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A crystalline Sm(Ⅲ)-containing antimonotungstate with efficient catalytic activity in three-component reaction for isoindolinones synthesis
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作者 Hao-Qi Liu Jia-Wei Cao +6 位作者 Wei Tang Zhou-Fu Lin Ke Li Wei-Jian Xu Zhi-Bin Zhang Yu-Feng Liu Guo-Ping Yang 《Rare Metals》 2025年第6期3995-4002,共8页
The development of the three-component catalytic system for constructing isoindolinones from simple feedstocks is both significant and challenging.In this study,a unique tartrate-linked dimeric samarium-antimonotungst... The development of the three-component catalytic system for constructing isoindolinones from simple feedstocks is both significant and challenging.In this study,a unique tartrate-linked dimeric samarium-antimonotungstate[Sm_(2)(H_(2)O)_(6)(tar)(Sb_(2)W_(21)O_(72))]_(2)^(20-)(Sm_(4)tar_(2),H_(4)tar=tartaric acid)was synthesized via a one-step method at room temperature using an acetate buffer solution.The dimeric polyanion of Sm4tar2shows a centrosymmetric structure with a parallelogram-like arrangement and comprises two enantiomeric{Sm_(2)(H_(2)O)_(6)(Sb_(2)W_(21)O_(72))}moieties connected by two enantiomeric tar ligands.Sm_(4)tar_(2)demonstrates efficient catalytic activity in the three-component reaction involving 2-acylbenzoic acids,primary amines,and phosphine oxides to form 3,3-disubstituted isoindolinones.The advantages of this catalytic system include simple feedstocks,green and reusable catalyst,and operational simplicity with water as the sole by-product.This finding enables an effective molecular fragment assembly strategy for synthesizing isoindolinone drug precursor skeletons. 展开更多
关键词 SAMARIUM Antimonotungstate Tartaric acid three-component reaction ISOINDOLINONES
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Three-component soliton states in spinor F=1 Bose-Einstein condensates with PT-symmetric generalized Scarf-Ⅱpotentials
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作者 Zhang-Lei Han Jun-Yi Lao +1 位作者 Jia-Rui Zhang Yu-Jia Shen 《Communications in Theoretical Physics》 2025年第4期1-11,共11页
Introducing PT-symmetric generalized Scarf-Ⅱpotentials into the three-coupled nonlinear Gross-Pitaevskii equations offers a new way to seek stable soliton states in quasi-onedimensional spin-1 Bose-Einstein condensat... Introducing PT-symmetric generalized Scarf-Ⅱpotentials into the three-coupled nonlinear Gross-Pitaevskii equations offers a new way to seek stable soliton states in quasi-onedimensional spin-1 Bose-Einstein condensates.In scenarios where the spin-independent parameter c_(0)and the spin-dependent parameter c_(2)vary,we use both analytical and numerical methods to investigate the three-coupled nonlinear Gross-Pitaevskii equations with PT-symmetric generalized Scarf-Ⅱpotentials.We obtain analytical soliton states and find that simply modulating c_(2)may change the analytical soliton states from unstable to stable.Additionally,we obtain numerically stable double-hump soliton states propagating in the form of periodic oscillations,exhibiting distinct behavior in energy exchange.For further investigation,we discuss the interaction of numerical double-hump solitons with Gaussian solitons and observe the transfer of energy among the three components.These findings may contribute to a deeper understanding of solitons in Bose-Einstein condensates with PT-symmetric potentials and may hold significance for both theoretical understanding and experimental design in related physics experiments. 展开更多
关键词 three-component soliton states PT-symmetric generalized Scarf-Ⅱpotentials Bose-Einstein condensates Three-coupled nonlinear Gross-Pitaevskii equations
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A H_(4)SiW_(12)O_(40)-catalyzed three-component tandem reaction for the synthesis of 3,3-disubstituted isoindolinones 被引量:1
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作者 Yufeng Liu Guodong Zeng +4 位作者 Yutao Cheng Lei Chen Yunhai Liu Yongge Wei Guoping Yang 《Chinese Chemical Letters》 SCIE CAS CSCD 2024年第1期233-236,共4页
