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BibTeX records: Hiroyuki Okazaki
@article{DBLP:journals/fm/Okazaki23, author = {Hiroyuki Okazaki}, title = {On the Formalization of Gram-Schmidt Process for Orthonormalizing a Set of Vectors}, journal = {Formaliz. Math.}, volume = {31}, number = {1}, pages = {53--57}, year = {2023}, url = {https://doi.org/10.2478/forma-2023-0005}, doi = {10.2478/FORMA-2023-0005}, timestamp = {Wed, 04 Oct 2023 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/Okazaki23.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/Okazaki22, author = {Hiroyuki Okazaki}, title = {Formalization of Orthogonal Decomposition for Hilbert Spaces}, journal = {Formaliz. Math.}, volume = {30}, number = {4}, pages = {295--299}, year = {2022}, url = {https://doi.org/10.2478/forma-2022-0023}, doi = {10.2478/FORMA-2022-0023}, timestamp = {Wed, 01 Mar 2023 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/Okazaki22.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/NakashoOS21, author = {Kazuhisa Nakasho and Hiroyuki Okazaki and Yasunari Shidama}, title = {Real Vector Space and Related NotionsThis study was supported in part by {JSPS} {KAKENHI} Grant Numbers 17K00182 and 20K19863}, journal = {Formaliz. Math.}, volume = {29}, number = {3}, pages = {117--127}, year = {2021}, url = {https://doi.org/10.2478/forma-2021-0012}, doi = {10.2478/FORMA-2021-0012}, timestamp = {Fri, 21 Jan 2022 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/NakashoOS21.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/NakashoOS21a, author = {Kazuhisa Nakasho and Hiroyuki Okazaki and Yasunari Shidama}, title = {Finite Dimensional Real Normed Spaces are Proper Metric Spaces}, journal = {Formaliz. Math.}, volume = {29}, number = {4}, pages = {175--184}, year = {2021}, url = {https://doi.org/10.2478/forma-2021-0017}, doi = {10.2478/FORMA-2021-0017}, timestamp = {Mon, 25 Jul 2022 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/NakashoOS21a.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/OkazakiN21, author = {Hiroyuki Okazaki and Kazuhisa Nakasho}, title = {The 3-Fold Product Space of Real Normed Spaces and its Properties}, journal = {Formaliz. Math.}, volume = {29}, number = {4}, pages = {241--248}, year = {2021}, url = {https://doi.org/10.2478/forma-2021-0022}, doi = {10.2478/FORMA-2021-0022}, timestamp = {Mon, 25 Jul 2022 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/OkazakiN21.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@inproceedings{DBLP:conf/aina/TokuyamaFSO21, author = {Ryo Tokuyama and Yuichi Futa and Hikofumi Suzuki and Hiroyuki Okazaki}, editor = {Leonard Barolli and Isaac Woungang and Tomoya Enokido}, title = {Virtual Environment for Analysis and Evaluation of DDoS Attacks}, booktitle = {Advanced Information Networking and Applications - Proceedings of the 35th International Conference on Advanced Information Networking and Applications (AINA-2021), Toronto, ON, Canada, 12-14 May, 2021, Volume 3}, series = {Lecture Notes in Networks and Systems}, volume = {227}, pages = {459--468}, publisher = {Springer}, year = {2021}, url = {https://doi.org/10.1007/978-3-030-75078-7\_46}, doi = {10.1007/978-3-030-75078-7\_46}, timestamp = {Thu, 12 Aug 2021 13:39:25 +0200}, biburl = {https://dblp.org/rec/conf/aina/TokuyamaFSO21.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@inproceedings{DBLP:conf/isita/MienoYOFA20, author = {Takehiko Mieno and Togo Yoshimura and Hiroyuki Okazaki and Yuichi Futa and Kenichi Arai}, title = {Formal Verification of Merkle-Damg{\aa}rd Construction in ProVerif}, booktitle = {International Symposium on Information Theory and Its Applications, {ISITA} 2020, Kapolei, HI, USA, October 24-27, 2020}, pages = {602--606}, publisher = {{IEEE}}, year = {2020}, url = {https://ieeexplore.ieee.org/document/9366163}, timestamp = {Mon, 22 Mar 2021 15:48:59 +0100}, biburl = {https://dblp.org/rec/conf/isita/MienoYOFA20.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/OkazakiNF19, author = {Hiroyuki Okazaki and Koh{-}ichi Nagao and Yuichi Futa}, title = {Maximum Number of Steps Taken by Modular Exponentiation and Euclidean Algorithm}, journal = {Formaliz. Math.