This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional ...This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.展开更多
In this paper,we are concerned with solutions to the fractional Schrodinger-Poisson system■ with prescribed mass ∫_(R^(3))|u|^(2)dx=a^(2),where a> 0 is a prescribed number,μ> 0 is a paremeter,s ∈(0,1),2 <...In this paper,we are concerned with solutions to the fractional Schrodinger-Poisson system■ with prescribed mass ∫_(R^(3))|u|^(2)dx=a^(2),where a> 0 is a prescribed number,μ> 0 is a paremeter,s ∈(0,1),2 <q <2_(s)^(*),and 2_(s)^(*)=6/(3-2s) is the fractional critical Sobolev exponent.In the L2-subcritical case,we show the existence of multiple normalized solutions by using the genus theory and the truncation technique;in the L^(2)-supercritical case,we obtain a couple of normalized solutions by developing a fiber map.Under both cases,to recover the loss of compactness of the energy functional caused by the doubly critical growth,we need to adopt the concentration-compactness principle.Our results complement and improve upon some existing studies on the fractional Schrodinger-Poisson system with a nonlocal critical term.展开更多
This paper presents a study on CO<sub>2</sub> atmospheric transformation which was reacted directly with lithium hydroxide solution and metallic lithium. This solution was obtained through the reaction bet...This paper presents a study on CO<sub>2</sub> atmospheric transformation which was reacted directly with lithium hydroxide solution and metallic lithium. This solution was obtained through the reaction between metallic lithium and deionized water where hydrogen is produced and by exposing the metal at ambient conditions. In the transformation process, atmospheric CO<sub>2</sub> gas reacts directly with LiOH solution, in both cases, the CO<sub>2</sub> transformation kinetics was different. For this purpose, reactions between CO<sub>2</sub> and LiOH solution were carried out under controlled temperature and the second process only with metallic lithium, which was exposed at room temperature, however, in these two processes lithium carbonate oxide was formed and identified. According to the results, the efficiency in CO<sub>2</sub> transformation is a function of temperature value which was variable until completely obtaining the by-product, its XRD characterization indicated the formation only of Li<sub>2</sub>CO<sub>3</sub> in both procedures. Under laboratory conditions lithium compounds selectively reacted with CO<sub>2</sub>. In the same way, there is an alternative procedure to obtain LiOH and Li<sub>2</sub>CO<sub>3</sub> for different applications in various areas.展开更多
This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé...This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé analysis.On the basis of the bilinear form,the forms of two-soliton solutions,three-soliton solutions,and four-soliton solutions are studied specifically.The appropriate parameter values are chosen and the corresponding figures are presented.The breather waves solutions,lump solutions,periodic solutions and the interaction of breather waves solutions and soliton solutions,etc.are given.In addition,we also analyze the different effects of the parameters on the figures.The figures of the same set of parameters in different planes are presented to describe the dynamical behavior of solutions.These are important for describing water waves in nature.展开更多
In this study, we will introduce the modified (G'/G<sup>2</sup>)-expansion method to explore some of the exact traveling wave solutions of some nonlinear partial differential equations namely, Phi-4 eq...In this study, we will introduce the modified (G'/G<sup>2</sup>)-expansion method to explore some of the exact traveling wave solutions of some nonlinear partial differential equations namely, Phi-4 equation, Joseph-Egri (TRLW) equation, and Calogro-Degasperis (CD) equation. As a result, we have obtained solutions for the equations expressed in terms of trigonometric, hyperbolic and rational functions. Moreover, some selected solutions are plotted using some specific values for the parameters.展开更多
