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Visible-light-promoted multi-component carbene transfer reactions of diazo compounds via ring-opening of cyclic ethers
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作者 Feng Zhao Hongyu Ding +4 位作者 Ting Sun Chao Shen Zu-Li Wang Wei Wei Dong Yi 《Chinese Chemical Letters》 2026年第2期206-217,共12页
Carbenes as one of the most important class of intermediates have been widely utilized in various organic synthetic transformations.Carbene insertion-initiated ring-opening reactions of cyclic ethers offer a valuable ... Carbenes as one of the most important class of intermediates have been widely utilized in various organic synthetic transformations.Carbene insertion-initiated ring-opening reactions of cyclic ethers offer a valuable strategy for constructing new carbon-oxygen bonds.In comparison with traditional thermal or metal-mediated carbene transfer reactions,visible-light-promoted multi-component reaction strategy provides a mild and eco-friendly approach to access densely functionalized molecules.Recently,visible-light-induced multi-component carbene transfer reactions of diazo compounds have been rapidly developed and attracted a great deal of research interest of chemists owing to their advantages of simple operation,mild condition,high atom economy and rich structural diversity.This paper summarizes the recent research progress on the visible-light-promoted multi-component carbene transfer reactions of diazo compounds via ring-opening of cyclic ethers with various nucleophiles.The reaction patterns of different nucleophiles and their corresponding mechanism are described in this review.The future research direction and challenges in this area are also discussed. 展开更多
关键词 VISIBLE-LIGHT multi-component reaction Carbene insertion Diazo compounds Ring-opening reaction
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Multi-component decompositions,linear superpositions,and new nonlinear integrable coupled KdV-type systems
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作者 Xiazhi Hao S Y Lou 《Communications in Theoretical Physics》 2025年第2期1-12,共12页
In the realm of nonlinear integrable systems,the presence of decompositions facilitates the establishment of linear superposition solutions and the derivation of novel coupled systems exhibiting nonlinear integrabilit... In the realm of nonlinear integrable systems,the presence of decompositions facilitates the establishment of linear superposition solutions and the derivation of novel coupled systems exhibiting nonlinear integrability.By focusing on single-component decompositions within the potential BKP hierarchy,it has been observed that specific linear superpositions of decomposition solutions remain consistent with the underlying equations.Moreover,through the implementation of multi-component decompositions within the potential BKP hierarchy,successful endeavors have been undertaken to formulate linear superposition solutions and novel coupled Kd V-type systems that resist decoupling via alterations in dependent variables. 展开更多
关键词 integrable system single-component decomposition multi-component decomposition linear superposition integrable coupled KdV-type system
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AVAILABILITY SIMULATION OF MULTI-COMPONENT SYSTEM BASED ON OPPORTUNISTIC MAINTENANCE POLICY 被引量:5
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作者 蔡景 左洪福 吕德峰 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2009年第3期219-223,共5页
A multi-component system has the long fixed maintenance time, so the opportunistic maintenance policy is adopted to put preventive replacement and corrective replacement together, so that the long fixed maintenance ti... A multi-component system has the long fixed maintenance time, so the opportunistic maintenance policy is adopted to put preventive replacement and corrective replacement together, so that the long fixed maintenance time can be shared by more than one component, and the system availability can be improved. Then, the generation characteristics of the random failure time are researched based on the replacement maintenance and the minima[ maintenance. Furthermore, by choosing the opportunistic replacement ages of each component as opti- mized variables, a simulation algorithm based on an opportunistic maintenance policy is designed to maximize the total availability. Finally, the simulation result shows the validity of the algorithm by an example. 展开更多
关键词 AVAILABILITY multi-component system ALGORITHMS opportunistic maintenance minimal maintenance
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Multi-component Dirac equation hierarchy and its multi-component integrable couplings system 被引量:8
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作者 夏铁成 尤福财 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第3期605-610,共6页
A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M- dimensional loop algebra ~X is produced. By taking advantage of ~X a new isospectral problem is established and... A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M- dimensional loop algebra ~X is produced. By taking advantage of ~X a new isospectral problem is established and then by making use of the Tu scheme the multi-component Dirac equation hierarchy is obtained. Finally, an expanding loop algebra ~FM of the loop algebra ~X is presented. Based on the ~FM, the multi-component integrable coupling system of the multi-component Dirac equation hierarchy is investigated. The method in this paper can be applied to other nonlinear evolution equation hierarchies. 展开更多
