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DYNAMIcS OF THE STOcHASTIc g-NAvIEr-STOKES EQUATIONS DrIvEN BY NONLINEAr NOISE

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Acta Mathematica Scientia 2023年第5期43卷 2108-2120页

作者：晏涛张露邹爱红舒级 school of mathematical sciences Laurent Mathematics Center and V.C.&V.R.Key LabSichuan Normal UniversityChengdu 610066China

This paper deals with the asymptotic behavior of solutions of the stochastic g-Navier-Stokes equation driven by nonlinear *** existence and uniqueness of weak pullback mean random attractors for the equation in Bochner space is proven for when the diffusion terms are Lipschitz nonlinear ***,we also establish the existence of invariant measures for the equation.

关键词： non-Newtonian fuid weak pullback attractor mean random dynamical system nonlinear noise invariant measure

Existence and Approximation of Statistical Solutions of the 3D MHD Equations

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Journal of Partial Differential Equations 2024年第3期37卷 326-354页

作者： ZHANG Yuanyuan cHEN Guanggan school of Mathematics and Physics Southwest University of Science and TechnologyMianyang 621010China school of mathematical sciences and V.C.&V.R.Key Lab of Sichuan ProvinceSichuan Normal UniversityChengdu 610068China.

This paper focuses on the statistical characteristics of the 3D MHD *** firstly establish an existence theorem of a vishik-Fursikov measure of the 3D MHD equations by taking advantage of the Krein-Milman theorem along with some functional and measure *** by applying the Topsoe lemma on the constructed trajectory space possessing some special topological properties,we show that the vishik-Fursikov measure and the stationary vishik-Fursikov statistical solution of the 3D MHD system are approximated by the counterparts of the 3D MHD-αsystem,respectively,as the parameterαdecreases to zero.

关键词： 3D MHD equations vishik-Fursikov measures stationary statistical solutions convergence of measures.

Pre-Locator Incorporating Swin-Transformer refined classifier for Traffic Sign recognition

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Intelligent Automation & Soft computing 2023年第8期37卷 2227-2246页

作者： Qiang Luo Wenbin Zheng school of Software Engineering Chengdu University of Information TechnologyChengdu610225China v.c.&v.r.key lab of sichuan province Sichuan Normal UniversityChengdu610068China

In the field of traffic sign recognition,traffic signs usually occupy very small areas in the input *** object detection algorithms directly reduce the original image to a specific size for the input model during the detection process,which leads to the loss of small object ***-tionally,classification tasks are more sensitive to information loss than local-ization *** paper proposes a novel traffic sign recognition approach,in which a lightweight pre-locator network and a refined classification network are *** pre-locator network locates the sub-regions of the traffic signs from the original image,and the refined classification network performs the refinement recognition task in the ***,an innovative module(named SPP-ST)is proposed,which combines the Spatial Pyramid Pool module(SPP)and the Swin-Transformer module as a new feature extractor to learn the special spatial information of traffic sign *** results show that the proposed method is superior to the state-of-the-art methods(82.1 mAP achieved on 218 categories in the TT100k dataset,an improvement of 19.7 percentage points compared to the previous method).Moreover,both the result analysis and the output visualizations further demonstrate the effectiveness of our proposed *** source code and datasets of this work are available at https://***/DijiesitelaQ/TSOD.

关键词： Traffic sign recognition swin-transformer YOLOX small object

chen-ruan cohomology and Stringy Orbifold K-Theory for Stable Almost complex Orbifolds

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chinese Annals of Mathematics,Series B 2020年第5期41卷 741-760页

作者： chengyong DU Tiyao LI school of mathematics and v.c.&v.r.key lab Sichuan Normal UniversityChengdu 610068China school of Mathematics Chongqing Normal UniversityChongqing 401331China

comparing to the construction of stringy cohomology ring of equivariant sta-ble almost complex manifolds and its relation with the chen-ruan cohomology ring of the quotient almost complex orbifolds,the authors construct in this note a chen-ruan cohomology ring for a stable almost complex *** authors show that for a finite group G and a G-equivariant stable almost complex manifold X,the G-invariant part of the stringy cohomology ring of(X,G)is isomorphic to the chen-ruan cohomology ring of the global quotient stable almost complex orbifold[X/G].Similar result holds when G is a torus and the action is locally ***,for a compact presentable stable almost complex orbifold,they study the stringy orbifold K-theory and its relation with chen-ruan cohomology ring.

