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Interpolation of closed ideals of bilinear operators

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Acta Mathematica Sinica,English Series 2024年

作者： Fernando COBOS Luz M.FERNáNdeZ-CABRERA Antón MARTíNEZ departamento de Análisis matemático y matemática Aplicada Facultad de MatemáticasUniversidad Complutense de Madrid Sección departamental del departamento de Análisis matemático y matemática Aplicada Facultad de Estudios EstadísticosUniversidad Complutense de Madrid departamento de matemática Aplicada I Escuela de Ingeniería IndustrialUniversidad de Vigo

AbstractWe extend the （outer） measureγIassociated to an operator ideal I to a measureγJfor bounded bilinear operators.If I is surjective and closed,and J is the class of those bilinear operators such thatγJ（T）=0,we prove that J coincides with the composition bideal I o B.If I satisfies the ∑r-condition,we establish a simple necessary and sufficient condition for an interpolated operator by the real method to belong to J.Furthermore,if in addition I is symmetric,we prove a formula for the measureγJof an operator interpolated by the real method.In particular,results apply to weakly compact operators.

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A Value for Games defined on Graphs

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Applied Mathematics 2024年第5期15卷 331-348页

作者： Néstor Bravo departamento de matemá ticas Universidad de Guanajuato Guanajuato Mexico

Given a graph g=( V,A ) , we define a space of subgraphs M with the binary operation of union and the unique decomposition property into blocks. This space allows us to discuss a notion of minimal subgraphs (minimal coalitions) that are of interest for the game. Additionally, a partition of the game is defined in terms of the gain of each block, and subsequently, a solution to the game is defined based on distributing to each player (node and edge) present in each block a payment proportional to their contribution to the coalition.

关键词： Graph Theory Values for Graphs Cooperation Games Potential Function

Cosmological Model in Four Time and Four Space Dimensions

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Journal of Applied Mathematics and Physics 2024年第3期12卷 829-840页

作者： Juan Antonio Nieto Facultad de Ciencias Físico-matemáticas de la Universidad Autónoma de Sinaloa Culiacán Sinaloa México

We develop a cosmological model in a physical background scenario of four time and four space dimensions ((4+4)-dimensions or (4+4)-universe). We show that in this framework the (1+3)-universe is deeply connected with the (3+1)-universe. We argue that this means that in the (4+4)-universe there exists a duality relation between the (1+3)-universe and the (3+1)-universe.

关键词： Cosmological Model (4+4)-Dimensions Duality Symmetry

Verdier quotients of homotopy categories of rings and Gorenstein-projective precovers

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Science China Mathematics 2024年

作者： Manuel Cortés-Izurdiaga departamento de matemática Aplicada Universidad de Málaga

Let R be a ring, Proj be the class of all the projective right R-modules, K be the full subcategory of the homotopy category K(Proj) whose class of objects consists of all the totally acyclic complexes, and MorK be the class of all the morphisms in K(Proj) whose cones belong to K. We prove that if K(Proj) has enough MorK-injective objects, then the Verdier quotient K(Proj)/K has small Hom-sets, and this last condition implies the existence of Gorenstein-projective precovers in Mod-R and of totally acyclic precovers in C(Mod-R).

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Rheological properties and concentration evolution of thickened tailings under the coupling effect of compression and shear

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International Journal of Minerals,Metallurgy and Materials 2024年第5期31卷 862-876页

作者： Aixiang Wu Zhenqi Wang Zhuen Ruan Raimund Bürger Shaoyong Wang Yi Mo Key Laboratory of the Ministry of Education of China for High-efficient Mining and Safety of Metal Mines University of Science and Technology BeijingBeijing 100083China Shunde Innovation School University of Science and Technology BeijingFoshan 528399China CI2MA and departamento de Ingeniería matemática Facultad de Ciencias Físicas y MatemáticasUniversidad de ConcepciónCasilla 160-CConcepciónChile School of Civil and Resource Engineering University of Science and Technology BeijingBeijing 100083China China Railway Construction Tongguan Investment Co. Ltd.Tongling 244000China

Cemented paste backfill(CPB)is a key technology for green mining in metal mines,in which tailings thickening comprises the primary link of CPB technology.However,difficult flocculation and substandard concentrations of thickened tailings often occur.The rheological properties and concentration evolution in the thickened tailings remain unclear.Moreover,traditional indoor thickening experiments have yet to quantitatively characterize their rheological properties.An experiment of flocculation condition optimization based on the Box-Behnken design(BBD)was performed in the study,and the two response values were investigated:concentration and the mean weighted chord length(MWCL)of flocs.Thus,optimal flocculation conditions were obtained.In addition,the rheological properties and concentration evolution of different flocculant dosages and ultrafine tailing contents under shear,compression,and compression-shear coupling experimental conditions were tested and compared.The results show that the shear yield stress under compression and compression-shear coupling increases with the growth of compressive yield stress,while the shear yield stress increases slightly under shear.The order of shear yield stress from low to high under different thickening conditions is shear,compression,and compression-shear coupling.Under compression and compression-shear coupling,the concentration first rapidly increases with the growth of compressive yield stress and then slowly increases,while concentration increases slightly under shear.The order of concentration from low to high under different thickening conditions is shear,compression,and compression-shear coupling.Finally,the evolution mechanism of the flocs and drainage channels during the thickening of the thickened tailings under different experimental conditions was revealed.

