In order to ascertain the effects of atmospheric pressure on developmental characteristics and the stability of AEA(air-entraining agent)solution bubbles,AEA solution experiments and AEA solution bubble experiments we...In order to ascertain the effects of atmospheric pressure on developmental characteristics and the stability of AEA(air-entraining agent)solution bubbles,AEA solution experiments and AEA solution bubble experiments were,respectively,conducted in Peking(50 m,101.2 kPa)and Lhasa(3,650 m,63.1 kPa).Surface tensions and inflection-point concentrations were tested based on AEA solutions,whilst developmental characteristics,thicknesses and elastic coefficients of liquid films were tested based on air bubbles of AEA solutions.The study involved three types of AEAs,which were TM-O,226A,and 226S.The experimental results show that initial sizes of TM-O,226A,and 226S are,respectively,increased by 43.5%,17.5%,and 3.8%.With the decrease of ambient pressure,the drainage rate and the drainage index of AEA solution bubbles increase.Interference experiments show that the liquid film thicknesses of all tested AEA solution bubbles are in micron scales.When the atmospheric pressure decreases from 101.2 to 63.1 kPa,the liquid film thicknesses of three types of AEA solutions decrease in various degrees;and film elasticities at critical thicknesses increase.Liquid film of 226S solution bubbles is the most stable,presenting as a minimum thickness variation.It should be noted that elastic coefficient of liquid film only represents the level at critical thickness,thus it can not be applied as the only evaluating indicator of bubble stability.For a type of AEA,factors affecting the stability of its bubbles under low atmospheric pressure include initial bubbles size,liquid film thickness,liquid film elasticity,ambient temperature,etc.展开更多
In this paper, we put our focus on a variable-coe^cient fifth-order Korteweg-de Vries (fKdV) equation, which possesses a great number of excellent properties and is of current importance in physical and engineering ...In this paper, we put our focus on a variable-coe^cient fifth-order Korteweg-de Vries (fKdV) equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out.展开更多
The pulse amplification in the dispersion-decreasing fiber (DDF) is investigated via symbolic computation to solve the variable-coefficient higher-order nonlinear Schrfdinger equation with the effects of third-order...The pulse amplification in the dispersion-decreasing fiber (DDF) is investigated via symbolic computation to solve the variable-coefficient higher-order nonlinear Schrfdinger equation with the effects of third-order dispersion, self-steepening, and stimulated Raman scattering. The analytic one-soliton solution of this model is obtained with a set of parametric conditions. Based on this solution, the fundamental soliton is shown to be amplified in the DDF. The comparison of the amplitude of pulses for different dispersion profiles of the DDF is also performed through the graphical analysis. The results of this paper would be of certain value to the study of signal amplification and pulse compression.展开更多
A bilinear Baecklund transformation is presented for the three coupled higher-order nonlinear Schroedinger equations with the inclusion of the group velocity dispersion, third-order dispersion and Kerr-law nonlinearit...A bilinear Baecklund transformation is presented for the three coupled higher-order nonlinear Schroedinger equations with the inclusion of the group velocity dispersion, third-order dispersion and Kerr-law nonlinearity, which can describe the dynamics of alpha helical proteins in living systems as well as the propagation of ultrashort pulses in wavelength-division multiplexed system. Starting from the Baecklund transformation, the analytical soliton solution is obtained from a trivial solution. Simultaneously, the N-soliton-like solution in double Wronskian form is constructed, and the corresponding proof is also given via the Wronskian technique. The results obtained from this paper might be valuable in studying the transfer of energy in biophysics and the transmission of light pulses in optical communication systems.展开更多
With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrodinger equations with the effects of group-velocity dispersion, self-phase modulation and cross-phase modulation, which have pot...With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrodinger equations with the effects of group-velocity dispersion, self-phase modulation and cross-phase modulation, which have potential applications in the long-distance communication of two-pulse propagation in inhomogeneous optical fibers. Based on the obtained nonisospectral linear eigenvalue problems (i.e. Lax pair), we construct the Darboux transformation for such a model to derive the optical soliton solutions. In addition, through the one- and two-soliton-like solutions, we graphically discuss the features of picosecond solitons in inhomogeneous optical fibers.展开更多
