Pub Date : 2020-04-13DOI: 10.1142/S2661335220500033
Satoshi Yabuoku
We consider the non-hermitian matrix-valued process of Elliptic Ginibre Ensemble. This model includes Dyson's Brownian motion model and the time evolution model of Ginibre ensemble by using hermiticity parameter. We show the complex eigenvalue processes satisfy the stochastic differential equations which are very similar to Dyson's model and give an explicit form of overlap correlations. As a corollary, in the case of 2-by-2 matrix, we also mention the relation between the diagonal overlap, which is the speed of eigenvalues, and the distance of the two eigenvalues.
{"title":"Eigenvalue processes of Elliptic Ginibre Ensemble and their overlaps","authors":"Satoshi Yabuoku","doi":"10.1142/S2661335220500033","DOIUrl":"https://doi.org/10.1142/S2661335220500033","url":null,"abstract":"We consider the non-hermitian matrix-valued process of Elliptic Ginibre Ensemble. This model includes Dyson's Brownian motion model and the time evolution model of Ginibre ensemble by using hermiticity parameter. We show the complex eigenvalue processes satisfy the stochastic differential equations which are very similar to Dyson's model and give an explicit form of overlap correlations. As a corollary, in the case of 2-by-2 matrix, we also mention the relation between the diagonal overlap, which is the speed of eigenvalues, and the distance of the two eigenvalues.","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":"71 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83940366","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 : 2020-01-01DOI: 10.1007/978-981-15-6062-0
A. Icha
{"title":"Mathematical Analysis of Continuum Mechanics and Industrial Applications III","authors":"A. Icha","doi":"10.1007/978-981-15-6062-0","DOIUrl":"https://doi.org/10.1007/978-981-15-6062-0","url":null,"abstract":"","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":"16 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85328401","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 : 2019-09-16DOI: 10.1142/S2661335219500047
Kouji Yamamuro
Two-dimensional flow is considered in the complex plane. We discuss Blasius’ formula in a perfect fluid through stochastic complex integrals. This formula is also investigated in a viscous fluid. We mention the theorems corresponding to Green’s formulae last.
{"title":"Random representation of Blasius’ formula through stochastic complex integrals","authors":"Kouji Yamamuro","doi":"10.1142/S2661335219500047","DOIUrl":"https://doi.org/10.1142/S2661335219500047","url":null,"abstract":"Two-dimensional flow is considered in the complex plane. We discuss Blasius’ formula in a perfect fluid through stochastic complex integrals. This formula is also investigated in a viscous fluid. We mention the theorems corresponding to Green’s formulae last.","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":"77 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82048833","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 : 2019-06-07DOI: 10.1142/S2661335219500035
K. Akiyama, Shuhei Nakamura, Masaru Ito, Noriko Hirata-Kohno
In this paper, we propose a key exchange protocol using multivariate polynomial maps whose security relies on the hardness in finding a solution to a certain system of nonlinear polynomial equations. Under the hardness assumption of solving the system of equations, we prove that our protocol is secure against key recovery attacks by passive attackers if the protocol is established honestly.
{"title":"A key exchange protocol relying on polynomial maps","authors":"K. Akiyama, Shuhei Nakamura, Masaru Ito, Noriko Hirata-Kohno","doi":"10.1142/S2661335219500035","DOIUrl":"https://doi.org/10.1142/S2661335219500035","url":null,"abstract":"In this paper, we propose a key exchange protocol using multivariate polynomial maps whose security relies on the hardness in finding a solution to a certain system of nonlinear polynomial equations. Under the hardness assumption of solving the system of equations, we prove that our protocol is secure against key recovery attacks by passive attackers if the protocol is established honestly.","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":"11 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80765886","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 : 2019-05-28DOI: 10.1142/S2661335219500023
T. Nakamoto, R. Nishii, S. Eguchi
In this paper, as data, ellipsoids in a color coordinate called the Commission Internationale de l’Eclairage (CIE)-Lab system are given as data for 19 colors. Each ellipsoid is a region where all points are visually recognized as the same color at the center of the coordinate system. Our aim here is to predict the shape of an ellipsoid whose center is given by a new color. We proposed two prediction methods of positive definite matrices determining ellipsoids. The first one is a nonparametric method with Gaussian kernel. The prediction is provided as a weighted sum of positive definite matrices corresponding to 19 ellipsoids in the training data. The second one is to use a matrix-valued regression model applied to a logarithm of positive definite matrices where explanatory variables are three elements of color centers. The best result was obtained by the nonparametric methods with three bandwidth parameters. The log normal regression had a weaker performance, but even so the model estimation was easily carried out.
{"title":"Predicting precision matrices for color matching problem","authors":"T. Nakamoto, R. Nishii, S. Eguchi","doi":"10.1142/S2661335219500023","DOIUrl":"https://doi.org/10.1142/S2661335219500023","url":null,"abstract":"In this paper, as data, ellipsoids in a color coordinate called the Commission Internationale de l’Eclairage (CIE)-Lab system are given as data for 19 colors. Each ellipsoid is a region where all points are visually recognized as the same color at the center of the coordinate system. Our aim here is to predict the shape of an ellipsoid whose center is given by a new color. We proposed two prediction methods of positive definite matrices determining ellipsoids. The first one is a nonparametric method with Gaussian kernel. The prediction is provided as a weighted sum of positive definite matrices corresponding to 19 ellipsoids in the training data. The second one is to use a matrix-valued regression model applied to a logarithm of positive definite matrices where explanatory variables are three elements of color centers. The best result was obtained by the nonparametric methods with three bandwidth parameters. The log normal regression had a weaker performance, but even so the model estimation was easily carried out.","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":"91 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83048721","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 : 2019-04-18DOI: 10.1142/S2661335220500045
Masaru Hasegawa, Y. Kabata, K. Saji
Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal projections in a number of directions. We discuss relations between (1) a space curve and the projected curves from several distinct directions, and (2) a surface and the apparent contours of projections from several distinct directions, in terms of differential geometry and singularity theory. In particular, formulae for recovering certain information on the original curves or surfaces from their projected images are given.
