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Extending the solid solution range of sodium ferric pyrophosphate:Off‐stoichiometric Na_(3)Fe(2.5)(P_(2)O_(7))_(2)as a novel cathode for sodium‐ion batteries 被引量:1
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作者 Xiang jun Pu Kunran Yang +6 位作者 Zibing Pan Chunhua Song Yangyang Lai Renjie Li Zheng‐Long Xu Zhongxue Chen Yuliang Cao 《Carbon Energy》 SCIE EI CAS CSCD 2024年第4期128-139,共12页
Iron‐based pyrophosphates are attractive cathodes for sodium‐ion batteries due to their large framework,cost‐effectiveness,and high energy density.However,the understanding of the crystal structure is scarce and on... Iron‐based pyrophosphates are attractive cathodes for sodium‐ion batteries due to their large framework,cost‐effectiveness,and high energy density.However,the understanding of the crystal structure is scarce and only a limited candidates have been reported so far.In this work,we found for the first time that a continuous solid solution,Na_(4−α)Fe_(2+α)_(2)(P_(2)O_(7))_(2)(0≤α≤1,could be obtained by mutual substitution of cations at center‐symmetric Na3 and Na4 sites while keeping the crystal building blocks of anionic P_(2)O_(7) unchanged.In particular,a novel off‐stoichiometric Na_(3)Fe(2.5)(P_(2)O_(7))_(2)is thus proposed,and its structure,energy storage mechanism,and electrochemical performance are extensively investigated to unveil the structure–function relationship.The as‐prepared off‐stoichiometric electrode delivers appealing performance with a reversible discharge capacity of 83 mAh g^(−1),a working voltage of 2.9 V(vs.Na^(+)/Na),the retention of 89.2%of the initial capacity after 500 cycles,and enhanced rate capability of 51 mAh g^(−1)at a current density of 1600 mA g^(−1).This research shows that sodium ferric pyrophosphate could form extended solid solution composition and promising phase is concealed in the range of Na_(4−α)Fe_(2+α)_(2)(P_(2)O_(7))_(2),offering more chances for exploration of new cathode materials for the construction of high‐performance SIBs. 展开更多
关键词 extending solid‐solution range off‐stoichiometric Na_(3)Fe_(2.5)(P_(2)O_(7))_(2) sodium‐ion batteries structure-function relationship
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Abundant invariant solutions of extended(3+1)-dimensional KP-Boussinesq equation
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作者 Hengchun Hu Jiali Kang 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第11期167-174,共8页
Lie group analysis method is applied to the extended(3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generator... Lie group analysis method is applied to the extended(3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generators.By selecting suitable arbitrary functions in the similarity reduction solutions,we obtain abundant invariant solutions,including the trigonometric solution,the kink-lump interaction solution,the interaction solution between lump wave and triangular periodic wave,the two-kink solution,the lump solution,the interaction between a lump and two-kink and the periodic lump solution in different planes.These exact solutions are also given graphically to show the detailed structures of this high dimensional integrable system. 展开更多
关键词 extended(3+1)-dimensional KP-Boussinesq equation Lie group method similarity reduction invariant solution
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Analytical Solutions for Testing of Baroclinic and Wind-Driven Three-Dimensional Hydrodynamic Models
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作者 Cheng He 《Journal of Applied Mathematics and Physics》 2024年第8期2866-2884,共19页
