九州大学 研究者情報
論文一覧
鍛冶 静雄(かじ しずお) データ更新日:2019.06.29

准教授 /  マス・フォア・インダストリ研究所 数理計算インテリジェント社会実装推進部門


原著論文
1. S. Kaji, A. Derouet-Jourdan, H. Ochiai, Dappled tiling, Mathematical Insights into Advanced Computer Graphics Techniques, 10.1007/978-981-13-2850-3, 59-72, 2019.03.
2. Adrien Fauré, Shizuo Kaji, A circuit-preserving mapping from multilevel to Boolean dynamics, Journal of Theoretical Biology, 10.1016/j.jtbi.2017.12.013, 440, 71-79, 2018.03, [URL].
3. Neşet Deniz Turgay, Shizuo Kaji, The mod 2 dual Steenrod algebra as a subalgebra of the mod 2 dual Leibniz-Hopf algebra, Journal of Homotopy and Related Structures, 10.1007/s40062-016-0163-x, 12, 3, 727-739, 2017.09, [URL].
4. Suyoung Choi, Shizuo Kaji, Stephen Theriault, Homotopy decomposition of a suspended real toric space, Boletin de la Sociedad Matematica Mexicana, 10.1007/s40590-016-0090-1, 23, 1, 153-161, 2017.04, [URL].
5. Ho Kyoung Ko, Hyung Won Kim, Shizuo Kaji, Suyoung Choi, Elementary school students who give up on learning mathematics: Correlations with non-cognitive learner characteristics, J. Korea Soc. Math. Ed. Ser. C, 20, 2, 143-151, 2017.04.
6. Shizuo Kaji, Michihiro Sakai, Stephen Theriault, Counting the number of homotopy associative multiplications on certain H-spaces, Topology and its Applications, 10.1016/j.topol.2016.10.008, 214, 137-149, 2016.12, [URL].
7. Shizuo Kaji, Hiroyuki Ochiai, A concise parametrization of affine transformation, SIAM Journal on Imaging Sciences, 10.1137/16M1056936, 9, 3, 1355-1373, 2016.09, [URL].
8. S. Kaji, Tetrisation of triangular meshes and its application in shape blending, Mathematical Progress in Expressive Image Synthesis III, 10.1007/978-981-10-1076-7_2, 7-19, 2016.05.
9. Shizuo Kaji, Akihiro Ohsita, Stephen Theriault, Mod p decompositions of the loop spaces of compact symmetric spaces, Algebraic and Geometric Topology, 10.2140/agt.2015.15.1771, 15, 3, 1771-1811, 2015.06, [URL].
10. S. Kaji and G. Liu, Probe-type deformers, Mathematical Progress in Expressive Image Synthesis I, 10.1007/978-4-431-55483-7_6, 63-77, 2015.05.
11. S. Kaji, Three presentations of torus equivariant cohomology of flag manifolds, Perspectives and Developments in Mathematics, Proceedings of the International Mathematics Conference in honour of the 70th Birthday of Professor S. A. Ilori, 37-54, 2015.05.
12. Koji Nuida, Takuro Abe, Shizuo Kaji, Toshiaki Maeno, Yasuhide Numata, A mathematical problem for security analysis of hash functions and pseudorandom generators, International Journal of Foundations of Computer Science, 10.1142/S0129054115500100, 26, 2, 169-194, 2015.02, [URL].
13. Shizuo Kaji, Weyl group symmetry on the gkm graph of a gkm manifold with an extended lie group action, Osaka Journal of Mathematics, 52, 1, 31-41, 2015.01.
14. G. Matsuda, S. Kaji, H. Ochiai, Anti-commutative Dual Complex Numbers and 2D Rigid Transformation, Mathematical Progress in Expressive Image Synthesis I, 10.1007/978-4-431-55007-5_17, 131-138, 2014.05.
15. Shizuo Kaji, S. Hirose, S. Sakata, Yoshihiro Mizoguchi, K. Anjyo, Mathematical analysis on affine maps for 2D shape interpolation, 11th ACM SIGGRAPH / Eurographics Symposium on Computer Animation, SCA 2012
Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012
, 71-76, 2012.07.
16. Shizuo Kaji, Equivariant Schubert calculus of Coxeter groups, Proceedings of the Steklov Institute of Mathematics, 10.1134/S0081543811080177, 275, 1, 239-250, 2011.12, [URL], We consider an equivariant extension for Hiller's Schubert calculus on the coinvariant ring of a finite Coxeter group..