关键词 loop algebra zero curvature equation multi-component Dirac equation hierarchy multi-component integrable couplings system
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Layout problem of multi-component systems arising for improving maintainability 被引量:5
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作者 罗旭 杨拥民 +2 位作者 葛哲学 温熙森 官凤娇 《Journal of Central South University》 SCIE EI CAS 2014年第5期1833-1841,共9页
To improve the mainlainability design efficiency and quality, a layout optimization method for maintainability of multi-component systems was proposed. The impact of the component layout design on system maintainabili... To improve the mainlainability design efficiency and quality, a layout optimization method for maintainability of multi-component systems was proposed. The impact of the component layout design on system maintainability was analyzed, and the layout problem for maintainability was presented. It was formulated as an optimization problem, where maintainability, layout space and distance requirement were formulated as objective functions. A multi-objective particle swarm optimization algorithm, in which the constrained-domination relationship and the update strategy of the global best were simply modified, was then used to obtain Pareto optimal solutions for the maintainability layout design problem. Finally, application in oxygen generation system of a spacecraft was studied in detail to illustrate the effectiveness and usefulness of the proposed method. The results show that the concurrent maintainability design can be carried out during the layout design process by solving the layout optimization problem for maintainability. 展开更多
关键词 MAINTAINABILITY layout problem OPTIMIZATION multi-component system multi-objective particle swarm optimization
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Opportunistic maintenance for multi-component systems considering structural dependence and economic dependence 被引量:6
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作者 Junbao Geng Michael Azarian Michael Pecht 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2015年第3期493-501,共9页
Although opportunistic maintenance strategies are widely used for multi-component systems, all opportunistic mainte- nance strategies only consider economic dependence and do not take structural dependence into accoun... Although opportunistic maintenance strategies are widely used for multi-component systems, all opportunistic mainte- nance strategies only consider economic dependence and do not take structural dependence into account. An opportunistic main- tenance strategy is presented for a multi-component system that considers both structural dependence and economic dependence. The cost relation and time relation among components based on structural dependence are developed. The maintenance strategy for each component of a multi-component system involves one of five maintenance actions, namely, no-maintenance, a minimal maintenance action, an imperfect maintenance action, a perfect maintenance action, and a replacement action. The maintenance action is determined by the virtual age of the component, the life expectancy of the component, and the age threshold values. Monte Carlo simulation is designed to obtain the optimal oppor- tunistic maintenance strategy of the system over its lifetime. The simulation result reveals that the minimum maintenance cost with a strategy that considers structural dependence is less than that with a strategy that does not consider structural dependence. The availability with a strategy that considers structural dependence is greater than that with a strategy that does not consider structural dependence under the same conditions. 展开更多
关键词 opportunistic maintenance multi-component system structural dependence Monte Carlo simulation maintenance cost.
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Data Mining-Based Maintenance Management Framework of Multi-component System 被引量:4
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作者 周瑜 《Journal of Donghua University(English Edition)》 EI CAS 2015年第6期950-953,共4页
Complex repairable system is composed of thousands of components.Some maintenance management and decision problems in maintenance management and decision need to classify a set of components into several classes based... Complex repairable system is composed of thousands of components.Some maintenance management and decision problems in maintenance management and decision need to classify a set of components into several classes based on data mining.Furthermore,with the complexity of industrial equipment increasing,the managers should pay more attention to the key components and carry out the lean management is very important.Therefore,the idea"customer segmentation"of"precise marketing"can be used in the maintenance management of the multi-component system.Following the idea of segmentation,the components of multicomponent systems should be subdivied into groups based on specific attributes relevant to maintenance,such as maintenance cost,mean time between failures,and failure frequency.For the target specific groups of parts,the optimal maintenance policy,health assessment and maintenance scheduling can be determined.The proposed analysis framework will be given out.In order to illustrate the effectiveness of this method,a numerical example is given out. 展开更多