For describing various complex nonlinear phenomena in the realistic world,the higher-dimensional nonlinearevolution equations appear more attractive in many fields of physical and engineering sciences.In this paper,by...For describing various complex nonlinear phenomena in the realistic world,the higher-dimensional nonlinearevolution equations appear more attractive in many fields of physical and engineering sciences.In this paper,by virtueof the Hirota bilinear method and Riemann theta functions,the periodic wave solutions for the(2+1)-dimensionalBoussinesq equation and(3+1)-dimensional Kadomtsev-Petviashvili(KP)equation are obtained.Furthermore,it isshown that the known soliton solutions for the two equations can be reduced from the periodic wave solutions.展开更多
目的采用非对称采集与迭代最小二乘估算法迭代水脂分离(iteraterative decomposition of water and fat with echo asymmetry and least-squares estimation quantitation,IDEAL-IQ)方法定量评估冈上肌腱损伤的严重程度与肩袖肌群脂肪...目的采用非对称采集与迭代最小二乘估算法迭代水脂分离(iteraterative decomposition of water and fat with echo asymmetry and least-squares estimation quantitation,IDEAL-IQ)方法定量评估冈上肌腱损伤的严重程度与肩袖肌群脂肪浸润程度及受试者特征之间的关系。材料与方法回顾性分析2022年8月至2024年6月本院经肩关节镜证实的33例冈上肌腱部分撕裂患者及89例完全撕裂患者,均进行了常规MRI扫描及IDEAL-IQ序列扫描。由两名放射科医生分别对所有受试者的MRI图像进行独立评估,根据常规MRI图像的冈上肌腱损伤表现,将完全撕裂组的冈上肌腱按照Patte分型分为Patte 1型(Ⅱ级)、Patte 2型(Ⅲ级)、Patte 3型(Ⅳ级),将部分撕裂组定义为Ⅰ级。同时在斜矢状位上进行Goutallier分级及Thomazeau萎缩分级,并通过GE ADW 4.7工作站后处理软件在IDEAL-IQ序列生成的脂肪分数图像上测量冈上肌、冈下肌、肩胛下肌及小圆肌脂肪分数(fat fraction,FF)。用组内相关系数(intra-class correlation coefficient,ICC)及Kappa一致性检验评估观察者间及观察者内的一致性。采用Kruskal-Wallis H检验、单因素ANOVA检验分析FF值在不同分组之间的差异,组间两两比较用Bonferroni检验。采用Pear_(s)on相关性分析肩袖肌肉FF值与年龄、症状持续时间的相关性(相关系数r),Spearman相关性分析冈上肌腱损伤分级与肩袖肌群FF值、Goutallier分级及Thomazeau萎缩分级之间的相关性(相关系数r_(s))。结果(1)冈上肌、冈下肌、肩胛下肌的FF值在冈上肌腱损伤Ⅳ级中显著高于Ⅲ级,高于Ⅱ级和Ⅰ级,差异有统计学意义(P值分别为<0.001、<0.001、0.005);小圆肌的FF值在不同分级之间差异无统计学意义(P=0.073)。组内比较Ⅰ级和Ⅱ级的冈上肌、冈下肌、肩胛下肌、小圆肌FF值差异无统计学意义(P值分别为0.026、0.102);Ⅲ级和Ⅳ级的FF值差异有统计学意义(P<0.001)。(2)冈上肌、冈下肌、小圆肌的FF值与年龄呈中等相关(r值分别为0.381、0.339、0.349,P均<0.001),肩胛下肌的FF值与年龄呈弱相关(r=0.216,P=0.017);冈上肌、冈下肌、肩胛下肌FF值与症状持续时间呈中等程度相关(r分别为0.442、0.412、0.314,P均<0.001),小圆肌的FF值与症状持续时间呈弱相关(r=0.277,P=0.002);冈上肌腱损伤程度与冈上肌FF值呈显著相关(r_(s)=0.740,P<0.001),与冈下肌的FF值呈强相关性(r_(s)=0.596,P<0.001),与肩胛下肌、小圆肌的FF值呈弱相关(r_(s)分别为0.257、0.212,P值分别为0.004、0.019);冈上肌损伤程度分级与Goutallier分级、Thomazeau分级之间呈显著正相关(r_(s)分别为0.757、0.737,P均<0.001),且冈上肌FF值在Goutallier和Thomazeau的分级中差异具有统计学意义(P均<0.001)。结论3.0 T MR IDEAL-IQ序列能量化和客观评估肩袖肌群脂肪浸润程度,肩袖肌群脂肪浸润程度与冈上肌腱损伤分级呈正相关,与年龄、症状持续时间呈正相关。展开更多
基金Funded by the National Natural Science Foundation of China(Nos.52178428,52178427,and 52308454)the Science and Technology Project of Tibet Department of Transportation(No.XZJTKJ[2020]04)。
文摘In order to ascertain the effects of atmospheric pressure on developmental characteristics and the stability of AEA(air-entraining agent)solution bubbles,AEA solution experiments and AEA solution bubble experiments were,respectively,conducted in Peking(50 m,101.2 kPa)and Lhasa(3,650 m,63.1 kPa).Surface tensions and inflection-point concentrations were tested based on AEA solutions,whilst developmental characteristics,thicknesses and elastic coefficients of liquid films were tested based on air bubbles of AEA solutions.The study involved three types of AEAs,which were TM-O,226A,and 226S.The experimental results show that initial sizes of TM-O,226A,and 226S are,respectively,increased by 43.5%,17.5%,and 3.8%.With the decrease of ambient pressure,the drainage rate and the drainage index of AEA solution bubbles increase.Interference experiments show that the liquid film thicknesses of all tested AEA solution bubbles are in micron scales.When the atmospheric pressure decreases from 101.2 to 63.1 kPa,the liquid film thicknesses of three types of AEA solutions decrease in various degrees;and film elasticities at critical thicknesses increase.Liquid film of 226S solution bubbles is the most stable,presenting as a minimum thickness variation.It should be noted that elastic coefficient of liquid film only represents the level at critical thickness,thus it can not be applied as the only evaluating indicator of bubble stability.For a type of AEA,factors affecting the stability of its bubbles under low atmospheric pressure include initial bubbles size,liquid film thickness,liquid film elasticity,ambient temperature,etc.
