By using integral transform methods, the Green(s functions of horizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equ...By using integral transform methods, the Green(s functions of horizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique. Utilizing the above- mentioned general solutions, and the boundary conditions of the surface of the half-space and the continuous conditions at the plane of the horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse Hankel transforms method, the Green(s functions of the harmonic horizontal force are obtainable. The degenerate case of the results deduced from this paper agrees well with the known results. Two numerical examples are given in the paper.展开更多
The general expressions of finite Hankel transform are naturally deduced with the help of the property of Bessel functions.The equations in this paper can degenerate into three kinds of boundaries since all the coeffi...The general expressions of finite Hankel transform are naturally deduced with the help of the property of Bessel functions.The equations in this paper can degenerate into three kinds of boundaries since all the coefficients in the boundary conditions are taken into consideration.The results can be adopted in solving physics problems involving the finite Hankel transform.展开更多
Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with...Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with a realizable (rational) transfer function thanks to the Adamjan, Arov and Krein (AAK) theorem. It is well known that the one dimensional AAK results give the best approximation of a polynomial as a rational function in the Hankel semi norm. We suppose that the Hankel matrix associated to the transfer function has a finite rank.展开更多
We introduce a primitive class of analytic functions, by specializing in many wellknown classes, classify Ma-Minda functions based on its conditions and their interesting geometrical aspects. Further, study a newly de...We introduce a primitive class of analytic functions, by specializing in many wellknown classes, classify Ma-Minda functions based on its conditions and their interesting geometrical aspects. Further, study a newly defined subclass of starlike functions involving a special type of Ma-Minda function introduced here for obtaining inclusion and radius results. We also establish some majorization, Bloch function norms, and other related problems for the same class.展开更多
The Hankel transform is an important transform. In this paper, westudy the wavelets associated with the Hankel transform, thendefine the Weyl transform of the wavelets. We give criteria of itsboundedness and compactne...The Hankel transform is an important transform. In this paper, westudy the wavelets associated with the Hankel transform, thendefine the Weyl transform of the wavelets. We give criteria of itsboundedness and compactness on the Lp-spaces.展开更多
基金State Natural Science Foundation (59879012) and Doctoral Foundation from State Education Commission (98024832).
文摘By using integral transform methods, the Green(s functions of horizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique. Utilizing the above- mentioned general solutions, and the boundary conditions of the surface of the half-space and the continuous conditions at the plane of the horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse Hankel transforms method, the Green(s functions of the harmonic horizontal force are obtainable. The degenerate case of the results deduced from this paper agrees well with the known results. Two numerical examples are given in the paper.
基金supported by the National Natural Scientific Foundation of China (Grant Nos.10972103 and 10902055)the National Science Foundation for Postdoctoral Scientists of China (Grant No.20070411046)
文摘The general expressions of finite Hankel transform are naturally deduced with the help of the property of Bessel functions.The equations in this paper can degenerate into three kinds of boundaries since all the coefficients in the boundary conditions are taken into consideration.The results can be adopted in solving physics problems involving the finite Hankel transform.
文摘Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with a realizable (rational) transfer function thanks to the Adamjan, Arov and Krein (AAK) theorem. It is well known that the one dimensional AAK results give the best approximation of a polynomial as a rational function in the Hankel semi norm. We suppose that the Hankel matrix associated to the transfer function has a finite rank.
基金supported by the Faculty Research Project grant of DTU(DTU/Council/BOM-AC/Notification-/31/2018/5738)Research Fellowship from the Department of Science and Technology,New Delhi(IF170272)。
文摘We introduce a primitive class of analytic functions, by specializing in many wellknown classes, classify Ma-Minda functions based on its conditions and their interesting geometrical aspects. Further, study a newly defined subclass of starlike functions involving a special type of Ma-Minda function introduced here for obtaining inclusion and radius results. We also establish some majorization, Bloch function norms, and other related problems for the same class.
基金This work was supported by the National Natural Science Foundation of China(Grant No.90104004)973 Project of China(Grant No.G1999075105).
文摘The Hankel transform is an important transform. In this paper, westudy the wavelets associated with the Hankel transform, thendefine the Weyl transform of the wavelets. We give criteria of itsboundedness and compactness on the Lp-spaces.
