By using the technique of integration within an ordered product （IWOP） of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we...By using the technique of integration within an ordered product （IWOP） of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator.展开更多
First we calculate the Wigner phase-space distribution function for the Klein-Gordan Landau problem ona commmutative space.Then we study the modifications introduced by the coordinate-coordinate noncommuting andmoment...First we calculate the Wigner phase-space distribution function for the Klein-Gordan Landau problem ona commmutative space.Then we study the modifications introduced by the coordinate-coordinate noncommuting andmomentum-momentum noncommuting, namely, by using a generalized Bopp’s shift method we construct the Wignerfunction for the Klein-Gordan Landau problem both on a noncommutative space (NCS) and a noncommutative phasespace (NCPS).展开更多
In this paper,we obtain the fractal dimension of the graph of the Weierstrass function, its derivative of the fractional order and the relation between the dimension and the order of the fractional derivative.
Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method wa...Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.展开更多
In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the （2＋1）-dimensional variable coefficients Broer-Kaup （VCBK） equations. The...In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the （2＋1）-dimensional variable coefficients Broer-Kaup （VCBK） equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.展开更多
In this paper, the dimension formulaes of multivariate weak spline are discussed. The dimension formulaes of non-degree multivariate weak spline on a vertex are presented. The dimension formulaes on triangulation are ...In this paper, the dimension formulaes of multivariate weak spline are discussed. The dimension formulaes of non-degree multivariate weak spline on a vertex are presented. The dimension formulaes on triangulation are also discussed. At last, the local supported bases of W31(I1Δ) are presented.展开更多
In this paper, the author considers equations with critical exponent in n ≥4 space tions on the initial data, it is proved that there small the initial data are. the Cauchy problem for semilinear wave dimensions. Und...In this paper, the author considers equations with critical exponent in n ≥4 space tions on the initial data, it is proved that there small the initial data are. the Cauchy problem for semilinear wave dimensions. Under some positivity condican be no global solutions no matter how展开更多
This research aimed to study the sound absorption properties of natural fibers and their reinforced composites.Sound absorption coefficients of three types of natural fibers,i.e.,ramie,flax and jute fibers and their c...This research aimed to study the sound absorption properties of natural fibers and their reinforced composites.Sound absorption coefficients of three types of natural fibers,i.e.,ramie,flax and jute fibers and their composites were measured by the two-microphone transfer function technique in the impedance tube.The results were compared with synthetic fibers and their composites.It was found that both natural fibers and their composites had superior capability of noise reduction.The multi-scale and hollow lumen structures of natural fibers contributed to the high sound absorption performance.Moreover,the sound absorption properties of these natural fibers were also calculated by the Delany-Bazley and Garai-Pompoli models.They showed good agreement with the experimental data.It was concluded that multi-functional composite materials can be made by natural fibers so that both the mechanical and acoustical functions can be achieved.展开更多
In this paper,we consider sets of points with some restricts on the digits of theirα-Lroth expansions.More precisely,for any countable partitionα={An,n∈N}of the unit interval I,we completely determine the Hausdorf ...In this paper,we consider sets of points with some restricts on the digits of theirα-Lroth expansions.More precisely,for any countable partitionα={An,n∈N}of the unit interval I,we completely determine the Hausdorf dimensions of the sets F(α,φ)=x=[l1(x),l2(x),...]α∈I:ln(x)φ(n),n 1,whereφis an arbitrary positive function defined on N satisfyingφ(n)→∞as n→∞.展开更多
With the speed upgrade of the high-speed train,the aerodynamic drag becomes one of the key factors to restrain the train speed and energy saving.In order to reduce the aerodynamic drag of train head,a new parametric a...With the speed upgrade of the high-speed train,the aerodynamic drag becomes one of the key factors to restrain the train speed and energy saving.In order to reduce the aerodynamic drag of train head,a new parametric approach called local shape function(LSF) was adopted based on the free form surface deformation(FFD) method and a new efficient optimization method based on the response surface method(RSM) of GA-GRNN.The optimization results show that the parametric method can control the large deformation with a few design parameters,and can ensure the deformation zones smoothness and smooth transition of different deformation regions.With the same sample points for training,GA-GRNN performs better than GRNN to get the global optimal solution.As an example,the aerodynamic drag for a simplified shape with head + one carriage + tail train is reduced by 8.7%.The proposed optimization method is efficient for the engineering design of high-speed train.展开更多
This paper proves that the first eigenfunctions of the Finsler p-Lapalcian are C^(1,α). Using a gradient comparison theorem and one-dimensional model, we obtain the sharp lower bound of the first Neumann and closed e...This paper proves that the first eigenfunctions of the Finsler p-Lapalcian are C^(1,α). Using a gradient comparison theorem and one-dimensional model, we obtain the sharp lower bound of the first Neumann and closed eigenvalue of the p-Laplacian on a compact Finsler manifold with nonnegative weighted Ricci curvature,on which a lower bound of the first Dirichlet eigenvalue of the p-Laplacian is also obtained.展开更多
基金the Natural Science Foundation of Heze University of Shandong Province of China under Grant Nos.XY07WL01 and XY05WL01the University Experimental Technology Foundation of Shandong Province of China under Grant No.S04W138
文摘By using the technique of integration within an ordered product （IWOP） of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10965006 and 10875035
文摘First we calculate the Wigner phase-space distribution function for the Klein-Gordan Landau problem ona commmutative space.Then we study the modifications introduced by the coordinate-coordinate noncommuting andmomentum-momentum noncommuting, namely, by using a generalized Bopp’s shift method we construct the Wignerfunction for the Klein-Gordan Landau problem both on a noncommutative space (NCS) and a noncommutative phasespace (NCPS).
