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Hochschild(Co)homology of Galois Coverings of Grassmann Algebras

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Acta Mathematica Sinica,English Series 2009年第10期25卷 1693-1702页

作者： yun ge xu Xin TANG School of Mathematics and Computer Science Hubei University Wuhan 430062 P.R. China Department of Mathematics and Computer Science Fayetteville State University Fayetteville NC 28301 USA

Let ∧ be the Z2-Galois covering of the Grassmann algebra A over a field k of characteristic not equal to 2. In this paper, the dimensional formulae of Hochschild homology and cohomology groups of ∧ are calculated explicitly. And the cyclic homology of∧ can also be calculated when the underlying field is of characteristic zero. As a result, we prove that there is an isomorphism from i≥1 HH^i（∧） to i≥1 HH^i（∧）.

关键词： Galois covering Grassmann algebra Hochschild (co)homology minimal projective resolution

Characteristic Modules of Dual Extensions and Grobner Bases

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Acta Mathematica Sinica,English Series 2004年第6期20卷 1119-1130页

作者： yun ge xu Long Cai LI Faculty of Mathematics and Computer Science Hubei University Academy of Mathematics and Systems Science Chinese Academy of Sciences

Let C be a finite dimensional directed algebra over an algebraically closed field k and A=A(C) the dual extension of *** characteristic modules of A are constructed explicitly for a class of directed algebras,which generalizes the results of ***,it is shown that the characteristic modules of dual extensions of a certain class of directed algebras admit the left Gr(?)bner basis theory in the sense of ***.

关键词： Quasi-hereditary algebra Dual extension Characteristic module (Left)Gr(?)bner basis

Hochschild cohomology of truncated quiver algebras

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Science China Mathematics 2007年第5期50卷 727-736页

作者： yun-ge xu Yang HAN Wen-feng JIANG Faculty of Mathematics&Computer Science Hubei UniversityWuhan 430062China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100080China

For a truncated quiver algebra over a field of an arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finitedimensional if and only if its... 详细信息

关键词： truncated quiver algebra Hochschild cohomology global dimension oriented cycle 16E40 16E10 16G10

Hochschild cohomology of special biserial algebras

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Science China Mathematics 2007年第8期50卷 1117-1128页

作者： yun-ge xu Faculty of Mathematics & Computer Science,Hubei University,Wuhan 430062,China Faculty of Mathematics & Computer Science Hubei University Wuhan 430062 China

Based on a four-term exact sequence,the formulae on the dimensions of the first and the second Hochschild cohomology groups of special biserial algebras with normed bases are obtained in terms of combinatorics.

关键词： special biserial algebra Hochschild cohomology medal 16E40 16G10

Soft coarse-grained particle model for particle-fluid systems

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Particuology 2024年第1期84卷 178-193页

作者： Yanhao Ye Ji xu Wei ge State Key Laboratory of Multiphase Complex Systems Institute of Process EngineeringChinese Academy of SciencesBeijing100190China School of Chemical Engineering University of Chinese Academy of SciencesBeijing100049China Innovation Academy for Green Manufacture Chinese Academy of SciencesBeijing100190China

By modeling a group of neighboring real particles as a single coarse-grained particle(CGP),discrete particle method(DPM)is now capable of simulating industrial-scale particle-fluid ***,a systematic approach to determine the CGP properties and develop their interaction models is still lacking,which casts uncertainty on the predictivity of the *** this study,collisions between predefined particle groups are analyzed to construct kernel functions for modeling the CGPs and then the model parameters are determined by equating the statistical properties of the CGPs and the real particles in the physical process *** approach is implemented for homogeneous cooling of granular gas,then demonstrated effective in simulating experimental fluidized beds.

关键词： Coarse-grain(CG) Discrete particle method(DPM) Fluidized bed Multi-scale simulation

△-tame quasi-hereditary algebras

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Science China Mathematics 2007年第2期50卷 240-252页

作者： yun-ge xu & Ying-bo ZHANG Faculty of Mathematics and Computer Science, Hubei University, Wuhan 430062, China School of Mathematics Sciences, Beijing Normal University, Beijing 100875, China Faculty of Mathematics and Computer Science Hubei University Wuhan China School of Mathematics Sciences Beijing Normal University Beijing China

Let (K, M,H) be an upper triangular bimodule problem. Briistle and Hille showed that the opposite algebra A of the endomorphism algebra of a projective generator P of the matrices category of (K., M, H) is quasi-hereditary, and there is an equivalence between the category of△-good modules of A and Mat(K, M). In this note, based on the tame theorem for bimodule problems, we show that if the algebra A associated with an upper triangular bimodule problem is of△-tame representation type, then the category F(△) has the homogeneous property, i.e. almost all modules in F(△) are isomorphic to their Auslander-Reiten translations. Moreover, if (K, M,H)is an upper triangular bipartite bimodule problem, then A is of△-tame representation type if and only if F(△) is homogeneous.

