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Topological Stability and Entropy for Certain Set-valued Maps

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Acta Mathematica Sinica,English Series 2024年第4期40卷 962-984页

作者： Yu zhang Yu jun ZHU School of Mathematical Sciences Xiamen UniversityXiamen 361005P.R.China

In this paper,the dynamics(including shadowing property,expansiveness,topological stability and entropy)of several types of upper semi-continuous set-valued maps are mainly considered from differentiable dynamical systems points of *** is shown that(1)if f is a hyperbolic endomorphism then for eachε>0 there exists a C^(1)-neighborhood U of f such that the induced set-valued map F_(f,U)has theε-shadowing property,and moreover,if f is an expanding endomorphism then there exists a C^(1)-neighborhood U of f such that the induced set-valued map F_(f,U)has the Lipschitz shadowing property;(2)when a set-valued map F is generated by finite expanding endomorphisms,it has the shadowing property,and moreover,if the collection of the generators has no coincidence point then F is expansive and hence is topologically stable;(3)if f is an expanding endomorphism then for eachε>0 there exists a C^(1)-neighborhood U of f such that h(F_(f,U,ε))=h(f);(4)when F is generated by finite expanding endomorphisms with no coincidence point,the entropy formula of F is ***,the dynamics of the set-valued maps based on discontinuous maps on the interval are also considered.

关键词： Set-valued map orbit space hyperbolic endomorphism perturbation shadowing expansiveness topological stability entropy

Camera,LiDAR,and IMU Based Multi-Sensor Fusion SLAM:A Survey

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Tsinghua Science and Technology 2024年第2期29卷 415-429页

作者： jun Zhu Hongyi Li Tao zhang Department of Automation Tsinghua UniversityBeijing 100084China

In recent years,Simultaneous Localization And Mapping(SLAM)technology has prevailed in a wide range of applications,such as autonomous driving,intelligent robots,Augmented Reality(AR),and Virtual Reality(VR).Multi-sensor fusion using the most popular three types of sensors(e.g.,visual sensor,LiDAR sensor,and IMU)is becoming ubiquitous in SLAM,in part because of the complementary sensing capabilities and the inevitable shortages(e.g.,low precision and long-term drift)of the stand-alone sensor in challenging *** this article,we survey thoroughly the research efforts taken in this field and strive to provide a concise but complete review of the related ***,a brief introduction of the state estimator formation in SLAM is ***,the state-of-the-art algorithms of different multi-sensor fusion algorithms are *** we analyze the deficiencies associated with the reviewed approaches and formulate some future research *** paper can be considered as a brief guide to newcomers and a comprehensive reference for experienced researchers and engineers to explore new interesting orientations.

关键词： multi-sensor fusion Simultaneous Localization And Mapping(SLAM) navigation localization

Weakly Approximate Diagonalization of Homomorphisms into Finite von Neumann Algebras

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Acta Mathematica Sinica,English Series 2024年第9期40卷 2187-2194页

作者： Wen Hua QIAN jun Hao SHEN Wen ming WU School of Mathematical Sciences Chongqing Normal UniversityChongqing 401331P.R.China Department of Mathematics and Statistics University of New HampshireDurhamNH 03824USA

Let A be a unital C^(∗)-algebra and B a unital C^(∗)-algebra with a faithful traceτ.Let n be a positive *** give the definition of weakly approximate diagonalization(with respect toτ)of a unital homomorphismφ:A→Mn(B).We give an equivalent characterization of McDuff II1 *** show that,if A is a unital nuclear C^(∗)-algebra and B is a type II1 factor with faithful traceτ,then every unital^(∗)-homomorphismφ:A→Mn(B)is weakly approximately *** B is a unital simple infinite dimensional separable nuclear C^(∗)-algebra,then any finitely many elements in Mn(B)can be simultaneously weakly approximately diagonalized while the elements in the diagonals can be required to be the same.