}, volume = {27}, number = {1}, pages = {87--91}, year = {2019}, url = {https://doi.org/10.2478/forma-2019-0009}, doi = {10.2478/FORMA-2019-0009}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/OkazakiNF19.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/FutaOS19, author = {Yuichi Futa and Hiroyuki Okazaki and Yasunari Shidama}, title = {Operations of Points on Elliptic Curve in Affine Coordinates}, journal = {Formaliz. Math.}, volume = {27}, number = {3}, pages = {315--320}, year = {2019}, url = {https://doi.org/10.2478/forma-2019-0026}, doi = {10.2478/FORMA-2019-0026}, timestamp = {Thu, 07 Jan 2021 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/FutaOS19.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/Okazaki18, author = {Hiroyuki Okazaki}, title = {Binary Representation of Natural Numbers}, journal = {Formaliz. Math.}, volume = {26}, number = {3}, pages = {223--229}, year = {2018}, url = {https://doi.org/10.2478/forma-2018-0020}, doi = {10.2478/FORMA-2018-0020}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/Okazaki18.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@inproceedings{DBLP:conf/isita/OkazakiFA18, author = {Hiroyuki Okazaki and Yuichi Futa and Kenichi Arai}, title = {Suitable Symbolic Models for Cryptographic Verification of Secure Protocols in ProVerif}, booktitle = {International Symposium on Information Theory and Its Applications, {ISITA} 2018, Singapore, October 28-31, 2018}, pages = {326--330}, publisher = {{IEEE}}, year = {2018}, url = {https://doi.org/10.23919/ISITA.2018.8664273}, doi = {10.23919/ISITA.2018.8664273}, timestamp = {Wed, 11 Aug 2021 11:51:25 +0200}, biburl = {https://dblp.org/rec/conf/isita/OkazakiFA18.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/NakashoYOS16, author = {Kazuhisa Nakasho and Hiroshi Yamazaki and Hiroyuki Okazaki and Yasunari Shidama}, title = {Conservation Rules of Direct Sum Decomposition of Groups}, journal = {Formaliz. Math.}, volume = {24}, number = {1}, pages = {81--94}, year = {2016}, url = {https://doi.org/10.1515/forma-2016-0007}, doi = {10.1515/FORMA-2016-0007}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/NakashoYOS16.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@inproceedings{DBLP:conf/cikm/OkazakiF16, author = {Hiroyuki Okazaki and Yuichi Futa}, editor = {Andrea Kohlhase and Paul Libbrecht and Bruce R. Miller and Adam Naumowicz and Walther Neuper and Pedro Quaresma and Frank Wm. Tompa and Martin Suda}, title = {Formalization of Polynomially Bounded and Negligible Functions Using the Computer-Aided Proof-Checking System Mizar}, booktitle = {Joint Proceedings of the FM4M, MathUI, and ThEdu Workshops, Doctoral Program, and Work in Progress at the Conference on Intelligent Computer Mathematics 2016 co-located with the 9th Conference on Intelligent Computer Mathematics {(CICM} 2016), Bialystok, Poland, July 25-29, 2016}, series = {{CEUR} Workshop Proceedings}, volume = {1785}, pages = {117--131}, publisher = {CEUR-WS.org}, year = {2016}, url = {https://ceur-ws.org/Vol-1785/W38.pdf}, timestamp = {Fri, 10 Mar 2023 16:22:32 +0100}, biburl = {https://dblp.org/rec/conf/cikm/OkazakiF16.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@inproceedings{DBLP:conf/isita/Okazaki16, author = {Hiroyuki Okazaki}, title = {Formalization of statistical indistinguishability of probability distribution ensembles in Mizar}, booktitle = {2016 International Symposium on Information Theory and Its Applications, {ISITA} 2016, Monterey, CA, USA, October 30 - November 2, 2016}, pages = {517--521}, publisher = {{IEEE}}, year = {2016}, url = {https://ieeexplore.ieee.org/document/7840478/}, timestamp = {Wed, 11 Aug 2021 01:00:00 +0200}, biburl = {https://dblp.org/rec/conf/isita/Okazaki16.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@inproceedings{DBLP:conf/semco/YamaguchiTOS16, author = {Hiroshi Yamaguchi and Shigeo Tsujii and Hiroyuki Okazaki and Yasunari Shidama}, title = {Privacy Preserving Logic Formula Calculation in Cloud}, booktitle = {Tenth {IEEE} International Conference on Semantic Computing, {ICSC} 2016, Laguna Hills, CA, USA, February 4-6, 2016}, pages = {329--332}, publisher = {{IEEE} Computer Society}, year = {2016}, url = {https://doi.org/10.1109/ICSC.2016.99}, doi = {10.1109/ICSC.2016.99}, timestamp = {Thu, 23 Mar 2023 00:00:00 +0100}, biburl = {https://dblp.org/rec/conf/semco/YamaguchiTOS16.