关键词： Stable almost complex orbifolds chen-ruan cohomology Orbifold K-theory Stringy product

Orbifold Gromov-Witten theory of weighted blowups

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Science china Mathematics 2020年第12期63卷 2475-2522页

作者： Bohui chen cheng-Yong Du rui Wang Department of Mathematics and Yangtze center of Mathematics Sichuan UniversityChengdu 610064China school of mathematical sciences and v.c.&v.r.key lab Sichuan Normal UniversityChengdu 610068China Department of Mathematics University of CaliforniaBerkeleyBerkeleyCA 94720USA

consider a compact symplectic sub-orbifold groupoid S of a compact symplectic orbifold groupoid(X,ω).LetXabe the weight-a blowup of X along S,and Da=PNa be the exceptional divisor,where N is the normal bundle of S in *** this paper we show that the absolute orbifold Gromov-Witten theory ofXacan be effectively and uniquely reconstructed from the absolute orbifold Gromov-Witten theories of X,S and Da,the natural restriction homomorphism Hcr^*(X)→Hcr*(S)and the first chern class of the tautological line bundle over *** achieve this we first prove similar results for the relative orbifold Gromov-Witten theories of(Xa|Da)and(Na|Da).As applications of these results,we prove an orbifold version of a conjecture of Maulik and Pandharipande(Topology,2006)on the Gromov-Witten theory of blowups along complete intersections,a conjecture on the Gromov-Witten theory of root constructions and a conjecture on the Leray-Hirsch result for the orbifold Gromov-Witten theory of Tseng and You(J Pure Appl Algebra,2016).

关键词： orbifold Gromov-Witten theory Leray-Hirsch result weighted projective bundle weighted blowup root stack blowup along complete intersection

Wong-Zakai approximations and long term behavior of stochastic FitzHugh-Nagumo system

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International Journal of Biomathematics 2021年第3期14卷 23-52页

作者： Ling Qin Dandan Ma Ji Shu school of Mathematics Science Laurent Mathematics center and v.c.&v.r.key lab sichuan Normal University Chengdu 610066P.R.China

This paper is concerned with the Wong-Zakai approximations given by a stationary process via the Wiener shift and their associated long term behavior of stochastic FitzHugh-Nagumo system driven by white *** prove the existence and uniqueness of pullback random attractors for the approximate system under much weaker conditions than the original *** the system is driven by additive white noise,we also prove the convergence of solutions of Wong-Zakai approximations and the upper semicontinuity of random attractors of the approximate random system as the size of approximation approaches zero.

关键词： Wong-Zakai approximation random attractor FitzHugh-Nagumo system upper semicontinuity white noise

Double ramification cycles with Orbifold Targets

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Acta Mathematica Sinica,English Series 2022年第8期38卷 1333-1376页

作者： Bo Hui cHEN cheng Yong DU rui WANG Department of Mathematics Sichuan UniversityChengdu 610064P.R.China school of mathematical sciences V.C.&V.R.Key Lab and Laurent Mathematics CenterSichuan Normal UniversityChengdu 610068P.R.China Department of Mathematics University of CaliforniaBerkeleyCA 94720-3840USA

In this paper,we consider double ramification cycles with orbifold *** explicit formula for double ramification cycles with orbifold targets,which is parallel to and generalizes the one known for the smooth case,is **... 详细信息

关键词： root of orbifold line bundles polynomiality double ramification cycle absolute/relative orbifold Gromov–Witten theory

Fractal Dimension of random Attractors for Non-autonomous Fractional Stochastic Ginzburg–Landau Equations

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Acta Mathematica Sinica,English Series 2020年第3期36卷 318-336页

作者： chun Xiao GUO Ji SHU Xiao Hu WANG Department of Mathematics China University of Mining and Technology BeijingBeijing 100083P.R.China school of mathematical Science and v.c.&v.r.key lab Sichuan Normal UniversityChengdu 610068P.R.China Department of Mathematics Sichuan UniversityChengdu 610064P.R.China

This paper considers the dynamical behavior of solutions for non-autonomous stochastic fractional Ginzburg–Landau equations driven by additive noise with α∈(0, 1). First, we give some conditions for bounding the fractal dimension of a random invariant set of non-autonomous random dynamical system. Second, we derive uniform estimates of solutions and establish the existence and uniqueness of tempered pullback random attractors for the equation in H. At last, we prove the finiteness of fractal dimension of random attractors.

关键词： Non-autonomous stochastic fractional Ginzburg–Landau equation random dynamical system random attractor additive noise fractal dimension

Fractal Dimension of random Attractors for Non-autonomous Fractional Stochastic reaction-diffusion Equations

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Journal of Partial Differential Equations 2020年第4期33卷 377-394页

作者： SHU Ji BAI Qianqian HUANG Xin ZHANG Jian school of Mathematics sciences and v.c.&v.r.key lab Sichuan Normal UniversityChengdu 610068China Department of Basic courses Sichuan Vocational College of Finance and EconomicsChengdu 610101China school of mathematical sciences University of Electronic Science and Technology of ChinaChengdu 611731China

This paper deals with non-autonomous fractional stochastic reaction-diffusion equations driven by multiplicative noise with s∈(0,1).We first present some conditions for estimating the boundedness of fractal dimension of a random invariant *** we establish the existence and uniqueness of tempered pullback random ***,the finiteness of fractal dimension of the random attractors is proved.

关键词： random dynamical system random attractor fractal dimension fractional reactiondiffusion equation multiplicative noise