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GLOBAL UNIQUE SOLUTIONS FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH VARIABLE DENSITY AND ELECTRICAL CONDUCTIVITY

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Acta Mathematica Scientia 2024年第5期44卷 1747-1765页

作者： Xueli KE school of mathematics and Computational {2. Xiangtan UniversityXiangtan411105China school of mathematics and Information {2. Henan Polytechnic UniversityJiaozuo454000China

We study the global unique solutions to the 2.D inhomogeneous incompressible MHD equations,with the initial data(u0,B0)being located in the critical Besov space■and the initial densityρ0 being close to a positive *** using weighted global estimates,maximal regularity estimates in the Lorentz space for the Stokes system,and the Lagrangian approach,we show that the 2.D MHD equations have a unique global solution.

关键词： inhomogeneous MHD equations electrical conductivity global unique solutions

Solitary,periodic,kink wave solutions of a perturbed high-order nonlinear Schrödinger equation via bifurcation theory

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Propulsion and Power Research 2024年第3期13卷 433-444页

作者： Qiancheng Ouyang Zaiyun Zhang Qiong Wang Wenjing Ling Pengcheng Zou Xinping Li school of mathematics Hunan Institute of Science and TechnologyYueyangHunan 414006China school of mathematics and Computational {2. Hunan University of Science and TechnologyXiangtanHunan 411201China

In this paper,by using the bifurcation theory for dynamical system,we construct traveling wave solutions of a high-order nonlinear Schrödinger equation with a quintic ***,based on wave variables,the equation is transformed into an ordinary differential ***,under the parameter conditions,we obtain the Hamiltonian system and phase ***,traveling wave solutions which contains solitary,periodic and kink wave so-lutions are constructed by integrating along the homoclinic or heteroclinic *** addition,by choosing appropriate values to parameters,different types of structures of solutions can be displayed ***,the computational work and it’sfigures show that this tech-nique is influential and efficient.

关键词： Traveling wave solution High-order nonlinear Schrödinger equation Bifurcation theory Dynamical system Hamiltonian system

Essentially Commuting Truncated Toeplitz Operators

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Acta Mathematica Sinica,English Series 2024年第10期40卷 2453-2480页

作者： Xi ZHAO Tao YU school of mathematics and {2. Hebei GEO University school of Mathematical sciences Dalian University of Technology

A model space is a subspace of the Hardy space which is invariant under the backward shift,and a truncated Toeplitz operator is the compression of a Toeplitz operator on some model space. In this paper we prove a necessary and sufficient condition for the commutator of two truncated Toeplitz operators on a model space to be compact.

关键词： 47B32 47B35 commutator compact operator maximal ideal space model space Truncated Toeplitz operator

The joint Laplace transforms for killed diffusion occupation times

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Applied mathematics(A Journal of Chinese Universities) 2024年第3期39卷 398-415页

作者： LI Ying-qiu CHEN Ye school of mathematics and Statistics Changsha University of Science and TechnologyChangsha 410114China College of mathematics and Computational science Hunan University of Arts and ScienceChangde 415000China

The approach of Li and Zhou(2.14)is adopted to find the Laplace transform of occupation time over interval(0,a)and joint occupation times over semi-infinite intervals(-∞,a)and(b,∞)for a time-homogeneous diffusion pr... 详细信息

关键词： time-homogeneous diffusion process occupation time joint occupation time Laplace transform Brownian motion with drift

Semisymmetric Graphs of Order 2.^(3)with Valency p^(2.

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Algebra Colloquium 2024年第2期31卷 199-208页

作者： Li Wang Songtao Guo Genghua Fan school of mathematics and Information {2. Henan Polytechnic University JiaozuoHenan 454000China school of mathematics and Statistics Henan University of Science and Technology LuoyangHenan 471023China 不详

A simple undirected regular graph is said to be semisymmetric if it is edge-transitive but not *** a semisymmetric graphΓof order 2.^(3),p a prime,it is well known thatΓis bipartite with two biparts having equal *** complete classification of such graphs has been given for the full automorphism group Aut(Γ)acting unfaithfully on at least one bipart ofΓ,which shows that there is only one infinite family of such graphs with valency p^(2..The graphs of this kind have been determined when Aut(Γ)acts faithfully and primitively on at least one bipart ofΓ,and thus there is only one remaining case for classifying such graphs of valency p^(2.,Aut(Γ)acting faithfully and imprimitively on both biparts ofΓ,which is dealt with in this *** a result,there is only one infinite family of semisymmetric graphs of order 2.^(3)with valency p^(2..

关键词： semisymmetric graph semitransitive graph bi-coset graph

One-step hydrothermal synthesis of Cit-NaYbF_(4):Er^(3+)nanocrystals with enhanced red upconversion emission for in vivo fluorescence molecular tomography

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Journal of Rare Earths 2024年第1期42卷 36-45,I0002页

作者： Xiaoli Luo Qichen Chen Hongbo Guo Heng Zhang Xiaowei He Wu Zhao school of mathematics and Computer {2. Ningxia Normal UniversityGuyuan756099China school of Information science and Technology Northwest UniversityXi'an710127China