目的探讨H3.3G34W、p63及SATB2在骨巨细胞瘤(giant cell tumor of bone,GCTB)中的表达情况及其联合应用对GCTB的诊断作用和价值。方法收集西安交通大学附属红会医院病理科2020年至2022年诊断的54例GCTB、83例非骨巨细胞瘤(non-giant cel...目的探讨H3.3G34W、p63及SATB2在骨巨细胞瘤(giant cell tumor of bone,GCTB)中的表达情况及其联合应用对GCTB的诊断作用和价值。方法收集西安交通大学附属红会医院病理科2020年至2022年诊断的54例GCTB、83例非骨巨细胞瘤(non-giant cell tumor of bone,NGCTB)(包含14例动脉瘤样骨囊肿、16例软骨母细胞瘤和53例非骨化性纤维瘤)患者的样本和病历资料,采用免疫组织化学EliVision法检测H3.3G34W、p63及SATB2的表达情况。通过χ^(2)检验判断H3.3G34W、p63及SATB2的阳性率在各组间是否存在统计学差异;通过Logistic回归分析建立包括H3.3G34W、p63及SATB2的联合诊断模型,通过受试者工作特征(ROC)曲线分析评价模型的诊断价值。结果H3.3G34W、p63及SATB2在GCTB组中阳性率分别为81.5%、90.7%、92.6%;在NGCTB组中阳性率分别为2.4%、28.9%、62.7%。与NGCTB组相比,GCTB组患者年龄显著较大[(41.222±14.849)vs.(16.566±9.439);P<0.001],女性比男性患病率更高(51.9%vs.48.1%,P<0.001)。与NGCTB组相比,GCTB组中H3.3G34W(81.5%vs.2.4%,P<0.001);p63(90.7%vs.28.9%,P<0.001)和SATB2(92.6%vs.62.7%,P<0.001)的阳性率更高。单因素Logistic回归分析构建单因素预测模型,同时行ROC曲线分析,表明年龄(AUC=92.9%,P<0.001)、性别(AUC=64.5%,P=0.004)、H3.3G34W阳性率(AUC=89.5%,P<0.001)、p63阳性率(AUC=80.9%,P<0.001)、SATB2阳性率(AUC=65.0%,P=0.003)是GCTB诊断的独立预测因素。进一步的多因素Logistic回归分析构建混合预测模型,并行ROC曲线分析,发现混合模型展现出比单因素模型更好的预测价值(AUC=98.4%,P<0.001)。结论H3.3G34W、p63及SATB2是有效诊断GCTB的分子标记物,且三者联合应用更能提高GCTB的诊断预测效能。展开更多
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
Recently, a new （2＋1）-dimensional shallow water wave system, the （2＋1）-dlmenslonal displacement shallow water wave system （2DDSWWS）, was constructed by applying the variational principle of the analytic mechan...Recently, a new （2＋1）-dimensional shallow water wave system, the （2＋1）-dlmenslonal displacement shallow water wave system （2DDSWWS）, was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS, which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis, we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS （M2DDSWWS） is studied and four similarity solutions are obtained. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the M2DDSWWS will degenerate to the 2DDSWWS.展开更多
Based on the travelling wave method, a(2 + 1)-dimensional AKNS equation is considered. Elliptic solution and soliton solution are presented and it is shown that the soliton solution can be reduced from the elliptic so...Based on the travelling wave method, a(2 + 1)-dimensional AKNS equation is considered. Elliptic solution and soliton solution are presented and it is shown that the soliton solution can be reduced from the elliptic solution. It also proves that the result is consistent with the soliton solution of simplify Hirota bilinear method by Wazwaz and illustrate the solution are right travelling wave solution.展开更多
Based on the B/icklund method and the multilinear variable separation approach （MLVSA）, this paper finds a general solution including two arbitrary functions for the （2＋1）-dimensional Burgers equations. Then a cl...Based on the B/icklund method and the multilinear variable separation approach （MLVSA）, this paper finds a general solution including two arbitrary functions for the （2＋1）-dimensional Burgers equations. Then a class of new doubly periodic wave solutions for （2＋l）-dimensional Burgers equations is obtained by introducing appropriate Jacobi elliptic functions, Weierstrass elliptic functions and their combination in the general solutions （which contains two arbitrary functions）. Two types of limit cases are considered. Firstly, taking one of the moduli to be unity and the other zero, it obtains particular wave （called semi-localized） patterns, which is periodic in one direction, but localized in the other direction. Secondly, if both moduli are tending to 1 as a limit, it derives some novel localized excitations （two-dromion solution）.展开更多
In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for （2＋1）-dimensional dispersive long wave equations in mathematical physics, which are...In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for （2＋1）-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions （m → 1）. This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12275172 and 11905124)。
文摘This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.
