Pub Date : 2023-08-30DOI: 10.1142/s2661335223500028
Kouji Yamamuro
{"title":"Iterated stochastic integrals and random velocity fluctuations","authors":"Kouji Yamamuro","doi":"10.1142/s2661335223500028","DOIUrl":"https://doi.org/10.1142/s2661335223500028","url":null,"abstract":"","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75170728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-20DOI: 10.1142/s2661335223500053
Satomi Watanabe
Let $mathcal{U}$ be the uniform spanning tree on $mathbb{Z}^3$, whose probability law is denoted by $mathbf{P}$. For $mathbf{P}$-a.s. realization of $mathcal{U}$, the recurrence of the the simple random walk on $mathcal{U}$ is proved in [5] and it is also demonstrated in [8] that two independent simple random walks on $mathcal{U}$ collide infinitely often. In this article, we will give a quantitative estimate on the number of collisions of two independent simple random walks on $mathcal{U}$, which provides another proof of the infinite collision property of $mathcal{U}$.
{"title":"Infinite collision property for the three-dimensional uniform spanning tree","authors":"Satomi Watanabe","doi":"10.1142/s2661335223500053","DOIUrl":"https://doi.org/10.1142/s2661335223500053","url":null,"abstract":"Let $mathcal{U}$ be the uniform spanning tree on $mathbb{Z}^3$, whose probability law is denoted by $mathbf{P}$. For $mathbf{P}$-a.s. realization of $mathcal{U}$, the recurrence of the the simple random walk on $mathcal{U}$ is proved in [5] and it is also demonstrated in [8] that two independent simple random walks on $mathcal{U}$ collide infinitely often. In this article, we will give a quantitative estimate on the number of collisions of two independent simple random walks on $mathcal{U}$, which provides another proof of the infinite collision property of $mathcal{U}$.","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2023-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80044715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-04DOI: 10.1142/s2661335222500046
Yoshiki Jikumaru, Yohei Yokosuka
{"title":"Differential geometric formulation of hanging membranes: shell membrane theory and variational principle","authors":"Yoshiki Jikumaru, Yohei Yokosuka","doi":"10.1142/s2661335222500046","DOIUrl":"https://doi.org/10.1142/s2661335222500046","url":null,"abstract":"","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84518196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-04DOI: 10.1142/s266133522250006x
Thi Thanh Mai Ta1, P. Hoang
{"title":"The Elastic Deformation Process of Bimetallic Objects","authors":"Thi Thanh Mai Ta1, P. Hoang","doi":"10.1142/s266133522250006x","DOIUrl":"https://doi.org/10.1142/s266133522250006x","url":null,"abstract":"","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82751028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-28DOI: 10.1142/s2661335222500058
Naoki Kubota, Masato Takei
. We consider Bernoulli first-passage percolation on the d dimensional hypercubic lattice with d ≥ 2. The passage time of edge e is 0 with probability p and 1 with probability 1 − p , independently of each other. Let p c be the critical probability for percolation of edges with passage time 0. When 0 ≤ p < p c , there exists a nonrandom, nonempty compact convex set B p such that the set of vertices to which the first-passage time from the origin is within t is well-approximated by t B p for all large t , with probability one. The aim of this paper is to prove that for 0 ≤ p < q < p c , the Hausdorff distance between B p and B q grows linearly in q − p . Moreover, we mention that the approach taken in the paper provides a lower bound for the expected size of the intersection of geodesics, that gives a nontrivial consequence for the critical case.