It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analyt... It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analytical solutions. In this paper, exact solutions for the periodic forcing by surface heat flux and wind stress are given by solving the linearized equations of motion neglecting the rotation, advection and horizontal diffusion terms. The temperature at the bottom is set to a prescribed periodic value and a slip condition on flow is enforced at the bottom. The geometry of the quarter annulus, which has been extensively studied for two- and three-dimensional analytical solutions of unstratified water bodies, is used with a general power law variation of the bottom slope in the radial direction and is constant in the azimuthal direction. The analytical solutions are derived in a cylindrical coordinate system, which describes the three-dimensional fluid field in a Cartesian coordinate system. The results presented in this paper should provide a foundation for studying and verifying the baroclinic term over a varied topography in a three-dimensional numerical model. 展开更多
关键词 3D Model Baroclinic Force Analytical solutions Model Verification
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美国ABBOTT AXSYM免疫发光分析仪Solution3和Solution4的研制开发及临床应用 被引量:3
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作者 张国元 唐中 +1 位作者 王兰兰 郭晓兰 《陕西医学检验》 CAS 2001年第4期62-64,共3页
目的 研制开发美国雅培 AXSYM免疫发光分析仪 Solution3、Soution4。方法 检测研制试剂理化指标、精密度、准确度、稳定性试验与原装试剂进行对比分析。结果 分别测定三种不同方法学 (MEIA法、FPIA法、ICIA法 )的 Free T3 等项目共 ... 目的 研制开发美国雅培 AXSYM免疫发光分析仪 Solution3、Soution4。方法 检测研制试剂理化指标、精密度、准确度、稳定性试验与原装试剂进行对比分析。结果 分别测定三种不同方法学 (MEIA法、FPIA法、ICIA法 )的 Free T3 等项目共 2 1项 ,所有项目的 x均接近 ,与原装试剂对比 ,P>0 .0 5 ,相关系数 r均 >0 .991 ;日内、日间重复性与原装试剂相比其 CV值非常接近。自制试剂放置 1 2 mo后 ,与原装试剂相比 ,P均 >0 .0 5 ,相关系数 r均 >0 .992。结论 自研试剂与进口试剂检测结果无显著差异 ,可以替代原装试剂。 展开更多
关键词 solution3 solution4 研制 应用 免疫发光分析
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自配AXSYM全自动免疫分析仪Solution 3、Solution 4试剂与原装试剂的比较分析
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作者 秦雪 李山 +4 位作者 刘志明 林发全 黄军强 黄敏承 覃锦耀 《广西医学》 CAS 2002年第1期7-9,共3页
目的 :为解决美国雅培AXSYM免疫分析仪Solution 3、Solution 4试剂国产化问题 ,采用自配试剂以代替原装试剂。方法 :将自配试剂的理化性质、精密度、准确度与原装试剂进行对比分析。结果 :自配试剂与原装试剂理化性质一致 ,采用MEIA法、... 目的 :为解决美国雅培AXSYM免疫分析仪Solution 3、Solution 4试剂国产化问题 ,采用自配试剂以代替原装试剂。方法 :将自配试剂的理化性质、精密度、准确度与原装试剂进行对比分析。结果 :自配试剂与原装试剂理化性质一致 ,采用MEIA法、FPIA法、ICAI法分别测定AFP、T4、Folate质控液 10次 ,其CV值均小于 5 % ,与原装试剂对比 ,两者无显著性差异 (P >0 0 5 )。结论 :自配美国雅培AXSYM免疫分析仪Solution 3、Solution 展开更多
关键词 solution3试剂 solution4试剂 指示剂 试剂 AXSYM免疫分析仪
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Effects of reaction parameters on preparation of Cu nanoparticles via aqueous solution reduction method with NaBH_4 被引量:1
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作者 刘清明 周德璧 +2 位作者 Yu-ya YAMAMOTO Kensuke KURUDA Masazumi OKIDO 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2012年第12期2991-2996,共6页
The preparation of Cu nanoparticles by the aqueous solution reduction method was investigated. The effects of different reaction parameters on the preparation of Cu nanoparticles were studied. The optimum conditions f... The preparation of Cu nanoparticles by the aqueous solution reduction method was investigated. The effects of different reaction parameters on the preparation of Cu nanoparticles were studied. The optimum conditions for preparing well-dispersed nanoparticles were found as follows: 0.4 mol/L NaBH4 was added into solution containing 0.2 mol/L Cu2+, 1.0% gelatin dispersant in mass fraction, and 1.2 mol/L NH3?H2O at pH 12 and 313 K. In addition, a series of experiments were performed to discover the reaction process. NH3?H2O was found to be able to modulate the reaction process. At pH=10, Cu2+ was transformed to Cu(NH3)42+ as precursor after the addition of NH3?H2O, and then Cu(NH3)42+ was reduced by NaBH4 solution. At pH=12, Cu2+ was transformed to Cu(OH)2 as precursor after the addition of NH3?H2O, and Cu(OH)2 was then reduced by NaBH4 solution. 展开更多