Fluorescence imaging techniques represent essential tools in in vitro,preclinical,and clinical *** this study,an improved one-step hydrothermal method to synthesize citric acid(CA)modifiedα-NaYbF_(4):2.Er^(3+)nanocrystals was *** introduction of various doping ions into NaYbF_(4):2.Er^(3+)and the different valence states of the same ions affect both the crystal size and upconversion luminesce *** fore,we investigated the upconversion luminesce nce enha ncement of NaYbF_(4):2.Er^(3+)by ion doping and find that the upconversion luminescence intensity of the upconversion nanoparticles(UCNPs)co-doped with 5 mol%Fe^(2.)ions shows the greatest enhancement,especially for red emission at654 ***,HeLa cells incubated with UCNPs allow for imaging with strong red upconversion emission detectio *** laser scanning microscope(CLSM)fluorescent images of HeLa cells indicate that NaYbF_(4):2.Er/5%Fe^(2.)leads to a clear outline and improves visualization of the cell *** addition,the CA coated NaYbF_(4):2.Er^(3+)/5%Fe^(2.)nanoparticles and NaYbF_(4):2.Er^(3+)/5%Fe^(2.)show low cytotoxicity in HeLa *** imaging reveals the efficiency of these UCNPs to analyze the lungs,liver,and ***,these results indicate that the Cit-NaYbF_(4):2.Er^(3+)/5%Fe^(2.)UCNPs are efficient nanoprobes for fluorescence molecular to mography.

关键词： Hydrothermal method Fe^(2.)ion doping Tuning size Nanoprobes Fluorescence imaging Rare earths

Computer vision tasks for intelligent aerospace perception: An overview

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science China(Technological sciences) 2024年第9期67卷 2727-2748页

作者： CHEN HuiLin SUN QiYu LI FangFei TANG Yang school of Information science and Engineering East China University of Science and TechnologyShanghai 200237China school of mathematics East China University of Science and TechnologyShanghai 200237China

Computer vision tasks are crucial for aerospace missions as they help spacecraft to understand and interpret the space environment,such as estimating position and orientation, reconstructing 3D models, and recognizing objects, which have been extensively studied to successfully carry out the missions. However, traditional methods like Kalman filtering, structure from motion, and multi-view stereo are not robust enough to handle harsh conditions, leading to unreliable results. In recent years, deep learning(DL)-based perception technologies have shown great potential and outperformed traditional methods, especially in terms of their robustness to changing environments. To further advance DL-based aerospace perception, various frameworks, datasets,and strategies have been proposed, indicating significant potential for future applications. In this survey, we aim to explore the promising techniques used in perception tasks and emphasize the importance of DL-based aerospace perception. We begin by providing an overview of aerospace perception, including classical space programs developed in recent years, commonly used sensors, and traditional perception methods. Subsequently, we delve into three fundamental perception tasks in aerospace missions: pose estimation, 3D reconstruction, and recognition, as they are basic and crucial for subsequent decision-making and control. Finally, we discuss the limitations and possibilities in current research and provide an outlook on future developments,including the challenges of working with limited datasets, the need for improved algorithms, and the potential benefits of multisource information fusion.

关键词： deep learning perception aerospace missions pose estimation 3D reconstruction recognition

Novel Cs-Mg-Al mixed oxide with improved mobility of oxygen species for passive NOx adsorption

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Green Energy & Environment 2024年第10期9卷 1581-1591页

作者： Yimeng Yin Chizhong Wang Lei Qiu Xing Li Feilin Zhao Jie Yu Jinchi Han Huazhen Chang school of Environment and Natural Resources Renmin University of China Department of Earth system science Tsinghua University

The development of passive NOxadsorbers with cost-benefit and high NOxstorage capacity remains an on-going challenge to after-treatment technologies at lower temperatures associated with cold-start ***,Cs1Mg3Al catalyst prepared by sol±gel method was cyclic tested in NOxstorage under 5 vol%*** 100°C,the NOxstorage capacity (12.9μmol g-1) was much higher than that of Pt/Ba O/Al2.3(610μmol g-1).This provided new insights for non-noble metal catalysts in low-temperature passive *** addition of Cs improved the mobility of oxygen species and thus improved the NOxstorage *** XRD,XPS,IR spectra and in situ DRIFTs with NH3probe showed an interaction between CsOxand AlOxsites via oxygen species formed on Cs1Mg3Al *** improved mobility of oxygen species inferred from O2.TPD was consistent with high NOxstorage capacity related to enhanced formation of nitrate and additional nitrite species by ***,the addition of Mg might improve the stability of Cs1Mg3Al by stabilizing surface active oxygen species in cyclic experiments.

关键词： Passive NO x adsorber Low-temperature NO x storage Cesium Oxygen mobility

THE LIMIT CYCLE BIFURCATIONS OF A WHIRLING PENDULUM WITH PIECEWISE SMOOTH PERTURBATIONS

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Acta Mathematica Scientia 2024年第3期44卷 1115-1144页

作者：杨纪华 school of mathematics and Computer {2. Ningxia Normal UniversityGuyuan756000China Ningxia Basic science Research Center of mathematics Yinchuan750000China

This paper deals with the problem of limit cycles for the whirling pendulum equation x=y,y=sin x(cosx-r)under piecewise smooth perturbations of polynomials of cos x,sin x and y of degree n with the switching line x=*** upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained using the Picard-Fuchs equations,which the generating functions of the associated first order Melnikov functions ***,the exact bound of a special case is given using the Chebyshev *** the end,some numerical simulations are given to illustrate the existence of limit cycles.

关键词： whirling pendulum limit cycle Melnikov function Picard-Fuchs equation Chebyshev system