关键词： thickened tailings compression-shear coupling compressive yield stress shear yield stress concentration

Positive solutions for some almost critical Brezis-Nirenberg type problems in bounded and exterior domains

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Acta Mathematica Sinica,English Series 2024年

作者： Salomón ALARCóN Pablo QUIJADA departamento de matemática Universidad Técnica Federico Santa María

We study the equation-Δu=|x|~αu(p_α~*+ε)+λ_ε|x|~βu in Ω,under the condition u=0 on ?Ω,where Ω is a smooth bounded domain in RN,N≥ 5,which is symmetric respect to x1,x2,…,xNand contains the origin,α>-2,-2 0 is a small parameter and λ_ε> 0 depends on ε,with λ_ε→ 0 as ε→ 0.Our main focus lies in finding positive solutions that take the form of a tower of bubbles of order α,exhibiting concentration at the origin as ε tends to zero.Furthermore,we extend our study to the equation-Δu=|x|~αup_α~*-ε+λ_ε|x|~βu in RN\ B1,where B1is the unit ball centered at the origin,under Dirichlet zero boundary condition and an additional vanishing condition at infinity.In this context,we discover positive solutions that take the form of a tower of bubbles of order α,progressively flattening as ε tends to zero.

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Solution of the Center Problem for a Class of Polynomial Differential Systems

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1685-1696页

作者： Chang Jian Liu Jaume Llibre Rafael Ramírez Valentín Ramírez School of Mathematics(Zhuhai) Sun Yat-sen UniversityZhuhai519086P.R.China departament de matemàtiques Universitat Autònoma de Barcelona08193BellaterraBarcelonaCataloniaSpain departament d’Enginyeria Informàtica i matemàtiques Universitat Rovira i VirgiliAvinguda dels Paiïsos Catalans 2643007TarragonaCataloniaSpain

Consider the polynomial differential system of degree m of the form x=-y(1+μ(a_(2)x-a_(1)y))+x(v(a_(1)x+a_(2)y)+Ω_(m-1)(x,y)),y=x(1+μ(a_(2)x-a_(1)y))+y(v(a_(1)x+a_(2)y)+Ω_(m-1)(x,y)),whereμandνare real numbers such that(μ^(2)+v^(2))(μ+v(m-2))(a_(1)^(2)+a_(2)^(2))≠m>2 andΩ_(m−1)(x,y)is a homogenous polynomial of degree m−1.A conjecture,stated in J.Differential Equations 2019,suggests that whenν=1,this differential system has a weak center at the origin if and only if after a convenient linear change of variable(x,y)→(X,Y)the system is invariant under the transformation(X,Y,t)→(−X,Y,−t).For every degree m we prove the extension of this conjecture to any value ofνexcept for a finite set of values ofμ.

关键词： Center problem polynomial differential system

Twisted and Absolute degrees of Maps into the Projective Plane

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Acta Mathematica Sinica,English Series 2024年

作者： Marcio Colombo FENILLE Daciberg Lima GON?ALVES Universidade Federal de Uberlandia – Instituto de matemática e Estatística.Av.Jo?o Naves deávila 2121 Santa M?nica Universidade de S?o Paulo – Instituto de matemática e Estatística.Rua do Mat?o 1010 Cidade Universitária

For each based map f : X → RP2from a closed surface into the real projective plane, we compute its absolute and twisted degrees and describe the action of the fundamental group of RP2over the based homotopy class of f. We emphasize the finding that for any nonorientable closed surface,there exists only one based homotopy class of maps from it into RP2whose maps have twisted degree zero and absolute degree nonzero – which shows that, unlike the absolute degree, the twisted degree is not able to detect the strong surjectivity in this setting. In all the other scenarios, the absolute degree of each map is either equal to the twisted degree or its absolute value – and so the twisted degree detects strong surjectivity.

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Area Operators on Bergman Spaces

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Acta Mathematica Sinica,English Series 2024年第5期40卷 1161-1176页

作者： Xiao Fen LV Jordi PAU Mao Fa WANG department of Mathematics Huzhou UniversityHuzhou 313000P.R.China departament de matemàtiques i Informàtica Universitat de Barcelona08007 BarcelonaCataloniaSpain School of Mathematics and Statistics Wuhan UniversityWuhan 430072P.R.China

We completely characterize the boundedness of area operators from the Bergman spaces A_(α)^(p)(Bn)to the Lebesgue spaces L^(q)(S_(n))for all 0 详细信息

We completely characterize the boundedness of area operators from the Bergman spaces A_(α)^(p)(Bn)to the Lebesgue spaces L^(q)(S_(n))for all 0ded.We solve the cases left open there and extend the results to n-complex dimension.

关键词： Area operator Bergman space tent space area formula