In recent years,polarization remote sensing has garnered increasing attention,particularly within the realm of meteorology.To accurately simulate polarization information,the vector discrete-ordinate radiative transfe...In recent years,polarization remote sensing has garnered increasing attention,particularly within the realm of meteorology.To accurately simulate polarization information,the vector discrete-ordinate radiative transfer(VDISORT)model developed earlier by the community is further enhanced to an advanced version(referred to as A-VDISORT)through an improved ocean surface reflection.The Fresnel reflection matrix,which includes wind-generated roughness and shading effects,is served by an ocean bidirectional reflection distribution function(BRDF).The simulation from AVDISORT is compared with SCIATRAN for a Rayleigh scattering atmosphere,and the influence of water-leaving radiance is analyzed by the PSTAR(Polarized System for Transfer of Atmospheric Radiation) model.For GaoFen-5 Directional Polarimetric Camera(DPC) observations with polarization and multi-angle information,clear-sky pixel recognition over the ocean is first carried out.The DPC reflectance of clear conditions is normalized and compared with the observations.It is shown that A-VDISORT has a high simulation accuracy with a bias of –0.0053.The difference between simulation and observation exhibits a standard normal probability distribution function.展开更多
We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions(BCs):the homogeneous Robin BCs and the mixed...We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions(BCs):the homogeneous Robin BCs and the mixed Neumann/Dirichlet BCs.The construction is based on the so-called dressing the boundary,which generates soliton solutions by preserving the integrable BCs at each step of the Darboux-dressing process.Under the Robin BCs,examples,including boundary-bound solitons,are explicitly derived;under the mixed Neumann/Dirichlet BCs,the boundary can act as a polarizer that tunes different components of the vector solitons.Connection of our construction to the inverse scattering transform is also provided.展开更多
MacCormack explicit scheme and Baldwin-Lomax algebraic turbulent model are employed to solve the axisymmetric compressible Navier-Stokes equations for the numerical simulation of the supersonic mustanl floats interact...MacCormack explicit scheme and Baldwin-Lomax algebraic turbulent model are employed to solve the axisymmetric compressible Navier-Stokes equations for the numerical simulation of the supersonic mustanl floats interacted with transverse injection at the base of a cone. A temperature switch function must be added to the artificial viscous model suggested by jameson etc to enhance the scheme's ability to eliminate oscillation for some injection case.The typical code optimization techniques about vectorization and some useful concepts and terminology about multiprocessing of YH-2 parallel supercmputer is given and explatined with some examples After reconstruction and optimization the code gets a spedup 5 .973 on pipeline computer YH- 1 and gets a speedup 1 886 for 2 processors and 3.545 for 4 processors on YH-2 parallel supeercomputer by using domain decomposition method..展开更多
This paper is concerned with the following second-order vector boundary value problem ：x^R=f（t,Sx,x,x＇）,0〈t〈1,x（0）=A,g（x（1）,x＇（1））=B,where x,f,g,A and B are n-vectors. Under appropriate assumptions,exis...This paper is concerned with the following second-order vector boundary value problem ：x^R=f（t,Sx,x,x＇）,0〈t〈1,x（0）=A,g（x（1）,x＇（1））=B,where x,f,g,A and B are n-vectors. Under appropriate assumptions,existence and uniqueness of solutions are obtained by using upper and lower solutions method.展开更多
The multi-cavity soft actuator is assembled from single-cavity soft actuator through a reasonable geometric distribution.It has the characteristic that the pneumatic soft actuator is driven by its own deformation and ...The multi-cavity soft actuator is assembled from single-cavity soft actuator through a reasonable geometric distribution.It has the characteristic that the pneumatic soft actuator is driven by its own deformation and has more degrees of freedom.Pneumatic soft actuator is widely used as an emerging discipline and its strong compliance has been greatly developed and applied.However,as the most application potential type of soft actuators,there is still a lack of simple and effective deformation prediction methods for studying the spatial deformation of multi-cavity soft actuators.To solve this problem,a vector equation method is proposed based on the analysis of the principle of the space deformation of the two-cavity,three-cavity and four-cavity soft actuators.Furthermore,a nonlinear mathematical model of the air pressure,space position and deformation trajectory of the soft actuator end is established by combining the vector equation method.Finally,the three-channel soft actuator is verified through experiments.The results show that the mathematical model can better predict the space deformation trajectory of the soft actuator,which provides a new research method for studying the space deformation of the multi-channel soft actuator.展开更多