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/NakashoYOS15, author = {Kazuhisa Nakasho and Hiroshi Yamazaki and Hiroyuki Okazaki and Yasunari Shidama}, title = {Definition and Properties of Direct Sum Decomposition of Groups1}, journal = {Formaliz. Math.}, volume = {23}, number = {1}, pages = {15--27}, year = {2015}, url = {https://doi.org/10.2478/forma-2015-0002}, doi = {10.2478/FORMA-2015-0002}, timestamp = {Fri, 10 Dec 2021 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/NakashoYOS15.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/FutaOS15, author = {Yuichi Futa and Hiroyuki Okazaki and Yasunari Shidama}, title = {Matrix of {\(\mathbb{Z}\)}-module1}, journal = {Formaliz. Math.}, volume = {23}, number = {1}, pages = {29--49}, year = {2015}, url = {https://doi.org/10.2478/forma-2015-0003}, doi = {10.2478/FORMA-2015-0003}, timestamp = {Fri, 10 Dec 2021 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/FutaOS15.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/NakashoOYS15, author = {Kazuhisa Nakasho and Hiroyuki Okazaki and Hiroshi Yamazaki and Yasunari Shidama}, title = {Equivalent Expressions of Direct Sum Decomposition of Groups1}, journal = {Formaliz. Math.}, volume = {23}, number = {1}, pages = {67--73}, year = {2015}, url = {https://doi.org/10.2478/forma-2015-0006}, doi = {10.2478/FORMA-2015-0006}, timestamp = {Fri, 10 Dec 2021 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/NakashoOYS15.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/OkazakiF15, author = {Hiroyuki Okazaki and Yuichi Futa}, title = {Polynomially Bounded Sequences and Polynomial Sequences}, journal = {Formaliz. Math.}, volume = {23}, number = {3}, pages = {205--213}, year = {2015}, url = {https://doi.org/10.1515/forma-2015-0017}, doi = {10.1515/FORMA-2015-0017}, timestamp = {Fri, 10 Dec 2021 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/OkazakiF15.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/FutaOS15a, author = {Yuichi Futa and Hiroyuki Okazaki and Yasunari Shidama}, title = {Torsion Part of {\(\mathbb{Z}\)}-module}, journal = {Formaliz. Math.}, volume = {23}, number = {4}, pages = {297--307}, year = {2015}, url = {https://doi.org/10.1515/forma-2015-0024}, doi = {10.1515/FORMA-2015-0024}, timestamp = {Fri, 10 Dec 2021 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/FutaOS15a.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/Okazaki15, author = {Hiroyuki Okazaki}, title = {Algebra of Polynomially Bounded Sequences and Negligible Functions}, journal = {Formaliz. Math.}, volume = {23}, number = {4}, pages = {371--378}, year = {2015}, url = {https://doi.org/10.1515/forma-2015-0029}, doi = {10.1515/FORMA-2015-0029}, timestamp = {Fri, 10 Dec 2021 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/Okazaki15.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@inproceedings{DBLP:conf/brain/OkazakiMSMM15, author = {Hiroyuki Okazaki and Hiroki Matsumoto and Yoshiki Shibata and Shinichi Motomura and Naoyuki Masada}, editor = {Yike Guo and Karl J. Friston and A. Aldo Faisal and Sean L. Hill and Hanchuan Peng}, title = {Application to Women's Healthcare of Health Management System Using a Tablet Phone}, booktitle = {Brain Informatics and Health - 8th International Conference, {BIH} 2015, London, UK, August 30 - September 2, 2015. Proceedings}, series = {Lecture Notes in Computer Science}, volume = {9250}, pages = {262--271}, publisher = {Springer}, year = {2015}, url = {https://doi.org/10.1007/978-3-319-23344-4\_26}, doi = {10.1007/978-3-319-23344-4\_26}, timestamp = {Sat, 09 Apr 2022 12:45:05 +0200}, biburl = {https://dblp.org/rec/conf/brain/OkazakiMSMM15.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/NakashoFOS14, author = {Kazuhisa Nakasho and Yuichi Futa and Hiroyuki Okazaki and Yasunari Shidama}, title = {Rank of Submodule, Linear Transformations and Linearly Independent Subsets of Z-module}, journal = {Formaliz. Math.}, volume = {22}, number = {3}, pages = {189--198}, year = {2014}, url = {https://doi.org/10.2478/forma-2014-0021}, doi = {10.2478/FORMA-2014-0021}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/NakashoFOS14.