关键词 maintenance management multi-component system data mining association rules CLUSTERING
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Dynamic probabilistic design technique for multi-component system with multi-failure modes 被引量:4
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作者 ZHANG Chun-yi LU Cheng +2 位作者 FEI Cheng-wei JING Hui-zhe LI Cheng-wei 《Journal of Central South University》 SCIE EI CAS CSCD 2018年第11期2688-2700,共13页
For unacceptable computational efficiency and accuracy on the probabilistic analysis of multi-component system with multi-failure modes,this paper proposed multi-extremum response surface method(MERSM).MERSM model was... For unacceptable computational efficiency and accuracy on the probabilistic analysis of multi-component system with multi-failure modes,this paper proposed multi-extremum response surface method(MERSM).MERSM model was established based on quadratic polynomial function by taking extremum response surface model as the sub-model of multi-response surface method.The dynamic probabilistic analysis of an aeroengine turbine blisk with two components,and their reliability of deformation and stress failures was obtained,based on thermal-structural coupling technique,by considering the nonlinearity of material parameters and the transients of gas flow,gas temperature and rotational speed.The results show that the comprehensive reliability of structure is 0.9904 when the allowable deformations and stresses of blade and disk are 4.78×10–3 m and 1.41×109 Pa,and 1.64×10–3 m and 1.04×109 Pa,respectively.Besides,gas temperature and rotating speed severely influence the comprehensive reliability of system.Through the comparison of methods,it is shown that the MERSM holds higher computational precision and speed in the probabilistic analysis of turbine blisk,and MERSM computational precision satisfies the requirement of engineering design.The efforts of this study address the difficulties on transients and multiple models coupling for the dynamic probabilistic analysis of multi-component system with multi-failure modes. 展开更多
关键词 probabilistic analysis multi-extremum response surface method multi-component multi-failure modes
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Generalized Multi-component TC Hierarchy and Its Multi-component Integrable Coupling System 被引量:1
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作者 XIA Tie-Cheng YOU Fu-Cai 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第5X期793-798,共6页
A new 3M-dimensional Lie algebra X is constructed firstly. Then, the corresponding loop algebra X is produced, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra A1.... A new 3M-dimensional Lie algebra X is constructed firstly. Then, the corresponding loop algebra X is produced, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra A1.It follows that a generalscheme for generating multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then well-known multi-component TC hierarchy is obtained. Finally,an expanding loop algebra FM of the loop algebra X is presented. Based on the FM, the multi-component integrable coupling system of the generalized multi-component TC hierarchy has been worked out. The method in this paper can be applied to other nonlinear evolution equations hierarchies. It is easy to find that we can construct any finite-dimensional Lie algebra by this approach. 展开更多
关键词 loop algebra multi-component TC hierarchy multi-component integrable coupling system
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Fretting Wear Behavior of Medium Carbon Steel Modified by Low Temperature Gas Multi-component Thermo-chemical Treatment 被引量:3
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作者 LUO Jun ZHENG Jianfeng +2 位作者 PENG Jinfang HE Liping ZHU Minhao 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2010年第3期288-296,共9页
The introduction of surface engineering is expected to be an effective strategy against fretting damage.A large number of studies show that the low gas multi-component(such as carbon,nitrogen,sulphur and oxygen,etc)th... The introduction of surface engineering is expected to be an effective strategy against fretting damage.A large number of studies show that the low gas multi-component(such as carbon,nitrogen,sulphur and oxygen,etc)thermo-chemical treatment(LTGMTT)can overcome the brittleness of nitriding process,and upgrade the surface hardness and improve the wear resistance and fatigue properties of the work-pieces significantly.However,there are few reports on the anti-fretting properties of the LTGMTT modified layer up to now,which limits the applications of fretting.So this paper discusses the fretting wear behavior of modified layer on the surface of LZ50(0.48%C)steel prepared by low temperature gas multi-component thermo-chemical treatment(LTGMTT)technology.The fretting wear tests of the modified layer flat specimens and its substrate(LZ50 steel)against 52100 steel balls with diameter of 40 mm are carried out under normal load of 150 N and displacement amplitudes varied from 2μm to 40μm.Characterization of the modified layer and dynamic analyses in combination with microscopic examinations were performed through the means of scanning electron microscope(SEM),optical microscope(OM),X-ray diffraction(XRD)and surface profilometer.The experimental results showed that the modified layer with a total thickness