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Embedding Tensors on 3-Hom-Lie Algebras

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Journal of Mathematical Research with Applications 2024年第2期44卷 187-198页

作者： Wen TENG Jiulin JIN Yu ZHANG school of mathematics and Statistics Guizhou University of Finance and Economics school of Science Guiyang University

In this paper, we introduce the notion of embedding tensors on 3-Hom-Lie algebras and show that embedding tensors induce naturally 3-Hom-Leibniz algebras. Moreover, the cohomology theory of embedding tensors on 3-Hom-Lie algebras is defined. As an application,we show that if two linear deformations of an embedding tensor on a 3-Hom-Lie algebra are equivalent, then their infinitesimals belong to the same cohomology class in the first cohomology group.

关键词： 3-Hom-Lie algebra embedding tensor representation cohomology deformation

On the inviscid limit of the compressible Navier-Stokes equations near Onsager's regularity in bounded domains

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Science China mathematics 2024年第1期67卷 1-22页

作者： Robin Ming Chen Zhilei Liang Dehua Wang Runzhang Xu Department of mathematics University of PittsburghPittsburghPA 15260USA school of mathematics Southwestern University of Finance and EconomicsChengdu 611130China College of Mathematical Sciences Harbin Engineering UniversityHarbin 150001China

The viscous dissipation limit of weak solutions is considered for the Navier-Stokes equations of compressible isentropic flows confined in a bounded *** establish a Kato-type criterion for the validity of the inviscid limit for the weak solutions of the Navier-Stokes equations in a function space with the regularity index close to Onsager’s critical *** particular,we prove that under such a regularity assumption,if the viscous energy dissipation rate vanishes in a boundary layer of thickness in the order of the viscosity,then the weak solutions of the Navier-Stokes equations converge to a weak admissible solution of the Euler *** approach is based on the commutator estimates and a subtle foliation technique near the boundary of the domain.

关键词： inviscid limit Navier-Stokes equations Euler equations weak solutions bounded domain Katotype criterion Onsager’s regularity

AN EXPLANATION ON FOUR NEW DEFINITIONS OF FRACTIONAL OPERATORS

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Acta Mathematica Scientia 2024年第4期44卷 1271-1279页

作者： Jiangen LIU Fazhan GENG school of mathematics and Statistics Changshu Institute of TechnologyChangshu 215500China Qin institute of mathematics Shanghai Hanjing Centre for Science and TechnologyShanghai 201609China

Fractional calculus has drawn more attentions of mathematicians and engineers in recent years.A lot of new fractional operators were used to handle various practical *** this article,we mainly study four new fractional operators,namely the CaputoFabrizio operator,the Atangana-Baleanu operator,the Sun-Hao-Zhang-Baleanu operator and the generalized Caputo type operator under the frame of the k-Prabhakar fractional integral ***,the theory of the k-Prabhakar fractional integral is regarded as a much broader than classical fractional ***,we firstly give a series expansion of the k-Prabhakar fractional integral by means of the k-Riemann-Liouville ***,a connection between the k-Prabhakar fractional integral and the four new fractional operators of the above mentioned was shown,*** terms of the above analysis,we can obtain this a basic fact that it only needs to consider the k-Prabhakar fractional integral to cover these results from the four new fractional operators.

关键词： k-Prabhakar fractional operator Caputo-Fabrizio operator Atangana-Baleanu operator Sun-Hao-Zhang-Baleanu operator generalized Caputo type operator

Pseudoeffective thresholds and cohomology of twisted symmetric tensor fields on irreducible Hermitian symmetric spaces

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Science China mathematics 2024年第11期67卷 2433-2452页

作者： Feng Shao institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences school of Mathematical Sciences University of Chinese Academy of Sciences

Let X be an irreducible Hermitian symmetric space of compact type(IHSS for short).In this paper,we give the irreducible decomposition of *** a by-product,we give a cohomological characterization of the rank of ***,we introduce pseudoeffective thresholds to measure the bigness of tangent bundles of smooth complex projective varieties precisely and calculate them for irreducible Hermitian symmetric spaces of compact type.

关键词： tangent bundle pseudoeffective threshold irreducible Hermitian symmetric space of compact type (IHSS) multiplicity free action

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Which Factors Influence the Effect of Deep Synthesized Video Propagation

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Journal of Systems Science and Information 2024年第3期12卷 393-411页

作者： Lixia MA Jingjing WANG Yiwei RU Yunjie WEI school of Economics and Management University of Chinese Academy of Sciences school of Economics and finance Xi'an Jiaotong University institute of Automation Chinese Academy of Sciences Academy of mathematics and Systems Science Chinese Academy of Sciences

Deep synthesis technology is an emerging artificial intelligence technology. There have been a large number of audio and video contents based on deep synthesis technology spreading in the Internet. In this paper, we take the deep synthetic videos on YouTube platform as the research object,and investigate the factors influencing the propagation effect of deep synthetic videos by establishing an ordered probit model. It is found that the effect of deep synthesized video transmission of YouTube platform is mainly influenced by factors such as the video type, video duration, influence of publishers and forms of fraud. In addition, the comparative analysis of ordinary video and in-depth synthesized video reveals that both the video transmission effect are significantly affected by the video type, video duration and the influence of publishers.