17. Koji Nuida, Takuro Abe, Shizuo Kaji, Toshiaki Maeno, Yasuhide Numata, A mathematical problem for security analysis of hash functions and pseudorandom generators, 6th International Workshop on Security, IWSEC 2011
Advances in Information and Computer Security - 6th International Workshop, IWSEC 2011, Proceedings
, 10.1007/978-3-642-25141-2_10, 144-160, 2011.11, [URL], The aim of this paper is to emphasize the significance of a certain mathematical problem in research on information security. We point out that the mathematical problem, which we refer to as "Function Density Problem," has connections to the following two major cryptographic topics; security analysis of hash functions in the real world (like SHA-1), and construction of pseudorandom generators with some enhanced security property. We also provide a first example to show how a study of Function Density Problem can contribute to the progress of the above-mentioned two topics. Other potential applications of Function Density Problem to information security are also discussed..
18. S. Kaji, Schubert calculus, seen from torus equivariant topology, Trends in Mathematics - New Series, 12, 1, 71-89, 2010.05.
19. Shizuo Kaji, Daisuke Kishimoto, Homotopy nilpotency in p-regular loop spaces, Mathematische Zeitschrift, 10.1007/s00209-008-0459-6, 264, 1, 209-224, 2010.01, [URL], We consider the problem how far from being homotopy commutative is a loop space having the homotopy type of the p-completion of a product of finite numbers of spheres. We determine the homotopy nilpotency of those loop spaces as an answer to this problem..
20. Hiroaki Hamanaka, Shizuo Kaji, Akira Kono, Samelson products in Sp (2), Topology and its Applications, 10.1016/j.topol.2008.02.008, 155, 11, 1207-1212, 2008.06, [URL], We calculate certain Samelson products of Sp (2). Using the result, we classify the homotopy types of the gauge groups of principal Sp (2) bundles over S8 and we also derive the homotopy commutativity of Sp (2) localized at 3..
21. Shizuo Kaji, Mod 2 cohomology of 2-compact groups of low rank, Kyoto Journal of Mathematics, 10.1215/kjm/1250281055, 47, 2, 441-450, 2007.01, [URL], We determine the mod 2 cohomology algebra over the Steenrod algebra A 2 of the classifying space of loop groups LG where G = Spin(7), Spin(8), Spin(9), F4 and DI(4). Then we show they are isomorphic as algebras over A2 to the mod 2 cohomology of the 2-compact groups of type G..
22. Shizuo Kaji, Low rank cohomology of the classifying spaces of gauge groups over 3-manifolds, Publications of the Research Institute for Mathematical Sciences, 10.2977/prims/1166642116, 42, 2, 581-587, 2006.06, [URL], The purpose of this paper is to calculate the cohomology of the function space Map(M, BG) for degree less than or equal to 3, where G is a simply connected compact Lie group and M is a closed orientable 3-manifold. The calculation enables us to obtain a simple proof and an improvement of the result [4, Theorem 1.2]..
23. Shizuo Kaji, On the nilpotency of rational H-spaces, Journal of the Mathematical Society of Japan, 10.2969/jmsj/1150287307, 57, 4, 1153-1165, 2005.10, [URL], In [BG], it is proved that the Whitehead length of a space Z is less than or equal to the nilpotency of ΩZ. As for rational spaces, those two invariants are equal. We show this for a 1-connected rational space Z by giving a way to calculate those invariants from a minimal model for Z. This also gives a way to calculate the nilpotency of an homotopy associative rational H-space..

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