关键词： Weakly approximately diagonalizable McDuff factors nuclear hyperfinite

New method for multibody dynamics based on unknown constraint force

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Science China(Technological Sciences) 2024年第3期67卷 791-808页

作者： TIAN Ying JIA YingHong zhang jun School of Astronautics Beihang UniversityBeijing 100191China Beijing Institute of Control Engineering Beijing 100190China National Laboratory of Space Intelligent Control Beijing 100190China

This paper presents a new method for the dynamics of multibody systems based on unknown constraint force. The method can uniformly solve multibody systems with typical configurations, including the system with rigid-flexible coupling, the system in tree topology, and the system with loop constraints. Unlike common methods, the proposed method can model the loop system without “cutting off” loop constraints, leading to the exact same modelling process as the tree-like system performs. Based on graph theory, a topological record matrix M_(rec) is proposed to capture the arbitrary system configuration. Moreover, constraint forces are selected as the key variables in semi-recursive framework. With the recursive kinematics relationship between adjacent bodies, the constraint force equation is further assembled to achieve the full-state system solution. The numerical simulations demonstrate the accuracy of the proposed method.

关键词： multibody system dynamic modelling rigid-flexible coupling unknown constraint force graph theory semi-recursive algorithm

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Unraveling role of double-exchange interaction in electrochemical water oxidation by external magnetic field

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Rare Metals 2024年第1期43卷 289-297页

作者： jun Li jun-ming Li Hong Hong Dong-Xue Liu Qing-Qi Cao Dun-Hui Wang National Laboratory of Solid State Microstructures and Jiangsu Provincial Key Laboratory for Nanotechnology Nanjing UniversityNanjing 210093China School of Electronics and Information Hangzhou Dianzi UniversityHangzhou 310018China

Double-exchange(DE) interaction plays an important role in electrocatalytic oxygen evolution reaction(OER).However,precise achievement of DE interaction often requires foreign dopants or vacancy engineering,leading to destabilization of the catalysts and deterioration of *** contrast,the utilization of environmentally friendly,contactless,and continuously adjustable magnetic fields to study the OER process is profitable to avoid aforementioned interference factors and further elucidate the direct relationship_(0.5)between DE interaction and OER ***,by using cobalt hydroxide carbonate(Co(OH)(CO_(3))·xH_(2)O,CoHC) nanostructures as a proof-of-concept study,external magnetic fields are carefully implemented to verify the role of DE interaction during water oxidation *** studies reveal that external magnetic fields effectively enhance the reaction rate of the catalyst,the overpotential decreases from 386 to 355 mV(100 mA·cm^(-2)),while Tafel slopes drastically decline from 93 to 67 mV·dec^(-1)(1.0 T).Moreover,magnetic field increment exhibits robust *** in situ Raman and impedance measurements under external field,it can be found that magnetic field promotes the electron migration between Co^(2+) and Co^(3+) in the CoHC catalysts with the assistance of DE interactions,thus boosting the OER efficiency.

关键词： Magnetic field Double-exchange(DE)interaction Electrocatalysis Oxygen evolution reaction(OER) Cobalt hydroxide carbonate

Self-Triggered Set Stabilization of Boolean Control Networks and Its Applications

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IEEE/CAA Journal of Automatica Sinica 2024年第7期11卷 1631-1642页

作者： Rong Zhao jun-e Feng Dawei zhang the School of Mathematics Shandong UniversityShandong UniversityJinan 250100China

Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control systems with limited communication resources. In this study, the set stabilization problem and STC design of Boolean control networks are investigated via the semi-tensor product technique. On the one hand, the largest control invariant subset is calculated in terms of the strongly connected components of the state transition graph, by which a graph-theoretical condition for set stabilization is derived. On the other hand, a characteristic function is exploited to determine the triggering mechanism and feasible controls. Based on this, the minimum-time and minimum-triggering open-loop, state-feedback and output-feedback STCs for set stabilization are designed,respectively. As classic applications of self-triggered set stabilization, self-triggered synchronization, self-triggered output tracking and self-triggered output regulation are discussed as well. Additionally, several practical examples are given to illustrate the effectiveness of theoretical results.

关键词： Boolean control networks(BCNs) output regulation self-triggered control semi-tensor product of matrices set stabilization synchronization

Central aromatic-core fluorination in non-fullerene acceptor advances binary organic solar cells to a record efficiency of 19.7%

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Science China Materials 2024年第8期67卷 2713-2714页

作者： ming zhang Zhi-Guo zhang State Key Laboratory of Organic/Inorganic Composites Beijing Advanced Innovation Center for Soft Matter Science and EngineeringBeijing University of Chemical TechnologyBeijing 100029China

Organic solar cells(OSCs)hold great promise for the conversion of solar energy into electricity,showing advantages such as lightweight,flexibility,semi-transparency,and solution *** field has witnessed significant adv... 详细信息