关键词： deep synthesized video transmission effect ordered probit model

Can whole steps of grain production be outsourced? Empirical analysis based on the three provinces of Jiangsu,Jilin,and Sichuan in China

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Journal of Integrative Agriculture 2024年第1期23卷 336-347页

作者： Jiacheng Liu Shengzhi Mao Qiufen Zheng Zhigang Xu school of finance and Taxation Nanjing University of Finance and EconomicsJiangsu 210023China school of Economics Southwestern University of Finance and EconomicsSichuan 611130China school of Economics and Management Nanjing Agricultural UniversityJiangsu 210095China

Certain outsourcing services for agricultural management in China,such as pest control in grain production,have experienced prolonged sluggishness,contrasting with the relatively high level of outsourcing services observed in harvesting,land preparation,and *** study examines the feasibility of implementing whole-step outsourcing in grain production by conducting a case study of rice and maize production in Jiangsu,Jilin,and Sichuan provinces in *** provision of outsourcing services hinges on two essential conditions:technological advancements fostering specialized production and economies of scale,coupled with a market size sufficient to realize the aforementioned potential economies of *** results showed that outsourcing pest control or harvesting services had varying economies of *** outsourcing services in pest control were less common than in harvesting services,and their marginal growth space of the economies of scale with technological change was also *** by the operational characteristics of pest control itself,the market scale of its professional services is ***,achieving the whole-step outsourcing of grain production necessitates not only technological innovation but also effective policy interventions to overcome the constraints of market *** interventions include(1)optimizing crop layouts between planning regions and reducing land fragmentation and(2)supplying timely and effective inter-regional agricultural information for service providers aided by information technology.

关键词： outsourcing services economy of scale technical conditions market scale

MATHEMATICAL MODELING AND BIFURCATION ANALYSIS FOR A BIOLOGICAL MECHANISM OF CANCER DRUG RESISTANCE

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Acta Mathematica Scientia 2024年第3期44卷 1165-1188页

作者：包康博梁桂珍田天海张兴安 school of Information Engineering and Artificial Intelligence Lanzhou University of Finance and EconomicsLanzhou730020China school of mathematics and Statistics Central China Normal UniversityWuhan430079China school of mathematics and Information Science Xinxiang UniversityXinxiang453003China school of Mathematical Sciences Monash UniversityMelbourneVIC3800Australia

Drug resistance is one of the most intractable issues in targeted therapy for cancer *** has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory cancer cell *** on how cancer cells develop resistance during the encounter with targeted drugs and the immune system,we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune *** analyze the local geometric properties of the equilibria of the *** simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant ***,the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation *** analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.

关键词： mathematical model drug resistance cancer heterogeneity immune system targeted therapy

Spectral flow, Llarull's rigidity theorem in odd dimensions and its generalization

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Science China mathematics 2024年第5期67卷 1103-1114页

作者： Yihan Li Guangxiang Su Xiangsheng Wang Chern institute of mathematics&LPMC Nankai UniversityTianjin 300071China school of mathematics Shandong UniversityJinan 250100China

For a compact spin Riemannian manifold(M,g^(TM))of dimension n such that the associated scalar curvature kT M verifies that k^(TM)≥n(n-1),Llarull’s rigidity theorem says that any area-decreasing smooth map f from M to the unit sphere Sn of nonzero degree is an *** this paper,we present a new proof of Llarull’s rigidity theorem in odd dimensions via a spectral flow *** approach also works for a generalization of Llarull’s theorem when the sphere Sn is replaced by an arbitrary smooth strictly convex closed hypersurface in Rn+*** results answer two questions by Gromov(2023).

关键词： Dirac operator scalar curvature spectral flow

Global Zero-relaxation Limit Problem of the Electro-diffusion Model Arising in Electro-Hydrodynamics

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 241-268页

作者： Ming-hua Yang Si-ming Huang Jin-yi Sun Department of mathematics Jiangxi University of Finance and EconomicsNanchang330032China school of Public Administration Guangdong University of Foreign StudiesGuangzhou510006China College of mathematics and Statistics Northwest Normal UniversityLanzhou730070China

In this paper,we study a global zero-relaxation limit problem of the electro-diffusion model arising in electro-hydrodynamics which is the coupled Planck-Nernst-Poisson and Navier-Stokes *** is,the paper deals with a singular limit problem of{u^(∈)_(t)+u^(∈)·▽u^(∈)-Δu^(∈)+▽P^(∈)=Δφ^(∈)▽φ^(∈),in R^(3)×(0,∞),▽·u^(∈)=0,in R^(3)×(0,∞),n^(∈)_(t)+u^(∈)·▽n^(∈)-Δn^(∈)=-▽·(n^(∈)▽φ^(∈)),in R^(3)×(0,∞),ct+u^(∈)·▽c^(∈)-Δc^(∈)=▽·(c^(∈)▽φ^(∈)),in R^(3)×(0,∞),∈^(-1)φ^(∈)_(t)=Δφ^(∈)-n^(∈)+c^(∈),in R^(3)×(0,∞),(u^(∈),n^(∈),c^(∈),φ^(∈))|t=0=(u0,n0,c0,φ0),in R^(3) involving with a positive,large parameter^(∈).The present work show a case that(u^(∈),n^(∈),c^(∈))stabilizes to(u^(∞),n∞,c∞):=(u,n,c)uniformly with respect to the time variable as^(∈)→+∞with respect to the strong topology in a certain Fourier-Herz space.

关键词： fourier-Herz space littlewood-Paley decomposition stability limit dissipative system