In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L 2(? s ). Suppose ψ = (ψ1,..., ψ r ) T and $ \tilde \psi = (\tilde \psi ^1 ,...,\tilde \psi ^r )^T $ ...In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L 2(? s ). Suppose ψ = (ψ1,..., ψ r ) T and $ \tilde \psi = (\tilde \psi ^1 ,...,\tilde \psi ^r )^T $ are two compactly supported vectors of functions in the Sobolev space (H μ(? s )) r for some μ > 0. We provide a characterization for the sequences {ψ jk l : l = 1,...,r, j ε ?, k ε ? s } and $ \tilde \psi _{jk}^\ell :\ell = 1,...,r,j \in \mathbb{Z},k \in \mathbb{Z}^s $ to form two Riesz sequences for L 2(? s ), where ψ jk l = m j/2ψ l (M j ·?k) and $ \tilde \psi _{jk}^\ell = m^{{j \mathord{\left/ {\vphantom {j 2}} \right. \kern-0em} 2}} \tilde \psi ^\ell (M^j \cdot - k) $ , M is an s × s integer matrix such that lim n→∞ M ?n = 0 and m = |detM|. Furthermore, let ? = (?1,...,? r ) T and $ \tilde \phi = (\tilde \phi ^1 ,...,\tilde \phi ^r )^T $ be a pair of compactly supported biorthogonal refinable vectors of functions associated with the refinement masks a, $ \tilde a $ and M, where a and $ \tilde a $ are finitely supported sequences of r × r matrices. We obtain a general principle for characterizing vectors of functions ψν = (ψν1,...,ψνr ) T and $ \tilde \psi ^\nu = (\tilde \psi ^{\nu 1} ,...,\tilde \psi ^{\nu r} )^T $ , ν = 1,..., m ? 1 such that two sequences {ψ jk νl : ν = 1,..., m ? 1, l = 1,...,r, j ε ?, k ε ? s } and { $ \tilde \psi _{jk}^\nu $ : ν=1,...,m?1,?=1,...,r, j ∈ ?, k ∈ ? s } form two Riesz multiwavelet bases for L 2(? s ). The bracket product [f, g] of two vectors of functions f, g in (L 2(? s )) r is an indispensable tool for our characterization.展开更多
This paper is concerned with the finite time blow-up phenomena for the vector nonlinear Schrdinger equations with a magnetic field which describe the spontaneous generation of a magnetic field in a cold plasma in the ...This paper is concerned with the finite time blow-up phenomena for the vector nonlinear Schrdinger equations with a magnetic field which describe the spontaneous generation of a magnetic field in a cold plasma in the subsonic limit. After obtaining some a priori estimates,we prove under certain natural conditions that the solutions to the Cauchy problem of the vector nonlinear Schrdinger equations in two and three spatial dimensions blow up in a finite time. Assuming that a solution to the aforementioned vector nonlinear Schrdinger equations is radially symmetric with respect to spatial variables x,we show that if the initial energy is non-positive,then the solution blows up in three dimensions in a finite time.展开更多
The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate a...The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.展开更多
In this paper, we consider a class of nonlinear vector differential equations of sixth order. By constructing appropriate Lyapunov functions, the non-existence of periodic solutions is established. Moreover, we provid...In this paper, we consider a class of nonlinear vector differential equations of sixth order. By constructing appropriate Lyapunov functions, the non-existence of periodic solutions is established. Moreover, we provide an example to show the feasibility of our results. Our results extend and improve two related results in the previous literature from scalar cases to vectorial cases.展开更多