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/AraiWO14, author = {Kenichi Arai and Ken Wakabayashi and Hiroyuki Okazaki}, title = {Difference of Function on Vector Space over {F}}, journal = {Formaliz. Math.}, volume = {22}, number = {3}, pages = {269--275}, year = {2014}, url = {https://doi.org/10.2478/forma-2014-0027}, doi = {10.2478/FORMA-2014-0027}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/AraiWO14.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/FutaONS14, author = {Yuichi Futa and Hiroyuki Okazaki and Kazuhisa Nakasho and Yasunari Shidama}, title = {Torsion Z-module and Torsion-free Z-module}, journal = {Formaliz. Math.}, volume = {22}, number = {4}, pages = {277--289}, year = {2014}, url = {https://doi.org/10.2478/forma-2014-0028}, doi = {10.2478/FORMA-2014-0028}, timestamp = {Fri, 10 Dec 2021 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/FutaONS14.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/aires/OkazakiFS13, author = {Hiroyuki Okazaki and Yuichi Futa and Yasunari Shidama}, title = {Formal definition of probability on finite and discrete sample space for proving security of cryptographic systems using Mizar}, journal = {Artif. Intell. Res.}, volume = {2}, number = {4}, pages = {37--48}, year = {2013}, url = {https://doi.org/10.5430/air.v2n4p37}, doi = {10.5430/AIR.V2N4P37}, timestamp = {Wed, 10 Feb 2021 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/aires/OkazakiFS13.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/KanazashiOS13, author = {Katuhiko Kanazashi and Hiroyuki Okazaki and Yasunari Shidama}, title = {The Ck Space}, journal = {Formaliz. Math.}, volume = {21}, number = {1}, pages = {25--31}, year = {2013}, url = {https://doi.org/10.2478/forma-2013-0002}, doi = {10.2478/FORMA-2013-0002}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/KanazashiOS13.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/OkazakiS13, author = {Hiroyuki Okazaki and Yasunari Shidama}, title = {Random Variables and Product of Probability Spaces}, journal = {Formaliz. Math.}, volume = {21}, number = {1}, pages = {33--39}, year = {2013}, url = {https://doi.org/10.2478/forma-2013-0003}, doi = {10.2478/FORMA-2013-0003}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/OkazakiS13.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/OkazakiYS13, author = {Hiroyuki Okazaki and Hiroshi Yamazaki and Yasunari Shidama}, title = {Isomorphisms of Direct Products of Finite Commutative Groups}, journal = {Formaliz. Math.}, volume = {21}, number = {1}, pages = {65--74}, year = {2013}, url = {https://doi.org/10.2478/forma-2013-0007}, doi = {10.2478/FORMA-2013-0007}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/OkazakiYS13.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/AraiO13, author = {Kenichi Arai and Hiroyuki Okazaki}, title = {N-Dimensional Binary Vector Spaces}, journal = {Formaliz. Math.}, volume = {21}, number = {2}, pages = {75--81}, year = {2013}, url = {https://doi.org/10.2478/forma-2013-0008}, doi = {10.2478/FORMA-2013-0008}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/AraiO13.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/FutaOMS13, author = {Yuichi Futa and Hiroyuki Okazaki and Daichi Mizushima and Yasunari Shidama}, title = {Gaussian Integers}, journal = {Formaliz. Math.}, volume = {21}, number = {2}, pages = {115--125}, year = {2013}, url = {https://doi.org/10.2478/forma-2013-0013}, doi = {10.2478/FORMA-2013-0013}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/FutaOMS13.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/OkazakiFS13, author = {Hiroyuki Okazaki and Yuichi Futa and Yasunari Shidama}, title = {Constructing Binary Huffman Tree}, journal = {Formaliz. Math.}, volume = {21}, number = {2}, pages = {133--143}, year = {2013}, url = {https://doi.org/10.2478/forma-2013-0015}, doi = {10.2478/FORMA-2013-0015}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/OkazakiFS13.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/EndouOS13, author = {Noboru Endou and Hiroyuki Okazaki and Yasunari Shidama}, title = {Double Sequences and Limits}, journal = {Formaliz. Math.