研究者詳細 - 永井　敦

論文 - 永井　敦

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The best constant of discrete Sobolev inequalities corresponding to braced grids : deformability and rigidity (Various aspects of integrable systems) 査読

NAGAI Atsushi, KANO Akari, KIKUCHI Maho, UEHARA Rikako

RIMS Kokyuroku Bessatsu B91 37 - 44 2023年2月

The best constant of discrete Sobolev inequality on 1812 C60 fullerene isomers 査読

Kametaka Yoshinori, Watanabe Kohtaro, Nagai Atsushi, Takemura Kazuo, Yamagishi Hiroyuki, Sekido Hiroto

JSIAM Letters 12 ( 0 ) 49 - 52 2020年

記述言語：英語出版者・発行元：The Japan Society for Industrial and Applied Mathematics

<p> The best constants of discrete Sobolev inequalities corresponding to 1812 isomers of C60 fullerene are found. Classical mechanical models of these isomers with a linear spring on each edge are investigated. The best constants stand for rigidities of these models. We show the best constants of 1812 isomers are distinct rational numbers and among these, Buckyball (or equivalently truncated icosahedron) takes the least. In other words, one can say that the Buckyball is the most rigid among 1812 C60 fullerene isomers. </p>

DOI： 10.14495/jsiaml.12.49

CiNii Research

Discrete Bernoulli polynomials and the best constant of discrete Sobolev inequality 査読

A. Nagai, Y. Kametaka, H. Yamagishi, K. Takemura and K. Watanabe

Funkcialaj Ekvacioj 51 307 - 327 2008年7月

Best constant of Sobolev inequality in an $n$-dimensional Euclidean space 査読

Y. Kametaka, K. Watanabe and A. Nagai

Proceedings of Japan Academy Ser. A 81 57 - 60 2005年4月

Proof of solitonical natures of box and ball systems by means of inverse ultra-discretization 査読

T. Tokihiro, A. Nagai and J. Satsuma

Inverse Problems 15 1639 - 1662 1999年12月

Positivity and Hierarchical Structure of four Green Functions Corresponding to a Bending Problem of a Beam on a half line 査読

Kametaka Yoshinori , Watanabe Kohtaro , Nagai Atsushi , Takemura Kazuo , Yamagishi Hiroyuki

Mathematical Journal of Okayama University 65 ( 1 ) 145 - 173 2023年1月

The best constant of discrete Sobolev inequality corresponding to a discrete bending problem of a string 査読

Hiroyuki Yamagishi and Atsushi Nagai

Saitama Mathematical Journal 34 19 - 46 2022年2月

A Hierarchical Structure for the Sharp Constants of Discrete Sobolev Inequalities on a Weighted Complete Graph (jointly worked) 査読

Kazuo Takemura, Yoshinori Kametaka and Atsushi Nagai

Symmetry 2018 ( 10 ) 1 - 13 2017年12月

Two types of discrete Sobolev inequalities on a weighted Toeplitz graph 査読

K. Takemura, A. Nagai and Y. Kametaka

Linear Algebra and its Applications 507 344 - 355 2016年6月

The Best Constant of Discrete Sobolev Inequality on the C60 Fullerene Buckyball 査読

Y. Kametaka, A. Nagai, H. Yamagishi, K. Takemura, and K. Watanabe

Journal of the Physical Society of Japan 84 2015年7月

A direct approach to the ultradiscrete KdV equation with negative and non-integer site values 査読

C R Gilson, J J C Nimmo and A. Nagai

J. Phys. A: Math. Theor. 48 2015年7月

Sobolev inequality of free boundary value problem for $(-1)^M (d/dx)^{2M}$ 査読

K. Takemura, A. Nagai, Y. Kametaka, K. Watanabe and H. Yamagishi

Journal of Inequalities and Applications 2015年2月

切頂正4,6,8面体上の離散ソボレフ不等式の最良定数査読

亀高惟倫, 永井敦

日本応用数理学会論文誌 25 2015年

The best estimation corresponding to continuous model of Thomson cable 査読

H. Yamagishi, Y. Kametaka, A. Nagai, K. Watanabe and K. Takemura

JSIAM Letters 5 53 - 56 2013年8月

The Best Constant of Three Kinds of Discrete Sobolev Inequalities on Regular Polyhedron 査読

H. Yamagishi, Y. Kametaka, K. Watanabe and A. Nagai

Tokyo J. Math. 36 253 - 268 2013年6月

Positivity and hierarchical structure of 16 Green functions corresponding to a bending problem of a beam 査読

Y. Kametaka, K. Takemura, H. Yamagishi, and A. Nagai

Saitama Math. J. 29 1 - 24 2013年2月

Complete low-cut filter and the best constant of Sobolev inequality 査読

H. Yamagishi, Y. Kametaka, A. Nagai, K. Watanabe and K. Takemura

JSIAM Lettters 5 33 - 36 2013年1月

Lyapunov-type inequalities for $2M$-th order equations under clamped-free boundary conditions 査読

K. Watanabe, K. Takemura, Y. Kametaka, A. Nagai and H. Yamagishi

Journal of Inequalities and Applications 2012年12月

Sobolev type inequalities of time-periodic boundary value problems for Heaviside and Thomson cables 査読

K. Takemura, Y. Kametaka, K. Watanabe, A. Nagai and H. Yamagishi

Boundary Value Problems 2012年11月

Elliptic theta function and the best constants of Sobolev-type inequalities 査読

H. Yamagishi, Y. Kametaka, A. Nagai, K. Watanabe and K. Takemura

JSIAM Letters 4 1 - 4 2012年2月

The best constant of Sobolev inequality corresponding to clamped boundary value problem 査読

