phytochemicals
发表于 2025-3-23 12:52:15
The Sommerfeld Theory of Diffraction by Half-PlaneIn 1896 Sommerfeld calculated for the first time an exact solution to the stationary diffraction by the half-plane with the Dirichlet and Neumann b.c., see Nagem et al. (Arnold Sommerfeld. Springer, New York, 1994; Arnold Sommerfeld. Springer, New York, 2004).
morale
发表于 2025-3-23 16:57:25
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outskirts
发表于 2025-3-23 20:25:02
Extension to the PlaneWe extend Eq. (.) to the whole plane which is necessary for application of the Fourier transform.
发现
发表于 2025-3-23 23:58:55
Connection Equation on the Riemann SurfaceHere we obtain the third equation for the Cauchy data using the identity (.). One of the central ideas of our method is that this identity also holds in the complex region, in the .. defined by
收集
发表于 2025-3-24 02:26:13
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SLING
发表于 2025-3-24 07:33:02
Undetermined Algebraic Equations on the Riemann SurfaceWe can rewrite (.), (.) as an algebraic system on the Riemann surface. . By Lemma . the sets . are nonempty. Obviously, .. Consider the functions
上下连贯
发表于 2025-3-24 13:22:30
Automorphic Functions on the Riemann SurfaceThe algebraic system (.) and Eq. (.) are both undetermined. Hence, we need additional equations for the Cauchy data... We obtain the additional equations by the method of automorphic functions, which was introduced by Malyshev in the context of difference equations in the quadrant of the plane.
textile
发表于 2025-3-24 14:57:42
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Dedication
发表于 2025-3-24 22:49:39
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知识
发表于 2025-3-25 01:43:45
The FactorizationTo study properties of the factorization (.), we need some preparatory steps. First, we start with the proof of Proposition .. Then we study the edge-point values. Finally, we will reduce the problem to the one with equal edge-point values.