In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linea...In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.展开更多
In this paper, the reverse order law for the Moore-Penrose inverse of closed linear operators with closed range is investigated by virtue of the Norm-preserving extension of the bounded linear operators. The results g...In this paper, the reverse order law for the Moore-Penrose inverse of closed linear operators with closed range is investigated by virtue of the Norm-preserving extension of the bounded linear operators. The results generalize some results obtained by S Izumino in [12].展开更多
Let K<sup>n×n</sup> be the set of all n×n matrices and K<sub>r</sub><sup>n×n</sup> the set {A∈K<sup>n×n</sup>|rankA=r} on askew field K. Zhuang [1] ...Let K<sup>n×n</sup> be the set of all n×n matrices and K<sub>r</sub><sup>n×n</sup> the set {A∈K<sup>n×n</sup>|rankA=r} on askew field K. Zhuang [1] denotes by A<sup>#</sup> the group inverse of A∈K<sup>n×n</sup> which is the solu-tion of the euqations:AXA=A, XAX=X, AX=AX.展开更多
In this paper, by using a block-operator matrix technique, we study mixed-type reverse order laws for {1,3}-, {1,2,3}- and {1,3,4}-generalized inverses over Hilbert spaces. It is shown that and when the ranges of are ...In this paper, by using a block-operator matrix technique, we study mixed-type reverse order laws for {1,3}-, {1,2,3}- and {1,3,4}-generalized inverses over Hilbert spaces. It is shown that and when the ranges of are closed. Moreover, a new equivalent condition of is given.展开更多
Using the order parameter of seismicity defined in natural time, we suggest a simple model for the expla- nation of Bath law, according to which a mainshock differs in magnitude from its largest aftershock by approxim...Using the order parameter of seismicity defined in natural time, we suggest a simple model for the expla- nation of Bath law, according to which a mainshock differs in magnitude from its largest aftershock by approximately 1.2 regardless of the mainshock magnitude. In addition, the validity of Bath law is studied in the Global Centroid Moment Tensor catalogue by using two different aftershock definitions. It is found that the mean of this difference, when considering all the pairs mainshock-largest aftershock, does not markedly differ from 1.2 and the corresponding distributions do not depend on the mainshock's magnitude threshold in a statistically significant manner. Finally, the analysis of the cumulative distribution functions provides evidence in favour of the proposed model.展开更多
With the assistance of the symbolic computation system Maple,rich higher order polynomial-type conservation laws and a sixth order t/x-dependent conservation law are constructed for a generalized seventh order nonline...With the assistance of the symbolic computation system Maple,rich higher order polynomial-type conservation laws and a sixth order t/x-dependent conservation law are constructed for a generalized seventh order nonlinear evolution equation by using a direct algebraic method.From the compatibility conditions that guaranteeing the existence of conserved densities,an integrable unnamed seventh order KdV-type equation is found.By introducing some nonlinear transformations,the one-,two-,and three-solition solutions as well as the solitary wave solutions are obtained.展开更多
Using a nonperturbative quantum electrodynamics theory of high-order harmonic generation (HHG), a scaling law of HHG is established. The scaling law states that when the atomic binding energy Eb, the wavelength ), ...Using a nonperturbative quantum electrodynamics theory of high-order harmonic generation (HHG), a scaling law of HHG is established. The scaling law states that when the atomic binding energy Eb, the wavelength ), and the intensity I of the laser field change simultaneously to kEb, λ/k, and k3I, respectively. The characteristics of the HHG spectrum remain unchanged, while the harmonic yield is enhanced k3 times. That HHG obeys the same scaling law with above-threshold ionization is a solid proof of the fact that the two physical processes have similar physical mechanisms. The variation of integrated harmonic yields is also discussed.展开更多
Scaling laws are addressed by analysing moments of velocity increments which obtained by Particle-image Velocimetry(PIV)system in the boundary layer of a flat plate.In the paper,we measure the moments of increments of...Scaling laws are addressed by analysing moments of velocity increments which obtained by Particle-image Velocimetry(PIV)system in the boundary layer of a flat plate.In the paper,we measure the moments of increments of upstream velocity(u'),longitudinal velocity(v')and ponderance of vorticity(dv'/dx)at Reθ=2167 in different wall distance and verify the anomaly of the scaling exponents of high-order structure functions with the increasing order of the moments,discuss the scaling of non-integer moments of order between+2 and-1.The difference of scaling exponents of low-order structure functions between the experimental data and Kolmogorov's,SL's(She & Leveque)prediction increases as the moment order decreases toward-1,which shows that the anomaly is manifested in low-oeder moments as well.However,for same order structure functions,the scaling exponents of v' and dv'/dx are not changeable in different wall distance.展开更多
To satisfy the terminal position and impact angel constraints,an optimal guidance problem was discussed for homing missiles. For a stationary or a slowly moving target on the ground,an extended trajectory shaping guid...To satisfy the terminal position and impact angel constraints,an optimal guidance problem was discussed for homing missiles. For a stationary or a slowly moving target on the ground,an extended trajectory shaping guidance lawconsidering a first-order autopilot lag( ETSG L-C FAL) was proposed. To derive the ETSG L-C FAL,a time-to-go- nth power weighted objection function was adopted and three different derivation methods were demonstrated while the Schwartz inequality method was mainly demonstrated.The performance of the ETSG L-C FAL and the ETSG L guidance laws was compared through simulation.Simulation results showthat although a first-order autopilot is introduced into the ETSG L-C FAL guidance system,the position miss distance and terminal impact angle error induced by the impact angle is zero for different guidance time.展开更多