of 60μm was consisted of three parts,i.e.,loose layer,compound layer and diffusion layer.Compared with the substrate,the range of the mixed fretting regime(MFR)of the LTGMTT modified layer diminished,and the slip regime(SR)of the modified layer shifted to the direction of smaller displacement amplitude.The coefficient of friction(COF)of the modified layer was lower than that of the substrate in the initial stage.For the modified layer,the damage in partial slip regime(PSR)was very slight.The fretting wear mechanism of the modified layer both in MFR and SR was abrasive wear and delamination.The modified layer presented better wear resistance than the substrate in PSR and MFR;however,in SR,the wear resistance of the modified layer decreased with the increase of the displacement amplitudes.The experimental results can provide some experimental bases for promoting industrial application of LTGMTT modified layer in anti-fretting wear. 展开更多
关键词 fretting wear fretting regimes low temperature gas multi-component thermo-chemical treatment(LTGMTT) modified layer medium carbon steel
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Overview of Condition-Based Maintenance Decision-Making Optimization Modeling of Multi-component System 被引量:1
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作者 WANG Lei ZHANG Yaohui 《Journal of Donghua University(English Edition)》 EI CAS 2018年第4期353-356,共4页
Overview about three key contents of condition-based maintenance decision-making of a multi-component system is analyzed based on maintenance optimization and modeling. The component deterioration model, the correlati... Overview about three key contents of condition-based maintenance decision-making of a multi-component system is analyzed based on maintenance optimization and modeling. The component deterioration model, the correlation between the degraded components and the system configuration are analyzed separately in the deterioration model of multi-component system.For the maintenance polices,the opportunistic maintenance( OM)policy and the grouping maintenance( GM) policy are analyzed and summarized in combination with the condition-based maintenance( CBM) modeling of multi-component system. It is put forward that CBM modeling of multi-component system should be further researched based on the inspection interval and the maintenance threshold of multi-component system in availability. 展开更多
关键词 multi-component SYStem condition-based maintenance maintenance polices
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Effects of V addition on the mechanical properties at elevated temperatures in a γ”-strengthened NiCoCr-based multi-component alloy 被引量:1
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作者 Yunwei Pan Anping Dong +4 位作者 Yang Zhou Dafan Du Donghong Wang Guoliang Zhu Baode Sun 《Journal of Materials Science & Technology》 SCIE EI CAS CSCD 2022年第12期290-300,共11页
Ni Co Cr-based multi-component alloys have drawn much attention due to their exceptional ductility and strain hardening capacity.However,insufficient strength-ductility synergy of NiCoCr alloy has always been an issue... Ni Co Cr-based multi-component alloys have drawn much attention due to their exceptional ductility and strain hardening capacity.However,insufficient strength-ductility synergy of NiCoCr alloy has always been an issue that prevents it from extensive applications.According to our previous research,the precipitation ofγ”phase can significantly improve the strength-ductility synergy of this alloy system at room temperature.In this study,the effects of V addition onγ”phase stability and high-temperature mechanical properties have been explicitly investigated.The results indicate that V addition can stabilize the metastableγ”phase in this alloy system and prevent it from transforming into a stableδphase at grain boundaries upon 650℃aging,resulting in improved mechanical properties at elevated temperatures.The specific strength ofγ”-strengthened multi-component NiCoCr-based alloy can reach up to 86.2 MPa gcmat 650℃,which is higher than those of Ni-based superalloys,IN 939 and Waspaloy.This work provides theoretical guidance for the novel design of γ”-strengthened alloy for high-temperature applications. 展开更多
关键词 multi-component alloys CALPHAD γ”phase Microstructural evolution High-temperature mechanical properties
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Similarity Reductions of(2+1)-Dimensional Multi-component Broer-Kaup System 被引量:1
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作者 DONG Zhong-Zhou CHEN Yong WANG Ling 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第10期803-808,共6页
Painleve property of the (2+1)-dimensional multi-component Broer-Kaup (BK) system is considered by using the standard Weiss Kruskal approaches. Applying the Clarkson and Kruskal (CK) direct method to the (2+1... Painleve property of the (2+1)-dimensional multi-component Broer-Kaup (BK) system is considered by using the standard Weiss Kruskal approaches. Applying the Clarkson and Kruskal (CK) direct method to the (2+1)- dimensional multi-component BK system, some types of similarity reductions are obtained. By solving the reductions, one can get the solutions of the (2+1)-dimensional multi-component BK system. 展开更多
关键词 multi-component Broer Kaup system similarity reduction direct method
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A facile high-efficiency preparation strategy for Al-containing multi-component boride microcrystals with superior comprehensive performance
