A technique based on the double Fourier series is developed to estimate the winds at different isobaric levels forthe limited area domain, 35°E to 140°E and 30°S to 40°N, using the observed winds a...A technique based on the double Fourier series is developed to estimate the winds at different isobaric levels forthe limited area domain, 35°E to 140°E and 30°S to 40°N, using the observed winds at 850 hPa lcvcl for the month ofJune. For this purpose the wind field at a level under consideration is taken in the ratio form with that of 850 hPa level and the coefficients of the double Fouricr series are computed. These coefficients are subsequently used to computethe winds which are compared with the actual winds. The results of the double Fourier series technique are comparedwith those of the polynomial surface fitting method developed by Bavadekar and Khaladkar (1 992). The technique isalso applied for the daily wind data of 11. June, 1979 and the validation of the technique is tested for a few radiosondestations of india. The computed winds for these radiosonde stations arc quite close to observed winds.展开更多
It this paper we construct a double Fourier series with a new linear summation factor, for the arbitrary continuous periodic function f(x,y)with period 2л, it converges to the function(fx,y) uniformly on total opl...It this paper we construct a double Fourier series with a new linear summation factor, for the arbitrary continuous periodic function f(x,y)with period 2л, it converges to the function(fx,y) uniformly on total oplane,and its convergence order is the best one.展开更多
We consider complex-valued functions f ∈ L^1 (R^2+), where R+ := [0,∞), and prove sufficient conditions under which the double sine Fourier transform fss and the double cosine Fourier transform fcc belong to o...We consider complex-valued functions f ∈ L^1 (R^2+), where R+ := [0,∞), and prove sufficient conditions under which the double sine Fourier transform fss and the double cosine Fourier transform fcc belong to one of the two-dimensional Lipschitz classes Lip(a,β) for some 0 〈 α,β ≤ 1; or to one of the Zygmund classes Zyg(α,β) for some 0 〈 α,β ≤ 2. These sufficient conditions are best possible in the sense that they are also necessary for nonnegative-valued functions f ∈ L^1 (R^2+).展开更多
A study on dynamic response of transversely isotropic saturated poroelastic media under a circular non-axisymmetrical harmonic source has been presented by Huang Yi et al. using the technique of Fourier expansion and ...A study on dynamic response of transversely isotropic saturated poroelastic media under a circular non-axisymmetrical harmonic source has been presented by Huang Yi et al. using the technique of Fourier expansion and Hankel transform. However, the method may not always be valid. The work is extended to the general case being in the rectangular coordinate. The purpose is to study the 3-d dynamic response of transversely isotropic saturated soils under a general source distributing in arbitrary rectangular zoon on the medium surface. Based on Biot's theory for fluid- saturated porous media, the 3-d wave motion equations in rectangular coordinate for transversely isotropic saturated poroelastic media were transformed into the two uncoupling governing differential equations of 6-order and 2-order respectively by means of the displacement functions. Then, using the technique of double Fourier transform, the governing differential equations were easily solved. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media were obtained. Furthermore, a systematic study on half-space problem in saturated soils was performed. Integral solutions for surface displacements under the general harmonic source distributing on arbitrary surface zone, considering both case of drained surface and undrained surface, were presented.展开更多
This paper presents a formulation for solving three-dimensional moving punch problem. It proves that Galin's theorem holds for the punch. As an example, the study offers some results (including numerical data) of ...This paper presents a formulation for solving three-dimensional moving punch problem. It proves that Galin's theorem holds for the punch. As an example, the study offers some results (including numerical data) of dynamic displacement over an ellipse contact region.展开更多
Starting with the governing equations in terms of displacements of 3D elastic media, the solutions to displacement components and their first derivatives are obtained by the application of a double Fourier transform a...Starting with the governing equations in terms of displacements of 3D elastic media, the solutions to displacement components and their first derivatives are obtained by the application of a double Fourier transform and an order reduction method based on the Cayley-Hamilton theorem. Combining the solutions and the constitutive equations which connect the displacements and stresses, the transfer matrix of a single soil layer is acquired. Then, the state space solution to multilayered elastic soils is further obtained by introducing the boundary conditions and continuity conditions between adjacent soil layers. The numerical analysis based on the present theory is carried out, and the vertical displacements of multilayered foundation with a weak and a hard underlying stratums are compared and discussed.展开更多
We prove the boundedness from Lp(T2) to itself, 1 〈 p 〈∞, of highly oscillatory singular integrals Sf(x, y) presenting singularities of the kind of the double Hilbert transform on a non-rectangular domain of in...We prove the boundedness from Lp(T2) to itself, 1 〈 p 〈∞, of highly oscillatory singular integrals Sf(x, y) presenting singularities of the kind of the double Hilbert transform on a non-rectangular domain of integration, roughly speaking, defined by |y′| 〉 |x′|, and presenting phases λ(Ax + By) with 0≤ A, B ≤ 1 and λ≥ 0. The norms of these oscillatory singular integrals are proved to be independent of all parameters A1 B and A involved. Our method extends to a more general family of phases. These results are relevant to problems of almost everywhere convergence of double Fourier and Walsh series.展开更多
文摘A technique based on the double Fourier series is developed to estimate the winds at different isobaric levels forthe limited area domain, 35°E to 140°E and 30°S to 40°N, using the observed winds at 850 hPa lcvcl for the month ofJune. For this purpose the wind field at a level under consideration is taken in the ratio form with that of 850 hPa level and the coefficients of the double Fouricr series are computed. These coefficients are subsequently used to computethe winds which are compared with the actual winds. The results of the double Fourier series technique are comparedwith those of the polynomial surface fitting method developed by Bavadekar and Khaladkar (1 992). The technique isalso applied for the daily wind data of 11. June, 1979 and the validation of the technique is tested for a few radiosondestations of india. The computed winds for these radiosonde stations arc quite close to observed winds.