The present work provides a novel method for calculating vertical velocity based on continuity equations in a pressure coordinate system.The method overcomes the disadvantage of accumulation of calculating errors of h...The present work provides a novel method for calculating vertical velocity based on continuity equations in a pressure coordinate system.The method overcomes the disadvantage of accumulation of calculating errors of horizontal divergence in current kinematics methods during the integration for calculating vertical velocity,and consequently avoids its subsequent correction.In addition,through modifications of the continuity equations,it shows that the vorticity of the vertical shear vector(VVSV) is proportional to-ω,the vertical velocity in p coordinates.Furthermore,if the change of ω in the horizontal direction is neglected,the vorticity of the horizontal vorticity vector is proportional to-ω.When ω is under a fluctuating state in the vertical direction,the updraft occurs when the vector of horizontal vorticity rotates counterclockwise;the downdraft occurs when rotating clockwise.The validation result indicates that the present method is generally better than the vertical velocity calculated by the ω equation using the wet Q-vector divergence as a forcing term,and the vertical velocity calculated by utilizing the kinematics method is followed by the O'Brien method for correction.The plus-minus sign of the vertical velocity obtained with this method is not correlated with the intensity of d BZ,but the absolute error increases when d BZ is >=40.This method demonstrates that it is a good reflection of the direction of the vertical velocity.展开更多
This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous liter...This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous literature,which is related to the instability of the zero solution to a nonlinear scalar differential equation of fourth order.展开更多
This paper gives sufficient conditions for the global asmptotic stability of the zero solution of the differential equation (1. 1). The result improves and generalizes the wellknown results.
In this paper, by constructing a Lyapunov functional, sufficient conditions for the uniform stability of the zero solution to a fourth-order vector delay differential equation are given.
The main purpose of verifiable secret sharing scheme is to solve the honesty problem of participants. In this paper, the concept of nonzero <em>k</em>-submatrix and theresidual vector of system of hyperpla...The main purpose of verifiable secret sharing scheme is to solve the honesty problem of participants. In this paper, the concept of nonzero <em>k</em>-submatrix and theresidual vector of system of hyperplane intersecting line equations is proposed. Based on certain projective transformations in projective space, a verifiable (<em>t</em>, <em>n</em>)-threshold secret sharing scheme is designed by using the structure of solutions of linear equations and the difficulty of solving discrete logarithm problems. The results show that this scheme can verify the correctness of the subkey provided by each participant before the reconstruction of the master key, and can effectively identify the fraudster. The fraudster can only cheat by guessing and the probability of success is only 1/<em>p</em>. The design of the scheme is exquisite and the calculation complexity is small. Each participant only needs to hold a subkey, which is convenient for management and use. The analysis shows that the scheme in this paper meets the security requirements and rules of secret sharing, and it is a computationally secure and effective scheme with good practical value.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.U2142212)National Key R&D Program of China(Grant No.2019QZKK,Qinghai Tibet KeKao)the National Natural Science Foundation of China(Grant No.U2242211)。
文摘In recent years,polarization remote sensing has garnered increasing attention,particularly within the realm of meteorology.To accurately simulate polarization information,the vector discrete-ordinate radiative transfer(VDISORT)model developed earlier by the community is further enhanced to an advanced version(referred to as A-VDISORT)through an improved ocean surface reflection.The Fresnel reflection matrix,which includes wind-generated roughness and shading effects,is served by an ocean bidirectional reflection distribution function(BRDF).The simulation from AVDISORT is compared with SCIATRAN for a Rayleigh scattering atmosphere,and the influence of water-leaving radiance is analyzed by the PSTAR(Polarized System for Transfer of Atmospheric Radiation) model.For GaoFen-5 Directional Polarimetric Camera(DPC) observations with polarization and multi-angle information,clear-sky pixel recognition over the ocean is first carried out.The DPC reflectance of clear conditions is normalized and compared with the observations.It is shown that A-VDISORT has a high simulation accuracy with a bias of –0.0053.The difference between simulation and observation exhibits a standard normal probability distribution function.