关键词： bimodule problem quasi-hereditary algebra △-tameness homogeneity.

Millimeter-wave PA design techniques in ISSCC 2024

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Journal of Semiconductors 2024年第4期45卷 16-18页

作者： yun Wang Hongtao xu State Key Laboratory of Integrated Chips and Systems School of MicroelectronicsFudan UniversityShanghai 201203China

Millimeter-wave systems with high integration level have been rapidly developed to enable modern wireless communication,sensing,and *** millimeter-wave power amplifier(PA)is one of the most challenging and critical components in a millimeter-wave transceiver,it is the last active stage in a transmitter amplifying spectrally efficient complex modulation signal for radiation with high output power.

关键词： millimeter Millimeter ISSCC

3D coarse-grained DPM simulation of the MIP reaction-regeneration loop

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Particuology 2024年第6期89卷 57-66页

作者： Yanhao Ye Shuai Zhang Ji xu Wei ge State Key Laboratory of Mesoscience and Engineering(formerly State Key Laboratory of Multiphase Complex Systems) Institute of Process EngineeringChinese Academy of SciencesBeijing100190China School of Chemical Engineering University of Chinese Academy of SciencesBeijing100049China

The reactor-regenerator loop is the core facility of the maximizing iso-paraffin(MIP)*** the discrete particle method(DPM)simulation can provide detailed information at the particle scale,it has been unable to simulate such a complex loop system due to limitations of coarse-grained(CG)models,computing software,and *** this study,a newly proposed soft-shell CG-DPM model with a CG ratio of up to 800 is used to simulate a 3.5 Mt/a industrial-scale MIP reactor-regenerator *** solid fraction distribution obtained is found to agree well with in-situ *** properties including the distribution of solid fraction,gas and solid velocity,standard derivation of solid fraction with time,temporal distribution of the flow field,and particle residence time distribution are measured in the simulation,which are meaningful to better design and operate such systems in the future.

关键词： Discrete particle method Coarse-grain Maximizing iso-paraffins Full-loop Reaction-regeneration system

Gas–solid reactor optimization based on EMMS-DPM simulation and machine learning

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Particuology 2024年第6期89卷 131-143页

作者： Haolei Zhang Aiqi Zhu Ji xu Wei ge State Key Laboratory of Mesoscience and Engineering Institute of Process EngineeringChinese Academy of SciencesBeijing 100190China State Key Laboratory of Multiphase Complex Systems Institute of Process EngineeringChinese Academy of SciencesBeijing 100190China School of Chemical Engineering University of Chinese Academy of SciencesBeijing 100049China Innovation Academy for Green Manufacture Chinese Academy of SciencesBeijing 100190China

Design,scaling-up,and optimization of industrial reactors mainly depend on step-by-step experiments and engineering experience,which is usually time-consuming,high cost,and high *** numerical simulation can reproduce high resolution details of hydrodynamics,thermal transfer,and reaction process in reactors,it is still challenging for industrial reactors due to huge computational *** this study,by combining the numerical simulation and artificial intelligence(AI)technology of machine learning(ML),a method is proposed to efficiently predict and optimize the performance of industrial reactors.A gas–solid fluidization reactor for the methanol to olefins process is taken as an example.1500 cases under different conditions are simulated by the coarse-grain discrete particle method based on the Energy-Minimization Multi-Scale model,and thus,the reactor performance data set is *** develop an efficient reactor performance prediction model influenced by multiple factors,the ML method is established including the ensemble learning strategy and automatic hyperparameter optimization technique,which has better performance than the methods based on the artificial neural ***,the operating conditions for highest yield of ethylene and propylene or lowest pressure drop are searched with the particle swarm optimization algorithm due to its strength to solve non-linear optimization *** show that decreasing the methanol inflow rate and increasing the catalyst inventory can maximize the yield,while decreasing methanol the inflow rate and reducing the catalyst inventory can minimize the pressure *** two objectives are thus conflicting,and the practical operations need to be compromised under different circumstance.

关键词： Discrete particle method Artificial intelligence Machine learning Particle swarm optimization Industrial reactor optimization