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Non-commutative Arithmetics on Thompson's Monoid

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Acta Mathematica Sinica,English Series 2021年第10期37卷 1586-1626页

作者： bo Qing XuE Institute of Mathematical Sciences ShanghaiTech UniversityShanghai 201210P.R.China

The main purpose of this paper is to define prime and introduce non-commutative arithmetics based on Thompson's group *** primes in a non-abelian monoid is highly non-trivial,which relies on a concept called"castling".Three types of castlings are essential to grasp the *** divisor functionτon Thompson's monoid S satisfiesτ(uv)≤τ(u)τ(v)for any u,v∈*** the limitτ_(0)(u)=lim_(n→∞)(τ(u~n))^(1/n)*** quantityC(S)=sup_(1≠u∈S)τ_(0)(u)/τ(u)describes the complexity for castlings in *** show thatC(S)=***,the MCbius function on S is *** the liouville functionCon S is studied.

关键词： Thompson's group non-commutative arithmetics castling complexity divisor function M?bius function

ERROR ESTIMATES FOR SPARSE OPTIMAl CONTROl PROBlEMS BY PIECEWISE lINEAR FINITE ElEMENT APPROXIMATION

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Journal of Computational Mathematics 2021年第3期39卷 471-492页

作者： Xiaoliang Song bo Chen bo Yu Dalian university of Technology Dalian 116024China Department of Mathematics National University of Singapore10 Lower Kent Ridge RoadSingapore School of Mathematical Sciences Dalian University of TechnologyDalian 116024China

Optimization problems with l^(1)-control cost functional subject to an elliptic partial differential equation(PDE)are ***,different from the finite dimensiona l^(1)-regularization optimization,the resulting discretized l^(1)norm does not have a decoupled form when the standard piecewise linear finite element is employed to discretize the continuous problem.A common approach to overcome this difficulty is employing a nodal quadrature formula to approximately discretize the l^(1)-*** this paper,a new discretized scheme for the l^(1)-norm is *** to the new discretized scheme for l^(1)-norm with the nodal quadrature formula,the advantages of our new discretized scheme can be demonstrated in terms of the order of ***,finite element error estimates results for the primal problem with the new discretized scheme for the l^(1)-norm are provided,which confirms that this approximation scheme will not change the order of error *** solve the new discretized problem,a symmetric Gauss-Seidel based majorized accelerated block coordinate descent(sGS-mABCD)method is introduced to solve it via its *** proposed sGS-mABCD algorithm is il.ustrated at two numerical *** results not only confirm the finite element error estimates,but also show that our proposed algorithm is efficient.

关键词： Finite element method ABCD method.Approximate discretization Error estimates

Comparative Studies of 1,4-Bis[2-(4-Pyridyl)ethenyl]-benzene using Density Functional Theory

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Chemical Research in Chinese universities 2007年第4期23卷 469-473页

作者： CHENG Jian-bo lǚ Jia-ping GONG Bao-an lI Wen-zuo Science and Engineering College of Chemistry and Biology Yantai University Yantai 264005 P. R. China

The optimized molecular structure and harmonic vibrational frequencies of a 1,4-bis [ 2-（4-pyridyl）ethenyl]- benzene（BPENB） molecule were cal.ulated via five popular density functional theory（DFI＇） methods. On the basis of the comparison between cal.ulated and experimental results, it is concluded that the B3PW91 and B3lYP methods are superior to the others in optimizing structures, and the BPW91 method reproduces the observed fundamental fre-quencies most satisfactorily.

关键词： 1,4-Bis[2-(4-pyridyl)ethenyl]-benzene Density functional theory Vibrational frequencies BPW91

部分柱顶滑移钢筋混凝土结构的滑移柱P-δ效应

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华南理工大学学报（自然科学版） 2016年第2期44卷 1-7页

作者：吴波吕文龙华南理工大学亚热带建筑科学国家重点实验室广东广州510640 广东省建筑科学研究院集团股份有限公司广东广州510500

为揭示部分柱顶滑移钢筋混凝土结构中滑移柱的P-δ效应,首先对该类柱的上端铰接简化模型的有效性进行了验证,在此基础上考察了不同情况下无侧移滑移柱因P-δ效应引发的二阶弯矩的特点,指出了需考虑二阶弯矩的界限条件,并就此提出了无侧... 详细信息

为揭示部分柱顶滑移钢筋混凝土结构中滑移柱的P-δ效应,首先对该类柱的上端铰接简化模型的有效性进行了验证,在此基础上考察了不同情况下无侧移滑移柱因P-δ效应引发的二阶弯矩的特点,指出了需考虑二阶弯矩的界限条件,并就此提出了无侧移滑移柱弯矩增大系数的确定方法,然后通过参数修正初步考虑了混凝土非线性对前述结果的影响,最后给出了算例分析.研究表明:小震阶段采用普通铰对滑移柱顶部的摩擦支座进行近似处理是可行的;在某些情况下,无侧移滑移柱因P-δ效应引发的二阶弯矩对柱身最大弯矩有增大效应,此时只需利用无侧移滑移柱的一阶弯矩和弯矩增大系数,即可方便地确定其考虑P-δ效应后的柱身最大弯矩.