文摘It this paper we construct a double Fourier series with a new linear summation factor, for the arbitrary continuous periodic function f(x,y)with period 2л, it converges to the function(fx,y) uniformly on total oplane,and its convergence order is the best one.
基金Supported partially by the Program TMOP-4.2.2/08/1/2008-0008 of the Hungarian National Development Agency
文摘We consider complex-valued functions f ∈ L^1 (R^2+), where R+ := [0,∞), and prove sufficient conditions under which the double sine Fourier transform fss and the double cosine Fourier transform fcc belong to one of the two-dimensional Lipschitz classes Lip(a,β) for some 0 〈 α,β ≤ 1; or to one of the Zygmund classes Zyg(α,β) for some 0 〈 α,β ≤ 2. These sufficient conditions are best possible in the sense that they are also necessary for nonnegative-valued functions f ∈ L^1 (R^2+).
文摘A study on dynamic response of transversely isotropic saturated poroelastic media under a circular non-axisymmetrical harmonic source has been presented by Huang Yi et al. using the technique of Fourier expansion and Hankel transform. However, the method may not always be valid. The work is extended to the general case being in the rectangular coordinate. The purpose is to study the 3-d dynamic response of transversely isotropic saturated soils under a general source distributing in arbitrary rectangular zoon on the medium surface. Based on Biot's theory for fluid- saturated porous media, the 3-d wave motion equations in rectangular coordinate for transversely isotropic saturated poroelastic media were transformed into the two uncoupling governing differential equations of 6-order and 2-order respectively by means of the displacement functions. Then, using the technique of double Fourier transform, the governing differential equations were easily solved. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media were obtained. Furthermore, a systematic study on half-space problem in saturated soils was performed. Integral solutions for surface displacements under the general harmonic source distributing on arbitrary surface zone, considering both case of drained surface and undrained surface, were presented.
文摘This paper presents a formulation for solving three-dimensional moving punch problem. It proves that Galin's theorem holds for the punch. As an example, the study offers some results (including numerical data) of dynamic displacement over an ellipse contact region.
文摘Starting with the governing equations in terms of displacements of 3D elastic media, the solutions to displacement components and their first derivatives are obtained by the application of a double Fourier transform and an order reduction method based on the Cayley-Hamilton theorem. Combining the solutions and the constitutive equations which connect the displacements and stresses, the transfer matrix of a single soil layer is acquired. Then, the state space solution to multilayered elastic soils is further obtained by introducing the boundary conditions and continuity conditions between adjacent soil layers. The numerical analysis based on the present theory is carried out, and the vertical displacements of multilayered foundation with a weak and a hard underlying stratums are compared and discussed.
文摘We prove the boundedness from Lp(T2) to itself, 1 〈 p 〈∞, of highly oscillatory singular integrals Sf(x, y) presenting singularities of the kind of the double Hilbert transform on a non-rectangular domain of integration, roughly speaking, defined by |y′| 〉 |x′|, and presenting phases λ(Ax + By) with 0≤ A, B ≤ 1 and λ≥ 0. The norms of these oscillatory singular integrals are proved to be independent of all parameters A1 B and A involved. Our method extends to a more general family of phases. These results are relevant to problems of almost everywhere convergence of double Fourier and Walsh series.