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作者 Yong Fan Jinfeng Nie +7 位作者 Zhigang Ding Yujing Zhang Xiang Chen Wei Liu Sen Yang Sida Liu Xiangfa Liu Yonghao Zhao 《Journal of Materials Science & Technology》 2025年第1期190-203,共14页
Multi-component transition group metal borides(MMB_(2))have become a research hotspot due to their new composition design concepts and superior properties compared with conventional ceramics.Most of the current method... Multi-component transition group metal borides(MMB_(2))have become a research hotspot due to their new composition design concepts and superior properties compared with conventional ceramics.Most of the current methods,however,are complicated and time-consuming,the mass production remains a chal-lenge.Herein,we proposed a new high-efficiency strategy for synthesis of MMB_(2)using molten aluminum as the medium for the first time.The prepared Al-containing multi-component borides(TiZrHfNbTa)B_(2)microcrystals had a homogeneous composition with a hexagonal AlB_(2)structure and ultra-high hardness value of∼35.3 GPa,which was much higher than data reported in the literature and the rule of mix-ture estimations.Furthermore,combined with the First-principles calculation results,we found that the Poisson’s ratio(v)values exhibit a clearly ascending trend from 0.17 at VEC=3.5 to 0.18 at VEC=3.4,then to 0.201 at VEC=3.2 with the increasing of Al content.This indicates that the intrinsic toughness of multi-component boride microcrystals is obviously enhanced by the trace-doped Al elements.Besides,the fabricated Al-containing multi-component boride microcrystals have superior oxidation activation en-ergy and structural stability.The enhanced oxidation resistance is mainly attributed to the formation of a protective Al2 O3 oxide layer and the lattice distortion,both of which lead to sluggish diffusion of O_(2).These findings propose a new unexplored avenue for the fabrication of MMB_(2)materials with supe-rior comprehensive performance including ultra-hardness and intrinsically improved thermo-mechanical properties. 展开更多
关键词 multi-component borides First-principles calculations Crystal growth Mechanical properties Oxidation behavior
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Multi-component Levi Hierarchy and Its Multi-component Integrable Coupling System
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作者 XIA Tie-Cheng YOU Fu-Cai ZHAO Wen-Ying 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第6X期990-996,共7页
A simple 3M-dimensional loop algebra X is produced, whose commutation operation defined by us is A1 as simple and straightforward as that in the loop algebra A1. It follows that a general scheme for generating multi-... A simple 3M-dimensional loop algebra X is produced, whose commutation operation defined by us is A1 as simple and straightforward as that in the loop algebra A1. It follows that a general scheme for generating multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then by making use of the Tu scheme the well-known multi-component Levi hierarchy is obtained. Finally, an expanding loop algebra FM of the loop algebra .X is presented, based on the FM, the multi-component integrable coupling system of the multi-component Levi hierarchy is worked out. The method in this paper can be applied to other nonlinear evolution equation hierarchies. 展开更多
关键词 loop algebra multi-component Levi hierarchy multi-component integrable coupling system
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Uncovering the hardening mechanism of multi-component carbide ceramics based on the coupling effect of covalent bond enhancement and lattice distortion
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作者 Qingyi Kong Qinchen Liu +7 位作者 Lei Chen Sijia Huo Kunxuan Li Mingxuan Mao WeiWei Sun Yujin Wang Suk-Joong L.Kang Yu Zhou 《Journal of Materials Science & Technology》 2025年第31期102-112,共11页
The hardening mechanism of multi-component carbide ceramic has been investigated in detail through a combination of experiments,first-principles calculations,and ab initio molecular dynamics(AIMD).Eight dense carbide ... The hardening mechanism of multi-component carbide ceramic has been investigated in detail through a combination of experiments,first-principles calculations,and ab initio molecular dynamics(AIMD).Eight dense carbide ceramics were prepared by spark plasma sintering.Compulsorily,all the multi-component carbide samples have similar carbon content,grain size,and uniform compositional distribution by optimizing the sintering process and adjusting the initial raw materials.Hence the interference of other factors on the hardness of multi-component carbide ceramics is minimized.The effects of changes in the elemental species on the lattice distortion,bond strength,bonding properties,and electronic structure of multi-component carbide ceramics were thoroughly analyzed.These results show that the hardening of multi-component carbide ceramic can be attributed to the coupling of solid solution strengthening caused by lattice distortion and covalent bond strengthening.Besides,the“host lattice”of multi-component carbide ceramics is defined based on the concept of supporting lattice.The present work is of great significance for a deeper understanding of the hardening mechanism of multi-component carbide ceramics and the design of superhard multi-component carbides. 展开更多
