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Cohomology groups of a new class of Kadison-Singer algebras

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Science china Mathematics 2024年第3期67卷 593-606页

作者： Guangyu An Xing cheng Jun Sheng School of Mathematics and Data Science Shaanxi University of Science and TechnologyXi’an 710021China

Let N be a maximal discrete nest on an infinite-dimensional separable Hilbert space H,ξ=∑^(∞)_(n=1)en/2n be a separating vector for the commutant N',E_(ξ)be the projection from H onto the subspace[Cξ]spanned by the vectorξ,and Q be the projection from K=H⊕H⊕H onto the closed subspace{(η,η,η)^(T):η∈H}.Suppose that L is the projection lattice generated by the projections(E_(ξ) 0 0 0 0 0 0 0 0),{(E 0 0 0 0 0 0 0 0):E∈N},(I 0 0 0 I 0 0 0 0) and *** show that L is a Kadison-Singer lattice with the trivial ***,we prove that every n-th bounded cohomology group H~n(AlgL,B(K))with coefficients in B(K)is trivial for n≥1.

关键词： Kadison-Singer algebra Kadison-Singer lattice derivation cohomology group

Rational Schur Superalgebras

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Algebra Colloquium 2024年第2期31卷 209-220页

作者： Andrew Riesen Shun-Jen cheng Department of Mathematical and Statistical Sciences University of Alberta 1132489 Ave NWEdmontonAlbertaCanada 不详

We develop and study the generalization of rational Schur algebras to the super *** to the classical case,this provides a new method for studying rational supermodules of the general linear supergroup GL(m|n).Furthermore,we establish a Schur-Weyl duality result for rational Schur superalgebras and conclude that under certain conditions these objects will be semisimple.

关键词： Schur algebra supermathematics general linear supergroup

Construction of conservation laws for the Gardner equation,Landau-Ginzburg-Higgs equation,and Hirota-Satsuma equation

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Communications in Theoretical Physics 2024年第5期76卷 49-57页

作者： cheng Chen Faiza Afzal Yufeng Zhang School of Mathematics China University of Mining and TechnologyXuzhou221116China Jiangsu Center for Applied Mathematics(CUMT) XuzhouJiangsu 221116China

In this paper,two different methods for calculating the conservation laws are used,these are the direct construction of conservation laws and the conservation theorem proposed by *** these two methods,we obtain the co... 详细信息

关键词： conservation laws Landau-Ginzburg-Higgs equation Hirota-Satsuma equation Gardner equation

Friction Characteristics Between Marine Clay and Construction Materials

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Journal of Ocean University of china 2024年第2期23卷 427-437页

作者： KOU Hailei HUANG Jiaming cheng Yang College of Engineering Ocean University of ChinaQingdao 266100China Fourth Division Organization Department of the CPC Qingdao Municipal CommitteeQingdao 266100China

Structure-soil interface friction characteristics is of importance to investigate the interaction between engineering structures and soils,especially for offshore *** interface friction behavior between marine clay and structural materials with different roughness was studied in this paper by using 3D optical scanning tests,a modified direct shear device and numerical *** between the surface roughness of structures,water content and interface friction angle were presented by model *** increase of water contents decreased the interface friction *** interfaces with different roughness,the interface friction angles will be smaller than that of the soil when the water content exceeds a certain *** roughness of the interface and the water content of the soil are mutually coupled to influence the coefficient of friction(COF).This paper proposed a Finite Element Method(FEM)to simulate the interface direct shear tests of structures with different *** surface models with different roughness are established based on the structure data obtained by 3D *** Coupled Eulerian-Lagrangian(CEL)approach was employed to analyse soils sheared by irregular *** interface behavior for interfaces with different roughness under cyclic shear stresses was analyzed by FEM.

关键词： marine clay construction material interface friction behavior surface roughness Finite Element Method

Continuous Orbit Equivalence of Semigroup Actions

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1581-1598页

作者： Xiang Qi QIANG cheng Jun HOU School of Mathematical Science Yangzhou UniversityYangzhou 225002P.R.China

We introduce notions of continuous orbit equivalence and its one-sided version for countable left Ore semigroup actions on compact spaces by surjective local homeomorphisms,and characterize them in terms of the corresponding transformation groupoids and their operator *** particular,we show that two essentially free semigroup actions on totally disconnected compact spaces are continuously orbit equivalent if and only if there is a canonical abelian subalgebra preserving C^(∗)-isomorphism between the associated transformation groupoid C^(∗)-*** also give some examples of orbit equivalence,consider the special case of semigroup actions by homeomorphisms and relate continuous orbit equivalence of semigroup actions to that of the associated group actions.