基金The project supported by the Key Project of the Chinese Ministry of Education under Grant No.106033the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20060006024+2 种基金Chinese Ministry of Education,the National Natural Science Foundation of China under Grant Nos.60772023 and 60372095the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.SKLSDE-07-001Beijing University of Aeronautics and Astronautics,and by the National Basic Research Program of China(973 Program)under Grant No.2005CB321901
文摘In this paper, we put our focus on a variable-coe^cient fifth-order Korteweg-de Vries (fKdV) equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out.
基金Supported by the National Natural Science Foundation of China under Grant No.60772023the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.BUAA-SKLSDE-09KF-04+3 种基金Beijing University of Aeronautics and Astronauticsthe National Basic Research Program of China (973 Program) under Grant No.2005CB321901the Specialized Research Fund for the Doctoral Program of Higher Education under Grant Nos.20060006024 and 20080013006Chinese Ministry of Education
文摘The pulse amplification in the dispersion-decreasing fiber (DDF) is investigated via symbolic computation to solve the variable-coefficient higher-order nonlinear Schrfdinger equation with the effects of third-order dispersion, self-steepening, and stimulated Raman scattering. The analytic one-soliton solution of this model is obtained with a set of parametric conditions. Based on this solution, the fundamental soliton is shown to be amplified in the DDF. The comparison of the amplitude of pulses for different dispersion profiles of the DDF is also performed through the graphical analysis. The results of this paper would be of certain value to the study of signal amplification and pulse compression.
基金the Key Project of the Ministry of Education under Grant No.106033the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20060006024National Natural Science Foundation of China under Grant No.60372095
文摘A bilinear Baecklund transformation is presented for the three coupled higher-order nonlinear Schroedinger equations with the inclusion of the group velocity dispersion, third-order dispersion and Kerr-law nonlinearity, which can describe the dynamics of alpha helical proteins in living systems as well as the propagation of ultrashort pulses in wavelength-division multiplexed system. Starting from the Baecklund transformation, the analytical soliton solution is obtained from a trivial solution. Simultaneously, the N-soliton-like solution in double Wronskian form is constructed, and the corresponding proof is also given via the Wronskian technique. The results obtained from this paper might be valuable in studying the transfer of energy in biophysics and the transmission of light pulses in optical communication systems.
基金Supported by the National Natural Science Foundation of China under Grant No.60772023 the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.BUAA-SKLSDE-09KF-04+2 种基金Beijing University of Aeronautics and Astronautics,by the National Basic Research Program of China (973 Program) under Grant No.2005CB321901the Specialized Research Fund for the Doctoral Program of Higher Education under Grant Nos.20060006024 and 200800130006Chinese Ministry of Education
文摘With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrodinger equations with the effects of group-velocity dispersion, self-phase modulation and cross-phase modulation, which have potential applications in the long-distance communication of two-pulse propagation in inhomogeneous optical fibers. Based on the obtained nonisospectral linear eigenvalue problems (i.e. Lax pair), we construct the Darboux transformation for such a model to derive the optical soliton solutions. In addition, through the one- and two-soliton-like solutions, we graphically discuss the features of picosecond solitons in inhomogeneous optical fibers.
