• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.99-110
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• 2022

The main object of this paper is to provide necessary and sufficient conditions for the generalized Struve functions of first kind to be in the classes 𝒮(k, λ) and 𝒞(k, λ). Furthermore, we give conditions for the integral operator 𝓛(m, c, z) = ∫^z₀(2 - u_p(t))dt to be in the class 𝒞^*(k, λ). Several corollaries and consequences of the main results are also considered.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.2
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• pp.109-122
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• 2023

In this study, we consider the application of the bifocusing method (BFM) for identifying the locations and shapes of small anomalies from scattering parameter data when the exact values of background permittivity and conductivity are unknown. To this end, an imaging function using numerical focusing operator is introduced and its mathematical structure is revealed by establishing a relationship with an infinite series of Bessel functions, antenna arrangements, and anomaly properties. On the basis of the revealed structure, we demonstrate why inaccurate location and size of anomalies were retrieved via the BFM. Some simulation results are illustrated using synthetic data polluted by random noise to support the theoretical result.