A H_(4)SiW_(12)O_(40)-catalyzed three-component tandem reaction of 2-acylbenzoic acids,primary amines and phosphine oxides to form 3,3-disubstituted isoindolinones was developed.By employing A H_(4)SiW_(12)O_(40)as th... A H_(4)SiW_(12)O_(40)-catalyzed three-component tandem reaction of 2-acylbenzoic acids,primary amines and phosphine oxides to form 3,3-disubstituted isoindolinones was developed.By employing A H_(4)SiW_(12)O_(40)as the catalyst and dimethyl carbonate(DMC)as the solvent,a diverse range of 2-acylbenzoic acid derivatives and primary amines worked well to give the C3-phosphinoyl-functionalized 3,3-disubstituted isoindolinones with the yield range of 61%-87%.Advantages of this transformation include green catalyst and solvent,available starting materials,broad substrate scope,high efficiency and operational simplicity with water as the sole by-product.The strategy achieved an efficient and green molecular fragment assembly to access isoindolinones,which would provide opportunities for the synthesis of potential biologically active molecules in a green manner. 展开更多
关键词 POLYOXOMETALATES Dehydrative coupling three-component tandem reaction 3 3-Disubstituted isoindolinones Organic carbonate
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Light-responsive Self-Immolative L-glutamic Acid-based Polyester Nanoparticles for Controlled Drug Release via Passerini Three-Component Polymerization
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作者 Xiao-Fei Sun Xu Zhang +5 位作者 Shu-Ping Song Ya-Qun Yao Yan Zhang Cheng-Liang Wang Jing-Jiang Sun Qing-Fu Wang 《Chinese Journal of Polymer Science》 SCIE EI CAS CSCD 2024年第5期570-578,I0005,共10页
L-glutamic acid(LA)is a bio-based,non-toxic,environmentally friendly material derived from biomass.The present study reports the application of Passerini three-component polymerization(P-3CP)for the straightforward pr... L-glutamic acid(LA)is a bio-based,non-toxic,environmentally friendly material derived from biomass.The present study reports the application of Passerini three-component polymerization(P-3CP)for the straightforward preparation of LA-based light-responsive polyesters(PLTDs)under mild conditions.PLTDs with molar masses up to 8500 g/mol and high yields exceeding 90%are obtained.The chemical structures and light-responsive self-immolative behavior of PLTDs are comprehensively characterized by employing ultraviolet-visible(UV-Vis)spectroscopy,size exclusion chromatography(SEC),nuclear magnetic resonance(NMR)spectroscopy,and liquid chromatography mass spectrometry(LC-MS).Meanwhile,monodisperse PLTD-based doxorubicin-loaded nanoparticles(PLTD-DOX-NP)(size=193 nm,PDI=0.018)are formulated by nanoprecipitation method.Upon light-induced depolymerization,the PLTD-DOX-NP undergoes rapid decomposition,resulting in a burst release of 80%cargo within 13 s.Furthermore,according to biological toxicity tests,the PLTD-NP possesses adequate biosafety,both before and after irradiation.Overall,the incorporation of P-3CP with biorenewable LA-based monomer adheres to the principles of green chemistry,significantly simplifying the synthetic pathway of light-responsive polymers. 展开更多
关键词 L-glutamic acid Passerini three-component polymerization Light-responsive POLYESTER NANOPARTICLES
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Cu-catalyzed three-component C–S–P coupling for the synthesis of trisubstituted allenyl phosphorothioates
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作者 Bowen Wang Longwu Sun +5 位作者 Qianqian Cao Xinzhi Li Jianai Chen Shizhao Wang Miaolin Ke Fener Chen 《Chinese Chemical Letters》 SCIE CAS CSCD 2024年第12期462-465,共4页
A copper-catalyzed three-component reaction involving cyclic carbonates,elemental sulfur,and H-phosphonates is presented.It proceeds with excellent yields and provides an attractive approach for the construction of va... A copper-catalyzed three-component reaction involving cyclic carbonates,elemental sulfur,and H-phosphonates is presented.It proceeds with excellent yields and provides an attractive approach for the construction of valuable trisubstituted allenyl phosphorothioates using a one-step strategy.Moreover,this method can be easily adapted to large-scale preparation. 展开更多
关键词 Cu-catalyzed Construction of C–S–P bond three-component reaction Elemental sulfur Allenyl phosphorothioates
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Design of ground-airborne TEM three-component air-core coil sensor 被引量:6
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作者 YUAN Shao-ye LIN Jun +2 位作者 SONG Shuang SUN De-li TENG Fei 《Journal of Measurement Science and Instrumentation》 CAS CSCD 2019年第1期28-37,共10页