K. Watanabe, Y. Kametaka, H. Yamagishi, A. Nagai and K. Takemura

Boundary Value Problems 2011年3月

The best constant of Sobolev inequality corresponding　to a bending problem of a beam on an interval 査読

Y. Kametaka, A. Nagai, K. Watanabe, K. Takemura and H. Yamagishi

Tsukuba Journal of Mathematics 33 253 - 280 2009年12月

The best constant of discrete Sobolev inequality 招待査読

A. Nagai, Y. Kametaka and K. Watanabe

Journal of Physics A 42 2009年10月

The best constant of Sobolev inequality corresponding to antiperiodic boundary value problem for $(-1)^M(d/dx)^{2M}$ 査読

H. Yamagishi, Y. Kametaka and A. Nagai

Journal of Nonlinear and Convex Analysis 10 103 - 116 2009年1月

The best constant of Sobolev inequality which corresponds to Schr\"odinger operator with Dirac delta potential 査読

Y. Kametaka, H. Yamagishi, K. Watanabe, A. Nagai, K. Takemura and M. Arai

Scienticae Mathematicae Japonicae 69 211 - 225 2008年12月

The best constant of Sobolev inequality corresponding to Dirichlet boundary value problem for $(-1)^M(d/dx)^{2M}$ 査読

Y. Kametaka, H. Yamagishi, K. Watanabe, A. Nagai and K. Takemura

Scientiae Mathematicae Japonicae 68 299 - 311 2008年10月

リーマンゼータ関数と3系列のソボレフ不等式の最良定数査読

亀高惟倫，山岸弘幸，渡辺宏太郎，永井敦，武村一雄

日本応用数理学会論文誌 18 29 - 40 2008年3月

$(-1)^M(d/dx)^{2M}$に対する両端自由端条件境界値問題と対応するソボレフ不等式の最良定数査読

武村一雄，永井敦，亀高惟倫，渡辺宏太郎，山岸弘幸

日本応用数理学会論文誌 18 41 - 64 2008年3月

The best constants of Sobolev inequalities on a bounded interval 査読

K. Watanabe, Y. Kametaka, A. Nagai, K. Takemura and H. Yamagishi

Journal of Mathematical Analysis and its Applications 340 699 - 706 2008年1月

Heaviside cable, Thomson cable and the best constant of a Sobolev-type inequality 査読

Y. Kametaka, K. Takemura, H. Yamagishi, A. Nagai and K. Watanabe

Scientiae Mathematicae Japonicae e-2007 739 - 755 2007年12月

Solutions to Some Fractional Differential Equations and Their Integrable Discretizations 査読

Atsushi Nagai and Yoshinori Kametaka

Journal of the Physical Society of Japan 76 2007年9月

The best constant of $L^p$ Sobolev inequality corresponding to periodic boundary value problem for $(-1)^M(d/dx)^{2M}$ 査読

Y. Kametaka, Y. Oshime, K. Watanabe, H. Yamagishi, A. Nagai and K. Takemura

Scientiae Mathematicae Japonicae e-2007 269 - 281 2007年5月

The best constant of Sobolev inequality which corresponds to a bending problem of a string with periodic boundary condition 査読

Y. Kametaka, K. Watanabe, A. Nagai, H. Yamagishi and K. Takemura

Scientiae Mathematicae Japonicae e-2007 283 - 300 2007年5月

Riemann zeta function, Bernoulli polynomials and the best constant of Sobolev inequality 査読

Y. Kametaka, H. Yamagishi, K. Watanabe, A. Nagai and K. Takemura

Scientiae Mathematicae Japonicae e-2007 63 - 89 2007年1月

Best constant of Sobolev inequality in an $n$-dimensional Euclidean space 査読

Y. Kametaka, K. Watanabe , A. Nagai and S. Pyatkov

Scientiae Mathematicae Japonicae 61 15 - 23 2004年12月

Dependency of Green functions on an interval length to 2-point boundary value problems for bending of a beam 査読

K. Takemura, Y. Kametaka and A. Nagai

Japan Journal of Industrial and Applied Mathematics 21 237 - 258 2004年10月

On a certain fractional $q$-difference and $q$-Mittag-Leffler function 招待査読

A. Nagai

Journal of Nonlinear Mathematical Physics Supplement 10 133 - 142 2003年12月

An Integrable Mapping with Fractional Difference 査読

A. Nagai

Journal of the Physical Society of Japan 72 2181 - 2183 2003年9月

Conserved quantities of box and ball systems 査読

A. Nagai, T. Tokihiro and J. Satsuma

Glasgow Mathematical Journal 43A 91 - 98 2001年7月

Positivity and hierarchical structure of Green's functions of 2-point boundary value problems for bending of a beam 査読

Y. Kametaka, K. Takemura, Y. Suzuki and A. Nagai

Japan Journal of Industrial and Applied Mathematics 21 543 - 566 2001年6月

Soliton cellular automaton, Toda molecule equation and sorting algorithm 査読

A. Nagai, D. Takahashi and T. Tokihiro

Physics Letters A 255 265 - 271 1999年5月

The Toda molecule equation and the $\varepsilon$-algorithm 査読

A. Nagai, T. Tokihiro, and J. Satsuma

Mathematics of Computation 67 1565 - 1575 1998年10月

Ultra-discrete Toda molecule equation 査読

A. Nagai, T. Tokihiro and J. Satsuma

Physics Letters A 244 383 - 388 1998年7月

Two-dimensional soliton cellular automaton of deautonomized Toda-type 査読

A. Nagai, T. Tokihiro, J. Satsuma, R. Willox and K. Kajiwara

Physics Letters A 234 301 - 309 1997年9月

Discrete soliton equations and convergence acceleration algorithms 査読

Atsushi Nagai and Junkichi Satsuma

Physics Letters A 209 305 - 309 1995年12月

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