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Asymptotic Analysis of Diffraction Integrals in Gevrey Spaces
No full textWe present an overview on the state of the art of the research on the asymptotic
behavior of diffraction integrals, i.e., the oscillatory integrals employed in the Fresnel theory
of optics. We focus on the behavior of such integrals in the presence of standard caustics, in
particular the elliptic and the hyperbolic umbilics, adopting the functional setting of Gevrey
spaces. We also derive new estimates for the shadow region of the hyperbolic umbilic in
terms of the distance from the caustic under symmetry condition in the space of parameters
Gelfand–Shilov Spaces: Structural Properties and Applications to Pseudodifferential Operators in ℝ n
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Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Cauchy Problem for Second-order Hyperbolic Equations for Shubin Pseudodifferential Operators
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