It is shown that the two-component Camassa-Holm and Hunter-Saxton systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws are ...It is shown that the two-component Camassa-Holm and Hunter-Saxton systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws are directly constructed. In addition, a class of nonlocal symmetries depending on the pseudo-potentials are obtained.展开更多
The asymmetric photocatalytic organic synthesis(APOS)process is a sustainable and environmentally benign method for the production of optically active chemicals with sunlight as an energy source.However,it still lacks...The asymmetric photocatalytic organic synthesis(APOS)process is a sustainable and environmentally benign method for the production of optically active chemicals with sunlight as an energy source.However,it still lacks efficient semiconductors with tunable band structures and has a low recycling stability.Herein,we report the synthesis of tetrahydroquinoline-linked covalent organic frameworks(QH-COFs)with irreversible tetrahydroquinoline linkage as efficient semiconductors for the visible-light-driven asymmetricα-alkylation of aldehydes by merging with a chiral secondary amine.Up to 94%ee was obtained over QH-COFs,and the activity of QH-COFs was significantly higher than those of inorganic semiconductors(e.g.,Ti O2,Bi VO4,and WO3)under similar conditions,which is mainly attributed to their narrow band gap and suitable band edge.As far as we know,QH-COFs are the most active semiconductors for asymmetricα-alkylation of aldehydes ever reported.The QH-COFs were prepared via a one-pot Povarov cascade imine formation and cycloaddition reaction using Sc(OTf)3/Yb(OTf)3 as Lewis acid catalysts.Attributed to the tetrahydroquinoline linkage,QH-COFs showed extremely high recycling stability,which made practicals application possible.This work not only opens up a new avenue for asymmetric photocatalysis but also provides an efficient and general method for the construction of robust COFs.展开更多
In terms of our new exact definition of partial Lagrangian and approximate Euler-Lagrange-type equation, we investigate the nonlinear wave equation with damping via approximate Noether-type symmetry operators associat...In terms of our new exact definition of partial Lagrangian and approximate Euler-Lagrange-type equation, we investigate the nonlinear wave equation with damping via approximate Noether-type symmetry operators associated with partial Lagrangians and construct its approximate conservation laws in general form.展开更多
The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie gr...The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.展开更多
In this article, by means of the theory of majorization, Adamovic's inequality is extended to the cases of the general elementary symmetric functions and its duals, and the refined and reversed forms are also give...In this article, by means of the theory of majorization, Adamovic's inequality is extended to the cases of the general elementary symmetric functions and its duals, and the refined and reversed forms are also given. As applications, some new inequalities for simplex are established.展开更多
To have a deep understanding of the lateral stability of hypersonic lifting-configurations, wind-tunnel tests of roll static and dynamic stability for typical hypersonic lifting-configurations are carried out. The res...To have a deep understanding of the lateral stability of hypersonic lifting-configurations, wind-tunnel tests of roll static and dynamic stability for typical hypersonic lifting-configurations are carried out. The results show the roll is static unstable in small angles; the roll dynamic test curves present obvious non-linearity characteristics, and the model vibrates violently even When the angle of attack is small, which may be provoked by the non-symmetry transition from the small transverse flow around the nose of model. Subsequent research adopts longitudinal trips to generate symmetry transition at the fore-body of the model. As a result, the lateral stability of the aircrafts is apparently improved. The results show that the lateral stability of hypersonic aircrafts is very weak, and the main reason for this is lateral perturbation of flow over the nose, among which asymmetric transition weighs the most. Adoption of longitudinal trips could spur fixed transition of lateral flow, reduce the transition asymmetry of lateral flow, and strengthen the lateral stability of hypersonic aircrafts at the same time.展开更多
This study presents a new way to identify the sensitive areas,which are determined by invoking the negative anomalies of moist potential vorticity (MPV) for typhoon adaptive observations. It is found that the areas of...This study presents a new way to identify the sensitive areas,which are determined by invoking the negative anomalies of moist potential vorticity (MPV) for typhoon adaptive observations. It is found that the areas of negative MPV are the symmetric instability areas and can be taken as sensitive areas for typhoon adaptive observations. Three typhoons in 2008,Nuri,Fung-wong,and Fengshen,were simulated with the help of MM5 model. It is shown that these typhoons are well simulated in the first 12 hours. Based on these investigations,the calculations of MPV are carried out sequentially. The result shows that the negative maxima of MPV are always around the typhoon eyes for all the cases,which means that the sensitive areas are also near them all the time.展开更多