}, volume = {21}, number = {3}, pages = {163--170}, year = {2013}, url = {https://doi.org/10.2478/forma-2013-0018}, doi = {10.2478/FORMA-2013-0018}, timestamp = {Sun, 12 Feb 2023 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/EndouOS13.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/AraiO13a, author = {Kenichi Arai and Hiroyuki Okazaki}, title = {Formalization of the Advanced Encryption Standard. Part {I}}, journal = {Formaliz. Math.}, volume = {21}, number = {3}, pages = {171--184}, year = {2013}, url = {https://doi.org/10.2478/forma-2013-0019}, doi = {10.2478/FORMA-2013-0019}, timestamp = {Mon, 28 Aug 2023 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/AraiO13a.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/YamazakiONS13, author = {Hiroshi Yamazaki and Hiroyuki Okazaki and Kazuhisa Nakasho and Yasunari Shidama}, title = {Isomorphisms of Direct Products of Cyclic Groups of Prime Power Order}, journal = {Formaliz. Math.}, volume = {21}, number = {3}, pages = {207--211}, year = {2013}, url = {https://doi.org/10.2478/forma-2013-0022}, doi = {10.2478/FORMA-2013-0022}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/YamazakiONS13.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/FutaOS13, author = {Yuichi Futa and Hiroyuki Okazaki and Yasunari Shidama}, title = {Submodule of free Z-module}, journal = {Formaliz. Math.}, volume = {21}, number = {4}, pages = {273--282}, year = {2013}, url = {https://doi.org/10.2478/forma-2013-0029}, doi = {10.2478/FORMA-2013-0029}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/FutaOS13.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/jar/FutaOS13, author = {Yuichi Futa and Hiroyuki Okazaki and Yasunari Shidama}, title = {Formalization of Definitions and Theorems Related to an Elliptic Curve Over a Finite Prime Field by Using Mizar}, journal = {J. Autom. Reason.}, volume = {50}, number = {2}, pages = {161--172}, year = {2013}, url = {https://doi.org/10.1007/s10817-012-9265-2}, doi = {10.1007/S10817-012-9265-2}, timestamp = {Wed, 02 Sep 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/jar/FutaOS13.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/KanazashiOS12, author = {Katuhiko Kanazashi and Hiroyuki Okazaki and Yasunari Shidama}, title = {Functional Space \emph{C}({\(\omega\)}), \emph{C}\({}_{\mbox{0}}\)({\(\omega\)})}, journal = {Formaliz. Math.}, volume = {20}, number = {1}, pages = {15--22}, year = {2012}, url = {https://doi.org/10.2478/v10037-012-0003-3}, doi = {10.2478/V10037-012-0003-3}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/KanazashiOS12.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/FutaOS12, author = {Yuichi Futa and Hiroyuki Okazaki and Yasunari Shidama}, title = {Z-modules}, journal = {Formaliz. Math.}, volume = {20}, number = {1}, pages = {47--59}, year = {2012}, url = {https://doi.org/10.2478/v10037-012-0007-z}, doi = {10.2478/V10037-012-0007-Z}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/FutaOS12.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/FutaOMS12, author = {Yuichi Futa and Hiroyuki Okazaki and Daichi Mizushima and Yasunari Shidama}, title = {Operations of Points on Elliptic Curve in Projective Coordinates}, journal = {Formaliz. Math.}, volume = {20}, number = {1}, pages = {87--95}, year = {2012}, url = {https://doi.org/10.2478/v10037-012-0012-2}, doi = {10.2478/V10037-012-0012-2}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/FutaOMS12.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/EndouOS12, author = {Noboru Endou and Hiroyuki Okazaki and Yasunari Shidama}, title = {Higher-Order Partial Differentiation}, journal = {Formaliz. Math.}, volume = {20}, number = {2}, pages = {113--124}, year = {2012}, url = {https://doi.org/10.2478/v10037-012-0015-z}, doi = {10.2478/V10037-012-0015-Z}, timestamp = {Sun, 12 Feb 2023 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/EndouOS12.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/OkazakiS12, author = {Hiroyuki Okazaki and Yasunari Shidama}, title = {Formalization of the Data Encryption Standard}, journal = {Formaliz. Math.}, volume = {20}, number = {2}, pages = {125--146}, year = {2012}, url = {https://doi.org/10.2478/v10037-012-0016-y}, doi = {10.2478/V10037-012-0016-Y}, timestamp = {Mon, 28 Aug 2023 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/OkazakiS12.