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
Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamic...Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamical characteristics of these solutions were displayed through graphical,particularly revealing fusion and ssion phenomena in the interaction of lump and the one-stripe soliton.展开更多
When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, ...When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.展开更多
For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits ...For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.展开更多
目的:探究血清甘油三酯-葡萄糖(TyG)指数、摄食抑制因子-1(nesfatin-1)、视黄醇结合蛋白4(RBP4)联合预测糖尿病视网膜病变(DR)的价值,为DR早期预测提供支持。方法:回顾性分析。收集2022-02/2023-12我院接诊的2型糖尿病(T2DM)患者164例...目的:探究血清甘油三酯-葡萄糖(TyG)指数、摄食抑制因子-1(nesfatin-1)、视黄醇结合蛋白4(RBP4)联合预测糖尿病视网膜病变(DR)的价值,为DR早期预测提供支持。方法:回顾性分析。收集2022-02/2023-12我院接诊的2型糖尿病(T2DM)患者164例的临床资料,按照眼底检查结果分为DR组43例(其中增殖性DR 19例,非增殖性DR 24例),不合并DR的T2DM组121例。入院后记录患者基本资料,检查血清TyG指数、nesfatin-1、RBP4水平。结果:DR组病程长于T2DM组,空腹血糖、糖化血红蛋白、甘油三酯、总胆固醇、低密度脂蛋白及TyG指数、RBP4水平高于T2DM组,高密度脂蛋白、nesfatin-1水平低于T2DM组(均P<0.001)。多因素Logistic回归分析可知,T2DM病程(OR=1.338,95%CI:1.059-1.690)、糖化血红蛋白(OR=5.065,95%CI:1.659-15.470)、低密度脂蛋白(OR=12.715,95%CI:2.385-67.790)、TyG指数(OR=23.057,95%CI:2.936-181.073)、RBP4(OR=1.319,95%CI:1.028-1.692)是T2DM患者发生DR的危险因素,nesfatin-1(OR=0.007,95%CI:0.003-0.016)为保护因素。绘制ROC曲线显示,TyG指数、nesfatin-1、RBP4均对T2DM患者并发DR具有一定预测价值,曲线下面积(areas under curve,AUC)分别为0.804、0.878、0.738,各指标联合预测时AUC为0.946,预测敏感度为83.72%、特异度为92.56%。增殖性DR患者TyG指数、RBP4水平高于非增殖性DR患者,nesfatin-1水平低于非增殖性DR患者(均P<0.05)。Spearman相关性分析显示,TyG指数、RBP4水平与DR病情程度呈正相关,nesfatin-1水平与DR病情程度呈负相关(r_(s)=0.557、0.392、-0.359,均P<0.05)。Pearson相关分析显示,T2DM并发DR患者TyG指数与nesfatin-1水平呈负相关,与RBP4水平呈正相关,nesfatin-1与RBP4水平呈负相关(r=-0.486、0.538、-0.592,均P<0.05)。结论:血清TyG指数、nesfatin-1、RBP4水平与DR发病风险及病情程度有关,可作为DR早期预测的标志物,且联合预测效能更好。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 National Natural Science Foundation of China(12275172)。
文摘Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamical characteristics of these solutions were displayed through graphical,particularly revealing fusion and ssion phenomena in the interaction of lump and the one-stripe soliton.
文摘When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.
文摘For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.
文摘目的:探究血清甘油三酯-葡萄糖(TyG)指数、摄食抑制因子-1(nesfatin-1)、视黄醇结合蛋白4(RBP4)联合预测糖尿病视网膜病变(DR)的价值,为DR早期预测提供支持。方法:回顾性分析。收集2022-02/2023-12我院接诊的2型糖尿病(T2DM)患者164例的临床资料,按照眼底检查结果分为DR组43例(其中增殖性DR 19例,非增殖性DR 24例),不合并DR的T2DM组121例。入院后记录患者基本资料,检查血清TyG指数、nesfatin-1、RBP4水平。结果:DR组病程长于T2DM组,空腹血糖、糖化血红蛋白、甘油三酯、总胆固醇、低密度脂蛋白及TyG指数、RBP4水平高于T2DM组,高密度脂蛋白、nesfatin-1水平低于T2DM组(均P<0.001)。多因素Logistic回归分析可知,T2DM病程(OR=1.338,95%CI:1.059-1.690)、糖化血红蛋白(OR=5.065,95%CI:1.659-15.470)、低密度脂蛋白(OR=12.715,95%CI:2.385-67.790)、TyG指数(OR=23.057,95%CI:2.936-181.073)、RBP4(OR=1.319,95%CI:1.028-1.692)是T2DM患者发生DR的危险因素,nesfatin-1(OR=0.007,95%CI:0.003-0.016)为保护因素。绘制ROC曲线显示,TyG指数、nesfatin-1、RBP4均对T2DM患者并发DR具有一定预测价值,曲线下面积(areas under curve,AUC)分别为0.804、0.878、0.738,各指标联合预测时AUC为0.946,预测敏感度为83.72%、特异度为92.56%。增殖性DR患者TyG指数、RBP4水平高于非增殖性DR患者,nesfatin-1水平低于非增殖性DR患者(均P<0.05)。Spearman相关性分析显示,TyG指数、RBP4水平与DR病情程度呈正相关,nesfatin-1水平与DR病情程度呈负相关(r_(s)=0.557、0.392、-0.359,均P<0.05)。Pearson相关分析显示,T2DM并发DR患者TyG指数与nesfatin-1水平呈负相关,与RBP4水平呈正相关,nesfatin-1与RBP4水平呈负相关(r=-0.486、0.538、-0.592,均P<0.05)。结论:血清TyG指数、nesfatin-1、RBP4水平与DR发病风险及病情程度有关,可作为DR早期预测的标志物,且联合预测效能更好。