The asymmetric effects on the escape rates from the stable states x±in the bistable system are analyzed. The results indicate that the multiplicative noise and the additive noise always enhance the particle escap...The asymmetric effects on the escape rates from the stable states x±in the bistable system are analyzed. The results indicate that the multiplicative noise and the additive noise always enhance the particle escape from stable states x±of bistable.However,the asymmetric parameter r enhances the particle escape from stable state x_+,and holds back the particle escape from stable state x_-.展开更多
We investigate in detail the effects of R-parity lepton number violation onthe decay b_1 → bχ_1~0 in the R-parity violating minimal supersymmetric standard model (R_p-MSSM)under the present experimental constraints ...We investigate in detail the effects of R-parity lepton number violation onthe decay b_1 → bχ_1~0 in the R-parity violating minimal supersymmetric standard model (R_p-MSSM)under the present experimental constraints on R_p parameters. In our numerical calculations weconsider two cases of input parameters of the squark and slepton sectors, M_(squark) 【 M_(slepton)and M_(squark) 】 M_(slepton), for comparison. The results show that the relative R-parity violatingcorrection is not very sensitive to the mass of the lightest neutralino bχ_1~0 the degenerateR-parity violating coupling parameter λ′_2 but strongly depends on M_(squark), M_(slepton) tan βand tie degenerate R-parity violating coupling parameter λ′_1. The relative correction is about -4～ 3% and can exceed -6% in some region of parameter space. Therefore, precise experiment analyseson the decay b_1 → bχ_1~0 may provide a probe of the R-parity violation.展开更多
The linear stability of fiber suspensions between two concentric cylinders rotating independently is studied. The modified stability equation is obtained based on the fiber orientation model and Hinch-Leal closure app...The linear stability of fiber suspensions between two concentric cylinders rotating independently is studied. The modified stability equation is obtained based on the fiber orientation model and Hinch-Leal closure approximation. The primary instabilities and bicritical curves have been calculated numerically. The critical Reynolds number,wavenumber and wave speeds of fiber suspensions as functions of the aspect ratio,volume concentration of the fibers and the gap width of cylinders are obtained.展开更多
The algorithm for constructing conservation laws of Euler Lagvange type equations via Noether-type symmetry operators associated with partial Lagrangian has been presented. As applications, many new conservation laws ...The algorithm for constructing conservation laws of Euler Lagvange type equations via Noether-type symmetry operators associated with partial Lagrangian has been presented. As applications, many new conservation laws of some important systems of nonlinear partial differential equations have been obtained.展开更多
This paper describes the problem of stability for one-dimensional Cellular Neural Networks（CNNs）. A sufficient condition is presented to ensure complete stability for a class of special CNN＇s with nonsymmetric temp...This paper describes the problem of stability for one-dimensional Cellular Neural Networks（CNNs）. A sufficient condition is presented to ensure complete stability for a class of special CNN＇s with nonsymmetric templates, where the parameter in the output function is greater than or equal to zero. The main method is analysising the property of the equilibrium point of the CNNs system.展开更多
An analysis of the instability in the Taylor-Couette flow of fiber suspensions with respect to the non-axisymmetric disturbances was performed. The constitutive model proposed by Ericksen was used to represent the rol...An analysis of the instability in the Taylor-Couette flow of fiber suspensions with respect to the non-axisymmetric disturbances was performed. The constitutive model proposed by Ericksen was used to represent the role of fiber additives on the stress tensor. The generalized eigenvalue equation governing the hydrodynamic stability of the system was solved using a direct numerical procedure. The results showed that the fiber additives can suppress the instability of the flow. At the same time, the non-axisymmetric disturbance is the preferred mode that makes the fiber suspensions unstable when the ratio of the angular ve- locity of the outer cylinder to that of the inner cylinder is a large negative number.展开更多
We present beam solutions of the strongly nonlocal nonlinear Schrodinger equation in left-handed mate- rims （LHMs）. Different Laguerre-Ganssian （LG） necklace beams, such as symmetric and asymmetric single layer an...We present beam solutions of the strongly nonlocal nonlinear Schrodinger equation in left-handed mate- rims （LHMs）. Different Laguerre-Ganssian （LG） necklace beams, such as symmetric and asymmetric single layer and multilayer necklace beams are created by the superposition of two single beams with different topological charges. Such superpositions are then propagated through LHMs, displaying linear diffraction. It is found that the superposition of two LGnm beams with opposite topological charges does not show rotational behavior and that there exists rotation for other topological charge combinations. Our theory predicts that the accessible solitons cannot exist in LHMs.展开更多
基金Supported by the China NSF for Distinguished Young Scholars under Grant No.10925104
文摘It is shown that the two-component Camassa-Holm and Hunter-Saxton systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws are directly constructed. In addition, a class of nonlocal symmetries depending on the pseudo-potentials are obtained.
