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Science China Mathematics 2024年第11期67卷 2485-2514页

作者： Zefu Feng Guangyi hong Changjiang zhu School of Mathematical Sciences Chongqing Normal UniversityChongqing 401331China School of Mathematics South China University of TechnologyGuangzhou 510641China

In this paper,we consider 3D compressible magneto-micropolar fluids without resistivity and spin viscosity in a strip *** prominent character of the governing model is the presence of the microstructure,a linear coupling structure involving derivatives of the velocity fields,which along with the lack of spin viscosity brings several challenges to the *** exploiting the two-tier energy method developed in Guo and Tice(Arch Ration Mech Anal,2013),we prove the global existence of classical solutions to the governing model around a uniform magnetic field that is non-parallel to the horizontal ***,we show that the solution converges to the steady state at an almost exponential rate as time goes to *** of the main ingredients in our analysis,compared with previous works on micropolar fluids,is that we deal with the microstructure by establishing some delicate estimates based on the analysis of the div-curl decomposition,and the coupling between the fluid velocity and the vorticity of angular velocity.

关键词： magneto-micropolar fluids compressible global existence large-time behavior

Unsaturated Creep Behaviors of Weak Intercalated Soils in Soft Rock of Badong Formation

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Journal of Mountain Science 2015年第6期12卷 1460-1470页

作者： zhu Yan-Bo YU hong-Ming College of Geology Engineering and Geomatics Chang'an University Faculty of Engineering China University of Geosciences

The cutting slopes in soft rock of redbed appeared in Yichang-Badong highway often suffer from the instability along weak intercalations, so the creep behaviors of weak intercalated soils are crucially important for the stability of cutting slopes. Because the deformation of weak intercalated soils is significantly affected by water content due to the strong water sensitivity, it is necessary to study the influence of matric suction on the creep behaviors of weak intercalated soils. In order to find out the unsaturated creep characters of weak intercalated soils, a GDS unsaturated triaxial apparatus was used. Then the triaxial creep experiments on weak intercalated soil samples under varying matric suction were conducted to obtain the unsaturated creep curves. The results show that the weak intercalated soils have obvious creep behaviors, and the creep strain is in nonlinear relationship with stress and time. When the matric suction is constant, a larger deviator stress will lead to a larger creep strain; When the deviator stress is constant, a smaller matric suction will lead to a larger creep strain. Based on the Mesri creep model, an improved creep model for weak intercalated soils under varying matric suction was established, in which the relationship of stress-strain was expressed with a hyperbolic function, and the relationship of strain-time was expressed with power functions in stages. Then an unsaturated creep model including stress-matric suction-strain-time for weak intercalated soils was established based on the power function relationship between matric suction and Ed(a parameter of the improved creep model). The comparison of the calculated values of creep model and the experimental values shows that the creep behaviors of weak intercalated soils can be predicted by the unsaturated creep model by and large.

关键词： Badong formation Weak intercalated soils Unsaturated creep behaviors Soil triaxial apparatus Creep model

On Initial Data of the Monopole Equation

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Acta Mathematica Sinica,English Series 2009年第12期25卷 2127-2132页

作者： hong Yu WANG Xiu Juan zhu School of Mathematical Sciences Yangzhou University Yangzhou 225002 P. R. China

The space-time monopole equation is the reduction of anti-self-dual Yang-Mills equations in R2,2 to R2,1. This equation is a non-linear wave equation, and can be encoded in a Lax pair. An equivalent Lax pair is used by Dai and Terng to construct monopoles with continuous scattering data, and then the equation can be linearized by the scattering data, allowing one to use the inverse scattering method to solve the Cauchy problem with rapidly decaying small initial data. In this paper, we use the terminology of holomorphic bundle and transversality of certain maps, parametrized by initial data, to give more initial data, with which we can use scattering method to solve the Cauchy problem of the monopole equation up to gauge transformation.