关键词 Cu nanoparticles NABH4 CU(OH)2 Cu(NH3)42+ aqueous solution reduction method PRECURSOR reaction process
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美国ABBOTT AXSYM免疫分析仪Solution3、Solution4研制与应用
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作者 莫和国 陈艳青 《陕西医学检验》 2000年第4期34-35,共2页
目的 :研制美国雅培 AXSYM免疫分析仪 Solution 3、Solution 4。方法 :检测研制试剂理化性质 ,精密度、准确度试验及与原装试剂进行对比分析。结果 :分别测定三种不同方法学 ( MEIA法、FPIA法、ICIA法 )的项目 h TSH、T4、Folate的质控... 目的 :研制美国雅培 AXSYM免疫分析仪 Solution 3、Solution 4。方法 :检测研制试剂理化性质 ,精密度、准确度试验及与原装试剂进行对比分析。结果 :分别测定三种不同方法学 ( MEIA法、FPIA法、ICIA法 )的项目 h TSH、T4、Folate的质控液 1 0次 ,其均值均在 1 s之内 ,CV分别为 4.58% ,1 .78% ,3.1 % ;与原装试剂对比 ,P>0 .0 5,无显著性差异。结论 :配制试剂达到实验室要求 。 展开更多
关键词 solution3 solution4 研制 免疫分析仪
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Multiple solutions and fermion mass effect in QED_3
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作者 周雨青 《Journal of Southeast University(English Edition)》 EI CAS 2013年第4期456-462,共7页
Due to the negligible non-perturbation effect in the low-energy region, quantum chromodynamics (QCD) is limited to be applied to hadron problems in particle physics. However, QED has mature non-perturbation models w... Due to the negligible non-perturbation effect in the low-energy region, quantum chromodynamics (QCD) is limited to be applied to hadron problems in particle physics. However, QED has mature non-perturbation models which can be applied to Fermi acting-energy between quark and gluon. This paper applies quantum electrodynamics in 2 + 1 dimensions (QED3) to the Fermi condensation problems. First, the Dyson-Schwinger equation which the fermions satisfy is constructed, and then the Fermi energy gap is solved. Theoretical calculations show that within the chirality limit, there exist three solutions for the energy gap; beyond the chirality limit, there are two solutions; all these solutions correspond to different fermion condensates. It can be concluded that the fermion condensates within the chirality limit can be used to analyze the existence of antiferromagnetic, pseudogap, and superconducting phases, and two fermion condensates are discovered beyond the chirality limit. 展开更多
关键词 Dyson-Schwinger equation chiral limit beyond chiral limit FERMION CONDENSATE multiple solutions quantum electrodvnamics in 2 1 dimensions (OED3)
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乙酰丙酮铱Ir(acac)_(3)电子结构及光学性质的理论研究
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作者 樊依佳 蔚娇娇 +2 位作者 郭家成 陈扬尹 杜恭贺 《原子与分子物理学报》 CAS 北大核心 2025年第1期1-7,共7页
乙酰丙酮铱是一种由过渡金属Ir与乙酰丙酮酸(acetylcaetonato)有机部分组成的过渡金属有机配合物,它是一种重要的绿光磷光材料,同时其也是多种铱系发光材料的组成部分.采用密度泛函理论(DFT)对Ir(acac)_(3)单体及其二聚物的基态几何结... 乙酰丙酮铱是一种由过渡金属Ir与乙酰丙酮酸(acetylcaetonato)有机部分组成的过渡金属有机配合物,它是一种重要的绿光磷光材料,同时其也是多种铱系发光材料的组成部分.采用密度泛函理论(DFT)对Ir(acac)_(3)单体及其二聚物的基态几何结构进行了优化,在此基础上考察了它们的振动和红外光谱,并使用CIS方法对它们的激发态性质进行了理论研究.计算得到的单体和二聚物的吸收光谱均在紫外波段,单体的主要吸收峰有260 nm,350 nm,414 nm,二聚物的主要吸收峰有299 nm,353 nm,401 nm.计算得到了二者在乙腈CH_(3)CN溶液中的吸收光谱,与它们气相情况的结果相比,溶剂极性的影响使得电子吸收谱发生蓝移.计算结果表明Horst Kunkely和Arnd Vogler所得光谱中既含有单体的特征光谱,又含有二聚体的特征光谱,证明实验溶液中同时存在乙酰丙酮铱的低聚物,并且二者的组分比能被合理推算.最后,对多聚体的形成机理作了简单讨论. 展开更多
关键词 Ir(acac)_(3) 密度泛函理论(DFT) CIS 电子吸收光谱 溶液效应
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Solution combustion synthesis of Ni-Y_2O_3 nanocomposite powder
