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52 papers
A Quadratic Curve Analogue of the Taniyama-Shimura Conjecture
Masahito Hayashi, Kazuyasu Shigemoto, Takuya Tsukioka
For quadratic curves over , the number of solutions, which is governed by an analogue of the Mordell-Weil group, is expressed with the Legendre symbol of a coefficient of quad…
Various Logistic Curves in SIS and SIR Models
Kazuyasu Shigemoto
In our previous paper, the logistic curve of the removed number was derived from SIR and SEIR models in the case of the small basic reproduction number. In this paper, we derive va…
The Half-period Addition Formulae for Genus Two Hyperelliptic Functions and the Sp(4,) Lie Group Structure
Masahito Hayashi, Kazuyasu Shigemoto, Takuya Tsukioka
In the previous study, by using the two-flows Kowalevski top, we have demonstrated that the genus two hyperelliptic functions provide the Sp(4,)/ SO(3,2) L…
Comments on the Aharonov-Bohm Effect
Kazuyasu Shigemoto, Kunihiko Uehara
In the original setting of the Aharonov-Bohm, the gauge invariant physical longitudinal mode of the vector potential, which is written by the gauge invariant physical current $(-e)…
Two Flows Kowalevski Top as the Full Genus Two Jacobi's Inversion Problem and Sp(4,) Lie Group Structure
Masahito Hayashi, Kazuyasu Shigemoto, Takuya Tsukioka
By using the first and the second flows of the Kowalevski top, we can make the Kowalevski top into the two flows Kowalevski top, which has two time variales. Then we show that equa…
Differential Equations of Genus Four Hyperelliptic Functions
Masahito Hayashi, Kazuyasu Shigemoto, Takuya Tsukioka
In order to find higher dimensional integrable models, we study differential equations of hyperelliptic functions up to genus four. For genus two, differential equations of h…