Energy Physics Chinese Academy of SciencesBeijing 100049China School of Physics University of Chinese Academy of SciencesBeijing 100049China institute of mathematics Academy of Mathematics and System Science and Hua Loo-Keng Key Laboratory of MathematicsChinese Academy of SciencesBeijing 100190China School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100190China

We construct new black-to-white hole solutions which connect the geometry of spacetime at some gluing surface inside the *** continuity of the metric can be guaranteed up to the arbitrary order which is controlled by the power factor *** sort of black-to-white holes is characterized by the sub-Planckian scalar curvature,independent of the mass of black-to-white *** importantly,we show that the energy condition is only violated within a small region near the gluing *** geodesics of particles within the region from black hole to white hole is also *** turns out that the matter falling into the black hole may pass through the center without singularity and come out from the white *** scenario provides novel ideas for understanding the information loss paradox in traditional black hole physics.

关键词： regular black hole energy condition singularity quantum gravity

UNCONDiTiONAL CONvERGENCE AND ERROR ESTiMATES OF A FULLY DiSCRETE FiNiTE ELEMENT METHOD FOR THE MiCROPOLAR NAviER-STOKES EQUATiONS

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Journal of Computational mathematics 2024年第1期42卷 71-110页

作者： Shipeng Mao Jiaao Sun Wendong Xue NCMiS LSECInstitute of Computational Mathematics and Scientific/Enginnering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

in this paper,we consider the initial-boundary value problem(iBvP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element *** first establish some regularity results for the solution of MNSE,which seem to be not available in the ***,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete ***,certain regularity results for the time discrete solution are establishes *** on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of ***,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.

关键词： Micropolar fluids Regularity estimates Euler semi-implicit scheme Mixed finite element methods Unconditional convergence

On the convergence of tracking differentiator with multiple stochastic disturbances

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Science China(information sciences) 2024年第2期67卷 157-169页

作者： Zehao WU Huacheng ZHOU Baozhu GUO Feiqi DENG School of mathematics and Big Data Foshan University School of mathematics and Statistics Central South University academy of mathematics and Systems Science Chinese Academy of Sciences Systems Engineering institute South China University of Technology

This paper investigates the convergence, noise-tolerance, and filtering performance of a tracking differentiator in the presence of multiple stochastic disturbances for the first time. We consider a general case wherein the input signal is corrupted by additive colored noise, and the tracking differentiator is disturbed by additive colored noise and white noise. The tracking differentiator is shown to track the input signal and its generalized derivatives in the mean square sense. Further, the almost sure convergence can be achieved when the stochastic noise affecting the input signal is vanishing. Herein, numerical simulations are performed to validate the theoretical results.

关键词： tracking differentiator convergence noise-tolerance filtering performance multiple stochastic disturbances