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A Dual Yamabe Flow and Related Integral Flows

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Chinese Annals of Mathematics,Series B 2024年第3期45卷 319-348页

作者： Jingang XIONG school of mathematical sciences Laboratory of Mathematics and Complex SystemsMinistry of EducationBeijing Normal UniversityBeijing 100875China

The author studies a family of nonlinear integral flows that involve Riesz potentials on Riemannian manifolds. In the Hardy-Littlewood-Sobolev (HLS for short)subcritical regime, he presents a precise blow-up profile exhibited by the flows. In the HLS critical regime, by introducing a dual Q curvature he demonstrates the concentrationcompactness phenomenon. If, in addition, the integral kernel matches with the Green’s function of a conformally invariant elliptic operator, this critical flow can be considered as a dual Yamabe flow. Convergence is then established on the unit spheres, which is also valid on certain locally conformally flat manifolds.

关键词： Hardy-Littlewood-Sobolev functional Dual Q curvature Integral flow

Exclusive Hypothesis Testing for Cox's Proportional Hazards Model

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Journal of Systems Science & Complexity 2024年第5期37卷 2157-2172页

作者： WU Qiang TONG Xingwei DUAN Xiaogang school of Statistics Beijing Normal UniversityBeijing 100875China

Exclusive hypothesis testing is a new and special class of hypothesis *** kind of testing can be applied in survival analysis to understand the association between genomics information and clinical information about the survival ***,it is well known that Cox's proportional hazards model is the most commonly used model for regression analysis of failure *** this paper,the authors consider doing the exclusive hypothesis testing for Cox's proportional hazards model with right-censored *** authors propose the comprehensive test statistics to make decision,and show that the corresponding decision rule can control the asymptotic TypeⅠerrors and have good powers in *** numerical studies indicate that the proposed approach works well for practical situations and it is applied to a set of real data arising from Rotterdam Breast Cancer Data study that motivated this study.

关键词： Comprehensive test statistics Cox’s proportional hazards model exclusive hypothesis testing right-censored data Type I error

Scattering-based hybrid network for facial attribute classification

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Frontiers of Computer Science 2024年第3期18卷 105-116页

作者： Na LIU Fan ZHANG Liang CHANG Fuqing DUAN school of Artificial Intelligence Beijing Normal UniversityBeijing 100875China

Face attribute classification(FAC)is a high-profile problem in biometric verification and face *** recent research has been devoted to extracting more delicate image attribute features and exploiting the inter-attribute correlations,significant challenges still *** scattering transform(WST)is a promising non-learned feature *** has been shown to yield more discriminative representations and outperforms the learned representations in certain *** to the image classification task,WST can enhance subtle image texture information and create local deformation *** paper designs a scattering-based hybrid block,to incorporate frequency-domain(WST)and image-domain features in a channel attention manner(Squeezeand-Excitation,SE),termed WS-SE *** with CNN,WS-SE achieves a more efficient FAC performance and compensates for the model sensitivity of the small-scale affine *** addition,to further exploit the relationships among the attribute labels,we propose a learning strategy from a causal *** cause attributes defined using the causalityrelated information can be utilized to infer the effect attributes with a high confidence *** analysis experiments demonstrate the effectiveness of our model,and our hybrid model obtains state-of-the-art results in two public datasets.

关键词： wavelet scattering transform causality-related learning facial attribute classification

Scattered Co-anchored MoS_(2)synergistically boosting photothermal capture and storage of phase change materials

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Journal of Energy Chemistry 2024年第8期95卷 208-215,I0005页

作者： Yang Li Panpan Liu Yan Gao Yuhao Feng Peicheng Li Xiao Chen Institute of Advanced Materials Beijing Normal UniversityBeijing 100875China school of Materials Science and Engineering University of Science and Technology BeijingBeijing 100083China school of Environment Beijing Normal UniversityBeijing 100875China

Pristine phase change materials(PCMs)suffer from inherent deficiencies of poor solar absorption and photothermal ***,we proposed a strategy of co-incorporation of zero-dimensional(OD)metal nanoparticles and two-dimensional(2D)photothermal materials in PCMs for efficient capture and conversion of solar energy into thermal *** scattered Co-anchored MoS_(2)nanoflower cluster serving as photon and phonon triggers was prepared by in-situ hydrothermal growth of ZIF67 polyhedron on 2D MoS_(2)and subsequent high-temperature *** encapsulating thermal storage unit(paraffin wax),the obtained composite PCMs integrated high-performance photothermal conversion and thermal energy storage *** from the synergistic enhancement of OD Co nanoparticles with localized surface plasmon resonance effect,carbon layer with the conjugation effect and 2D MoS_(2)with strong solar absorption,composite PCMs exhibited a high photothermal conversion efficiency of 95.19%,Additionally,the resulting composite PCMs also demonstrated long-term thermal sto rage stability and durable structu ral stability after 300 thermal *** proposed collabo rative co-incorporation strategy provides some innovative references for developing next-generation photothermal PCMs in solar energy utilization.

