The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Teori matematik gelombang elektromagnet bikompleks dalam masalah serakan dan pembelauan dua dimensi dibangunkan. Ungkapan integral Vekua untuk medan dua dimensi yang sah hanya di kawasan bebas sumber tertutup digeneralisasikan ke dalam medan penyinaran. Masalah nilai sempadan untuk serakan dan pembelauan dirumuskan dalam ruang bikompleks. Fungsi kompleks pembolehubah tunggal, yang mematuhi hubungan Cauchy-Riemann dan dengan itu menyatakan aspek frekuensi rendah medan dekat pada baji penyerakan, disambungkan dengan medan penyinaran oleh pengendali kamiran yang mempunyai kernel yang sesuai. Tingkah laku fungsi kompleks ini di seluruh ruang dibincangkan bersama-sama dengan medan zon jauh atau amplitud spektrum sudut. Skim pemfaktoran Hilbert digunakan untuk mengetahui penjelmaan linear daripada medan zon jauh kepada fungsi bernilai dwikompleks bagi pembolehubah tunggal. Transformasi ini terbukti unik. Ungkapan kamiran baharu untuk medan yang bertaburan oleh jalur logam nipis juga diperolehi.
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Salinan
Masahiro HASHIMOTO, "Bicomplex Waves in Electromagnetic Scattering and Diffraction Problems" in IEICE TRANSACTIONS on Electronics,
vol. E83-C, no. 2, pp. 236-247, February 2000, doi: .
Abstract: The mathematical theory of bicomplex electromagnetic waves in two-dimensional scattering and diffraction problems is developed. The Vekua's integral expression for the two-dimensional fields valid only in the closed source-free region is generalized into the radiating field. The boundary-value problems for scattering and diffraction are formulated in the bicomplex space. The complex function of a single variable, which obeys the Cauchy-Riemann relations and thus expresses low-frequency aspects of the near field at a wedge of the scatterer, is connected with the radiating field by an integral operator having a suitable kernel. The behaviors of this complex function in the whole space are discussed together with those of the far-zone field or the amplitude of angular spectrum. The Hilbert's factorization scheme is used to find out a linear transformation from the far-zone field to the bicomplex-valued function of a single variable. This transformation is shown to be unique. The new integral expression for the field scattered by a thin metallic strip is also obtained.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/e83-c_2_236/_p
Salinan
@ARTICLE{e83-c_2_236,
author={Masahiro HASHIMOTO, },
journal={IEICE TRANSACTIONS on Electronics},
title={Bicomplex Waves in Electromagnetic Scattering and Diffraction Problems},
year={2000},
volume={E83-C},
number={2},
pages={236-247},
abstract={The mathematical theory of bicomplex electromagnetic waves in two-dimensional scattering and diffraction problems is developed. The Vekua's integral expression for the two-dimensional fields valid only in the closed source-free region is generalized into the radiating field. The boundary-value problems for scattering and diffraction are formulated in the bicomplex space. The complex function of a single variable, which obeys the Cauchy-Riemann relations and thus expresses low-frequency aspects of the near field at a wedge of the scatterer, is connected with the radiating field by an integral operator having a suitable kernel. The behaviors of this complex function in the whole space are discussed together with those of the far-zone field or the amplitude of angular spectrum. The Hilbert's factorization scheme is used to find out a linear transformation from the far-zone field to the bicomplex-valued function of a single variable. This transformation is shown to be unique. The new integral expression for the field scattered by a thin metallic strip is also obtained.},
keywords={},
doi={},
ISSN={},
month={February},}
Salinan
TY - JOUR
TI - Bicomplex Waves in Electromagnetic Scattering and Diffraction Problems
T2 - IEICE TRANSACTIONS on Electronics
SP - 236
EP - 247
AU - Masahiro HASHIMOTO
PY - 2000
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E83-C
IS - 2
JA - IEICE TRANSACTIONS on Electronics
Y1 - February 2000
AB - The mathematical theory of bicomplex electromagnetic waves in two-dimensional scattering and diffraction problems is developed. The Vekua's integral expression for the two-dimensional fields valid only in the closed source-free region is generalized into the radiating field. The boundary-value problems for scattering and diffraction are formulated in the bicomplex space. The complex function of a single variable, which obeys the Cauchy-Riemann relations and thus expresses low-frequency aspects of the near field at a wedge of the scatterer, is connected with the radiating field by an integral operator having a suitable kernel. The behaviors of this complex function in the whole space are discussed together with those of the far-zone field or the amplitude of angular spectrum. The Hilbert's factorization scheme is used to find out a linear transformation from the far-zone field to the bicomplex-valued function of a single variable. This transformation is shown to be unique. The new integral expression for the field scattered by a thin metallic strip is also obtained.
ER -