关键词： continuous scattering holomorphically trivial bundle transversality

On Corepresentations of Multiplier Hopf Algebras

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Acta Mathematica Sinica,English Series 2010年第6期26卷 1087-1114页

作者： Shuan-hong WANG Hai-xing zhu Department of Mathematics Southeast University Nanjing 210096 P. R. China

We present a general construction producing a unitary corepresentation of a multiplier Hopf algebra in itself and study RR-corepresentations of twisted tensor coproduct multiplier Hopf algebra. Then we investigate some properties of functors, integrals and morphisms related to the categories of the crossed modules and covariant modules over multiplier Hopf algebras. By doing so, we can apply our theory to the case of group-cograded multiplier Hopf algebras, in particular, the case of Hopf group-coalgebras.

关键词： (group-cograded) multiplier Hopf algebra copresentation crossed module covariant module Hopf group-coalgebra twisted tensor coproduct

Weak type(1, 1) of the Riesz transform on some direct product manifolds with exponential volume growth

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Science China Mathematics 2024年第7期67卷 1599-1622页

作者： hong-Quan Li Jie-Xiang zhu School of Mathematical Sciences Fudan UniversityShanghai200433China Center for Applied Mathematics Tianjin UniversityTianjin300072China

In this paper, we are concerned with the Riesz transform on the direct product manifold H^(n)× M,where H^(n) is the n-dimensional real hyperbolic space, and M is a connected complete non-compact Riemannian manifold satisfying the volume doubling property and generalized Gaussian or sub-Gaussian upper estimates for the heat kernel. We establish its weak type(1, 1) property. In addition, we obtain the weak type(1, 1) of the heat maximal operator in the same setting. Our arguments also work for a large class of direct product manifolds with exponential volume growth. Particularly, we provide a simpler proof of weak type(1, 1) boundedness of some operators considered in the work of Li et al.(2016).

关键词： Riesz transform heat kernel direct product real hyperbolic space

Implementation of Time-Scale Transformation Based on Continuous Wavelet Theory

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Journal of Systems Engineering and Electronics 2000年第1期11卷 32-37页

作者： zhu, Xiaoguang hong, Bingrong Wang, Dongmu Harbin Inst of Technology Harbin China

The basic objective of time-scale transformation is to compress or expand the signal in time field while keeping the same spectral properties. This paper presents two methods to derive time-scale transformation formula based on continuous wavelet transform. For an arbitrary given square-integrable function f(t),g(t) = f(t/λ) is derived by continuous wavelet transform and its inverse transform. The result shows that time-scale transformation may be obtained through the modification of the time-scale of wavelet function filter using equivalent substitution. The paper demonstrates the result by theoretic derivations and experimental simulation.

关键词： Frequency domain analysis Integral equations Signal processing Spectrum analysis Time domain analysis Time series analysis Wave filters

A Score Type Test for General Autoregressive Models in Time Series

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Acta Mathematicae Applicatae Sinica 2007年第3期23卷 439-450页

作者： Jian-hong Wu Li-xing zhu College of Statistics and Mathematics Zhejiang Gongshang University Hangzhou 310018 China hong Kong Baptist University Hong Kong China East China Normal University Shanghai 200062 China

This paper is devoted to the goodness-of-fit test for the general autoregressive models in time series. By averaging for the weighted residuals, we construct a score type test which is asymptotically standard chi-squared under the null and has some desirable power properties under the alternatives. Specifically, the test is sensitive to alternatives and can detect the alternatives approaching, along a direction, the null at a rate that is arbitrarily close to n-1/2. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of alternatives. The performance of the tests is evaluated through simulation studies.