基金supported by the BIT Research and Innovation Promoting Project(2023YCXY046)the NSFC(11771468,11971027,11971061,12171497 and 12271028)+1 种基金the BNSF(1222017)the Fundamental Research Funds for the Central Universities。
文摘In this paper,we are concerned with solutions to the fractional Schrodinger-Poisson system■ with prescribed mass ∫_(R^(3))|u|^(2)dx=a^(2),where a> 0 is a prescribed number,μ> 0 is a paremeter,s ∈(0,1),2 <q <2_(s)^(*),and 2_(s)^(*)=6/(3-2s) is the fractional critical Sobolev exponent.In the L2-subcritical case,we show the existence of multiple normalized solutions by using the genus theory and the truncation technique;in the L^(2)-supercritical case,we obtain a couple of normalized solutions by developing a fiber map.Under both cases,to recover the loss of compactness of the energy functional caused by the doubly critical growth,we need to adopt the concentration-compactness principle.Our results complement and improve upon some existing studies on the fractional Schrodinger-Poisson system with a nonlocal critical term.
文摘This paper presents a study on CO<sub>2</sub> atmospheric transformation which was reacted directly with lithium hydroxide solution and metallic lithium. This solution was obtained through the reaction between metallic lithium and deionized water where hydrogen is produced and by exposing the metal at ambient conditions. In the transformation process, atmospheric CO<sub>2</sub> gas reacts directly with LiOH solution, in both cases, the CO<sub>2</sub> transformation kinetics was different. For this purpose, reactions between CO<sub>2</sub> and LiOH solution were carried out under controlled temperature and the second process only with metallic lithium, which was exposed at room temperature, however, in these two processes lithium carbonate oxide was formed and identified. According to the results, the efficiency in CO<sub>2</sub> transformation is a function of temperature value which was variable until completely obtaining the by-product, its XRD characterization indicated the formation only of Li<sub>2</sub>CO<sub>3</sub> in both procedures. Under laboratory conditions lithium compounds selectively reacted with CO<sub>2</sub>. In the same way, there is an alternative procedure to obtain LiOH and Li<sub>2</sub>CO<sub>3</sub> for different applications in various areas.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11505090)Research Award Foundation for Outstanding Young Scientists of Shandong Province(Grant No.BS2015SF009)+2 种基金the Doctoral Foundation of Liaocheng University(Grant No.318051413)Liaocheng University Level Science and Technology Research Fund(Grant No.318012018)Discipline with Strong Characteristics of Liaocheng University–Intelligent Science and Technology(Grant No.319462208).
文摘This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé analysis.On the basis of the bilinear form,the forms of two-soliton solutions,three-soliton solutions,and four-soliton solutions are studied specifically.The appropriate parameter values are chosen and the corresponding figures are presented.The breather waves solutions,lump solutions,periodic solutions and the interaction of breather waves solutions and soliton solutions,etc.are given.In addition,we also analyze the different effects of the parameters on the figures.The figures of the same set of parameters in different planes are presented to describe the dynamical behavior of solutions.These are important for describing water waves in nature.
文摘In this study, we will introduce the modified (G'/G<sup>2</sup>)-expansion method to explore some of the exact traveling wave solutions of some nonlinear partial differential equations namely, Phi-4 equation, Joseph-Egri (TRLW) equation, and Calogro-Degasperis (CD) equation. As a result, we have obtained solutions for the equations expressed in terms of trigonometric, hyperbolic and rational functions. Moreover, some selected solutions are plotted using some specific values for the parameters.