关键词： Phase change materials Photothermal conversion Thermal energy storage

An Example of Embedded Singular Continuous Spectrum for Discrete Schrödinger Operators

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Acta Mathematica Sinica,English Series 2024年第8期40卷 1837-1849页

作者： Zheng Qi FU Xiong LI Laboratory of Mathematics and Complex Systems(Ministry of Education) School of Mathematical SciencesBeijing Normal UniversityBeijing 100875P.R.China

We present an example of a potential such that the corresponding discrete Schrödinger operator has singular continuous spectrum embedded in the absolutely continuous spectrum.

关键词： Sparse potentials singular continuous spectrum Prüfer variables

Uniqueness Problem for the Backward Differential Equation of a Continuous-State Branching Process

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Acta Mathematica Sinica,English Series 2024年第8期40卷 1825-1836页

作者： Pei Sen LI Zeng Hu LI school of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100872P.R.China school of mathematical sciences Beijing Normal UniversityBeijing 100875P.R.China

The distributional properties of a multi-dimensional continuous-state branching process are determined by its cumulant semigroup,which is defined by the backward differential *** provide a proof of the assertion of Rhyzhov and Skorokhod(Theory ***.,1970)on the uniqueness of the solutions to the equation,which is based on a characterization of the process as the pathwise unique solution to a system of stochastic equations.

关键词： Continuous-state branching process multi-dimensional backward differential equation stochastic equation generator

Projections of summer light rain frequency in typical terrain over eastern China under wind speed constraint

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Science China Earth sciences 2024年第6期67卷 1885-1894页

作者： Xuechen DONG Daoyi GONG Cuicui SHI Institute of Disaster Risk Science Faculty of Geographical ScienceBeijing Normal UniversityBeijing 100875China Key Laboratory of Environmental Change and Natural Disaster MOEFaculty of Geographical ScienceBeijing Normal UniversityBeijing 100875China school of National Safety and Emergency Management Beijing Normal UniversityBeijing 100875China school of Systems Science Beijing Normal UniversityBeijing 100875China

The variation in near-surface wind speed is a key dynamic parameter in the orographic effect of precipitation over eastern *** this study,we used the latest high-resolution outputs from six GCMs in CMIP6-HighResMIP to evaluate the performance of high-resolution models in simulating the orographic precipitation characteristics of typical mountainous areas in summer over eastern *** orographic precipitation under warming scenarios was projected and constrained according to observational *** results indicated that during the contemporary climate reference period(1979-2009),although the relationship between model-simulated near-surface wind speed and orographic light rain frequency was consistently stable,the sensitivity of the orographic light rain frequency to surface wind variability was generally underestimated,with a deviation approximately 24.1% lower than the observational *** estimated orographic light rain frequency corrected based on the observed near-surface wind speed under a 1.5℃ warming scenario,was 36.1% lower than that of the contemporary period;this reduction was 8.6 times that without the wind speed constraint(4.2%).The MRI-AGCM3-2-S model,with a longer dataset,demonstrated relatively stable reductions in orographic light rain frequency under different warming scenarios(1.5℃,2℃,3℃,and 4℃)after the application of wind speed *** all cases,the reductions exceeded those for the predictions made without the wind speed constraint.

关键词： Frequency of orographic light rain HighResMIP High-resolution projection Observational constraint Eastern China

Random change point model with an application to the China Household Finance Survey

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Science China Mathematics 2024年第10期67卷 2373-2386页

作者： Meng Li Lingxi Gao Guangming Lv Xingwei Tong school of Statistics Beijing Normal UniversityBeijing 100875China

We consider a linear model with a change point according to the unknown random threshold of a covariate. We give the expectation-maximization(EM) estimations of the regression and change point parameters. The existence of the random change point is detected by the supremum(SUP) test of score statistics. Theoretically, we establish the convergence and asymptotic distribution of the estimation and show that the EM estimates converge in distribution to a normal distribution. In addition, the numerical performance of the proposed approach is demonstrated through simulation studies. Finally, applying our methodology to household financial decisions, we see that the average debt tolerance of Chinese households is estimated to be 1.1364 times the sum of total household income and financial assets. The effect of assets and income on consumption shows a rapid decline if the household exceeds the average debt tolerance.

关键词： random change point EM algorithm SUP test debt nancial vulnerability

THE PERSISTENCE OF SOLUTIONS IN A NONLOCAL PREDATOR-PREY SYSTEM WITH A SHIFTING HABITAT

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Acta Mathematica Scientia 2024年第3期44卷 1096-1114页

作者：赵敏袁荣 school of Science Tianjin Chengjian UniversityTianjin300384China Laboratory of Mathematics and Complex Systems(Ministry of Education) School of Mathematical SciencesBeijing Normal UniversityBeijing100875China

In this paper,we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting *** is known that Choi et al.[J Differ Equ,2021,302:807-853]studied the persistence or extinction of the prey and of the predator separately in various moving *** particular,they achieved a complete picture in the local diffusion ***,the question of the persistence of the prey and of the predator in some intermediate moving frames in the nonlocal diffusion case was left open in Choi et al.'s *** using some a prior estimates,the Arzelà-Ascoli theorem and a diagonal extraction process,we can extend and improve the main results of Choi et *** achieve a complete picture in the nonlocal diffusion case.

关键词： predator-prey system persistence nonlocal dispersal shifting environment