{"title":"Capturing information on curves and surfaces from their projected images","authors":"Masaru Hasegawa, Y. Kabata, K. Saji","doi":"10.1142/S2661335220500045","DOIUrl":"https://doi.org/10.1142/S2661335220500045","url":null,"abstract":"Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal projections in a number of directions. We discuss relations between (1) a space curve and the projected curves from several distinct directions, and (2) a surface and the apparent contours of projections from several distinct directions, in terms of differential geometry and singularity theory. In particular, formulae for recovering certain information on the original curves or surfaces from their projected images are given.","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":"64 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89073497","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 : 2019-04-10DOI: 10.1142/S2661335219500011
T. Kumano, J. Nakagawa
Grain-oriented silicon steel is mainly used as the core material of transformers, and it is manufactured by applying secondary recrystallization. The driving force of this process is the grain boundary energy, based on the nature of the grain boundary, which is determined by coincidence site lattice (CSL) relations. CSL relations are determined by the arrangement of lattice points in three-dimensional space and have already been shown mathematically by using advanced mathematics. However, their derivation processes are abstract, making them difficult for material engineers to understand. Therefore, in this study, a derivation of CSL relations is attempted in order to enable material engineers to easily understand the derivation. This study contributes to industrial mathematics by helping material engineers understand the essence of the mathematical method in order to use it appropriately. Specifically, a derivation method for coincidence relations is proposed using the hexagonal lattice (in the case of an axial ratio of [Formula: see text]) as an example that avoids the need for advanced mathematics. This method involves applying the scale rotation of a quaternion, and it is thus named the quaternion-matrix method. The matrix specifying the [Formula: see text] coincidence relation of a certain lattice system is expressed by a similarity transformation using the matrix comprising its primitive translation vectors and is given as the following transformation matrix: [Formula: see text]. Based on the rational number property of the transformation matrix elements, the following formula is derived: [Formula: see text], [Formula: see text], [Formula: see text] value. Here, ([Formula: see text]) is specified by the integrality (lattice point) and irreducibility (unit cell) among the elements of [Formula: see text], and the quaternion for the CSL formation is thus derived. Finally, based on the polar form of this quaternion, the coincidence relation can be derived.
{"title":"A derivation of coincidence relations utilizing quaternion and matrix based on the hexagonal lattice for material engineers","authors":"T. Kumano, J. Nakagawa","doi":"10.1142/S2661335219500011","DOIUrl":"https://doi.org/10.1142/S2661335219500011","url":null,"abstract":"Grain-oriented silicon steel is mainly used as the core material of transformers, and it is manufactured by applying secondary recrystallization. The driving force of this process is the grain boundary energy, based on the nature of the grain boundary, which is determined by coincidence site lattice (CSL) relations. CSL relations are determined by the arrangement of lattice points in three-dimensional space and have already been shown mathematically by using advanced mathematics. However, their derivation processes are abstract, making them difficult for material engineers to understand. Therefore, in this study, a derivation of CSL relations is attempted in order to enable material engineers to easily understand the derivation. This study contributes to industrial mathematics by helping material engineers understand the essence of the mathematical method in order to use it appropriately. Specifically, a derivation method for coincidence relations is proposed using the hexagonal lattice (in the case of an axial ratio of [Formula: see text]) as an example that avoids the need for advanced mathematics. This method involves applying the scale rotation of a quaternion, and it is thus named the quaternion-matrix method. The matrix specifying the [Formula: see text] coincidence relation of a certain lattice system is expressed by a similarity transformation using the matrix comprising its primitive translation vectors and is given as the following transformation matrix: [Formula: see text]. Based on the rational number property of the transformation matrix elements, the following formula is derived: [Formula: see text], [Formula: see text], [Formula: see text] value. Here, ([Formula: see text]) is specified by the integrality (lattice point) and irreducibility (unit cell) among the elements of [Formula: see text], and the quaternion for the CSL formation is thus derived. Finally, based on the polar form of this quaternion, the coincidence relation can be derived.","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":"100 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88018570","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 : 2019-01-06DOI: 10.1007/978-981-15-6062-0_6
M. Kimura, Atsushi Suzuki
{"title":"Deformation Problem for Glued Elastic Bodies and an Alternative Iteration Method","authors":"M. Kimura, Atsushi Suzuki","doi":"10.1007/978-981-15-6062-0_6","DOIUrl":"https://doi.org/10.1007/978-981-15-6062-0_6","url":null,"abstract":"","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":"67 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72591247","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 : 2019-01-01DOI: 10.1007/978-4-431-55456-1
O. Matsushita, Masato Tanaka, H. Kanki, Masao Kobayashi, P. Keogh
{"title":"Vibrations of Rotating Machinery","authors":"O. Matsushita, Masato Tanaka, H. Kanki, Masao Kobayashi, P. Keogh","doi":"10.1007/978-4-431-55456-1","DOIUrl":"https://doi.org/10.1007/978-4-431-55456-1","url":null,"abstract":"","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":"130 6 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77446748","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 : 2016-07-20DOI: 10.1007/978-981-13-2850-3
Deskripsi Lengkap
{"title":"Mathematical Insights into Advanced Computer Graphics Techniques","authors":"Deskripsi Lengkap","doi":"10.1007/978-981-13-2850-3","DOIUrl":"https://doi.org/10.1007/978-981-13-2850-3","url":null,"abstract":"","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":"3 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2016-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73661069","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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