The lack of descriptions regarding the order of precedence between the local laws of cities with subordinate districts and the regulations of provincial governments in Legislation Law of the People's Republic of C...The lack of descriptions regarding the order of precedence between the local laws of cities with subordinate districts and the regulations of provincial governments in Legislation Law of the People's Republic of China(Legislation Law) has led to two divergent views. One holds that "the local laws of cities with subordinate districts should take precedence over the regulations of provincial governments," while the other supports the exact opposite. This is a value judgment issue in legislation. To reach a solution, we need to clarify the premises based on the characteristics of the laws in question so that a basic common ground can be established for discussion. The first premise for traditional legislation is that a law should be based on experience as well as logic; the second is that the experience of authority subjects, plus the three aspects of logic should outweigh the experience of social subjects, plus the three aspects of logic. With respect to postmodern legislation, the first premise is that experience should override logic, and the second is that the experience of the authority subject should take precedence over that of social subject, with no requirements for logical consistency. Since Legislation Law fal s into the category of postmodern legislation, according to the premises, the argument that the local laws of cities with subordinate districts should take precedence enjoys wider acceptance, but the view is logically challenged in terms of conceptual consistency, system consistency and principle consistency. More studies must be conducted to facilitate the discussion.展开更多
Equations of steady inviscid and laminar flows are solved by means of a third-order finite volume (FV) scheme. For this purpose, a cell-centered discretization technique is employed. In this technique, the flow para...Equations of steady inviscid and laminar flows are solved by means of a third-order finite volume (FV) scheme. For this purpose, a cell-centered discretization technique is employed. In this technique, the flow parameters at the cell faces are computed using a third-order weighted averages procedure. A fourth-order artificial dissipation is used for stability of the solution. In order to achieve the steady-state situation, four-step Runge-Kutta explicit time integration method is applied. An advanced progressive preconditioning method, named the power-law preconditioning method, is used for faster convergence. In this method, the preconditioning matrix is adjusted automatically from the velocity and/or pressure flow-field by a power-law relation. Attention is directed towards accuracy and convergence of the schemes. The results presented in the paper focus on steady inviscid and laminar flows around sheet-cavitating and fully-wetted bodies including hydrofoils and circular/elliptical cylinder. Excellent agreements are obtained when numerical predictions are compared with other available experimental and numerical results. In addition, it is found that using the power-law preconditioner significantly increases the numerical convergence speed.展开更多
基金supported by the NNSF of China(12261065)the NSF of Inner Mongolia(2022MS01005)+1 种基金the Basic Science Research Fund of the Universities Directly under the Inner Mongolia Autonomous Re-gion(JY20220084)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(NMGIRT2317).
文摘In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.
文摘In this paper, the reverse order law for the Moore-Penrose inverse of closed linear operators with closed range is investigated by virtue of the Norm-preserving extension of the bounded linear operators. The results generalize some results obtained by S Izumino in [12].
基金This work is Supported by NSF of Heilongjiang Provice
文摘Let K<sup>n×n</sup> be the set of all n×n matrices and K<sub>r</sub><sup>n×n</sup> the set {A∈K<sup>n×n</sup>|rankA=r} on askew field K. Zhuang [1] denotes by A<sup>#</sup> the group inverse of A∈K<sup>n×n</sup> which is the solu-tion of the euqations:AXA=A, XAX=X, AX=AX.
文摘In this paper, by using a block-operator matrix technique, we study mixed-type reverse order laws for {1,3}-, {1,2,3}- and {1,3,4}-generalized inverses over Hilbert spaces. It is shown that and when the ranges of are closed. Moreover, a new equivalent condition of is given.
文摘Using the order parameter of seismicity defined in natural time, we suggest a simple model for the expla- nation of Bath law, according to which a mainshock differs in magnitude from its largest aftershock by approximately 1.2 regardless of the mainshock magnitude. In addition, the validity of Bath law is studied in the Global Centroid Moment Tensor catalogue by using two different aftershock definitions. It is found that the mean of this difference, when considering all the pairs mainshock-largest aftershock, does not markedly differ from 1.2 and the corresponding distributions do not depend on the mainshock's magnitude threshold in a statistically significant manner. Finally, the analysis of the cumulative distribution functions provides evidence in favour of the proposed model.
文摘With the assistance of the symbolic computation system Maple,rich higher order polynomial-type conservation laws and a sixth order t/x-dependent conservation law are constructed for a generalized seventh order nonlinear evolution equation by using a direct algebraic method.From the compatibility conditions that guaranteeing the existence of conserved densities,an integrable unnamed seventh order KdV-type equation is found.By introducing some nonlinear transformations,the one-,two-,and three-solition solutions as well as the solitary wave solutions are obtained.