关键词： Autoregressive model goodness-of-fit maximin test model checking score type test time series

Comparative analysis shows high level of lineage sorting in genomic regions with low recombination in the extended Picea likiangensis species complex

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Plant Diversity 2024年第4期46卷 547-550页

作者： Hui zhu Weixiao Lei Qing Lai Yongshuai Sun Dafu ru State Key Laboratory of Grassland Agro-ecosystems College of EcologyLanzhou UniversityLanzhou 730000China CAS Key Laboratory of Tropical Forest Ecology Xishuangbanna Tropical Botanical GardenChinese Academy of SciencesMengla 666303China Xi'an Center for Disease Control and Prevention Xi'an 710068China

Genome-scale data,while promising for illuminating phylogenetic relationships,frequently pose a conundrum by yielding conflicting topologies and highly variable gene tree distributions(Pease et al.,2016).This complexity likely arises from the reticulate evolution observed in many taxa,where genetic information exchange occurs through diverse biological processes.

关键词： sorting processes yielding

A Variational ODE and its Application to an Elliptic Problem

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Acta Mathematicae Applicatae Sinica 2007年第4期23卷 685-696页

作者： Huan-song Zhou hong-bo zhu Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences P.O. Box 71010 Wuhan 430071 China

In this paper, we consider the following ODE problem { （-u＂（τ）＋（N-1）（N-3）/4τ^2 ）u（τ）＋λu（τ）=f（τ,τ（1-N）/2 u）u（τ）,τ〉0, u∈H, N≥3. （P）,where f ∈ C（（0,＋∞） ×R,R）, f（τ,s） goes t... 详细信息

In this paper, we consider the following ODE problem { （-u＂（τ）＋（N-1）（N-3）/4τ^2 ）u（τ）＋λu（τ）=f（τ,τ（1-N）/2 u）u（τ）,τ〉0, u∈H, N≥3. （P）,where f ∈ C（（0,＋∞） ×R,R）, f（τ,s） goes to p（τ） and q（τ） uniformly in τ 〉 0 as s→ 0 and s→＋∞ respectively, 0≤ p（τ） ≤ q（τ） ∈L^∞（0,∞）. Moreover, for τ 〉 0, f（τ, s） is nondecreasing in s≥ 0. Some existence and non-existence of positive solutions to problem （P） are proved without assuming that p（τ） = 0 and q（τ） has a limit at infinity. Based on these results, we get the existence of positive solutions for an elliptic problem.

关键词： Elliptic equation asymptotically linear mountain pass theorem

Elevated soluble 4-1BB is associated with serum markers of hepatitis B virus in patients with chronic hepatitis B

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World Journal of Clinical Cases 2021年第7期9卷 1619-1630页

作者： Meng-ru Zhan Xiu-zhu Gao Chang Wang Fei Peng Xiao-Mei Wang hong-Qin Xu Jun-Qi Niu Department of Hepatology The First Hospital of Jilin UniversityChangchun 130021Jilin ProvinceChina Phase I Clinical Research Center The First Hospital of Jilin UniversityChangchun 130021Jilin ProvinceChina

BACKGROUND Previous studies have suggested that the costimulatory molecule 4-1BB plays pivotal roles in regulating immunity during chronic viral ***,up to now,there are few studies about 4-1BB in chronic hepatitis B(CHB).AIM To clarify this issue,we report our comprehensive study results on the expression levels of 4-1BB in patients with *** From September 2018 to June 2019,a total of 64 patients with CHB were recruited from the Department of Hepatology,The First Hospital of Jilin *** blood samples were collected from 52 treatment-naïve and 12 entecavir-treated patients with CHB as well as 37 healthy donors(including 24 healthy adults and 13 healthy children).The levels of soluble 4-1BB(s4-1BB)in plasma were measured by ELISA.4-1BB mRNA expression in peripheral blood mononuclear cells was detected by real-time quantitative *** The s4-1BB levels in the plasma of patients with CHB were significantly higher than those in healthy adults(94.390±7.393 ng/mL vs 8.875±0.914 ng/mL,Prus DNA,hepatitis B e antigen,and triglyceride levels(r=0.748,Prus and therefore may be a promising biomarker for disease progression.

关键词： Hepatitis B virus Hepatitis B Chronic 4-1BB Soluble 4-1BB Hepatitis B virus serum marker