In this article,by employing the Hirota bilinear approach and the long wave limit method,we not only derive soliton solutions,lump solutions,and hybrid solutions for the(2+1)-dimensional Yu-Toda-Sasa-Fukuyama(YTSF)equ...In this article,by employing the Hirota bilinear approach and the long wave limit method,we not only derive soliton solutions,lump solutions,and hybrid solutions for the(2+1)-dimensional Yu-Toda-Sasa-Fukuyama(YTSF)equation,but also analyze the dynamical behaviors of nonlinear local wave propagation in shallow water.Firstly,based on the Hirota bilinear approach,one to four-order soliton solutions of the YTSF equation are obtained,and the effects of different parameters on the amplitude,propagation trajectory,and displacement of solitons are investigated.Secondly,using the long wave limit approach,one to three-order lump solutions and various physical quantities of the YTSF equation are derived.It is found that the real and imaginary parts of the parameter pi dominate the propagation trajectory and the shape of lump waves,respectively.Furthermore,we construct the hybrid solution for the YTSF equation,leading to the conclusion that the interaction between lumps and solitons constitutes an elastic collision.To intuitively understand the dynamic behaviors of these solutions,we conduct numerical simulations to present vivid three-dimensional visualizations.展开更多
Let H3 be the 9-dimensional Taft Hopf algebra,let r(H3)be the corresponding Green ring of H3,and let Aut(R(H3))be the automorphism group of Green algebra R(H3)=R■Zr(H3)over the real number fieldR.We prove that the qu...Let H3 be the 9-dimensional Taft Hopf algebra,let r(H3)be the corresponding Green ring of H3,and let Aut(R(H3))be the automorphism group of Green algebra R(H3)=R■Zr(H3)over the real number fieldR.We prove that the quotient group Aut(R(H3))/T1 is isomorphic to the direct product of the dihedral group of order 12 and the cyclic group of order 2,where T1 is the isomorphism class which contains the identity map and is isomorphic to a group G={(c,d)∈R^(2)∣∣(c,d)≠(−1/3,−1/6)}with multiplication given by(c1,d1)⋅(c2,d2)=(c1+c2+2c1c2−4d1d2+2c1d2+2d1c2,d1+d2−2c1c2−2d1d2+4c1d2+4d1c2).展开更多
目的通过研究缺氧缺血性脑病(HIE)新生儿血清神经纤维轻链(NF-L)、水通道蛋白9(AQP9)、纤维蛋白原样蛋白2(FGL2)水平的变化,分析三者与新生儿行为神经评估(NABA)评分的相关性。方法选取2022年1月~2024年7月山西省儿童医院收治的203例HI...目的通过研究缺氧缺血性脑病(HIE)新生儿血清神经纤维轻链(NF-L)、水通道蛋白9(AQP9)、纤维蛋白原样蛋白2(FGL2)水平的变化,分析三者与新生儿行为神经评估(NABA)评分的相关性。方法选取2022年1月~2024年7月山西省儿童医院收治的203例HIE患儿为研究组,根据病情程度分为轻度组(n=63)、中度组(n=81)和重度组(n=59),另选同期的健康新生儿203例为对照组,酶联免疫吸附试验(ELISA)检测血清NF-L、AQP9、FGL2水平,收集分析一般临床资料。受试者操作特征(ROC)曲线分析NF-L、AQP9、FGL2及NABA评分对新生儿重度HIE的诊断价值;Pearson法分析血清NF-L、AQP9、FGL2与NABA评分的相关性。结果与对照组相比,研究组血清NF-L(14.78±1.67ng/ml vs 10.65±1.21ng/ml)、AQP9(61.82±6.29pg/ml vs 42.62±4.31pg/ml)、FGL2(189.69±20.26ng/ml vs 132.51±14.84ng/ml)水平显著升高,差异具有统计学意义(t=28.533、35.877、32.440,均P<0.05);中度组、重度组血清NF-L(14.68±1.67ng/ml、18.62±2.03ng/ml),AQP9(63.51±6.44pg/ml、69.63±7.03pg/ml),FGL2(195.68±20.84ng/ml、210.65±22.36ng/ml)水平显著高于轻度组(11.32±1.33ng/ml、52.32±5.41pg/ml、162.35±17.55ng/ml),NABA(34.89±3.51分、29.88±3.43分)评分显著低于轻度组(36.54±1.52分),差异具有统计学意义(t_(中度组)=4.616~16.729,t_(重度组)=17.276~33.701,均P<0.05);NF-L、AQP9、FGL2与NABA评分均呈负相关(r=-0.432、-0.421、-0.402,均P<0.05);NF-L、AQP9、FGL2、NABA联合诊断患儿重度病情的曲线下面积(AUC)显著高于各项单独诊断,差异具有统计学意义(Z=2.066~3.307,均P<0.05)。结论HIE患儿血清NF-L、AQP9、FGL2水平显著升高,与NABA评分相关,可能成为评估HIE患儿病情的标志物。展开更多
基金Supported by the National Natural Science Foundation of China(12001424,12271324)the Natural Science Basic research program of Shaanxi Province(2021JZ-21)+1 种基金the China Postdoctoral Science Foundation(2020M673332)Xi’an University,Xi’an Science and Technology Plan Wutongshu Technology Transfer Action Innovation Team(25WTZD07)。
文摘In this article,by employing the Hirota bilinear approach and the long wave limit method,we not only derive soliton solutions,lump solutions,and hybrid solutions for the(2+1)-dimensional Yu-Toda-Sasa-Fukuyama(YTSF)equation,but also analyze the dynamical behaviors of nonlinear local wave propagation in shallow water.Firstly,based on the Hirota bilinear approach,one to four-order soliton solutions of the YTSF equation are obtained,and the effects of different parameters on the amplitude,propagation trajectory,and displacement of solitons are investigated.Secondly,using the long wave limit approach,one to three-order lump solutions and various physical quantities of the YTSF equation are derived.It is found that the real and imaginary parts of the parameter pi dominate the propagation trajectory and the shape of lump waves,respectively.Furthermore,we construct the hybrid solution for the YTSF equation,leading to the conclusion that the interaction between lumps and solitons constitutes an elastic collision.To intuitively understand the dynamic behaviors of these solutions,we conduct numerical simulations to present vivid three-dimensional visualizations.