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/OkazakiAS12, author = {Hiroyuki Okazaki and Yosiki Aoki and Yasunari Shidama}, title = {Extended Euclidean Algorithm and {CRT} Algorithm}, journal = {Formaliz. Math.}, volume = {20}, number = {2}, pages = {175--179}, year = {2012}, url = {https://doi.org/10.2478/v10037-012-0020-2}, doi = {10.2478/V10037-012-0020-2}, timestamp = {Mon, 03 Jan 2022 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/OkazakiAS12.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/FutaOS12a, author = {Yuichi Futa and Hiroyuki Okazaki and Yasunari Shidama}, title = {Quotient Module of Z-module}, journal = {Formaliz. Math.}, volume = {20}, number = {3}, pages = {205--214}, year = {2012}, url = {https://doi.org/10.2478/v10037-012-0024-y}, doi = {10.2478/V10037-012-0024-Y}, timestamp = {Mon, 03 Jan 2022 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/FutaOS12a.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/Okazaki12, author = {Hiroyuki Okazaki}, title = {Posterior Probability on Finite Set}, journal = {Formaliz. Math.}, volume = {20}, number = {4}, pages = {257--263}, year = {2012}, url = {https://doi.org/10.2478/v10037-012-0030-0}, doi = {10.2478/V10037-012-0030-0}, timestamp = {Fri, 10 Dec 2021 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/Okazaki12.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/SakuraiOS12, author = {Hideki Sakurai and Hiroyuki Okazaki and Yasunari Shidama}, title = {Banach's Continuous Inverse Theorem and Closed Graph Theorem}, journal = {Formaliz. Math.}, volume = {20}, number = {4}, pages = {271--274}, year = {2012}, url = {https://doi.org/10.2478/v10037-012-0032-y}, doi = {10.2478/V10037-012-0032-Y}, timestamp = {Mon, 03 Jan 2022 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/SakuraiOS12.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/FutaOS12b, author = {Yuichi Futa and Hiroyuki Okazaki and Yasunari Shidama}, title = {Free {\(\mathbb{Z}\)}-module}, journal = {Formaliz. Math.}, volume = {20}, number = {4}, pages = {275--280}, year = {2012}, url = {https://doi.org/10.2478/v10037-012-0033-x}, doi = {10.2478/V10037-012-0033-X}, timestamp = {Mon, 03 Jan 2022 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/FutaOS12b.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/AraiOS12, author = {Kenichi Arai and Hiroyuki Okazaki and Yasunari Shidama}, title = {Isomorphisms of Direct Products of Finite Cyclic Groups}, journal = {Formaliz. Math.}, volume = {20}, number = {4}, pages = {343--347}, year = {2012}, url = {https://doi.org/10.2478/v10037-012-0038-5}, doi = {10.2478/V10037-012-0038-5}, timestamp = {Mon, 03 Jan 2022 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/AraiOS12.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@inproceedings{DBLP:conf/isita/FutaMO12, author = {Yuichi Futa and Daichi Mizushima and Hiroyuki Okazaki}, title = {Formalization of Gaussian integers, Gaussian rational numbers, and their algebraic structures with Mizar}, booktitle = {Proceedings of the International Symposium on Information Theory and its Applications, {ISITA} 2012, Honolulu, HI, USA, October 28-31, 2012}, pages = {591--595}, publisher = {{IEEE}}, year = {2012}, url = {https://ieeexplore.ieee.org/document/6401006/}, timestamp = {Wed, 11 Aug 2021 01:00:00 +0200}, biburl = {https://dblp.org/rec/conf/isita/FutaMO12.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/OkazakiAS11, author = {Hiroyuki Okazaki and Kenichi Arai and Yasunari Shidama}, title = {Normal Subgroup of Product of Groups}, journal = {Formaliz. Math.}, volume = {19}, number = {1}, pages = {23--26}, year = {2011}, url = {https://doi.org/10.2478/v10037-011-0004-7}, doi = {10.2478/V10037-011-0004-7}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/OkazakiAS11.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/OkazakiES11, author = {Hiroyuki Okazaki and Noboru Endou and Yasunari Shidama}, title = {More on Continuous Functions on Normed Linear Spaces}, journal = {Formaliz. Math.}, volume = {19}, number = {1}, pages = {45--49}, year = {2011}, url = {https://doi.org/10.2478/v10037-011-0008-3}, doi = {10.2478/V10037-011-0008-3}, timestamp = {Sun, 12 Feb 2023 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/OkazakiES11.