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作者 刘烨 秦明礼 +4 位作者 章林 贾宝瑞 曹知勤 张德智 曲选辉 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2015年第1期129-136,共8页
Ni-Y2O3 nanocomposite powder with uniform distribution of fine oxide particles in the metal matrix was successfully fabricated via solution combustion process followed by hydrogen reduction. The combustion behavior wa... Ni-Y2O3 nanocomposite powder with uniform distribution of fine oxide particles in the metal matrix was successfully fabricated via solution combustion process followed by hydrogen reduction. The combustion behavior was investigated by DTA-TG analysis. The influence of urea to nickel nitrate(U/Ni) ratio on the combustion behavior and morphology evolution of the combusted powder was investigated. The morphological characteristics and phase transformation of the combusted powder and the reduced powder were characterized by FESEM, TEM and XRD. The HRTEM image of Ni-Y2O3 nanocomposite powder indicated that Y2O3 particles with average particle size of about 10 nm dispersed uniformly in the nickel matrix. 展开更多
关键词 NANOCOMPOSITES NANOPARTICLES solution combustion synthesis oxide dispersion strengthening NI Y2O3
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Mixed rare earth concentrate leaching with HCl-AlCl_3 solution 被引量:10
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作者 Mei Li Xiao-Wei Zhang +3 位作者 Zhao-Gang Liu Mi-Tang Wang Jia Liu Jian-Ping Yang 《Rare Metals》 SCIE EI CAS CSCD 2013年第3期312-317,共6页
Abstract A method of Baotou mixed rare earth concen- trate leaching was investigated. According to the principle of complex leaching, the quadratic orthogonal regression experiment was used to investigate effect of si... Abstract A method of Baotou mixed rare earth concen- trate leaching was investigated. According to the principle of complex leaching, the quadratic orthogonal regression experiment was used to investigate effect of six factors. An optimal condition of low energy and environment friendly was determined as follows: HCl acidity is 4 mol.L-1, AlCl3 concentration is 2 mol.L-l, reaction temperature is 85 ℃, reaction time is 90 rain, liquid to solid ratio is 35 ml.g-1, and stirring speed is 100 r.min-1. According to this condition, the leaching ratio of mixed rare earth con- centrate is 76.5 %. The analyses of X-ray diffraction shows that bastnasite disappears, and the main peaks of filter residue is monazite and cheralite after leaching of HCl- AlCl3 solution. The result indicates that REFCO3 of the mixed rare earth concentrate can be dissolved, but REPO4 remains in the leaching residue. This method provides a way to separate and extract rare earth. 展开更多
关键词 HCl-AlCl3 solution Mixed rare earthconcentrate LEACHING
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Temporal Floorplanning Using Solution Space Smoothing Based on 3D-BSSG Structure
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作者 郑舒一 董社勤 洪先龙 《Journal of Semiconductors》 EI CAS CSCD 北大核心 2005年第10期1916-1924,共9页
We develop a 3D bounded slice-surface grid (3D-BSSG) structure for representation and introduce the solution space smoothing technique to search for the optimal solution. Experiment results demonstrate that a 3D-BSS... We develop a 3D bounded slice-surface grid (3D-BSSG) structure for representation and introduce the solution space smoothing technique to search for the optimal solution. Experiment results demonstrate that a 3D-BSSG structure based algorithm is very effective and efficient. 展开更多
关键词 temporal floorplanning~ FPGA 3D-BSSG solution space smoothing