Transient electromagnetic method (TEM),as a non-seismic geophysical exploration mainstream electromagnetic method,is widely used in oil,gas,mineral and other underground resources exploration areas. The coil sensor is... Transient electromagnetic method (TEM),as a non-seismic geophysical exploration mainstream electromagnetic method,is widely used in oil,gas,mineral and other underground resources exploration areas. The coil sensor is generally used to collect data. In view of the problems of incomplete information of the abnormal body and the data loss in the existing TEM single-component coil sensor,a three-component TEM coil sensor is designed. By analyzing the relationship between sensor sensitivity and coil structure parameters,the coil structure and turns are designed. By analyzing the frequency response characteristics of the TEM magnetic field sensor,the signal distortion is reduced by using the under-damped matching mode. By analyzing the distribution of various noise sources of the magnetic sensor,the appropriate amplifier is selected to reduce the background noise. Finally,a three-component TEM induction magnetic field sensor is designed. The weight of the sensor is controlled at 3.2 kg and the working frequency is 10 mHz-10 kHz. The background noises of X and Y components probably keep in 1.5×10^-8 V/ Hz and sensitivities are 8.4 and 9.8 nT/s,respectively,the background noise of vertical component is 2.1× 10^-7 V/ Hz and sensitivity is 18.5 nT/s. Compared with the existing single-component TEM receiving magnetic field sensor,the designed sensor realizes the signal acquisition of three components. Without too much increase in volume and total weight,it improves the sensitivity of the sensor and reduces the background noise,thus the signal-to-noise ratio (SNR) of the signal is improved. 展开更多
关键词 transient electromagnetic method (TEM) three-component air-core coil sensor under-damped matching noise analysis
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Three-Component Model for Bidirectional Reflection Distribution Function of Thermal Coating Surfaces 被引量:3
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作者 刘宏 朱京平 +2 位作者 王凯 王秀红 徐蓉 《Chinese Physics Letters》 SCIE CAS CSCD 2016年第6期33-36,共4页
We present a bidirectional reflection distribution function (BRDF) model for thermal coating surfaces based on a three-component reflection assumption, in which the specular reflection is given according to the micr... We present a bidirectional reflection distribution function (BRDF) model for thermal coating surfaces based on a three-component reflection assumption, in which the specular reflection is given according to the microfacet theory and Snell's law, the multiple reflection is considered Nth cosine distributed, and the volume scattering is uniformly distributed in reflection angles according to the experimental results. This model describes the reflection characteristics of thermal coating surfaces more completely and reasonably. Simulation and measurement results of two thermal coating samples SR107 and S781 are given to validate that this three-component model significantly improves the modeling accuracy for thermal coating surfaces compared with the existing BRDF models. 展开更多
关键词 for in BRDF three-component Model for Bidirectional Reflection Distribution Function of Thermal Coating Surfaces of
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Facile three-component synthesis and insecticidal evaluation of hexahydroimidazo[1,2-a]pyridine derivatives 被引量:2
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作者 Ye-Feng Fan Wen-Wen Zhang +3 位作者 Xu-Sheng Shao Zhi-Ping Xu Xiao-Yong Xu Zhong Li 《Chinese Chemical Letters》 SCIE CAS CSCD 2015年第1期1-5,共5页
A series of new hexahydroimidazo[1,2-a]pyridine derivatives were synthesized via convenient and practical three-component reactions. Preliminary bioassays showed that majority of the target compounds exhibited moderat... A series of new hexahydroimidazo[1,2-a]pyridine derivatives were synthesized via convenient and practical three-component reactions. Preliminary bioassays showed that majority of the target compounds exhibited moderate to excellent insecticidal activity against cowpea aphids (Aphis craccivora). Among them, compound 91 demonstrated significant activity with LCso value of 0.00918 mmol/L which was about 3.8-fold higher than that of imidacloprid (IMI). Furthermore, the study of stereostructure-activity relationship of four isomers of 9k indicated that configuration played a key role in insecticidal activity of these compounds. 展开更多
关键词 NEONICOTINOIDS Hexahydroimidazo[ 1 2-a]pyridine three-component reaction CONFIGURATION Insecticidal activity
