In this paper, we discuss the estimation of the number of zeros of the Abelian integral for the quadratic system which has a periodic region with a parabola and a straight line as its boundary when we perturb the syst...In this paper, we discuss the estimation of the number of zeros of the Abelian integral for the quadratic system which has a periodic region with a parabola and a straight line as its boundary when we perturb the system inside the class of all polynomial systems of degree n. The main result is that the upper bound for the number of zeros of the Abelian integral associated to this system is 3n-1.展开更多
In this paper, a transfer matrix and a three-dimensional dynamic response of a layered half-space to an arbitrary buried source are derived with the aid of a technique which combines the Laplace and two-dimensional Fo...In this paper, a transfer matrix and a three-dimensional dynamic response of a layered half-space to an arbitrary buried source are derived with the aid of a technique which combines the Laplace and two-dimensional Fourier transforms in a rectangular coordinate system. This method is clear in concept, and the corresponding formulas given in the paper are simple and convenient for marine seismic prospecting and other fields' applications. An example is presented and the calculated results are in good agreement with those of the finite element method (FEM).展开更多
The new inversion formula of the Laplace transform is considered. In the formula we use only the positive values ofx SiCoLT（x） = c S（x）, L（S（x）） = T（x）, c = const., x 〉 O,from the real axis. Si is the sinus...The new inversion formula of the Laplace transform is considered. In the formula we use only the positive values ofx SiCoLT（x） = c S（x）, L（S（x）） = T（x）, c = const., x 〉 O,from the real axis. Si is the sinus transform, Co is the cosines transform of Fourier and L is the Laplace transform.展开更多
In this paper,we point out that the Fourier series of a classical function∑^∞k=1 sin kx/k has the Gibbs phenomenon in the neighborhood of zero.Furthermore,we estimate the upper bound of its partial sum and get：sup ...In this paper,we point out that the Fourier series of a classical function∑^∞k=1 sin kx/k has the Gibbs phenomenon in the neighborhood of zero.Furthermore,we estimate the upper bound of its partial sum and get：sup n≥1｜｜∑^n k=1sin kx/k｜｜=∫^x 0sin x/x dx=1.85194, which is better than that in[1].展开更多
Let λkbe the k-th Dirichlet eigenvalue of totally characteristic degenerate elliptic operator-ΔB defined on a stretched cone B0 ■ [0,1) × X with boundary on {x1 = 0}. More precisely,ΔB=(x1αx1)2+ α2x2+ + α2...Let λkbe the k-th Dirichlet eigenvalue of totally characteristic degenerate elliptic operator-ΔB defined on a stretched cone B0 ■ [0,1) × X with boundary on {x1 = 0}. More precisely,ΔB=(x1αx1)2+ α2x2+ + α2xnis also called the cone Laplacian. In this paper,by using Mellin-Fourier transform,we prove thatλk Cnk2 n for any k 1,where Cn=(nn+2)(2π)2(|B0|Bn)-2n,which gives the lower bounds of the Dirchlet eigenvalues of-ΔB. On the other hand,by using the Rayleigh-Ritz inequality,we deduce the upper bounds ofλk,i.e.,λk+1 1 +4n k2/nλ1. Combining the lower and upper bounds of λk,we can easily obtain the lower bound for the first Dirichlet eigenvalue λ1 Cn(1 +4n)-12n2.展开更多
The analytical solutions of non-Fourier Pennes and Chen Holmes equations are obtained using the Laplace transformation and particular solution method in the present paper. As an application, the effects of the thermal...The analytical solutions of non-Fourier Pennes and Chen Holmes equations are obtained using the Laplace transformation and particular solution method in the present paper. As an application, the effects of the thermal relaxation time % the blood perfusion wb, and the blood flow velocity v on the biological skin and inner tissue temperature T are stxldied in detail The results obtained in this study provide a good alternative method to study the bio-heat and a biophysical insight into the understanding of the heat transfer in the biotissue.展开更多
In the present study, using the Fourier analysis method and considering the Bianchi-type I spacetime, we investigate the dynamics of photon in the torsion gravity, and show that the free-space Maxwell equations give t...In the present study, using the Fourier analysis method and considering the Bianchi-type I spacetime, we investigate the dynamics of photon in the torsion gravity, and show that the free-space Maxwell equations give the same results. Furthermore, we also discuss the harmonic oscillator behavior of the solutions.展开更多
文摘In this paper, we discuss the estimation of the number of zeros of the Abelian integral for the quadratic system which has a periodic region with a parabola and a straight line as its boundary when we perturb the system inside the class of all polynomial systems of degree n. The main result is that the upper bound for the number of zeros of the Abelian integral associated to this system is 3n-1.
基金funded by the Natural Science Foundation Projeet of State(40174030)the Natural Science Foundation Project of Shandong Province(Y2000E05)
文摘In this paper, a transfer matrix and a three-dimensional dynamic response of a layered half-space to an arbitrary buried source are derived with the aid of a technique which combines the Laplace and two-dimensional Fourier transforms in a rectangular coordinate system. This method is clear in concept, and the corresponding formulas given in the paper are simple and convenient for marine seismic prospecting and other fields' applications. An example is presented and the calculated results are in good agreement with those of the finite element method (FEM).
文摘The new inversion formula of the Laplace transform is considered. In the formula we use only the positive values ofx SiCoLT（x） = c S（x）, L（S（x）） = T（x）, c = const., x 〉 O,from the real axis. Si is the sinus transform, Co is the cosines transform of Fourier and L is the Laplace transform.
基金Foundation item： the Natural Science Foundation of Zhejiang Province （No. 102058）.
文摘In this paper,we point out that the Fourier series of a classical function∑^∞k=1 sin kx/k has the Gibbs phenomenon in the neighborhood of zero.Furthermore,we estimate the upper bound of its partial sum and get：sup n≥1｜｜∑^n k=1sin kx/k｜｜=∫^x 0sin x/x dx=1.85194, which is better than that in[1].
基金supported by National Natural Science Foundation of China(Grant No.11131005)
文摘Let λkbe the k-th Dirichlet eigenvalue of totally characteristic degenerate elliptic operator-ΔB defined on a stretched cone B0 ■ [0,1) × X with boundary on {x1 = 0}. More precisely,ΔB=(x1αx1)2+ α2x2+ + α2xnis also called the cone Laplacian. In this paper,by using Mellin-Fourier transform,we prove thatλk Cnk2 n for any k 1,where Cn=(nn+2)(2π)2(|B0|Bn)-2n,which gives the lower bounds of the Dirchlet eigenvalues of-ΔB. On the other hand,by using the Rayleigh-Ritz inequality,we deduce the upper bounds ofλk,i.e.,λk+1 1 +4n k2/nλ1. Combining the lower and upper bounds of λk,we can easily obtain the lower bound for the first Dirichlet eigenvalue λ1 Cn(1 +4n)-12n2.
文摘The analytical solutions of non-Fourier Pennes and Chen Holmes equations are obtained using the Laplace transformation and particular solution method in the present paper. As an application, the effects of the thermal relaxation time % the blood perfusion wb, and the blood flow velocity v on the biological skin and inner tissue temperature T are stxldied in detail The results obtained in this study provide a good alternative method to study the bio-heat and a biophysical insight into the understanding of the heat transfer in the biotissue.
文摘In the present study, using the Fourier analysis method and considering the Bianchi-type I spacetime, we investigate the dynamics of photon in the torsion gravity, and show that the free-space Maxwell equations give the same results. Furthermore, we also discuss the harmonic oscillator behavior of the solutions.