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Grammian Determinant Solution and Pfaffianization for a (3+1)-Dimensional Soliton Equation 被引量:5
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作者 WU Jian-Ping GENG Xian-Guo2 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第11期791-794,共4页
Based on the Pfaffian derivative formulae,a Grammian determinant solution for a(3+1)-dimensionalsoliton equation is obtained.Moreover,the Pfaffianization procedure is applied for the equation to generate a newcoupled ... Based on the Pfaffian derivative formulae,a Grammian determinant solution for a(3+1)-dimensionalsoliton equation is obtained.Moreover,the Pfaffianization procedure is applied for the equation to generate a newcoupled system.At last,a Gram-type Pfaffian solution to the new coupled system is given. 展开更多
关键词 (3+1)-dimensional soliton equation Grammian determinant solution PFAFFIANIZATION Gram-type Pfaffian solution
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A more general form of lump solution,lumpoff,and instanton/rogue wave solutions of a reduced (3+1)-dimensional nonlinear evolution equation 被引量:2
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作者 Panfeng Zheng Man Jia 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第12期147-156,共10页
In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution ... In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution. 展开更多
关键词 a reduced(3 + 1)-dimensional nonlinear evolution equation more general form of lump solution soliton induced by lump lumpoff and instanton/rogue wave solutions
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Removal of hexavalent chromium in aquatic solutions by pomelo peel 被引量:7
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作者 Qiong Wang Cong Zhou +2 位作者 Yin-jie Kuang Zhao-hui Jiang Min Yang 《Water Science and Engineering》 EI CAS CSCD 2020年第1期65-73,共9页
This study investigated the removal of hexavalent chromium(Cr(VI)) in aqueous solutions using pomelo peel(PP) and FeCl3-modified pomelo peel(FPP) as novel biomass adsorbents.Batch adsorption experiments were performed... This study investigated the removal of hexavalent chromium(Cr(VI)) in aqueous solutions using pomelo peel(PP) and FeCl3-modified pomelo peel(FPP) as novel biomass adsorbents.Batch adsorption experiments were performed to evaluate the effects of pH,time,temperature,initial concentration,and adsorbent dose on Cr(VI) removal by PP and FPP.The results show that the maximum adsorption capacity of Cr(VI)was 21.55 mg/g for FPP and 0.57 mg/g for PP at a pH of 2.0 and a temperature of 40℃.The surface shape,microstructure,and chemical composition of FPP were analyzed with scanning electron microscopy(SEM),Fourier transform infrared spectroscopy(FTIR),and energy dispersive spectroscopy(EDS),and compared with those of PP.The results show that the adsorption performance of FPP was much better than that of PP,indicating that FPP can be an alternative high-efficiency adsorbent for Cr(VI) removal. 展开更多
关键词 Adsorption Hexavalent chromium REMOVAL Biomass ADSORBENT POMELO PEEL FeCl3-modified POMELO PEEL AQUATIC solution
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All Single Traveling Wave Solutions to (3+1)-Dimensional Nizhnok-Novikov-Veselov Equation 被引量:12
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作者 LIU Cheng-Shi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第6期991-992,共2页
Using elementary integral method, a complete classification of all possible exact traveling wave solutions to (3+1)-dimensional Nizhnok-Novikov-Veselov equation is given. Some solutions are new.