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/OkazakiES11a, author = {Hiroyuki Okazaki and Noboru Endou and Yasunari Shidama}, title = {Cartesian Products of Family of Real Linear Spaces}, journal = {Formaliz. Math.}, volume = {19}, number = {1}, pages = {51--59}, year = {2011}, url = {https://doi.org/10.2478/v10037-011-0009-2}, doi = {10.2478/V10037-011-0009-2}, timestamp = {Sun, 12 Feb 2023 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/OkazakiES11a.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/FutaOS11, author = {Yuichi Futa and Hiroyuki Okazaki and Yasunari Shidama}, title = {Formalization of Integral Linear Space}, journal = {Formaliz. Math.}, volume = {19}, number = {1}, pages = {61--64}, year = {2011}, url = {https://doi.org/10.2478/v10037-011-0010-9}, doi = {10.2478/V10037-011-0010-9}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/FutaOS11.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/OkazakiENS11, author = {Hiroyuki Okazaki and Noboru Endou and Keiko Narita and Yasunari Shidama}, title = {Differentiable Functions into Real Normed Spaces}, journal = {Formaliz. Math.}, volume = {19}, number = {2}, pages = {69--72}, year = {2011}, url = {https://doi.org/10.2478/v10037-011-0012-7}, doi = {10.2478/V10037-011-0012-7}, timestamp = {Sun, 12 Feb 2023 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/OkazakiENS11.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/KanazashiOS11, author = {Katuhiko Kanazashi and Hiroyuki Okazaki and Yasunari Shidama}, title = {Banach Algebra of Bounded Complex-Valued Functionals}, journal = {Formaliz. Math.}, volume = {19}, number = {2}, pages = {121--126}, year = {2011}, url = {https://doi.org/10.2478/v10037-011-0019-0}, doi = {10.2478/V10037-011-0019-0}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/KanazashiOS11.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/FutaOS11a, author = {Yuichi Futa and Hiroyuki Okazaki and Yasunari Shidama}, title = {Set of Points on Elliptic Curve in Projective Coordinates}, journal = {Formaliz. Math.}, volume = {19}, number = {3}, pages = {131--138}, year = {2011}, url = {https://doi.org/10.2478/v10037-011-0021-6}, doi = {10.2478/V10037-011-0021-6}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/FutaOS11a.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/OkazakiS10, author = {Hiroyuki Okazaki and Yasunari Shidama}, title = {Probability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables}, journal = {Formaliz. Math.}, volume = {18}, number = {1-4}, pages = {213--217}, year = {2010}, url = {https://doi.org/10.2478/v10037-010-0026-6}, doi = {10.2478/V10037-010-0026-6}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/OkazakiS10.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@inproceedings{DBLP:conf/fcs/AraiKO10, author = {Kenichi Arai and Nobuaki Kondo and Hiroyuki Okazaki}, editor = {Hamid R. Arabnia and George A. Gravvanis and Ashu M. G. Solo}, title = {Formalization of Probability and Random Sampling on a Finite and Discrete Sample Space Using the Mizar Proof Checker}, booktitle = {Proceedings of the 2010 International Conference on Foundations of Computer Science, {FCS} 2010, July 12-15, 2010, Las Vegas, Nevada, {USA}}, pages = {81--86}, publisher = {{CSREA} Press}, year = {2010}, timestamp = {Wed, 08 Dec 2010 08:03:41 +0100}, biburl = {https://dblp.org/rec/conf/fcs/AraiKO10.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/OkazakiS09, author = {Hiroyuki Okazaki and Yasunari Shidama}, title = {Probability on Finite Set and Real-Valued Random Variables}, journal = {Formaliz. Math.}, volume = {17}, number = {1-4}, pages = {129--136}, year = {2009}, url = {https://doi.org/10.2478/v10037-009-0014-x}, doi = {10.2478/V10037-009-0014-X}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/OkazakiS09.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/AraiO09, author = {Kenichi Arai and Hiroyuki Okazaki}, title = {Properties of Primes and Multiplicative Group of a Field}, journal = {Formaliz. Math.}, volume = {17}, number = {1-4}, pages = {151--155}, year = {2009}, url = {https://doi.org/10.2478/v10037-009-0017-7}, doi = {10.2478/V10037-009-0017-7}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/AraiO09.