伪善
发表于 2025-3-26 21:55:23
Typical Integrals of Catastrophe Theory,atastrophes and also some more complex integrals associated with caustics that occur in series. A novel point in this exposition is the one of Fresnel’s criteria for passing over from some normal forms to others when external parameters vary.
Indelible
发表于 2025-3-27 04:49:12
Uniform Caustic Asymptotics Derived with Standard Integrals,its derivatives with respect to external parameters (Kravtsov-Ludwig technique) renders the asymptotic uniformly valid, that is, applicable both at short and at long distances from the caustic. We introduce the concepts of transverse and longitudinal caustic scales to derive uniformly-valid applicability conditions for the asymptotic expressions.
SLING
发表于 2025-3-27 07:18:35
Penumbra Caustics,ctions and their extensions. A close type of caustics is formed by the diffracted rays in the region of a diffraction penumbra. Both types of caustic, treated first by Yu.I. Orlov, correspond to the so-called edge catastrophes.
evasive
发表于 2025-3-27 11:24:54
Caustics Revisited,less Maxwell’s equations. Nevertheless manageable asymptotic solutions can be obtained for caustics in dispersive and anisotropic media, in nonlinear and random media and for related problems of quantum mechanics.
Gastric
发表于 2025-3-27 14:07:04
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减至最低
发表于 2025-3-27 18:38:28
https://doi.org/10.1007/978-3-7643-8994-9 be overestimated. The new approach has allowed one to classify caustics, to select among them structurally stable species, and to establish a subordinance for caustics of different complexity. It has been the historically first breakthrough to understanding the nature of caustics.
招待
发表于 2025-3-27 22:46:34
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通知
发表于 2025-3-28 04:25:02
Birkhäuser Advanced Texts‘ Basler Lehrbücherits derivatives with respect to external parameters (Kravtsov-Ludwig technique) renders the asymptotic uniformly valid, that is, applicable both at short and at long distances from the caustic. We introduce the concepts of transverse and longitudinal caustic scales to derive uniformly-valid applicab
PIZZA
发表于 2025-3-28 06:20:01
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凹处
发表于 2025-3-28 12:01:55
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