Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the...Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the concept and representations of modified RotaBaxter Hom-Lie algebras. We develop a cohomology of modified Rota-Baxter Hom-Lie algebras with coefficients in a suitable representation. As applications, we study formal deformations and abelian extensions of modified Rota-Baxter Hom-Lie algebras in terms of second cohomology groups.展开更多
The finite-dimensional indecomposable solvable Lie algebras s with Q2n+1as their nilradical are studied and classified, it turns out that the dimension of s is dim Q2n+1+1.Then the Hom-Lie algebra structures on solvab...The finite-dimensional indecomposable solvable Lie algebras s with Q2n+1as their nilradical are studied and classified, it turns out that the dimension of s is dim Q2n+1+1.Then the Hom-Lie algebra structures on solvable Lie algebras s are calculated.展开更多
The aim of this article is to introduce the notion of Hom-Lie H-pseudo-superalgebras for any Hopf algebra H. This class of algebras is a natural generalization of the Hom-Lie pseudo-algebras as well as a special case ...The aim of this article is to introduce the notion of Hom-Lie H-pseudo-superalgebras for any Hopf algebra H. This class of algebras is a natural generalization of the Hom-Lie pseudo-algebras as well as a special case of the Hom-Lie superalgebras. We present some construction theorems of Hom-Lie H-pseudo-superalgebras, reformulate the equivalent definition of Hom-Lie H-pseudo-super-algebras, and consider the cohomology theory of Hom-Lie H-pseudo-superalgebras with coefficients in arbitrary Hom-modules as a generalization of Kac’s result.展开更多
In this paper,we consider compatible Hom-Lie triple systems.More precisely,compatible Hom-Lie triple systems are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra.We also define a...In this paper,we consider compatible Hom-Lie triple systems.More precisely,compatible Hom-Lie triple systems are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra.We also define a cohomology theory for compatible Hom-Lie triple systems.As applications of cohomology,we study linear deformations and abelian extensions of compatible Hom-Lie triple systems.展开更多
随着人工智能大模型训练与推理业务的快速发展,智算中心面临算网协同调度的新挑战。为优化分布式智算Ring Allreduce业务的部署问题,首先,通过扩展传统波平面,开发了算力波平面技术,实现了算力与网络资源的一体化虚拟管理。然后,基于算...随着人工智能大模型训练与推理业务的快速发展,智算中心面临算网协同调度的新挑战。为优化分布式智算Ring Allreduce业务的部署问题,首先,通过扩展传统波平面,开发了算力波平面技术,实现了算力与网络资源的一体化虚拟管理。然后,基于算力波平面,提出了一种高效路由、波长、算力和时隙分配(routing,wavelength,computing power and time slot assignment,RWCTA)算法用于环规约(Ring Allreduce)业务部署。仿真结果表明,与传统基于波平面的部署算法相比,基于算力波平面的RWCTA算法能有效降低62.4%的总业务完成时间和54.5%的平均业务计算时间。展开更多
Let A be a multiplicative Hom-associative algebra and L a multiplicative Hom-Lie algebra together with surjective twisting maps. We show that if A is a sum of two commutative Hom-associative subalgebras, then the comm...Let A be a multiplicative Hom-associative algebra and L a multiplicative Hom-Lie algebra together with surjective twisting maps. We show that if A is a sum of two commutative Hom-associative subalgebras, then the commutator Hom-ideal is nilpotent. Furthermore, we obtain an analogous result for Hom-Lie algebra L extending Kegel＇s Theorem. Finally, we discuss the Hom-Lie ideal structure of a simple Hom-associative algebra A by showing that any non-commutative Hom-Lie ideal of A must contain [A, A].展开更多
In this paper,potent index of an element and pseudo clean rings are considered.Some properties and examples of pseudo clean rings are given.We also show that Zm is pseudo clean for every 2≤m∈Z and pseudo clean rings...In this paper,potent index of an element and pseudo clean rings are considered.Some properties and examples of pseudo clean rings are given.We also show that Zm is pseudo clean for every 2≤m∈Z and pseudo clean rings are clean.Furthermore,we prove pseudo clean rings are directly finite and have stable range one.展开更多
Increasing temperatures and severe droughts threaten forest vitality globally.Prediction of forest response to climate change requires knowledge of the spatiotemporal patterns of monthly or seasonal climatic impacts o...Increasing temperatures and severe droughts threaten forest vitality globally.Prediction of forest response to climate change requires knowledge of the spatiotemporal patterns of monthly or seasonal climatic impacts on the growth of tree species,likely driven by local climatic aridity,climate trends,edaphic conditions,and the climatic adaption of tree species.The ability of tree species to cope with changing climate and the effects of environmental variables on growth trends and growth-climate relationships across diverse bioclimatic regions are still poorly understood for many species.This study investigated radial growth trends,interannual growth variability,and growth-climate sensitivity of two dominant tree species,Pinus tabulaeformis(PT)and Pinus sylvestris var.mongolica(PS),across a broad climatic gradient with a variety of soil properties in temperate Northern China.Using a network of 83 tree ring chronologies(54 for PT and 29 for PS)from 1971 to 2010,we documented that both species maintained constant growth trends