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Photocatalyst-free visible-light-mediated three-component reaction ofα-diazoesters, cyclic ethers and NaSCN to access organic thiocyanates 被引量:2
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作者 Zhiwei Wang Na Meng +3 位作者 Yufen Lv Wei Wei Huilan Yue Guofu Zhong 《Chinese Chemical Letters》 SCIE CAS CSCD 2023年第2期198-201,共4页
A facile and environmentally friendly visible-light-induced three-component reaction of α-diazoesters,cyclic ethers and Na SCN to construct organic thiocyanates has been developed at room temperature. This reaction c... A facile and environmentally friendly visible-light-induced three-component reaction of α-diazoesters,cyclic ethers and Na SCN to construct organic thiocyanates has been developed at room temperature. This reaction could occur under photocatalyst-and additive-free conditions to afford a number of organic thiocyanates with moderate to good yield and favorable functional group tolerance. 展开更多
关键词 Photocatalyst-free VISIBLE-LIGHT three-component reaction Organic thiocyanates
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Visible-light-induced three-component reaction of quinoxalin-2(1H)-ones,alkenes and CF_(3)SO_(2)Na leading to 3-trifluoroalkylated quinoxalin-2(1H)-ones 被引量:2
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作者 Na Menga Yufen Lv +3 位作者 Qishun Liu Ruisheng Liu Xiaohui Zhao Wei Wei 《Chinese Chemical Letters》 SCIE CAS CSCD 2021年第1期258-262,共5页
A facile and metal-free visible-light-enabled three-component reaction of quinoxalin-2(1 H)-ones,alkenes and CF_(3)SO_(2)Na has been developed under air at room temperature.This photocatalytic tandem reaction using 4 ... A facile and metal-free visible-light-enabled three-component reaction of quinoxalin-2(1 H)-ones,alkenes and CF_(3)SO_(2)Na has been developed under air at room temperature.This photocatalytic tandem reaction using 4 CzIPN as the photocatalyst and air as the green oxidant,provides a mild and environmentally friendly approach to access a series of 3-trifluoroalkylated quinoxalin-2(1 H)-ones. 展开更多
关键词 METAL-FREE Visible-light-catalysis three-component reaction Quinoxalin-2(1H)-ones
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Three-component reaction for synthesis of functionalized spiro[indoline-3,4'-pyrano[3,2-h]quinolines] 被引量:1
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作者 Rong-Guo Shi Chao-Guo Yan 《Chinese Chemical Letters》 SCIE CAS CSCD 2016年第4期575-578,共4页
The functionalized spiro[indoline-3,40-pyrano[3,2-h]quinolines] were efficiently prepared in high yields from three-component reaction of 8-hydroxyquinoline, isatins and malononitrile or ethyl cyanoacetate in ethanol ... The functionalized spiro[indoline-3,40-pyrano[3,2-h]quinolines] were efficiently prepared in high yields from three-component reaction of 8-hydroxyquinoline, isatins and malononitrile or ethyl cyanoacetate in ethanol at room temperature for about 12 h in the presence of piperidine. 展开更多
关键词 SPIROOXINDOLE CHROMENE ISATIN MALONONITRILE three-component reaction
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Metal-free one-pot synthesis of quinoline-2,4-carboxylates via a molecular iodine-catalyzed three-component reaction of arylamines, ethyl glyoxylate, and α-ketoesters 被引量:2
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作者 Guang-Ming Nan Wei Liu 《Chinese Chemical Letters》 SCIE CAS CSCD 2015年第10期1289-1292,共4页
A simple and metal-free method has been developed for the construction of quinoline-2,4-carboxylates under mild conditions via a molecular iodine-catalyzed three-component tandem reaction of arylamines, ethyl glyoxyla... A simple and metal-free method has been developed for the construction of quinoline-2,4-carboxylates under mild conditions via a molecular iodine-catalyzed three-component tandem reaction of arylamines, ethyl glyoxylate, and a-ketoesters. The present protocol provides a convenient and attractive approach to various quinoline-2,4-carboxylates in moderate to good yields with excellent functional group tolerance. 展开更多
关键词 Molecular iodine Quinoline-2 4-carboxylates three-component Tandem reaction
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Statistical Average of Spin Operators for Calculation of Three-Component Magnetization (II): Solution of Equation 被引量:1
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作者 WANG Huai-Yu LONG Yao CHEN Nan-Xian 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第1期175-179,共5页