文摘We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions(BCs):the homogeneous Robin BCs and the mixed Neumann/Dirichlet BCs.The construction is based on the so-called dressing the boundary,which generates soliton solutions by preserving the integrable BCs at each step of the Darboux-dressing process.Under the Robin BCs,examples,including boundary-bound solitons,are explicitly derived;under the mixed Neumann/Dirichlet BCs,the boundary can act as a polarizer that tunes different components of the vector solitons.Connection of our construction to the inverse scattering transform is also provided.
文摘MacCormack explicit scheme and Baldwin-Lomax algebraic turbulent model are employed to solve the axisymmetric compressible Navier-Stokes equations for the numerical simulation of the supersonic mustanl floats interacted with transverse injection at the base of a cone. A temperature switch function must be added to the artificial viscous model suggested by jameson etc to enhance the scheme's ability to eliminate oscillation for some injection case.The typical code optimization techniques about vectorization and some useful concepts and terminology about multiprocessing of YH-2 parallel supercmputer is given and explatined with some examples After reconstruction and optimization the code gets a spedup 5 .973 on pipeline computer YH- 1 and gets a speedup 1 886 for 2 processors and 3.545 for 4 processors on YH-2 parallel supeercomputer by using domain decomposition method..
文摘This paper is concerned with the following second-order vector boundary value problem ：x^R=f（t,Sx,x,x＇）,0〈t〈1,x（0）=A,g（x（1）,x＇（1））=B,where x,f,g,A and B are n-vectors. Under appropriate assumptions,existence and uniqueness of solutions are obtained by using upper and lower solutions method.
基金the National Natural Science Foundation of China(No.11604205)。
文摘The multi-cavity soft actuator is assembled from single-cavity soft actuator through a reasonable geometric distribution.It has the characteristic that the pneumatic soft actuator is driven by its own deformation and has more degrees of freedom.Pneumatic soft actuator is widely used as an emerging discipline and its strong compliance has been greatly developed and applied.However,as the most application potential type of soft actuators,there is still a lack of simple and effective deformation prediction methods for studying the spatial deformation of multi-cavity soft actuators.To solve this problem,a vector equation method is proposed based on the analysis of the principle of the space deformation of the two-cavity,three-cavity and four-cavity soft actuators.Furthermore,a nonlinear mathematical model of the air pressure,space position and deformation trajectory of the soft actuator end is established by combining the vector equation method.Finally,the three-channel soft actuator is verified through experiments.The results show that the mathematical model can better predict the space deformation trajectory of the soft actuator,which provides a new research method for studying the space deformation of the multi-channel soft actuator.
基金supported by National Natural Science Foundation of China (Grant Nos. 10771190, 10471123)
文摘In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L 2(? s ). Suppose ψ = (ψ1,..., ψ r ) T and $ \tilde \psi = (\tilde \psi ^1 ,...,\tilde \psi ^r )^T $ are two compactly supported vectors of functions in the Sobolev space (H μ(? s )) r for some μ > 0. We provide a characterization for the sequences {ψ jk l : l = 1,...,r, j ε ?, k ε ? s } and $ \tilde \psi _{jk}^\ell :\ell = 1,...,r,j \in \mathbb{Z},k \in \mathbb{Z}^s $ to form two Riesz sequences for L 2(? s ), where ψ jk l = m j/2ψ l (M j ·?k) and $ \tilde \psi _{jk}^\ell = m^{{j \mathord{\left/ {\vphantom {j 2}} \right. \kern-0em} 2}} \tilde \psi ^\ell (M^j \cdot - k) $ , M is an s × s integer matrix such that lim n→∞ M ?n = 0 and m = |detM|. Furthermore, let ? = (?1,...,? r ) T and $ \tilde \phi = (\tilde \phi ^1 ,...,\tilde \phi ^r )^T $ be a pair of compactly supported biorthogonal refinable vectors of functions associated with the refinement masks a, $ \tilde a $ and M, where a and $ \tilde a $ are finitely supported sequences of r × r matrices. We obtain a general principle for characterizing vectors of functions ψν = (ψν1,...,ψνr ) T and $ \tilde \psi ^\nu = (\tilde \psi ^{\nu 1} ,...,\tilde \psi ^{\nu r} )^T $ , ν = 1,..., m ? 1 such that two sequences {ψ jk νl : ν = 1,..., m ? 1, l = 1,...,r, j ε ?, k ε ? s } and { $ \tilde \psi _{jk}^\nu $ : ν=1,...,m?1,?=1,...,r, j ∈ ?, k ∈ ? s } form two Riesz multiwavelet bases for L 2(? s ). The bracket product [f, g] of two vectors of functions f, g in (L 2(? s )) r is an indispensable tool for our characterization.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171241, 10801102, 11071177)
文摘This paper is concerned with the finite time blow-up phenomena for the vector nonlinear Schrdinger equations with a magnetic field which describe the spontaneous generation of a magnetic field in a cold plasma in the subsonic limit. After obtaining some a priori estimates,we prove under certain natural conditions that the solutions to the Cauchy problem of the vector nonlinear Schrdinger equations in two and three spatial dimensions blow up in a finite time. Assuming that a solution to the aforementioned vector nonlinear Schrdinger equations is radially symmetric with respect to spatial variables x,we show that if the initial energy is non-positive,then the solution blows up in three dimensions in a finite time.