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/EndouOS09, author = {Noboru Endou and Hiroyuki Okazaki and Yasunari Shidama}, title = {Hopf Extension Theorem of Measure}, journal = {Formaliz. Math.}, volume = {17}, number = {1-4}, pages = {157--162}, year = {2009}, url = {https://doi.org/10.2478/v10037-009-0018-6}, doi = {10.2478/V10037-009-0018-6}, timestamp = {Sun, 12 Feb 2023 00:00:00 +0100}, biburl = {https://dblp.org/rec/journals/fm/EndouOS09.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/Okazaki09, author = {Hiroyuki Okazaki}, title = {Probability on Finite and Discrete Set and Uniform Distribution}, journal = {Formaliz. Math.}, volume = {17}, number = {1-4}, pages = {173--178}, year = {2009}, url = {https://doi.org/10.2478/v10037-009-0020-z}, doi = {10.2478/V10037-009-0020-Z}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/Okazaki09.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/fm/OkazakiS08, author = {Hiroyuki Okazaki and Yasunari Shidama}, title = {Uniqueness of Factoring an Integer and Multiplicative Group Z/pZ*}, journal = {Formaliz. Math.}, volume = {16}, number = {1-4}, pages = {103--107}, year = {2008}, url = {https://doi.org/10.2478/v10037-008-0015-1}, doi = {10.2478/V10037-008-0015-1}, timestamp = {Thu, 18 Jun 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/fm/OkazakiS08.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@inproceedings{DBLP:conf/gecco/AguirreOF07, author = {Hern{\'{a}}n E. Aguirre and Hiroyuki Okazaki and Yasushi Fuwa}, editor = {Hod Lipson}, title = {An evolutionary multiobjective approach to design highly non-linear Boolean functions}, booktitle = {Genetic and Evolutionary Computation Conference, {GECCO} 2007, Proceedings, London, England, UK, July 7-11, 2007}, pages = {749--756}, publisher = {{ACM}}, year = {2007}, url = {https://doi.org/10.1145/1276958.1277112}, doi = {10.1145/1276958.1277112}, timestamp = {Tue, 06 Nov 2018 00:00:00 +0100}, biburl = {https://dblp.org/rec/conf/gecco/AguirreOF07.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/iacr/OkazakiSK05, author = {Hiroyuki Okazaki and Ryuichi Sakai and Masao Kasahara}, title = {Meta Ring Signature}, journal = {{IACR} Cryptol. ePrint Arch.}, pages = {310}, year = {2005}, url = {http://eprint.iacr.org/2005/310}, timestamp = {Mon, 11 May 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/iacr/OkazakiSK05.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/jnsm/EiriPOH98, author = {Masayoshi Ejiri and Jong{-}Tae Park and Hiroyuki Okazaki and James Won{-}Ki Hong}, title = {Managing the New Telecommunications Paradigms: {A} Report on APNOMS'98}, journal = {J. Netw. Syst. Manag.}, volume = {6}, number = {4}, pages = {497--500}, year = {1998}, url = {https://doi.org/10.1023/A:1018793127649}, doi = {10.1023/A:1018793127649}, timestamp = {Thu, 21 Apr 2022 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/jnsm/EiriPOH98.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@inproceedings{DBLP:conf/noms/KawagoeKSTOH96, author = {T. Kawagoe and H. Kawakami and K. Soga and K. Tanaka and Hiroyuki Okazaki and Satoshi Hasegawa}, editor = {Masayoshi Ejiri and Shri K. Goyal}, title = {On the design and an implementation of broadband access management systems}, booktitle = {1996 Network Operations and Management Symposium, {NOMS} 1996, Kyoto, Japan, April 15-19, 1996. Proceedings}, pages = {382--391}, publisher = {{IEEE}}, year = {1996}, url = {https://doi.org/10.1109/NOMS.1996.539609}, doi = {10.1109/NOMS.1996.539609}, timestamp = {Wed, 16 Oct 2019 14:14:54 +0200}, biburl = {https://dblp.org/rec/conf/noms/KawagoeKSTOH96.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
@article{DBLP:journals/jnsm/SakauchiOOH93, author = {Hideki Sakauchi and Yasuyo Okanoue and Hiroyuki Okazaki and Satoshi Hasegawa}, title = {Distributed Self-Healing Control in {SONET}}, journal = {J. Netw. Syst. Manag.}, volume = {1}, number = {2}, pages = {123--141}, year = {1993}, url = {https://doi.org/10.1007/BF01035884}, doi = {10.1007/BF01035884}, timestamp = {Thu, 24 Sep 2020 01:00:00 +0200}, biburl = {https://dblp.org/rec/journals/jnsm/SakauchiOOH93.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
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