基金supported by the National Natural Science Foundation of China under Grant Nos.60772023 and 60372095the Key Project of the Ministry of Education under Grant No.106033+3 种基金the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.SKLSDE-07-001Beijing University of Aeronautics and Astronauticsthe National Basic Research Program of China(973 Program)under Grant No.2005CB321901the Specialized Research Fund for the Doctoral Program of Higher Education of the Ministry of Education under Grant No.20060006024
文摘For describing various complex nonlinear phenomena in the realistic world,the higher-dimensional nonlinearevolution equations appear more attractive in many fields of physical and engineering sciences.In this paper,by virtueof the Hirota bilinear method and Riemann theta functions,the periodic wave solutions for the(2+1)-dimensionalBoussinesq equation and(3+1)-dimensional Kadomtsev-Petviashvili(KP)equation are obtained.Furthermore,it isshown that the known soliton solutions for the two equations can be reduced from the periodic wave solutions.
文摘目的采用非对称采集与迭代最小二乘估算法迭代水脂分离(iteraterative decomposition of water and fat with echo asymmetry and least-squares estimation quantitation,IDEAL-IQ)方法定量评估冈上肌腱损伤的严重程度与肩袖肌群脂肪浸润程度及受试者特征之间的关系。材料与方法回顾性分析2022年8月至2024年6月本院经肩关节镜证实的33例冈上肌腱部分撕裂患者及89例完全撕裂患者,均进行了常规MRI扫描及IDEAL-IQ序列扫描。由两名放射科医生分别对所有受试者的MRI图像进行独立评估,根据常规MRI图像的冈上肌腱损伤表现,将完全撕裂组的冈上肌腱按照Patte分型分为Patte 1型(Ⅱ级)、Patte 2型(Ⅲ级)、Patte 3型(Ⅳ级),将部分撕裂组定义为Ⅰ级。同时在斜矢状位上进行Goutallier分级及Thomazeau萎缩分级,并通过GE ADW 4.7工作站后处理软件在IDEAL-IQ序列生成的脂肪分数图像上测量冈上肌、冈下肌、肩胛下肌及小圆肌脂肪分数(fat fraction,FF)。用组内相关系数(intra-class correlation coefficient,ICC)及Kappa一致性检验评估观察者间及观察者内的一致性。采用Kruskal-Wallis H检验、单因素ANOVA检验分析FF值在不同分组之间的差异,组间两两比较用Bonferroni检验。采用Pear_(s)on相关性分析肩袖肌肉FF值与年龄、症状持续时间的相关性(相关系数r),Spearman相关性分析冈上肌腱损伤分级与肩袖肌群FF值、Goutallier分级及Thomazeau萎缩分级之间的相关性(相关系数r_(s))。结果(1)冈上肌、冈下肌、肩胛下肌的FF值在冈上肌腱损伤Ⅳ级中显著高于Ⅲ级,高于Ⅱ级和Ⅰ级,差异有统计学意义(P值分别为<0.001、<0.001、0.005);小圆肌的FF值在不同分级之间差异无统计学意义(P=0.073)。组内比较Ⅰ级和Ⅱ级的冈上肌、冈下肌、肩胛下肌、小圆肌FF值差异无统计学意义(P值分别为0.026、0.102);Ⅲ级和Ⅳ级的FF值差异有统计学意义(P<0.001)。(2)冈上肌、冈下肌、小圆肌的FF值与年龄呈中等相关(r值分别为0.381、0.339、0.349,P均<0.001),肩胛下肌的FF值与年龄呈弱相关(r=0.216,P=0.017);冈上肌、冈下肌、肩胛下肌FF值与症状持续时间呈中等程度相关(r分别为0.442、0.412、0.314,P均<0.001),小圆肌的FF值与症状持续时间呈弱相关(r=0.277,P=0.002);冈上肌腱损伤程度与冈上肌FF值呈显著相关(r_(s)=0.740,P<0.001),与冈下肌的FF值呈强相关性(r_(s)=0.596,P<0.001),与肩胛下肌、小圆肌的FF值呈弱相关(r_(s)分别为0.257、0.212,P值分别为0.004、0.019);冈上肌损伤程度分级与Goutallier分级、Thomazeau分级之间呈显著正相关(r_(s)分别为0.757、0.737,P均<0.001),且冈上肌FF值在Goutallier和Thomazeau的分级中差异具有统计学意义(P均<0.001)。结论3.0 T MR IDEAL-IQ序列能量化和客观评估肩袖肌群脂肪浸润程度,肩袖肌群脂肪浸润程度与冈上肌腱损伤分级呈正相关,与年龄、症状持续时间呈正相关。