at wet sites,while both displayed rapid declines at dry sites.We reported the species-specific drivers of spatial heterogeneity in growth trends,interannual growth variability,and growth-climate relationships.Calculated climatic variables and soil properties were identified as the most critical factors affecting the growth trends and growth-climate relationships.However,climatic variables play more essential roles than soil properties in determining the spatial heterogeneity of the growth-climate relationship.Lower clay content and higher soil nutrient regimes can exacerbate the moisture-related susceptibility of tree growth.Our findings highlight that soil properties emerged as important modulating factors to predict the drought vulnerability of forests in addition to climatic variables.Considering the continued climate warmingdrying trend in the future,both pines will face a more severe growth decline and increase in drought vulnerability at drier sites with lower clayed soil or higher nutrient regimes.展开更多
Purpose–The brake pipe system was an essential braking component of the railway freight trains,but the existing E-type sealing rings had problems such as insufficient low-temperature resistance,poor heat stability an...Purpose–The brake pipe system was an essential braking component of the railway freight trains,but the existing E-type sealing rings had problems such as insufficient low-temperature resistance,poor heat stability and short service life.To address these issues,low-phenyl silicone rubber was prepared and tested,and the finite element analysis and experimental studies on the sealing performance of its sealing rings were carried out.Design/methodology/approach–The low-temperature resistance and thermal stability of the prepared lowphenyl silicone rubber were studied using low-temperature tensile testing,differential scanning calorimetry,dynamic thermomechanical analysis and thermogravimetric analysis.The sealing performance of the lowphenyl silicone rubber sealing ring was studied by using finite element analysis software abaqus and experiments.Findings–The prepared low-phenyl silicone rubber sealing ring possessed excellent low-temperature resistance and thermal stability.According to the finite element analysis results,the finish of the flange sealing surface and groove outer edge should be ensured,and extrusion damage should be avoided.The sealing rings were more susceptible to damage in high compression ratio and/or low-temperature environments.When the sealing effect was ensured,a small compression ratio should be selected,and rubbers with hardness and elasticity less affected by temperature should be selected.The prepared low-phenyl silicone rubber sealing ring had zero leakage at both room temperature(RT)and�508C.Originality/value–The innovation of this study is that it provides valuable data and experience for the future development of the sealing rings used in the brake pipe flange joints of the railway freight cars in China.展开更多
The big-tapered profiled ring disk is a key component of engines for rockets and missiles.A new forming technology,as called spinning-rolling process,has been proposed previously for the high performance,high efficien...The big-tapered profiled ring disk is a key component of engines for rockets and missiles.A new forming technology,as called spinning-rolling process,has been proposed previously for the high performance,high efficiency and low-cost manufacturing of the component.Blank design is the key part of plastic forming process design.For spinning-rolling process,the shape and size of the blank play a crucial role in process stability,deformation behavior and dimensional accuracy.So this work proposes a blank design method to determine the geometry structure and sizes of the blank.The mathematical model for calculating the blank size has been deduced based on volume conservation and neutral layer length invariance principle.The FE simulation and corresponding trial production of an actual big-tapered profiled ring disk show that the proposed blank design method is applicative.In order to obtain a preferred blank,the influence rules of blank size determined by different deformation degrees(rolling ratio k)on the spinning-rolling process are revealed by comprehensive FE simulations.Overall considering the process stability,circularity of the deformed ring disk and forming forces,a reasonable range of deformation degree(rolling ratio k)is recommended for the blank design of the new spinning-rolling process.展开更多
基金Supported by the Universities Key Laboratory of System Modeling and Data Mining in Guizhou Province(Grant No.2023013)the National Natural Science Foundation of China(Grant No.12161013)the Science and Technology Program of Guizhou Province(Grant No.ZK[2023]025)。
文摘Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the concept and representations of modified RotaBaxter Hom-Lie algebras. We develop a cohomology of modified Rota-Baxter Hom-Lie algebras with coefficients in a suitable representation. As applications, we study formal deformations and abelian extensions of modified Rota-Baxter Hom-Lie algebras in terms of second cohomology groups.