关键词 (3+1)-dimensional Nizhnok-Novikov-Veselov equation traveling wave solution elementary integral method
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New Exact Solutions and Conservation Laws to (3+1)-Dimensional Potential-YTSF Equation 被引量:10
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作者 ZHANG Li-Hua LIU Xi-Qiang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第3期487-492,共6页
Using the modified find some new exact solutions to Lie point symmetry groups and also get conservation laws, of the CK's direct method, we build the relationship between new solutions and old ones and the (3+1)-d... Using the modified find some new exact solutions to Lie point symmetry groups and also get conservation laws, of the CK's direct method, we build the relationship between new solutions and old ones and the (3+1)-dimensional potentiaial-YTSF equation. Baaed on the invariant group theory, Lie symmetries of the (3+1)-dimensional potential-YTSF equation are obtained. We equation with the given Lie symmetry. 展开更多
关键词 new exact solutions Lie point symmetry groups conservation laws (3+1)-dimensional potential-YTSF equation
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Lump-type solutions of a generalized Kadomtsev–Petviashvili equation in(3+1)-dimensions 被引量:1
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作者 Xue-Ping Cheng Wen-Xiu Ma Yun-Qing Yang 《Chinese Physics B》 SCIE EI CAS CSCD 2019年第10期245-252,共8页
Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized(3+1)-dimensional Kadomtsev-Petviashvili(KP) equation in three cases of the coeffi... Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized(3+1)-dimensional Kadomtsev-Petviashvili(KP) equation in three cases of the coefficients in the equation. Then the sufficient and necessary conditions to guarantee the analyticity of the resulting lump-type solutions(or the positivity of the corresponding quadratic solutions to the associated bilinear equation) are discussed. To illustrate the generality of the obtained solutions, two concrete lump-type solutions are explicitly presented, and to analyze the dynamic behaviors of the solutions specifically, the three-dimensional plots and contour profiles of these two lump-type solutions with particular choices of the involved free parameters are well displayed. 展开更多
关键词 lump-type solution generalized(3+1)-dimensional Kadomtsev-Petviashvili equation HIROTA bilinear form symbolic computation
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One-Step Synthesis of Nanocrytalline Perovskite LaMnO_3 Powders via Microwave-Induced Solution Combustion Route 被引量:3
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作者 陈伟凡 李凤生 +1 位作者 刘磊力 刘洋 《Journal of Rare Earths》 SCIE EI CAS CSCD 2006年第6期782-787,共6页
Perovskite LaMnO3 powders with an average crystallite size of 12.5 nm were rapidly synthesized via a microwave-induced autocombustion reaction using glycine as a fuel and nitrate as an oxidant. After self-propagating ... Perovskite LaMnO3 powders with an average crystallite size of 12.5 nm were rapidly synthesized via a microwave-induced autocombustion reaction using glycine as a fuel and nitrate as an oxidant. After self-propagating combustion, the desired nanocrystalline perovskite LaMnO3 was obtained and no further calcination was carried out. The possible processes of combustion reaction were discussed according to the principle of propellant chemistry. The autocombustion and thermal decomposition of the precursor were investigated using the TG-DTA and FT-IR techniques. The influences of glycine-nitrate molar ratio and heat-treatment temperature on the perovskite phase formation and crystallite size of as-burnt powder were studied by XRD. The morphology and size of the as-burnt powder before and after milling were characterized and compared by TEM. 展开更多
关键词 microwave-induced solution combustion synthesis LaMnO3 perovskite NANOCRYSTALLINE rare earths
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Symmetry analysis and explicit solutions of the (3+1)-dimensional baroclinic potential vorticity equation 被引量:1
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作者 胡晓瑞 陈勇 黄菲 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第8期35-45,共11页
This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-(3+1)- dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method. Its symmet... This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-(3+1)- dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method. Its symmetry algebra, symmetry group and group-invariant solutions are analysed. Otherwise, some exact explicit solutions are obtained from the corresponding (2+1)-dimensional equation, the inviscid barotropic nondivergent vorticy equation. To show the properties and characters of these solutions, some plots as well as their possible physical meanings of the atmospheric circulation are given out. 展开更多
关键词 (3+1)-dimensional nonlinear baroclinic potential vorticity equation symmetry group group-invariant solution explicit solution
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