关键词： Semigroup action continuous one-sided orbit equivalence continuous orbit equivalence groupoid C^(∗)-algebras

Effects of the Rainfall-Triggered Lisse Effect on the Stability of Loess Slopes

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Journal of Earth Science 2024年第4期35卷 1254-1262页

作者： Zhizhou Yang Donghui cheng Jun Xia School of Water and Environment Chang’an UniversityXi’an710054China Key Laboratory of Subsurface Hydrology and Ecological Effects in Arid Region of the Ministry of Education Chang’an UniversityXi’an710054China Key Laboratory of Eco-Hydrology and Water Security in Arid and Semi-Arid Regions of the Ministry of Water Resources Chang’an UniversityXi’an710054China Key Laboratory of Water Cycle&Related Land Surface Processes Institute of Geographic Sciences and Natural Resources ResearchChinese Academy of SciencesBeijing100101China State Key Laboratory of Water Resources&Hydropower Engineering Sciences Wuhan UniversityWuhan430000China

This paper coupled a water-air two-phase hydrodynamic(WATPH)model with the Iverson’s method to analyze the influence of the Lisse effect on the fast groundwater pressure(P_(w))response and the slope ***,the sensitivities of the driving force and loess soil parameters were *** showed that the WATPH model simulated the height and rise of the depth to the water table reasonably *** depth to water table before rainfall(H0)had a significant impact on the Lisse effect and the slope *** the H_(0) was less than approximately 1 m,the rainfall triggered a significant Lisse effect and decreased the slope factor of safety(F_(s)).When the rainfall intensity(R_(i))was higher than the saturated hydraulic conductivity(K_(s)),the Lisse effect and the F_(s) slightly changed with the increase of the R_(i),and the slope tended to be unstable with continuous *** increasing K_(s),the Lisse effect noticeably increased,and the minimum F_(s) quickly *** analysis of the normalized sensitivity coefficient revealed that H_(0) had a dramatic impact on the Lisse effect and loess slope *** different R_(i) and K_(s) values had prominent influences on the Lisse effect and slight impacts on F_(s).

关键词： Lisse effect landslides safety factor rainfall

On the global smooth solutions of 3D incompressible Hall-MHD equations

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Applied Mathematics(A Journal of chinese Universities) 2024年第2期39卷 319-327页

作者： YUE Gao-cheng SUN Wen-da School of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China

The present paper is devoted to the well-posedness issue for the 3D incompressible Hall-MHD system obtained from kinetic models. Our analysis strongly relies on the use of the Fourier analysis. We establish the global existence of smooth solutions for a class of large initial data, this result implies the initial velocity and magnetic field can be arbitrarily large.

关键词： 3D Hall-MHD well-posedness Fourier analysis

A SCALAR AUXILIARY VARIABLE (SAV) FINITE ELEMENT NUMERICAL SCHEME FOR THE CAHN-HILLIARD-HELE-SHAW SYSTEM WITH DYNAMIC BOUNDARY CONDITIONS

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Journal of Computational Mathematics 2024年第2期42卷 544-569页

作者： Changhui Yao Fengdan Zhang cheng Wang School of Mathematics and Statistics Zhengzhou UniversityZhengzhou 450001China Department of Mathematics University of MassachusettsNorth DartmouthMA 02747USA

In this paper,we consider the Cahn-Hilliard-Hele-Shaw(CHHS)system with the dynamic boundary conditions,in which both the bulk and surface energy parts play important *** scalar auxiliary variable approach is introduced for the physical system;the mass conservation and energy dissipation is proved for the CHHS ***,a fully discrete SAV finite element scheme is proposed,with the mass conservation and energy dissipation laws established at a theoretical *** addition,the convergence analysis and error estimate is provided for the proposed SAV numerical scheme.

关键词： Cahn-Hilliard-Hele-Shaw system Dynamic boundary conditions Bulk energy and surface energy Scalar auxiliary variable formulation Energy stability Convergence analysis

Ti_(3)C_(2)T_(x)MXene wrapped,carbon-coated porous Si sheets for improved lithium storage performance

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chinese Chemical Letters 2024年第2期35卷 617-621页

作者： Hui cheng Yueming Liu Zhongling cheng Xianying Wang Na Huang Haijiao Zhang Institute of Nanochemistry and Nanobiology School of Environmental and Chemical EngineeringShanghai UniversityShanghai 200444China Shanghai Key Laboratory of Green Chemistry and Chemical Processes School of Chemistry and Molecular EngineeringEast China Normal UniversityShanghai 200062China Energy Materials Research Center AG Hydrogen Materials & Devices CAS Key Laboratory of Materials for Energy ConversionShanghai Institute of CeramicsChinese Academy of Sciences (SICCAS)Shanghai 200050China

Si-based materials have shown great potential as lithium-ion batteries(LIBs)anodes due to their natural reserves and high theoretical ***,the large volume changes during cycles and poor conductivity of Si lead to rapid capacity decay and poor cycling stability,ultimately limiting their commercial ***,we have skillfully utilized the microporous MCM-22 zeolite as the unique silicon source to produce porous Si(pSi)sheets by a simple magnesiothermic reduction,followed by a carbon coating and further Ti_(3)C_(2)T_(x)MXene assembly,obtaining the ternary pSi@NC@TNSs *** the design,porous Si sheets provide more active sites and shorten Li-ion transport paths for electrochemical *** N-doped carbon(NC)layer serves as a bonding layer to couple pSi and Ti_(3)C_(2)T_(x).The conductive network formed by 2D Ti_(3)C_(2)T_(x)and medium NC layer effectively enhances the overall charge transport of the electrode material,and helps to stabilize the electrode ***,the as-made pSi@NC@TNSs anode delivers an improved lithium storage performance,exhibiting a high reversible capacity of 925 mAh/g at 0.5 A/g after 100 *** present strategy provides an effective way towards high-performance Si-based anodes for LIBs.

关键词： Si anodes Ti_(3)C_(2)Ti_(x)MXene Porous structure Interfacial assembly Lithium-ion batteries