In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin... In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin quantum number S. The Chebyshev equation is transformed from an ordinary differential equation obtained when we dealt with Heisenberg model, in order to calculate all three components of magnetization, by many-body Green's function under random phase approximation. The Chebyshev functions with argument being greater than 1 are discussed. This paper shows that the Chebyshev polynomials with their argument being greater than 1 have their physical application. 展开更多
关键词 three-component magnetization Heisenberg model many-body Green's function method ordinary differential equation Chebyshev functions
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A mild and highly efficient one-pot three-component reaction for carbon-sulfur bond formation catalyzed by potassium tert-butoxide 被引量:1
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作者 Barahman Movassagh Amir Rakhshani 《Chinese Chemical Letters》 SCIE CAS CSCD 2011年第10期1179-1182,共4页
Potassium tert-butoxide has been found to be a highly efficient catalyst for one-pot,three-component reaction of aryl aldehydes, acetophenones,and thiols via Claisen-Schmidt/Michael addition reactions for the synthesi... Potassium tert-butoxide has been found to be a highly efficient catalyst for one-pot,three-component reaction of aryl aldehydes, acetophenones,and thiols via Claisen-Schmidt/Michael addition reactions for the synthesis of thia-Michael adducts in high yields. The reactions are best carried out in tert-butyl alcohol at room temperature. 展开更多
关键词 Potassium tert-butoxide Thia-Michael adduct three-component reaction C-S bond formation THIOLS
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Low-Frequency Waves in Cold Three-Component Plasmas 被引量:1
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作者 FU Qiang TANG Ying +1 位作者 ZHAO Jinsong LU Jianyong 《Plasma Science and Technology》 SCIE EI CAS CSCD 2016年第9期897-901,共5页
The dispersion relation and electromagnetic polarization of the plasma waves are comprehensively studied in cold electron, proton, and heavy charged particle plasmas. Three modes are classified as the fast, intermedia... The dispersion relation and electromagnetic polarization of the plasma waves are comprehensively studied in cold electron, proton, and heavy charged particle plasmas. Three modes are classified as the fast, intermediate, and slow mode waves according to different phase velocities. When plasmas contain positively-charged particles, the fast and intermediate modes can interact at the small propagating angles, whereas the two modes are separate at the large propagating angles. The near-parallel intermediate and slow waves experience the linear polarization, circular polarization, and linear polarization again, with the increasing wave number. The wave number regime corresponding to the above circular polarization shrinks as the propagating angle increases. Moreover, the fast and intermediate modes cause the reverse change of the electromagnetic polarization at the special wave number. While the heavy particles carry the negative charges, the dispersion relations of the fast and intermediate modes are always separate, being independent of the propagating angles. Furthermore, this study gives new expressions of the three resonance frequencies corresponding to the highly-oblique propagation waves in the general three-component plasmas, and shows the dependence of the resonance frequencies on the propagating angle, the concentration of the heavy particle, and the mass ratio among different kinds of particles. 展开更多
关键词 three-component plasma plasma wave dispersion relation electromagneticpolarization
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Dark and multi-dark solitons in the three-component nonlinear Schrodinger equations on the general nonzero background 被引量:1
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作者 Zhi-Jin Xiong Qing Xu Liming Ling 《Chinese Physics B》 SCIE EI CAS CSCD 2019年第12期60-67,共8页
We exhibit some new dark soliton phenomena on the general nonzero background for a defocusing three-component nonlinear Schrodinger equation. As the plane wave background undergoes unitary transformation SU(3), we obt... We exhibit some new dark soliton phenomena on the general nonzero background for a defocusing three-component nonlinear Schrodinger equation. As the plane wave background undergoes unitary transformation SU(3), we obtain the general nonzero background and study its modulational instability by the linear stability analysis. On the basis of this background, we study the dynamics of one-dark soliton and two-dark-soliton phenomena, which are different from the dark solitons studied before. Furthermore, we use the numerical method for checking the stability of the one-dark-soliton solution. These results further enrich the content in nonlinear Schrodinger systems, and require more in-depth studies in the future. 展开更多
