An asymptotic existence of balanced incomplete block (BIB) designs and pairwise balanced designs (PBD) has been discussed in [1]-[3]. On the other hand, the existence of additive BIB designs and pairwise additive BIB ...An asymptotic existence of balanced incomplete block (BIB) designs and pairwise balanced designs (PBD) has been discussed in [1]-[3]. On the other hand, the existence of additive BIB designs and pairwise additive BIB designs with k = 2?and?λ = 1?has been discussed with direct and recursive constructions in [4]-[8]. In this paper, an asymptotic existence of pairwise additive BIB designs is proved by use of Wilson’s theorem on PBD, and?also for some l?and k the exact existence of l?pairwise additive BIB designs with block size k and?λ = 1?is discussed.展开更多
We present some convergence and boundedness theorems with respect to filter convergence for lattice group-valued measures. We give a direct proof, based on the sliding hump argument. Furthermore we pose some open prob...We present some convergence and boundedness theorems with respect to filter convergence for lattice group-valued measures. We give a direct proof, based on the sliding hump argument. Furthermore we pose some open problems.展开更多
The scattering and reflection of SH waves by a slope on an elastic wedged space is investigated. A series solution is obtained by using the wave function expansion method. The slope on a wedged space is divided into t...The scattering and reflection of SH waves by a slope on an elastic wedged space is investigated. A series solution is obtained by using the wave function expansion method. The slope on a wedged space is divided into two subregions by an artificial, auxiliary circular arc. The wave fields with unknown complex coefficients within each sub-region are derived. Applying Graf addition theorem, the scattered waves in the sub-regions are expressed in a global coordinate system. Fourier transform is adopted to derive a consistent form of standing waves in the inner region using the orthogonality of the cosine functions. The boundary-valued problem is solved by stress and displacement continuity along the artificial, auxiliary arc to obtain the unknown complex coefficients. Parametric studies are next performed to investigate how the topography from the slope on the wedged space will affect the scattering and diffraction, and hence the amplification and de-amplification of the SH waves. Numerical results show that the surface motions on the slope of the wedged space is influenced greatly by the topography. Amplification of the surface motions near the slope vertex is significant. The corresponding phases along the wedged space surfaces are consistent with the direction that the SH waves are propagating.展开更多
In this paper, the principle of mirror image is used to transform the problem of wave diffraction from a circular cylinder in front of orthogonal vertical walls into the problem of diffraction of four symmetric incide...In this paper, the principle of mirror image is used to transform the problem of wave diffraction from a circular cylinder in front of orthogonal vertical walls into the problem of diffraction of four symmetric incident waves from four symmetrically arranged circular cylinders, and then the eigenfunction expansion of velocity potential and Grafs addition theorem are used to give the analytical solution to the wave diffraction problem. The relation of the total wave force on cylinder to the distance between the cylinder and orthogonal vertical walls and the incidence angle of wave is also studied by numerical computation.展开更多
My previous work dealt finding numbers which relatively prime to factorial value of certain number, high exponents and also find the way for finding mod values on certain number’s exponents. Firstly, I retreat my pre...My previous work dealt finding numbers which relatively prime to factorial value of certain number, high exponents and also find the way for finding mod values on certain number’s exponents. Firstly, I retreat my previous works about Euler’s phi function and some works on Fermat’s little theorem. Next, I construct exponent parallelogram to find coherence numbers of Euler’s phi functioned numbers and apply to Fermat’s little theorem. Then, I test the primality of prime numbers on Pascal’s triangle and explore new ways to construct Pascal’s triangle. Finally, I find the factorial value for certain number by using exponent triangle.展开更多
文摘An asymptotic existence of balanced incomplete block (BIB) designs and pairwise balanced designs (PBD) has been discussed in [1]-[3]. On the other hand, the existence of additive BIB designs and pairwise additive BIB designs with k = 2?and?λ = 1?has been discussed with direct and recursive constructions in [4]-[8]. In this paper, an asymptotic existence of pairwise additive BIB designs is proved by use of Wilson’s theorem on PBD, and?also for some l?and k the exact existence of l?pairwise additive BIB designs with block size k and?λ = 1?is discussed.
文摘We present some convergence and boundedness theorems with respect to filter convergence for lattice group-valued measures. We give a direct proof, based on the sliding hump argument. Furthermore we pose some open problems.
文摘The scattering and reflection of SH waves by a slope on an elastic wedged space is investigated. A series solution is obtained by using the wave function expansion method. The slope on a wedged space is divided into two subregions by an artificial, auxiliary circular arc. The wave fields with unknown complex coefficients within each sub-region are derived. Applying Graf addition theorem, the scattered waves in the sub-regions are expressed in a global coordinate system. Fourier transform is adopted to derive a consistent form of standing waves in the inner region using the orthogonality of the cosine functions. The boundary-valued problem is solved by stress and displacement continuity along the artificial, auxiliary arc to obtain the unknown complex coefficients. Parametric studies are next performed to investigate how the topography from the slope on the wedged space will affect the scattering and diffraction, and hence the amplification and de-amplification of the SH waves. Numerical results show that the surface motions on the slope of the wedged space is influenced greatly by the topography. Amplification of the surface motions near the slope vertex is significant. The corresponding phases along the wedged space surfaces are consistent with the direction that the SH waves are propagating.
基金financially supported by the National Natural Science Foundation of China(Grant No.50025924).
文摘In this paper, the principle of mirror image is used to transform the problem of wave diffraction from a circular cylinder in front of orthogonal vertical walls into the problem of diffraction of four symmetric incident waves from four symmetrically arranged circular cylinders, and then the eigenfunction expansion of velocity potential and Grafs addition theorem are used to give the analytical solution to the wave diffraction problem. The relation of the total wave force on cylinder to the distance between the cylinder and orthogonal vertical walls and the incidence angle of wave is also studied by numerical computation.
文摘My previous work dealt finding numbers which relatively prime to factorial value of certain number, high exponents and also find the way for finding mod values on certain number’s exponents. Firstly, I retreat my previous works about Euler’s phi function and some works on Fermat’s little theorem. Next, I construct exponent parallelogram to find coherence numbers of Euler’s phi functioned numbers and apply to Fermat’s little theorem. Then, I test the primality of prime numbers on Pascal’s triangle and explore new ways to construct Pascal’s triangle. Finally, I find the factorial value for certain number by using exponent triangle.