文摘目的探讨H3.3G34W、p63及SATB2在骨巨细胞瘤(giant cell tumor of bone,GCTB)中的表达情况及其联合应用对GCTB的诊断作用和价值。方法收集西安交通大学附属红会医院病理科2020年至2022年诊断的54例GCTB、83例非骨巨细胞瘤(non-giant cell tumor of bone,NGCTB)(包含14例动脉瘤样骨囊肿、16例软骨母细胞瘤和53例非骨化性纤维瘤)患者的样本和病历资料,采用免疫组织化学EliVision法检测H3.3G34W、p63及SATB2的表达情况。通过χ^(2)检验判断H3.3G34W、p63及SATB2的阳性率在各组间是否存在统计学差异;通过Logistic回归分析建立包括H3.3G34W、p63及SATB2的联合诊断模型,通过受试者工作特征(ROC)曲线分析评价模型的诊断价值。结果H3.3G34W、p63及SATB2在GCTB组中阳性率分别为81.5%、90.7%、92.6%;在NGCTB组中阳性率分别为2.4%、28.9%、62.7%。与NGCTB组相比,GCTB组患者年龄显著较大[(41.222±14.849)vs.(16.566±9.439);P<0.001],女性比男性患病率更高(51.9%vs.48.1%,P<0.001)。与NGCTB组相比,GCTB组中H3.3G34W(81.5%vs.2.4%,P<0.001);p63(90.7%vs.28.9%,P<0.001)和SATB2(92.6%vs.62.7%,P<0.001)的阳性率更高。单因素Logistic回归分析构建单因素预测模型,同时行ROC曲线分析,表明年龄(AUC=92.9%,P<0.001)、性别(AUC=64.5%,P=0.004)、H3.3G34W阳性率(AUC=89.5%,P<0.001)、p63阳性率(AUC=80.9%,P<0.001)、SATB2阳性率(AUC=65.0%,P=0.003)是GCTB诊断的独立预测因素。进一步的多因素Logistic回归分析构建混合预测模型,并行ROC曲线分析,发现混合模型展现出比单因素模型更好的预测价值(AUC=98.4%,P<0.001)。结论H3.3G34W、p63及SATB2是有效诊断GCTB的分子标记物,且三者联合应用更能提高GCTB的诊断预测效能。
基金National Natural Science Foundation of China,Grant/Award Numbers:21972108,U20A20249,U22A20438Changzhou Science and Technology Bureau,Grant/Award Number:CM20223017Innovation and Technology Commission(ITC)of Hong Kong,The Innovation&Technology Fund(ITF)with Project No.ITS/126/21。
文摘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.
基金Project supported by the Natural Science Foundation of Guangdong Province of China (Grant No.10452840301004616)the National Natural Science Foundation of China (Grant No.61001018)the Scientific Research Foundation for the Doctors of University of Electronic Science and Technology of China Zhongshan Institute (Grant No.408YKQ09)
文摘Recently, a new （2＋1）-dimensional shallow water wave system, the （2＋1）-dlmenslonal displacement shallow water wave system （2DDSWWS）, was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS, which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis, we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS （M2DDSWWS） is studied and four similarity solutions are obtained. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the M2DDSWWS will degenerate to the 2DDSWWS.
文摘Based on the travelling wave method, a(2 + 1)-dimensional AKNS equation is considered. Elliptic solution and soliton solution are presented and it is shown that the soliton solution can be reduced from the elliptic solution. It also proves that the result is consistent with the soliton solution of simplify Hirota bilinear method by Wazwaz and illustrate the solution are right travelling wave solution.
基金Project supported by the National Natural Science Foundation of China (Grant No 10647112)the Foundation of Donghua University
文摘Based on the B/icklund method and the multilinear variable separation approach （MLVSA）, this paper finds a general solution including two arbitrary functions for the （2＋1）-dimensional Burgers equations. Then a class of new doubly periodic wave solutions for （2＋l）-dimensional Burgers equations is obtained by introducing appropriate Jacobi elliptic functions, Weierstrass elliptic functions and their combination in the general solutions （which contains two arbitrary functions）. Two types of limit cases are considered. Firstly, taking one of the moduli to be unity and the other zero, it obtains particular wave （called semi-localized） patterns, which is periodic in one direction, but localized in the other direction. Secondly, if both moduli are tending to 1 as a limit, it derives some novel localized excitations （two-dromion solution）.
基金Project supported by the Anhui Key Laboratory of Information Materials and Devices (Anhui University),China
文摘In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for （2＋1）-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions （m → 1）. This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations.