基金Project supported by National Natural Science Foundation of China.
文摘In this paper,we obtain the fractal dimension of the graph of the Weierstrass function, its derivative of the fractional order and the relation between the dimension and the order of the fractional derivative.
基金Supported by the National Natural Science Foundation of China under Grant No.50921001973 Program under Grant No. 2010CB83270
文摘Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.
基金The project supported by National Natural Science Foundation of China undcr Grant No. 10172056 .
文摘In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the （2＋1）-dimensional variable coefficients Broer-Kaup （VCBK） equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.
基金Project supported by the National Natural Science Foundation of China (19871010, 69973010)
文摘In this paper, the dimension formulaes of multivariate weak spline are discussed. The dimension formulaes of non-degree multivariate weak spline on a vertex are presented. The dimension formulaes on triangulation are also discussed. At last, the local supported bases of W31(I1Δ) are presented.
基金Project supported by the National Natural Science Foundation of China (No. 10225102)the 973 Project of the Ministry of Science and Technology of China.
文摘In this paper, the author considers equations with critical exponent in n ≥4 space tions on the initial data, it is proved that there small the initial data are. the Cauchy problem for semilinear wave dimensions. Under some positivity condican be no global solutions no matter how
基金supported by the National Basic Research Program of China ("973" Program) (Grant No. 2010CB631105)
文摘This research aimed to study the sound absorption properties of natural fibers and their reinforced composites.Sound absorption coefficients of three types of natural fibers,i.e.,ramie,flax and jute fibers and their composites were measured by the two-microphone transfer function technique in the impedance tube.The results were compared with synthetic fibers and their composites.It was found that both natural fibers and their composites had superior capability of noise reduction.The multi-scale and hollow lumen structures of natural fibers contributed to the high sound absorption performance.Moreover,the sound absorption properties of these natural fibers were also calculated by the Delany-Bazley and Garai-Pompoli models.They showed good agreement with the experimental data.It was concluded that multi-functional composite materials can be made by natural fibers so that both the mechanical and acoustical functions can be achieved.
基金supported by National Natural Science Foundation of China (Grant No.11071090)
文摘In this paper,we consider sets of points with some restricts on the digits of theirα-Lroth expansions.More precisely,for any countable partitionα={An,n∈N}of the unit interval I,we completely determine the Hausdorf dimensions of the sets F(α,φ)=x=[l1(x),l2(x),...]α∈I:ln(x)φ(n),n 1,whereφis an arbitrary positive function defined on N satisfyingφ(n)→∞as n→∞.
基金supported by the National Basic Research Program of China ("973" Project) (Grant No. 2011CB711100)the National Hi-Tech Research and Development Program of China ("863" Project) (Grant No.2009BAQG12A03)Computing Facility for Computational Mechanics,Institute of Mechanics,Chinese Academy of Sciences
文摘With the speed upgrade of the high-speed train,the aerodynamic drag becomes one of the key factors to restrain the train speed and energy saving.In order to reduce the aerodynamic drag of train head,a new parametric approach called local shape function(LSF) was adopted based on the free form surface deformation(FFD) method and a new efficient optimization method based on the response surface method(RSM) of GA-GRNN.The optimization results show that the parametric method can control the large deformation with a few design parameters,and can ensure the deformation zones smoothness and smooth transition of different deformation regions.With the same sample points for training,GA-GRNN performs better than GRNN to get the global optimal solution.As an example,the aerodynamic drag for a simplified shape with head + one carriage + tail train is reduced by 8.7%.The proposed optimization method is efficient for the engineering design of high-speed train.
基金supported by National Natural Science Foundation of China (Grant No. 11471246)Natural Science Foundation of Higher Education in Anhui Province (Grant No. KJ2014A257)
文摘This paper proves that the first eigenfunctions of the Finsler p-Lapalcian are C^(1,α). Using a gradient comparison theorem and one-dimensional model, we obtain the sharp lower bound of the first Neumann and closed eigenvalue of the p-Laplacian on a compact Finsler manifold with nonnegative weighted Ricci curvature,on which a lower bound of the first Dirichlet eigenvalue of the p-Laplacian is also obtained.
