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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(2014)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

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 science 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

Gorenstein projective modules over rings of Morita contexts

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science China mathematics 2024年第11期67卷 2453-2484页

作者： Qianqian Guo Changchang Xi school of Mathematical sciences Capital Normal University school of Mathematical sciences Laboratory of Mathematics and Complex Systems(Ministry of Education of China)Beijing Normal University school of mathematics and Statistics Shaanxi Normal University

Under semi-weak and weak compatibility conditions of bimodules,we establish necessary and sufficient conditions of Gorenstein-projective modules over rings of Morita contexts with one bimodule homomorphism *** extends greatly the results on triangular matrix Artin algebras and on Artin algebras of Morita contexts with two bimodule homomorphisms zero in the literature,where only sufficient conditions are given under a strong assumption of compatibility of *** application is provided to describe Gorenstein-projective modules over noncommutative tensor products arising from Morita *** results are proved under a general setting of noetherian rings and modules instead of Artin algebras and modules.

关键词： Gorenstein-projective module noetherian ring noncommutative tensor product totally exact complex weakly compatible bimodule

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

关键词： semisymmetric graph semitransitive graph bi-coset graph

Boundary Points,Minimal L^(2)Integrals and Concavity PropertyⅢ—Linearity on Riemann Surfaces and Fibrations over Open Riemann Surfaces

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Acta Mathematica Sinica,English Series 2024年第9期40卷 2091-2152页

作者： Qi An GUAN Zhi Tong MI Zheng YUAN school of Mathematical sciences Peking UniversityBeijing 100871P.R.China school of mathematics and Statistics Beijing Jiaotong UniversityBeijing 100044P.R.China Institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190P.R.China

In this article,we consider a modified version of minimal L^(2) integrals on sublevel sets of plurisubharmonic functions related to modules at boundary points,and obtain a concavity property of the modified *** applications,we give characterizations for the concavity degenerating to linearity on open Riemann surfaces and on fibrations over open Riemann surfaces.

关键词： Minimal L^(2)integrals plurisubharmonic functions boundary points weakly pseudoconvex Kähler manifold

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

Holder continuous weak solutions of the 2D Boussinesq equation with thermal diffusion

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science China mathematics 2024年第8期67卷 1777-1806页

作者： Tianwen Luo Tao Tao Liqun Zhang Yau Mathematical sciences Center Tsinghua UniversityBeijing 100084China school of mathematics Shandong UniversityJinan 250100China Institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

We show the existence of Holder continuous periodic weak solutions of the 2D Boussinesq equation with thermal diffusion which satisfy the prescribed kinetic *** precisely,for any smooth e(t):[0,1]→R+andε∈(0,110),there exist v∈C 110−ε([0,1]×T2)andθ∈C 1,120−εt 2 C 2,1 x 10−ε([0,1]×T2),which satisfy(1.1)in the sense of distribution and e(t)=ˆT2|v(t,x)|2 dx,∀t∈[0,1].

关键词： 2D Boussinesq equation with thermal diffusion Holder continuous periodic weak solutions prescribed kinetic energy

Quantum correlations in a chain-type quantum network

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Communications in Theoretical Physics 2024年第6期76卷 77-91页

作者： Xiaofei Qi Aihong Zhai Lihua Yang school of Mathematical science Shanxi UniversityTaiyuan 030006China Key Laboratory of Complex systems and Data science of Ministry of Education Shanxi UniversityTaiyuan 030006China school of mathematics and Information Technology Yuncheng UniversityYuncheng 044000China

A quantum network concerns several independent entangled resources and can create strong quantum correlations by performing joint measurements on some *** this paper,we discuss an n-partite chain network with each of two neighboring observers sharing an arbitrary Bell state and all intermediate observers performing some positive-operator-valued measurements with parameterλ.The expressions of all post-measurement states between any two observers are obtained,and their quantifications of Bell nonlocality,Einstein-Podolsky-Rosen steering and entanglement with different ranges ofλare respectively detected and analyzed.

关键词： quantum correlation nonlocality entanglement chain-type quantum network

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 science 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