文摘The asymmetric photocatalytic organic synthesis(APOS)process is a sustainable and environmentally benign method for the production of optically active chemicals with sunlight as an energy source.However,it still lacks efficient semiconductors with tunable band structures and has a low recycling stability.Herein,we report the synthesis of tetrahydroquinoline-linked covalent organic frameworks(QH-COFs)with irreversible tetrahydroquinoline linkage as efficient semiconductors for the visible-light-driven asymmetricα-alkylation of aldehydes by merging with a chiral secondary amine.Up to 94%ee was obtained over QH-COFs,and the activity of QH-COFs was significantly higher than those of inorganic semiconductors(e.g.,Ti O2,Bi VO4,and WO3)under similar conditions,which is mainly attributed to their narrow band gap and suitable band edge.As far as we know,QH-COFs are the most active semiconductors for asymmetricα-alkylation of aldehydes ever reported.The QH-COFs were prepared via a one-pot Povarov cascade imine formation and cycloaddition reaction using Sc(OTf)3/Yb(OTf)3 as Lewis acid catalysts.Attributed to the tetrahydroquinoline linkage,QH-COFs showed extremely high recycling stability,which made practicals application possible.This work not only opens up a new avenue for asymmetric photocatalysis but also provides an efficient and general method for the construction of robust COFs.
基金Supported by the National Natural Science Foundation of China under Grant No.10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.SJ08A05
文摘In terms of our new exact definition of partial Lagrangian and approximate Euler-Lagrange-type equation, we investigate the nonlinear wave equation with damping via approximate Noether-type symmetry operators associated with partial Lagrangians and construct its approximate conservation laws in general form.
基金supported by the Scientific Research Foundation for the Doctors of University of Electronic Science and Technology of China Zhongshan Institutethe National Natural Science Foundation of China under Grant Nos. 10735030 and 90503006
文摘The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.
文摘In this article, by means of the theory of majorization, Adamovic's inequality is extended to the cases of the general elementary symmetric functions and its duals, and the refined and reversed forms are also given. As applications, some new inequalities for simplex are established.
文摘To have a deep understanding of the lateral stability of hypersonic lifting-configurations, wind-tunnel tests of roll static and dynamic stability for typical hypersonic lifting-configurations are carried out. The results show the roll is static unstable in small angles; the roll dynamic test curves present obvious non-linearity characteristics, and the model vibrates violently even When the angle of attack is small, which may be provoked by the non-symmetry transition from the small transverse flow around the nose of model. Subsequent research adopts longitudinal trips to generate symmetry transition at the fore-body of the model. As a result, the lateral stability of the aircrafts is apparently improved. The results show that the lateral stability of hypersonic aircrafts is very weak, and the main reason for this is lateral perturbation of flow over the nose, among which asymmetric transition weighs the most. Adoption of longitudinal trips could spur fixed transition of lateral flow, reduce the transition asymmetry of lateral flow, and strengthen the lateral stability of hypersonic aircrafts at the same time.
基金State Key Development Program for Basic Research of China (2009CB421505)Meteorological Special Project of The Ministry of Sciences and Technology of the People’s Republic of China (GYHY200706020)+1 种基金Project of the Natural Science Foundation of China (40775031)Project of NO.2008 LASW-A01
文摘This study presents a new way to identify the sensitive areas,which are determined by invoking the negative anomalies of moist potential vorticity (MPV) for typhoon adaptive observations. It is found that the areas of negative MPV are the symmetric instability areas and can be taken as sensitive areas for typhoon adaptive observations. Three typhoons in 2008,Nuri,Fung-wong,and Fengshen,were simulated with the help of MM5 model. It is shown that these typhoons are well simulated in the first 12 hours. Based on these investigations,the calculations of MPV are carried out sequentially. The result shows that the negative maxima of MPV are always around the typhoon eyes for all the cases,which means that the sensitive areas are also near them all the time.