关键词 dark soliton three-component nonlinear Schrodinger equations general nonzero background
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Three-Component Coupling Catalyzed by Phosphine: Preparation of α-Amino γ-Oxo Acid Derivatives 被引量:1
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作者 Yohei Oe Takeshi Inoue +3 位作者 Hiroaki Kishimoto Mitsuhiro Sasaki Tetsuo Ohta Isao Furukawa 《International Journal of Organic Chemistry》 2012年第2期111-116,共6页
The three-component coupling reaction of ethyl propiolate (1), phthalimide (2), and aldehyde (3) catalyzed by tripheny- lphosphine, was developed. A solution of an equivalent amount of 1 and 2 in benzaldehyde (3a) in ... The three-component coupling reaction of ethyl propiolate (1), phthalimide (2), and aldehyde (3) catalyzed by tripheny- lphosphine, was developed. A solution of an equivalent amount of 1 and 2 in benzaldehyde (3a) in the presence of 30 mol% of PPh3 was heated at 100?C for 48 h to give N-(1-ethoxycarbonyl-3-oxo-3-phenylpropyl)phthalimide (4a) in 83% yield. This reaction was thought to proceed via vinylphosphonium salt formed from the reaction of ethyl propiolate (1) with triphenylphosphine in situ. 展开更多
关键词 three-component Coupling PHOSPHINE 2-Amino-4-Oxocarboxylic ACID
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A novel and green synthesis of indolone-N-amino acid derivatives via the Passerini three-component reactions in water 被引量:1
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作者 Rong-Kun Li Quan-Li Yang +3 位作者 Yi Liu Dong-Wei Li Nian-Yu Huang Ming-Guo Liu 《Chinese Chemical Letters》 SCIE CAS CSCD 2016年第3期345-348,共4页
A green Passerini three-component reaction of 2-(4-oxo-4,5,6,7-tetrahydro-1H-indol-1-yl)acetic acid with alkyl or aryl isocyanides and aldehydes was reported under aqueous conditions at 35 ℃ for 1 h, and21 indolone... A green Passerini three-component reaction of 2-(4-oxo-4,5,6,7-tetrahydro-1H-indol-1-yl)acetic acid with alkyl or aryl isocyanides and aldehydes was reported under aqueous conditions at 35 ℃ for 1 h, and21 indolone-N-amino acid derivatives were prepared in high yields of 42%–99%. Their structures were characterized by IR, ESI–MS, NMR and elemental analysis, and the possible mechanisms have been also proposed. The highly efficient and eco-friendly method provides a facile access to a library of indoloneN-amino acid derivatives for future research on bioactivity screening. 展开更多
关键词 Passerini three-component reaction Indolone-N-amino acid Green synthesis Heterocycles Isocyanide
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Localized waves in three-component coupled nonlinear Schrdinger equation 被引量:1
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作者 徐涛 陈勇 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第9期180-188,共9页
We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,... We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system. 展开更多
关键词 localized waves three-component coupled nonlinear Schr ¨odinger equation generalized Darboux transformation
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Statistical Average of Spin Operators for Calculation of Three-Component Magnetization
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作者 WANGHuai-Yu ZHOUBin CHENNan-Xian 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第4期753-758,共6页
When one wants to calculate all the three components of magnetization of Heisenberg model under random phase approximation, at least one of the components should be the solution of an ordinary differential equation. I... When one wants to calculate all the three components of magnetization of Heisenberg model under random phase approximation, at least one of the components should be the solution of an ordinary differential equation. In this paper such an equation is established. It is argued that the general expressions of magnetization for any spin quantum number S suggested before are the solution of the ordinary differential equation. 展开更多
关键词 three-component magnetization heisenberg model many-body Green's functionmethod ordinary differential equation
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