关键词 multi-component ceramics Mechanical properties Hardening mechanism First principle calculation Ab initio molecular dynamics
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Photocatalytic multi-component synthesis of ester-containing quinoxalin-2(1H)-ones using water as the hydrogen donor
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作者 Qiang Feng Jindong Hao +3 位作者 Ya Hu Rong Fu Wei Wei Dong Yi 《Chinese Chemical Letters》 2025年第6期484-488,共5页
A convenient photocatalytic multi-component reaction of alkenes,quinoxalin-2(1H)-ones,and diazo compounds has been developed in the presence of water.A number of ester-containing quinoxalin-2(1H)-ones could be efficie... A convenient photocatalytic multi-component reaction of alkenes,quinoxalin-2(1H)-ones,and diazo compounds has been developed in the presence of water.A number of ester-containing quinoxalin-2(1H)-ones could be efficiently obtained in moderate to good yields at room temperature.This metal-free visiblelight-driven tandem reaction was conducted through proton-coupled electron transfer(PCET)process using water as the hydrogen donor and 1,2,3,5-tetrakis(carbazol-9-yl)-4,6-dicyanobenzene(4CzIPN)as the photocatalyst. 展开更多
关键词 PHOTOCATALYTIC multi-component synthesis Diazo compounds Radical reaction Quinoxalin-2(1H)-ones
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Fast algorithm of borehole correction library construction for multi-component array induction tool in deviated boreholes
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作者 Ya-Zhou Wang Hong-Nian Wang +2 位作者 Lei Yu Yan Bai Shou-Wen Yang 《Petroleum Science》 2025年第12期5034-5046,共13页
The construction of a borehole correction library for the multi-component array induction tool in deviated boreholes involves extensive 3D forward modeling and typically requires significant computational resources.To... The construction of a borehole correction library for the multi-component array induction tool in deviated boreholes involves extensive 3D forward modeling and typically requires significant computational resources.To address this challenge,this paper proposes an efficient algorithm for the library construction based on the 3D finite volume method(FVM)and contraction high-order Born approximation(CHBA).First,the electromagnetic(EM)field solution region is divided into two symmetric subregions based on the symmetry of the correction library model and the EM field.Numerical solution on a single subregion,combined with the symmetry boundary extension technique,enhances the efficiency of the 3D numerical simulation.Second,three reference mud conductivities are selected based on the mud conductivity range,and the CHBA is applied to calculate the EM responses at all mud conductivity nodes rapidly.Third,the number of forward simulation operations is further reduced by exploiting the principle that models with different frequencies and different formation conductivities have equivalent EM responses.Numerical experiments demonstrate the correctness and feasibility of the proposed algorithm.Compared to conventional 3D modeling,the proposed algorithm achieves approximately a 20-fold speedup in library construction,effectively reducing computational resources and time consumption. 展开更多
关键词 multi-component array induction logging Borehole correction library 3D finite volume method Contraction high-order Born approximation
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Invariants of Multi-Component Ermakov Systems
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作者 屈长征 闫璐 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第9期393-396,共4页
It is shown that certain multi-component Ermakov systems admit Lewis-Ray-Reid invariants.This extendsthe result to the two-component Ermakov system.
关键词 multi-component Ermakov system Lewis-Ray-Reid invariant affine invariant SYMMETRY
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Calculation of Extraction Equilibrium in Multi-Component System by Newton-Raphson Algorithm
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作者 贾江涛 王建方 +3 位作者 严纯华 廖春生 吴声 李标国 《Journal of Rare Earths》 SCIE EI CAS CSCD 1999年第4期246-249,共4页
Based on the extraction equilibrium and mass balances in countercurrent extraction systems, a novel method was studied for dealing with the extraction equilibrium and the mass distribution in a multi-component(gamma-c... Based on the extraction equilibrium and mass balances in countercurrent extraction systems, a novel method was studied for dealing with the extraction equilibrium and the mass distribution in a multi-component(gamma-component) system. The relationships of mass distribution (x(i), y(i), i = 1, ..., lambda) between two phases were expressed by 2 lambda dimensional simultaneous equations. These simultaneous equations can be converted to a one-dimension nonlinear equation, then it was solved by Newton-Raphson algorithm within a few number of iteration. Compared with the regular calculation method for the 2 lambda dimensional simultaneous equations, Newton-Raphson algorithm can decrease the number of iteration, increase the convergence of the equations and accelerate the speed of simulation. It was verified in many multi-component systems with satisfactory results. As an example, a five-component system is demonstrated in this paper. 展开更多
关键词 rare earths multi-component system extraction equilibrium Newton-Raphson algorithm
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