关键词：钢筋混凝土结构柱顶滑移 P-δ效应弯矩增大系数

New algorithm for hub-and-spoke topological virtual networks embedding problem

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The Journal of China universities of Posts and Telecommunications 2012年第1期19卷 55-61页

作者： l.u Jiang HuANG Tao CHEN Jian-ya l.u Yun-jie lÜ bo Key laboratory of universal Wireless Communications Ministry of EducationBeijing University of Posts and TelecommunicationsBeijing 100876China

The virtual network embedding/mapping problem is a core issue of the network virtualization. It＇s mainly concerned with how to map virtual network requests to the substrate network efficiently. Previous researches mainly focus on developing heuristic algorithms for general topology virtual network request. In this paper, we propose a new algorithm for the hub-and-spoke （HAS） topology virtual request. The characters of the HAS topology are exploited to develop the new algorithm. The simulation results show that the new algorithm greatly enhances the performance of revenue/cost （R/C） ratio while the HAS topology request arrives.

关键词： virtual network embedding general topology HAS topology

New Heat Treatment Technology for Grain Refining of Structural Steel

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Journal of Iron and Steel Research International 2005年第6期12卷 49-53页

作者： lü bo ZHANG Fu-cheng CAO Guo-hua ZHANG Ji-ming Yanshan university Qinhuangdao 066004 China Key laboratory of Metastable MaterialsScience and Technology Qinhuangdao 066004 China）

The application of electrical contact heating （ECH） in austenitic grain refining of ultra-pure 42CrMoVNb steel was introduced. The ECH equipment was designed to reach uniform heating of uniform heat transfer in the sample. The 42CrMoVNb steel treated possesses uniform microstructure with an average austenite grain size of 1.4 μm, higher strength （1 538 MPa） and impact toughness （81J/cm^2）.

关键词： electrical contact heating medium carbon alloy steel ultrafine grain 42CrMoVNb

Static and Dynamic Mechanics Analysis on Artificial Hip Joints with Different Interface Designs by the Finite Element Method

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Journal of Bionic Engineering 2007年第2期4卷 123-131页

作者： Hai-bo Jiang College of Mechanic and Electrical Engineering China University of Mining and Technology Xuzhou 221008 P. R. China

Four different structural models of artificial joints were developed and the finite element method （FEM） was employed to investigate their mechanical characteristics under static and dynamic conditions. The materials used in the FEM cal.ulation were ultra-high molecular weight polyethylene （uHMWPE）, 316l stainless steel, CoCrMo alloy and Ti6A14V alloy. The stress distribution, strain, and elastic deformation under static and dynamic conditions were obtained. Analysis and comparison of the ~al.ulation results of different models were conducted. It is shown that with the same parameters the model of a metallic femur head covered with an artificial cartilage layer is more similar to the structure of the natural human joint and its mechanical characteristics are the best of the four models.

关键词： finite element analysis stress articular joint

Plastic deformation of a Zr-based bulk metallic glass fabricated by selective laser melting

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Journal of Materials Science & Technology 2021年第1期60卷 139-146页

作者： l.Deng K.Kosiba R.limbach l.Wondraczek u.Kühn S.Pauly IFW Dresden Institute for Complex MaterialsHelmholtzstraße 20D-01069DresdenGermany Otto Schott Institute of Materials Research University of JenaFraunhoferstraße 6D-07743JenaGermany university of Applied Sciences Aschaffenburg Würzburger Straße 45D-63743AschaffenburgGermany

Fully amorphous Zr_(52.5)Cu_(17.9)Ni_(14.6)Al_(10)Ti_(5) bulk metallic glass(BMG) samples with a relative density exceeding 98% were fabricated via selective laser melting(SlM).High fracture stresses of around1700 MPa and a reproducible plastic strain of about 0.5% were obtained for cylindrical SlM *** analysis of the observed serrations during compressive loading implies that the shear-band dynamics in the additively manufactured samples distinctly differ from those of the as-cast *** phenomenon appears to originate from the presence of uniformly dispersed spherical pores as well as from the more pronounced heterogeneity of the glass itself as revealed by instrumented *** these heterogeneities,the shear bands are straight and form in the plane of maximum shear *** manufacturing,hence,might not only allow for producing large BMG samples with complex geometries but also for manipulating their deformation behaviour through tailoring porosity and structural heterogeneity.

关键词： Powder bed fusion Selective laser melting Bulk metallic glass Serrated flow Heterogeneity

Teaching and learning Chinese through Immersion:A Case Study from the North American Context

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Frontiers of Education in China 2020年第1期15卷 99-141页

作者： Chan lÜ Department of Asian languages&literature University of WashingtonSeattleWA 98195-3521USA

With the promise of achieving bilingualism,biliteracy,and cul.ural pluralism,Chinese immersion programs for students from kindergarten to 12th grade(K-12)in North America,especially the uS,have been proliferating in the past two *** on this rapidly growing population of non-native Chinese learners is also *** research synthesis focuses on 35 selected studies published in recent years on Chinese immersion in both Chinese and English language journals and *** review found that researchers are exploring a wide range of issues with respect to language and literacy development in Chinese immersion programs,including academic achievement in English,language and literacy acquisition in Chinese,instructional strategies and classroom interaction,as well as learners’language use and its sociolinguistic *** studies reflect a growing interest in and demand for learning more about the lesser-researched Chinese foreign language(CFl)learner population,and this review concludes with suggestions for future research on Chinese immersion based on its curricular features as well as specific considerations for conducting research with young,emergent bilingual and biliterate learners.

关键词： K-12 education Chinese immersion programs Chinese as a foreign language(CFl) academic achievement bilingual and biliteracy acquisition instructional strategies classroom interaction learner language