文摘The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.
文摘In this paper, we consider a class of nonlinear vector differential equations of sixth order. By constructing appropriate Lyapunov functions, the non-existence of periodic solutions is established. Moreover, we provide an example to show the feasibility of our results. Our results extend and improve two related results in the previous literature from scalar cases to vectorial cases.
基金National Key Basic Research Development Program"973"(2013CB430103,2009CB421503)National Natural Science Funding(41375058,41530427)State Key Laboratory of Severe Weather,Chinese Academy of Meteorological Sciences(2015LASW-A07)
文摘The present work provides a novel method for calculating vertical velocity based on continuity equations in a pressure coordinate system.The method overcomes the disadvantage of accumulation of calculating errors of horizontal divergence in current kinematics methods during the integration for calculating vertical velocity,and consequently avoids its subsequent correction.In addition,through modifications of the continuity equations,it shows that the vorticity of the vertical shear vector(VVSV) is proportional to-ω,the vertical velocity in p coordinates.Furthermore,if the change of ω in the horizontal direction is neglected,the vorticity of the horizontal vorticity vector is proportional to-ω.When ω is under a fluctuating state in the vertical direction,the updraft occurs when the vector of horizontal vorticity rotates counterclockwise;the downdraft occurs when rotating clockwise.The validation result indicates that the present method is generally better than the vertical velocity calculated by the ω equation using the wet Q-vector divergence as a forcing term,and the vertical velocity calculated by utilizing the kinematics method is followed by the O'Brien method for correction.The plus-minus sign of the vertical velocity obtained with this method is not correlated with the intensity of d BZ,but the absolute error increases when d BZ is >=40.This method demonstrates that it is a good reflection of the direction of the vertical velocity.
文摘This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous literature,which is related to the instability of the zero solution to a nonlinear scalar differential equation of fourth order.
文摘This paper gives sufficient conditions for the global asmptotic stability of the zero solution of the differential equation (1. 1). The result improves and generalizes the wellknown results.
文摘In this paper, by constructing a Lyapunov functional, sufficient conditions for the uniform stability of the zero solution to a fourth-order vector delay differential equation are given.
文摘The main purpose of verifiable secret sharing scheme is to solve the honesty problem of participants. In this paper, the concept of nonzero <em>k</em>-submatrix and theresidual vector of system of hyperplane intersecting line equations is proposed. Based on certain projective transformations in projective space, a verifiable (<em>t</em>, <em>n</em>)-threshold secret sharing scheme is designed by using the structure of solutions of linear equations and the difficulty of solving discrete logarithm problems. The results show that this scheme can verify the correctness of the subkey provided by each participant before the reconstruction of the master key, and can effectively identify the fraudster. The fraudster can only cheat by guessing and the probability of success is only 1/<em>p</em>. The design of the scheme is exquisite and the calculation complexity is small. Each participant only needs to hold a subkey, which is convenient for management and use. The analysis shows that the scheme in this paper meets the security requirements and rules of secret sharing, and it is a computationally secure and effective scheme with good practical value.