关键词： aromatic acceptor transparency

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Effect of Wave Nonlinearity on the Instantaneous Seabed Liquefaction

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China Ocean Engineering 2024年第1期38卷 93-103页

作者： WANG Zhao-jun SUI Ti-ti zhang Chi PAN jun-ning Key Laboratory of Port Waterway and Sedimentation Engineering of the Ministry of TransportNanjing Hydraulic Research InstituteNanjing 210024China Key Laboratory of Coastal Disaster and Protection(Hohai University) Ministry of EducationNanjing 210098China The National Key Laboratory of Water Disaster Prevention Nanjing 210098China

The nonlinear variation of wave is commonly seen in nearshore area,and the resulting seabed response and liquefaction are of high concern to coastal *** this study,an analytical formula considering the nonlinear wave skewness and asymmetry is adopted to provide wave pressure on the seabed *** liquefaction depth attenuation coefficient and width growth coefficient are defined to quantitatively characterize the nonlinear effect of wave on seabed *** on the 2D full dynamic model of wave-induced seabed response,a detailed parametric study is carried out in order to evaluate the influence of the nonlinear variation of wave loadings on seabed ***,new empirical prediction formulas are proposed to fast predict the maximum liquefaction under nonlinear *** indicate that(1)Due to the influence of wave nonlinearity,the vertical transmission of negative pore water pressure in the seabed is hindered,and therefore,the amplitude decreases significantly.(2)In general,with the increase of wave nonlinearity,the liquefaction depth of seabed decreases *** under asymmetric and skewed wave loading,the attenuation of maximum seabed liquefaction depth is the most significant among all the nonlinear wave ***,highly skewed wave can cause the liquefaction depth of seabed greater than that under linear wave.(3)The asymmetry of wave pressure leads to the increase of liquefaction width,whereas the influence of skewedness is not significant.(4)Compared with the nonlinear waveform,seabed liquefaction is more sensitive to the variation of nonlinear degree of wave loading.

关键词： nonlinear wave seabed response seabed liquefaction numerical simulation liquefaction prediction

Discovery of the choristodere Hyphalosaurus baitaigouensis from the Lower Cretaceous Jiufotang Formation of western Liaoning,China and its paleobiogeographic significance

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Journal of Palaeogeography 2024年第3期13卷 547-562页

作者： Li-jun zhang Shu-An Ji Hai-Chun zhang South China Sea Culture Museum Hainan Tropical Ocean UniversitySanya 572022Hainan ProvinceChina Key Laboratory of Stratigraphy and Paleontology Ministry of Natural ResourcesInstitute of GeologyChinese Academy of Geological SciencesBeijing 100037China State Key Laboratory of Palaeobiology and Stratigraphy Nanjing Institute of Geology and Palaeontology and Center for Excellence in Life and PaleoenvironmentChinese Academy of SciencesNanjing 210008Jiangsu ProvinceChina

The water-living reptile genus Hyphalosaurus was previously discovered in the Lower Cretaceous Yixian Formation bearing the middle Jehol Biota in western Liaoning,*** complete skeletons of Hyphalosaurus are reported for the first time from the Jiufotang Formation bearing the late Jehol Biota at two sites in western *** show the typical characteristics of Hyphalosaurus baitaigouensis in terms of the contact between some cranial bones and the number of cervical and dorsal vertebrae,and therefore are assigned to *** discovery extends the stratigraphic range of this species from the Yixian Formation to the overlying Jiufotang *** paper further briefly compares the main characteristics of the two skeletons,summarizes the temporal and spatial distribution of Hyphalosaurus,and discusses the palaeogeographic evolution of western Liaoning at the middle and late Jehol Biota stages based on the aquatic habits of Hyphalosaurus and the geological background of western *** analytical results show that the volcanic downwarped lakes,with distinct geographical divisions in western Liaoning during the deposition of the Yixian Formation,had not completely disappeared till the deposition of the Jiufotang *** palaeo-lake in the Fuxin-Yixian Basin underwent the process of generation,expansion and shrinkage during the depositional period of the Yixian Formation and finally merged into a large *** palaeo-Dalinghe River,which connected the main basins in western Liaoning during the depositional period of the Jiufotang Formation,was formed simultaneously.

关键词： Western liaoning Jehol biota Jiufotang formation Hyphalosaurus baitaigouensis Palaeobiogeography