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- Noboru Endou, Kazuhisa Nakasho, Yasunari Shidama
- Formalized Mathematics
- 2015

In this article, semi-ring and semi-algebra of sets are formalized so as to construct a measure of a given set in the next step. Although a semi-ring of sets has already been formalized in [12], that is, strictly speaking, a definition of a quasi semi-ring of sets suggested in the last few decades [14]. We adopt a classical definition of a semi-ring of sets… (More)

- Kazuhisa Nakasho, Yuichi Futa, Yasunari Shidama
- Formalized Mathematics
- 2014

In this article, we formalize topological properties of real normed spaces. In the first few parts, open and closed, density, separability and sequence and its convergence are discussed. Then we argue properties of real normed subspace. In the middle of the article, we discuss linear functions between real normed speces. Several kinds of subspaces induced… (More)

- Kazuhisa Nakasho, Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama
- Formalized Mathematics
- 2014

In this article, we formalize some basic facts of Z-module. In the first section, we discuss the rank of submodule of Z-module and its properties. Especially, we formally prove that the rank of any Z-module is equal to or more than that of its submodules, and vice versa, there exists a submodule with any given rank that satisfies the above condition. In the… (More)

- Yuichi Futa, Hiroyuki Okazaki, Kazuhisa Nakasho, Yasunari Shidama
- Formalized Mathematics
- 2014

In this article, we formalize a torsion Z-module and a torsionfree Z-module. Especially, we prove formally that finitely generated torsion-free Z-modules are finite rank free. We also formalize properties related to rank of finite rank free Z-modules. The notion of Z-module is necessary for solving lattice problems, LLL (Lenstra, Lenstra, and Lovász) base… (More)

- Kazuhisa Nakasho, Yasunari Shidama
- CICM
- 2015

The purpose of this project is to collect symbol information in the Mizar Mathematical Library and manipulate it into practical and organized documentation. Inspired by the MathWiki project and API reference systems for computer programs, we developed a documentation generator focusing on symbols for the HTML-ized Mizar library. The system has several… (More)

- Keiko Narita, Kazuhisa Nakasho, Yasunari Shidama
- Formalized Mathematics
- 2016

- Takuya Sasaki, Cairos Cuadra, Hirokazu Madokoro, Kazuhisa Nakasho, Nobuhiro Shimoi
- 2016 16th International Conference on Control…
- 2016

At present, approximately 60% of world's population lives in masonry structures. Some of these structures are found in developing countries experiencing frequent earthquakes. Strong earthquakes tend to collapse these brittle, "non-engineered" structures, causing great harm to humans when these are residential structures. The purpose of this… (More)

- Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki, Yasunari Shidama
- Formalized Mathematics
- 2015

In this article, direct sum decomposition of group is mainly discussed. In the second section, support of element of direct product group is defined and its properties are formalized. It is formalized here the fact that an element of direct product group belongs to its direct sum if and only if support of the element is finite. In the third section, product… (More)

- Hirokazu Madokoro, Kazuhito Sato, Kazuhisa Nakasho, Nobuhiro Shimoi
- 2017 International Joint Conference on Neural…
- 2017

This study was conducted to create driving episodes using machine-learning-based algorithms that address long-term memory (LTM) and topological mapping. This paper presents a novel episodic memory model for driving safety according to traffic scenes. The model incorporates three important features: adaptive resonance theory (ART), which learns time-series… (More)

- Kazuhisa Nakasho, Noboru Endou
- Formalized Mathematics
- 2015

In this article, the separability of real normed spaces and its properties are mainly formalized. In the first section, it is proved that a real normed subspace is separable if it is generated by a countable subset. We used here the fact that the rational numbers form a dense subset of the real numbers. In the second section, the basic properties of the… (More)