基金Supported by the National Natural Science Foundation of China(Nos.11661014,11701499,11871063,and 11711530703)the Research Innovation Program Project of Academic Degree Graduate Students in Jiangsu(XKYCX17_029)the Excellent Doctoral Dissertation Foundation Project of Yangzhou University in 2018.
文摘Let H3 be the 9-dimensional Taft Hopf algebra,let r(H3)be the corresponding Green ring of H3,and let Aut(R(H3))be the automorphism group of Green algebra R(H3)=R■Zr(H3)over the real number fieldR.We prove that the quotient group Aut(R(H3))/T1 is isomorphic to the direct product of the dihedral group of order 12 and the cyclic group of order 2,where T1 is the isomorphism class which contains the identity map and is isomorphic to a group G={(c,d)∈R^(2)∣∣(c,d)≠(−1/3,−1/6)}with multiplication given by(c1,d1)⋅(c2,d2)=(c1+c2+2c1c2−4d1d2+2c1d2+2d1c2,d1+d2−2c1c2−2d1d2+4c1d2+4d1c2).
文摘目的通过研究缺氧缺血性脑病(HIE)新生儿血清神经纤维轻链(NF-L)、水通道蛋白9(AQP9)、纤维蛋白原样蛋白2(FGL2)水平的变化,分析三者与新生儿行为神经评估(NABA)评分的相关性。方法选取2022年1月~2024年7月山西省儿童医院收治的203例HIE患儿为研究组,根据病情程度分为轻度组(n=63)、中度组(n=81)和重度组(n=59),另选同期的健康新生儿203例为对照组,酶联免疫吸附试验(ELISA)检测血清NF-L、AQP9、FGL2水平,收集分析一般临床资料。受试者操作特征(ROC)曲线分析NF-L、AQP9、FGL2及NABA评分对新生儿重度HIE的诊断价值;Pearson法分析血清NF-L、AQP9、FGL2与NABA评分的相关性。结果与对照组相比,研究组血清NF-L(14.78±1.67ng/ml vs 10.65±1.21ng/ml)、AQP9(61.82±6.29pg/ml vs 42.62±4.31pg/ml)、FGL2(189.69±20.26ng/ml vs 132.51±14.84ng/ml)水平显著升高,差异具有统计学意义(t=28.533、35.877、32.440,均P<0.05);中度组、重度组血清NF-L(14.68±1.67ng/ml、18.62±2.03ng/ml),AQP9(63.51±6.44pg/ml、69.63±7.03pg/ml),FGL2(195.68±20.84ng/ml、210.65±22.36ng/ml)水平显著高于轻度组(11.32±1.33ng/ml、52.32±5.41pg/ml、162.35±17.55ng/ml),NABA(34.89±3.51分、29.88±3.43分)评分显著低于轻度组(36.54±1.52分),差异具有统计学意义(t_(中度组)=4.616~16.729,t_(重度组)=17.276~33.701,均P<0.05);NF-L、AQP9、FGL2与NABA评分均呈负相关(r=-0.432、-0.421、-0.402,均P<0.05);NF-L、AQP9、FGL2、NABA联合诊断患儿重度病情的曲线下面积(AUC)显著高于各项单独诊断,差异具有统计学意义(Z=2.066~3.307,均P<0.05)。结论HIE患儿血清NF-L、AQP9、FGL2水平显著升高,与NABA评分相关,可能成为评估HIE患儿病情的标志物。
