http://hdl.handle.net/11320/3583 2026-06-01T07:51:39Z http://hdl.handle.net/11320/3629 Tytuł: The Differentiable Functions from R into Rⁿ Autorzy: Narita, Keiko; Korniłowicz, Artur; Shidama, Yasunari Abstrakt: In control engineering, differentiable partial functions from R into Rⁿ play a very important role. In this article, we formalized basic properties of such functions. 2012-01-01T00:00:00Z http://hdl.handle.net/11320/3630 Tytuł: Some Basic Properties of Some Special Matrices. Part III Autorzy: Liang, Xiquan; Wang, Tao Abstrakt: This article describes definitions of subsymmetric matrix, anti-subsymmetric matrix, central symmetric matrix, symmetry circulant matrix and their basic properties. 2012-01-01T00:00:00Z http://hdl.handle.net/11320/3631 Tytuł: Riemann Integral of Functions from R into n-dimensional Real Normed Space Autorzy: Miyajima, Keiichi; Korniłowicz, Artur; Shidama, Yasunari Abstrakt: In this article, we define the Riemann integral on functions R into n-dimensional real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to the wider range. Our method refers to the [21] 2012-01-01T00:00:00Z http://hdl.handle.net/11320/3632 Tytuł: Operations of Points on Elliptic Curve in Projective Coordinates Autorzy: Futa, Yuichi; Okazaki, Hiroyuki; Mizushima, Daichi; Shidama, Yasunari Abstrakt: In this article, we formalize operations of points on an elliptic curve over GF(p). Elliptic curve cryptography [7], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security. We prove that the two operations of points: compellProjCo and addellProjCo are unary and binary operations of a point over the elliptic curve. 2012-01-01T00:00:00Z