@techreport{oai:ipsj.ixsq.nii.ac.jp:00222146,
 author = {永井, 信夫 and 真田, 博文 and 谷萩, 隆嗣 and Nobuo, Nagai and Hirofumi, Sanada and Takashi, Yahagi},
 issue = {7},
 month = {Nov},
 note = {電磁気現象の一つに屈折と同時に生じる部分反射があるが，物理学では電磁気を変分法で取り扱うことが多く，変分法では部分反射を無視している．数学の分野では，部分反射を意識することなく，波動方程式から Fuchs function が導かれ，それからモジュラー形式を導出した．回路理論で用いられる「縦続行列」は電圧と電流とが双対性を満たす二つの関数で表され，それらは同一の空間に存在していて，縦続行列はそれらを線形結合で表す数学的な道具であり，しかもモジュラー形式をも持つことが示された．今後の研究課題として，電磁気や量子力学に，モジュラー形式と双対性とを持った縦続行列を応用することにより，新しい機能や作用を明らかにする研究につなげることが期待できる．, Partial reflection is an electromagnetic phenomenon that occurs concurrently with refraction, but the presence of partial reflection is ignored in the variation method, which is frequently used to analyze electromagnetic phenomena in physics. In mathematics, Fuchs functions were derived from wave equations without considering partial reflection, and modular forms were then derived from the Fuchs functions. This paper shows that the cascade matrices used in circuit theory are expressed using two functions with duality, that is, voltage and current, serve as a mathematical tool expressed by a linear combination existing in an identical space, and have a modular form. In future work, it is expected that new functions and actions of the cascade matrices with a modular form and duality can be clarified through their application to electromagnetics and quantum mechanics.},
 title = {１次元波動方程式から導出される線形の方程式の数学的な性質},
 year = {2022}
}