． 考虑d≥2的d维超立方晶格上的伯努利第一通道渗流。边e的通过时间为0，概率为p，通过时间为1，概率为1 - p，它们彼此独立。设cp为通过时间为0的边渗透的临界概率。当0≤p < p c时，存在一个非随机、非空的紧凸集B p，使得到达原点的第一次经过时间在t内的顶点集合t B p对所有大t都很好地逼近，概率为1。本文的目的是证明当0≤p < q < p c时，B p与B q之间的Hausdorff距离在q−p内线性增长。此外，我们提到本文所采用的方法为测地线相交的期望大小提供了一个下界，这对于临界情况给出了一个非平凡的结果。
{"title":"Comparison of limit shapes for Bernoulli first-passage percolation","authors":"Naoki Kubota, Masato Takei","doi":"10.1142/s2661335222500058","DOIUrl":"https://doi.org/10.1142/s2661335222500058","url":null,"abstract":". We consider Bernoulli first-passage percolation on the d dimensional hypercubic lattice with d ≥ 2. The passage time of edge e is 0 with probability p and 1 with probability 1 − p , independently of each other. Let p c be the critical probability for percolation of edges with passage time 0. When 0 ≤ p < p c , there exists a nonrandom, nonempty compact convex set B p such that the set of vertices to which the first-passage time from the origin is within t is well-approximated by t B p for all large t , with probability one. The aim of this paper is to prove that for 0 ≤ p < q < p c , the Hausdorff distance between B p and B q grows linearly in q − p . Moreover, we mention that the approach taken in the paper provides a lower bound for the expected size of the intersection of geodesics, that gives a nontrivial consequence for the critical case.","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88530496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-10DOI: 10.1142/s2661335222500010
J. Naveen
{"title":"AVD Proper edge coloring of some families of graphs","authors":"J. Naveen","doi":"10.1142/s2661335222500010","DOIUrl":"https://doi.org/10.1142/s2661335222500010","url":null,"abstract":"","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90113635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-20DOI: 10.1142/s2661335221500027
Kouji Yamamuro
{"title":"Stochastic complex integrals in a two-dimensional flow","authors":"Kouji Yamamuro","doi":"10.1142/s2661335221500027","DOIUrl":"https://doi.org/10.1142/s2661335221500027","url":null,"abstract":"","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87977173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-01DOI: 10.1142/s2661335222500071
Sebastián Elías Graiff Zurita, K. Kajiwara, Toshitomo Suzuki
We construct a method to fair a given discrete planar curve by using the integrable discrete analogue of Euler’s elastica, which is a discrete version of the approximation algorithm presented by D. Brander, et al. We first give a brief review of the integrable discrete analogue of Euler’s elastica proposed by A. I. Bobenko and Yu. B. Suris, then we present a detailed account of the fairing algorithm, and we apply this method to an architectural problem of characterizing the keylines of Japanese handmade pantiles.
我们构造了一种方法，通过使用欧拉弹性的可积离散模拟来公平给定的离散平面曲线，这是D. Brander等人提出的近似算法的离散版本。我们首先简要回顾了a . I. Bobenko和Yu提出的欧拉弹性的可积离散模拟。B. Suris，然后我们详细介绍了整流光算法，并将该方法应用于描述日本手工内裤的关键线条的建筑问题。
{"title":"Fairing of Discrete Planar Curves to Integrable Discrete Analogue of Euler's Elasticae","authors":"Sebastián Elías Graiff Zurita, K. Kajiwara, Toshitomo Suzuki","doi":"10.1142/s2661335222500071","DOIUrl":"https://doi.org/10.1142/s2661335222500071","url":null,"abstract":"We construct a method to fair a given discrete planar curve by using the integrable discrete analogue of Euler’s elastica, which is a discrete version of the approximation algorithm presented by D. Brander, et al. We first give a brief review of the integrable discrete analogue of Euler’s elastica proposed by A. I. Bobenko and Yu. B. Suris, then we present a detailed account of the fairing algorithm, and we apply this method to an architectural problem of characterizing the keylines of Japanese handmade pantiles.","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73007745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.1007/978-981-16-5576-0
{"title":"Proceedings of the Forum \"Math-for-Industry\" 2018","authors":"","doi":"10.1007/978-981-16-5576-0","DOIUrl":"https://doi.org/10.1007/978-981-16-5576-0","url":null,"abstract":"","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83286220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-13DOI: 10.1142/S2661335221500015
K. Nuida
The group structure on the rational points of elliptic curves plays several important roles, in mathematics and recently also in other areas such as cryptography. However, the famous proofs for the group property (in particular, for its associative law) require somewhat advanced mathematics and therefore are not easily accessible by non-mathematician. On the other hand, there have been attempts in the literature to give an elementary proof, but those rely on computer-aided calculation for some part in their proofs. In this paper, we give a self-contained proof of the associative law for this operation, assuming mathematical knowledge only at the level of basic linear algebra and not requiring computer-aided arguments.
{"title":"An elementary linear-algebraic proof without computer-aided arguments for the group law on elliptic curves","authors":"K. Nuida","doi":"10.1142/S2661335221500015","DOIUrl":"https://doi.org/10.1142/S2661335221500015","url":null,"abstract":"The group structure on the rational points of elliptic curves plays several important roles, in mathematics and recently also in other areas such as cryptography. However, the famous proofs for the group property (in particular, for its associative law) require somewhat advanced mathematics and therefore are not easily accessible by non-mathematician. On the other hand, there have been attempts in the literature to give an elementary proof, but those rely on computer-aided calculation for some part in their proofs. In this paper, we give a self-contained proof of the associative law for this operation, assuming mathematical knowledge only at the level of basic linear algebra and not requiring computer-aided arguments.","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2020-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81709093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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