著者
大野 泰生 後藤 丈志
出版者
一般社団法人 日本応用数理学会
雑誌
日本応用数理学会論文誌 (ISSN:24240982)
巻号頁・発行日
vol.16, no.3, pp.187-195, 2006-09-25 (Released:2017-04-08)
参考文献数
20

Jenkins recently showed that an odd perfect number must be divisible by a prime greater than 10^7. The aim of this article is to give a new algorithm to obtain such a lower bound. The theory of cyclotomic numbers plays an important role in the algorithm. We also discuss some relation between cyclotomic numbers and ABC conjecture.
著者
斉藤 一哉
出版者
一般社団法人 日本応用数理学会
雑誌
応用数理 (ISSN:24321982)
巻号頁・発行日
vol.26, no.1, pp.9-14, 2016 (Released:2016-07-27)
参考文献数
18

This study presents a new method for designing self-deploying origami using the geometrically misaligned creases. In this method, some facets are replaced by “holes” such that the systems become a 1-DOF mechanism. These perforated origami models can be folded and unfolded similar to rigidfoldable(without misalignment) models because of their DOF despite the existence of the misalignment. Focusing on the removed facets, the holes will deform according to the motion of the frame of the remaining parts. In the proposed method, these holes are filled with elastic parts and store elastic energy for self-deployment. First, a new extended rigid-folding simulation technique is proposed to estimate the deformation of the holes. Next by using the above technique, the proposed method is applied on arbitrary-size quadrilateral mesh origami. Finally, by using the finite-element method, the authors conduct numerical simulations and confirm the deployment capabilities of the models.
著者
鈴木 増雄
出版者
一般社団法人 日本応用数理学会
雑誌
日本応用数理学会論文誌 (ISSN:24240982)
巻号頁・発行日
vol.7, no.3, pp.257-264, 1997-09-15 (Released:2017-04-08)
参考文献数
7

The purpose of the present paper is to formulate the quantum analysis of multivariate operator functions f({A_j}) by introducing auxiliary operators {H_j} satisfying the conditions that [H_j, H_κ]=0 , [H_j, A_κ ]=0 for j≠κ, and [H_j, [H_κ, A_κ]]=0. Then we have d^nf=Σ_<j1>...<jn> δ_H_<J1>・・・δ_H_<jn>f using the inner derivation δ_A : δ_AQ=[A, Q]=AQ-QA. The operator Taylor expansion formula is given in the form : f({A_j+x_jdA_j})=e^Σ_j^x_j^d_jf({A_j})=exp(Σ_jx_jδ_H_j)f({A_j})=Σ_nΣ_<j1>...<jn>x_<j1>・・・x_<jn>δ<j1>..., _<jn>f≡Σ_nΣ_<j1>..., _<jn>x_<j1>・・・x_<jn>f^<(n)>_<j1>..., _<jn> : dA_<J1>・・・dA_jn with dA_j≡[H_j, A_j]=δ_H_jA_j, and with the partial derivatives {d_j} with respect to {A_j}. Here, δ_<j1>..., _<jn> denotes an ordered partial inner derivation, and n!f^<(n)>_<j1>...<jn> denotes the n th derivative of f({A_j}).
著者
石原 辰雄
出版者
一般社団法人 日本応用数理学会
雑誌
日本応用数理学会論文誌 (ISSN:09172246)
巻号頁・発行日
vol.12, no.3, pp.197-207, 2002
参考文献数
6
被引用文献数
1 or 0

In this paper, I derive expressions for the probability density function and the cumulative distribution function of a random variable composed of the sum and the product of n-independent uniform random variables distributed at different intervals. The numerical examples are shown to derive the probability density function in the case of three uniform random variables.
著者
冨岡 亮太
出版者
一般社団法人 日本応用数理学会
雑誌
日本応用数理学会論文誌 (ISSN:09172246)
巻号頁・発行日
vol.23, no.3, pp.485-515, 2013

本サーベイ論文では機械学習を中心とした分野で近年注目されているスパース性を導く様々な正則化法を加法的なスパース正則化と構造的なスパース正則化に分類し,それぞれに対する最適化法を議論する.前者は,条件数の悪化に対して頑健な手法が重要であり,相対拡張ラグランジュ法を紹介する.一方,後者に対しては,線形演算で表現される構造とスパース正則化項を分離することを可能にする手法として交互方向乗数法を紹介する.
著者
Jeff Irion Naoki Saito
出版者
一般社団法人 日本応用数理学会
雑誌
JSIAM Letters (ISSN:18830609)
巻号頁・発行日
vol.6, pp.21-24, 2014 (Released:2014-05-16)
参考文献数
16

We describe a new transform that generates a dictionary of bases for handling data on a graph by combining recursive partitioning of the graph and the Laplacian eigenvectors of each subgraph. Similar to the wavelet packet and local cosine dictionaries for regularly sampled signals, this dictionary of bases on the graph allows one to select an orthonormal basis that is most suitable to one's task at hand using a best-basis type algorithm. We also describe a few related transforms including a version of the Haar wavelet transform on a graph, each of which may be useful in its own right.
著者
杉山 将
出版者
一般社団法人 日本応用数理学会
雑誌
日本応用数理学会論文誌 (ISSN:24240982)
巻号頁・発行日
vol.23, no.3, pp.439-452, 2013-09-25 (Released:2017-04-08)
被引用文献数
1 or 0

確率分布間の距離の推定は機械学習における基礎的な研究課題の一つであり,二標本検定,変化点検知,クラスバランス推定など様々な目的に応用することができる.本稿では,確率分布の推定を介さない直接距離近似法,特に,カルバック・ライブラー距離,ピアソン距離,相対ピアソン距離,L^2距離の直接近似法を概観する.
著者
牧野 淳一郎
出版者
一般社団法人 日本応用数理学会
雑誌
応用数理 (ISSN:24321982)
巻号頁・発行日
vol.8, no.4, pp.277-287, 1998-12-15 (Released:2017-04-08)
参考文献数
18

I overview the Fast Multipole Method (FMM) and the Barnes-Hut tree method. These algorithms evaluate mutual gravitational interaction between N particles in O(N) or O(N log N) times, respectively. I present basic algorithms as well as recent developments, such as Anderson's method of using Poisson's formula, the use of FFT, and other optimization techniques. I also summarize the current states of two algorithms. Though FMM with O(N) scaling is theoretically preferred over O(N log N) tree method, comparisons of existing implementations proved otherwise. This result is not surprizing, since the calculation cost of FMM scales as O(Np^2) where p is the order of expansion, while that of the tree method scales as O(N log Np).
著者
Atsushi Iwasaki Ken Umeno
出版者
一般社団法人 日本応用数理学会
雑誌
JSIAM Letters (ISSN:18830609)
巻号頁・発行日
vol.9, pp.5-8, 2015 (Released:2017-02-18)
参考文献数
8

Permutation polynomials over a ring of modulo $2^w$ are well adopted to digital computers and digital signal processors, and so they are in particular expected to be useful for cryptography and pseudo random number generator{s}. For a longer period of the polynomial is demanded in general, we derive a necessary and sufficient condition that polynomials are permutating and their periods are the longest over the ring. We call polynomials which satisfy the condition ``one-stroke polynomials over the ring''.