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2016
The focus of this chapter is a detailed analysis of two specific positive definite functions, each one defined in a fixed finite interval, centered at x = 0. Rationale: The examples serve to make explicit some of the many connections between our general theme (locally defined p.d. functions and their extensions), on the one hand; and probability theory
Palle Jorgensen +2 more
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The focus of this chapter is a detailed analysis of two specific positive definite functions, each one defined in a fixed finite interval, centered at x = 0. Rationale: The examples serve to make explicit some of the many connections between our general theme (locally defined p.d. functions and their extensions), on the one hand; and probability theory
Palle Jorgensen +2 more
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2019
Green’s functions provide a simple and elegant way to solve differential equations, such as the wave equation in electrodynamics, and play an important role in nano optics. In this chapter we start by introducing the basic concepts of Green’s functions for the simplified scalar wave equation, and then ponder on the solutions of the full Maxwell’s ...
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Green’s functions provide a simple and elegant way to solve differential equations, such as the wave equation in electrodynamics, and play an important role in nano optics. In this chapter we start by introducing the basic concepts of Green’s functions for the simplified scalar wave equation, and then ponder on the solutions of the full Maxwell’s ...
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1992
In this chapter we derive Green’s functions useful for scattering and propagation problems. We present a thorough discussion of one-dimensional problems as well as many examples. The Green’s functions for the wave and Helmholtz equations are derived and interrelated for one, two, and three dimensions.
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In this chapter we derive Green’s functions useful for scattering and propagation problems. We present a thorough discussion of one-dimensional problems as well as many examples. The Green’s functions for the wave and Helmholtz equations are derived and interrelated for one, two, and three dimensions.
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2006
Earlier we considered the phenomenon of a grounded conducting surface surrounding a charged body. We saw that the surface acquired an induced charge, and the combined potential of the charge on the body and the induced charge on the surface equals zero on the surface.
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Earlier we considered the phenomenon of a grounded conducting surface surrounding a charged body. We saw that the surface acquired an induced charge, and the combined potential of the charge on the body and the induced charge on the surface equals zero on the surface.
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1978
One approach to the solution of non-homogeneous boundary value problems is by means of the construction of functions known as Green’s functions. Historically, the concept originated with work on potential theory published by Green in 1828. Green’s work has provided the germs of a much wider formulation for solving a variety of eigenvalue, boundary ...
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One approach to the solution of non-homogeneous boundary value problems is by means of the construction of functions known as Green’s functions. Historically, the concept originated with work on potential theory published by Green in 1828. Green’s work has provided the germs of a much wider formulation for solving a variety of eigenvalue, boundary ...
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1998
Green’s functions are useful in solving the first boundary value problem (Dirichlet problem) of potential theory in itself and in the case of conformal mapping of a region onto a disk. In the latter case a relationship is needed between the conformal map and Green’s function for the region.
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Green’s functions are useful in solving the first boundary value problem (Dirichlet problem) of potential theory in itself and in the case of conformal mapping of a region onto a disk. In the latter case a relationship is needed between the conformal map and Green’s function for the region.
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2009
The goal of theoretical physics consists in developing methods for the calculation of measurable physical quantities.
Wolfgang Nolting, William D. Brewer
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The goal of theoretical physics consists in developing methods for the calculation of measurable physical quantities.
Wolfgang Nolting, William D. Brewer
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1988
An open subset D of ₵n is called pseudoconvex if −log d(z, CD) is plurisubharmonic. \(\left( {d\left( {z,CD} \right) = _{w \in CD}^{\inf }\left| {z - w} \right|} \right)\).
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An open subset D of ₵n is called pseudoconvex if −log d(z, CD) is plurisubharmonic. \(\left( {d\left( {z,CD} \right) = _{w \in CD}^{\inf }\left| {z - w} \right|} \right)\).
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2016
In Chap. 2, Sect. 2.1.1, we considered one method, variation of parameters (or variation of constants ), for solving the linear inhomogeneous differential equation. In the method considered here, rather than determining the solution to the differential equation with the inhomogeneous term defined at each point of the interval, we consider the equation ...
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In Chap. 2, Sect. 2.1.1, we considered one method, variation of parameters (or variation of constants ), for solving the linear inhomogeneous differential equation. In the method considered here, rather than determining the solution to the differential equation with the inhomogeneous term defined at each point of the interval, we consider the equation ...
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Forced vibration of pipe conveying fluid by the Green function method
, 2014Yun-dong Li, Yi-ren Yang
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