基金Supported by the Natural Science Foundation of China under Grant No.10865006the Natural Science Foundation of Shaanxi Province under Grant No.2010JQ1014the Science Foundation of Baoji University of Science and Arts of China under Grant No.ZK0954
文摘The asymmetric effects on the escape rates from the stable states x±in the bistable system are analyzed. The results indicate that the multiplicative noise and the additive noise always enhance the particle escape from stable states x±of bistable.However,the asymmetric parameter r enhances the particle escape from stable state x_+,and holds back the particle escape from stable state x_-.
文摘We investigate in detail the effects of R-parity lepton number violation onthe decay b_1 → bχ_1~0 in the R-parity violating minimal supersymmetric standard model (R_p-MSSM)under the present experimental constraints on R_p parameters. In our numerical calculations weconsider two cases of input parameters of the squark and slepton sectors, M_(squark) 【 M_(slepton)and M_(squark) 】 M_(slepton), for comparison. The results show that the relative R-parity violatingcorrection is not very sensitive to the mass of the lightest neutralino bχ_1~0 the degenerateR-parity violating coupling parameter λ′_2 but strongly depends on M_(squark), M_(slepton) tan βand tie degenerate R-parity violating coupling parameter λ′_1. The relative correction is about -4～ 3% and can exceed -6% in some region of parameter space. Therefore, precise experiment analyseson the decay b_1 → bχ_1~0 may provide a probe of the R-parity violation.
基金Project (Nos. 10632070 and 40231017) supported by the National Natural Science Foundation of China
文摘The linear stability of fiber suspensions between two concentric cylinders rotating independently is studied. The modified stability equation is obtained based on the fiber orientation model and Hinch-Leal closure approximation. The primary instabilities and bicritical curves have been calculated numerically. The critical Reynolds number,wavenumber and wave speeds of fiber suspensions as functions of the aspect ratio,volume concentration of the fibers and the gap width of cylinders are obtained.
基金supported by the State Key Basic Research Program of China under Grant No.2004CB318000
文摘The algorithm for constructing conservation laws of Euler Lagvange type equations via Noether-type symmetry operators associated with partial Lagrangian has been presented. As applications, many new conservation laws of some important systems of nonlinear partial differential equations have been obtained.
基金Supported by the NSF of Zhejiang Province(M103087) Supported by the Science Research Fund of Hushou Teacher's College
文摘This paper describes the problem of stability for one-dimensional Cellular Neural Networks（CNNs）. A sufficient condition is presented to ensure complete stability for a class of special CNN＇s with nonsymmetric templates, where the parameter in the output function is greater than or equal to zero. The main method is analysising the property of the equilibrium point of the CNNs system.
基金Project (No. 10372090) supported by the National Natural ScienceFoundation of China
文摘An analysis of the instability in the Taylor-Couette flow of fiber suspensions with respect to the non-axisymmetric disturbances was performed. The constitutive model proposed by Ericksen was used to represent the role of fiber additives on the stress tensor. The generalized eigenvalue equation governing the hydrodynamic stability of the system was solved using a direct numerical procedure. The results showed that the fiber additives can suppress the instability of the flow. At the same time, the non-axisymmetric disturbance is the preferred mode that makes the fiber suspensions unstable when the ratio of the angular ve- locity of the outer cylinder to that of the inner cylinder is a large negative number.
基金Supported by the Science Research Foundation of Shunde Polytechnic (2008-KJ06), ChinaWork at the Texas A&M University at Qatar is supported by the NPRP 25-6-7-2 project with the Qatar National Research Foundation
文摘We present beam solutions of the strongly nonlocal nonlinear Schrodinger equation in left-handed mate- rims （LHMs）. Different Laguerre-Ganssian （LG） necklace beams, such as symmetric and asymmetric single layer and multilayer necklace beams are created by the superposition of two single beams with different topological charges. Such superpositions are then propagated through LHMs, displaying linear diffraction. It is found that the superposition of two LGnm beams with opposite topological charges does not show rotational behavior and that there exists rotation for other topological charge combinations. Our theory predicts that the accessible solitons cannot exist in LHMs.