基金Foundation item： Supported by the National Natural Science Foundation of China（11071187） Supported by the Natural Science Foundation of Henan Province（13A110785）
文摘The finite-dimensional indecomposable solvable Lie algebras s with Q2n+1as their nilradical are studied and classified, it turns out that the dimension of s is dim Q2n+1+1.Then the Hom-Lie algebra structures on solvable Lie algebras s are calculated.
文摘The aim of this article is to introduce the notion of Hom-Lie H-pseudo-superalgebras for any Hopf algebra H. This class of algebras is a natural generalization of the Hom-Lie pseudo-algebras as well as a special case of the Hom-Lie superalgebras. We present some construction theorems of Hom-Lie H-pseudo-superalgebras, reformulate the equivalent definition of Hom-Lie H-pseudo-super-algebras, and consider the cohomology theory of Hom-Lie H-pseudo-superalgebras with coefficients in arbitrary Hom-modules as a generalization of Kac’s result.
基金Supported by the Scientifc Research Foundation for Advanced Talents of GUFE(Grant No.2022YJ007)the Innovation Exploration and Academic Talent Project of GUFE(Grant No.2022XSXMB11)+4 种基金the Science and Technology Program of Guizhou Province(Grant Nos.QKHZC[2023]372QKHJC-[2024]QN081)the Research Foundation for Science&Technology Innovation Team of Guizhou Province(Grant Nos.QJJ[2023]063QJJ[2024]190)the Doctoral Research Start-Up Fundation of Guiyang University(Grant No.GYU-KY-2024)。
文摘In this paper,we consider compatible Hom-Lie triple systems.More precisely,compatible Hom-Lie triple systems are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra.We also define a cohomology theory for compatible Hom-Lie triple systems.As applications of cohomology,we study linear deformations and abelian extensions of compatible Hom-Lie triple systems.
文摘随着人工智能大模型训练与推理业务的快速发展,智算中心面临算网协同调度的新挑战。为优化分布式智算Ring Allreduce业务的部署问题,首先,通过扩展传统波平面,开发了算力波平面技术,实现了算力与网络资源的一体化虚拟管理。然后,基于算力波平面,提出了一种高效路由、波长、算力和时隙分配(routing,wavelength,computing power and time slot assignment,RWCTA)算法用于环规约(Ring Allreduce)业务部署。仿真结果表明,与传统基于波平面的部署算法相比,基于算力波平面的RWCTA算法能有效降低62.4%的总业务完成时间和54.5%的平均业务计算时间。
基金Supported by the Excellent Young Talents Fund Project of Anhui Province(Grant No.2013SQRL092ZD)the Natural Science Foundation of Anhui Province(Grant Nos.1408085QA06+2 种基金1408085QA08)the Excellent Young Talents Fund Project of Chuzhou University(Grant No.2013RC001)the Research and Innovation Projectfor College Graduates of Jiangsu Province(Grant No.CXLX12-0071)
文摘Let A be a multiplicative Hom-associative algebra and L a multiplicative Hom-Lie algebra together with surjective twisting maps. We show that if A is a sum of two commutative Hom-associative subalgebras, then the commutator Hom-ideal is nilpotent. Furthermore, we obtain an analogous result for Hom-Lie algebra L extending Kegel＇s Theorem. Finally, we discuss the Hom-Lie ideal structure of a simple Hom-associative algebra A by showing that any non-commutative Hom-Lie ideal of A must contain [A, A].
基金Supported by National Natural Science Foundation of China(12301041)。
文摘In this paper,potent index of an element and pseudo clean rings are considered.Some properties and examples of pseudo clean rings are given.We also show that Zm is pseudo clean for every 2≤m∈Z and pseudo clean rings are clean.Furthermore,we prove pseudo clean rings are directly finite and have stable range one.
基金funded by the National Key Research and Development Plan of China(No.2022YFE0127900)the National Natural Science Foundation of China(Nos.32071558,32171559)+2 种基金the Natural Science Foundation Key Project of Inner Mongolia Autonomous Region,China(No.2023ZD23)the Hulunbuir Science and Technology Plan Project(No.SF2022001)the Fundamental Research Funds of CAF(CAFYBB2023ZA002).