基金supported by the National Natural Science Foundation of China (Grant Nos.10774153 and 61078080)the National Basic Research Program of China (Grant Nos.2010CB923203 and 2011CB808103)
文摘Using a nonperturbative quantum electrodynamics theory of high-order harmonic generation (HHG), a scaling law of HHG is established. The scaling law states that when the atomic binding energy Eb, the wavelength ), and the intensity I of the laser field change simultaneously to kEb, λ/k, and k3I, respectively. The characteristics of the HHG spectrum remain unchanged, while the harmonic yield is enhanced k3 times. That HHG obeys the same scaling law with above-threshold ionization is a solid proof of the fact that the two physical processes have similar physical mechanisms. The variation of integrated harmonic yields is also discussed.
基金Sponsored by the National Natural Science Foundation of China(Grant No.10372033)
文摘Scaling laws are addressed by analysing moments of velocity increments which obtained by Particle-image Velocimetry(PIV)system in the boundary layer of a flat plate.In the paper,we measure the moments of increments of upstream velocity(u'),longitudinal velocity(v')and ponderance of vorticity(dv'/dx)at Reθ=2167 in different wall distance and verify the anomaly of the scaling exponents of high-order structure functions with the increasing order of the moments,discuss the scaling of non-integer moments of order between+2 and-1.The difference of scaling exponents of low-order structure functions between the experimental data and Kolmogorov's,SL's(She & Leveque)prediction increases as the moment order decreases toward-1,which shows that the anomaly is manifested in low-oeder moments as well.However,for same order structure functions,the scaling exponents of v' and dv'/dx are not changeable in different wall distance.
基金Supported by the National Natural Science Foundation of China(61172182)
文摘To satisfy the terminal position and impact angel constraints,an optimal guidance problem was discussed for homing missiles. For a stationary or a slowly moving target on the ground,an extended trajectory shaping guidance lawconsidering a first-order autopilot lag( ETSG L-C FAL) was proposed. To derive the ETSG L-C FAL,a time-to-go- nth power weighted objection function was adopted and three different derivation methods were demonstrated while the Schwartz inequality method was mainly demonstrated.The performance of the ETSG L-C FAL and the ETSG L guidance laws was compared through simulation.Simulation results showthat although a first-order autopilot is introduced into the ETSG L-C FAL guidance system,the position miss distance and terminal impact angle error induced by the impact angle is zero for different guidance time.
基金part of the results(presented in stages)of"Research on the Legislative System of Cities with Subordinate Districts"(16XFX004)-a program of National Social Sciences Fund in Western China"Empirical Research on Local Legislation"(16XW16)-a research focus of Sichuan Academy of Social Sciences under a key program launched by the Publicity Department of the CPC Sichuan Provincial Committee
文摘The lack of descriptions regarding the order of precedence between the local laws of cities with subordinate districts and the regulations of provincial governments in Legislation Law of the People's Republic of China(Legislation Law) has led to two divergent views. One holds that "the local laws of cities with subordinate districts should take precedence over the regulations of provincial governments," while the other supports the exact opposite. This is a value judgment issue in legislation. To reach a solution, we need to clarify the premises based on the characteristics of the laws in question so that a basic common ground can be established for discussion. The first premise for traditional legislation is that a law should be based on experience as well as logic; the second is that the experience of authority subjects, plus the three aspects of logic should outweigh the experience of social subjects, plus the three aspects of logic. With respect to postmodern legislation, the first premise is that experience should override logic, and the second is that the experience of the authority subject should take precedence over that of social subject, with no requirements for logical consistency. Since Legislation Law fal s into the category of postmodern legislation, according to the premises, the argument that the local laws of cities with subordinate districts should take precedence enjoys wider acceptance, but the view is logically challenged in terms of conceptual consistency, system consistency and principle consistency. More studies must be conducted to facilitate the discussion.
基金the Shahrood University of Technology for financial support of this study
文摘Equations of steady inviscid and laminar flows are solved by means of a third-order finite volume (FV) scheme. For this purpose, a cell-centered discretization technique is employed. In this technique, the flow parameters at the cell faces are computed using a third-order weighted averages procedure. A fourth-order artificial dissipation is used for stability of the solution. In order to achieve the steady-state situation, four-step Runge-Kutta explicit time integration method is applied. An advanced progressive preconditioning method, named the power-law preconditioning method, is used for faster convergence. In this method, the preconditioning matrix is adjusted automatically from the velocity and/or pressure flow-field by a power-law relation. Attention is directed towards accuracy and convergence of the schemes. The results presented in the paper focus on steady inviscid and laminar flows around sheet-cavitating and fully-wetted bodies including hydrofoils and circular/elliptical cylinder. Excellent agreements are obtained when numerical predictions are compared with other available experimental and numerical results. In addition, it is found that using the power-law preconditioner significantly increases the numerical convergence speed.