文摘Increasing temperatures and severe droughts threaten forest vitality globally.Prediction of forest response to climate change requires knowledge of the spatiotemporal patterns of monthly or seasonal climatic impacts on the growth of tree species,likely driven by local climatic aridity,climate trends,edaphic conditions,and the climatic adaption of tree species.The ability of tree species to cope with changing climate and the effects of environmental variables on growth trends and growth-climate relationships across diverse bioclimatic regions are still poorly understood for many species.This study investigated radial growth trends,interannual growth variability,and growth-climate sensitivity of two dominant tree species,Pinus tabulaeformis(PT)and Pinus sylvestris var.mongolica(PS),across a broad climatic gradient with a variety of soil properties in temperate Northern China.Using a network of 83 tree ring chronologies(54 for PT and 29 for PS)from 1971 to 2010,we documented that both species maintained constant growth trends at wet sites,while both displayed rapid declines at dry sites.We reported the species-specific drivers of spatial heterogeneity in growth trends,interannual growth variability,and growth-climate relationships.Calculated climatic variables and soil properties were identified as the most critical factors affecting the growth trends and growth-climate relationships.However,climatic variables play more essential roles than soil properties in determining the spatial heterogeneity of the growth-climate relationship.Lower clay content and higher soil nutrient regimes can exacerbate the moisture-related susceptibility of tree growth.Our findings highlight that soil properties emerged as important modulating factors to predict the drought vulnerability of forests in addition to climatic variables.Considering the continued climate warmingdrying trend in the future,both pines will face a more severe growth decline and increase in drought vulnerability at drier sites with lower clayed soil or higher nutrient regimes.
基金supported by the Science and Technology Research and Development Plan of the China State Railway Group Company Limited(No.Q2023J012).
文摘Purpose–The brake pipe system was an essential braking component of the railway freight trains,but the existing E-type sealing rings had problems such as insufficient low-temperature resistance,poor heat stability and short service life.To address these issues,low-phenyl silicone rubber was prepared and tested,and the finite element analysis and experimental studies on the sealing performance of its sealing rings were carried out.Design/methodology/approach–The low-temperature resistance and thermal stability of the prepared lowphenyl silicone rubber were studied using low-temperature tensile testing,differential scanning calorimetry,dynamic thermomechanical analysis and thermogravimetric analysis.The sealing performance of the lowphenyl silicone rubber sealing ring was studied by using finite element analysis software abaqus and experiments.Findings–The prepared low-phenyl silicone rubber sealing ring possessed excellent low-temperature resistance and thermal stability.According to the finite element analysis results,the finish of the flange sealing surface and groove outer edge should be ensured,and extrusion damage should be avoided.The sealing rings were more susceptible to damage in high compression ratio and/or low-temperature environments.When the sealing effect was ensured,a small compression ratio should be selected,and rubbers with hardness and elasticity less affected by temperature should be selected.The prepared low-phenyl silicone rubber sealing ring had zero leakage at both room temperature(RT)and�508C.Originality/value–The innovation of this study is that it provides valuable data and experience for the future development of the sealing rings used in the brake pipe flange joints of the railway freight cars in China.
基金the National Natural Science Foundation of China(No.52275378)the National Key Laboratory for Precision Hot Processing of Metals(6142909200208)。
文摘The big-tapered profiled ring disk is a key component of engines for rockets and missiles.A new forming technology,as called spinning-rolling process,has been proposed previously for the high performance,high efficiency and low-cost manufacturing of the component.Blank design is the key part of plastic forming process design.For spinning-rolling process,the shape and size of the blank play a crucial role in process stability,deformation behavior and dimensional accuracy.So this work proposes a blank design method to determine the geometry structure and sizes of the blank.The mathematical model for calculating the blank size has been deduced based on volume conservation and neutral layer length invariance principle.The FE simulation and corresponding trial production of an actual big-tapered profiled ring disk show that the proposed blank design method is applicative.In order to obtain a preferred blank,the influence rules of blank size determined by different deformation degrees(rolling ratio k)on the spinning-rolling process are revealed by comprehensive FE simulations.Overall considering the process stability,circularity of the deformed ring disk and forming forces,a reasonable range of deformation degree(rolling ratio k)is recommended for the blank design of the new spinning-rolling process.
