In this paper we investigate normalized conformal mappings of the exterior of the reciprocal of the Multibrot set and analyze the growth of the denominator of the coefficients. Our inequality improves Ewing and Schober’s result which was presented in [6]. We use the coefficient formula of [13]. The straightforward adaptation of the proof in this paper slightly improves the main theorem of [12].
{"title":"Taylor Coefficients of the Conformal Map for the Exterior of the Reciprocal of the Multibrot Set","authors":"Hirokazu Shimauchi","doi":"10.4036/iis.2019.a.03","DOIUrl":"https://doi.org/10.4036/iis.2019.a.03","url":null,"abstract":"In this paper we investigate normalized conformal mappings of the exterior of the reciprocal of the Multibrot set and analyze the growth of the denominator of the coefficients. Our inequality improves Ewing and Schober’s result which was presented in [6]. We use the coefficient formula of [13]. The straightforward adaptation of the proof in this paper slightly improves the main theorem of [12].","PeriodicalId":91087,"journal":{"name":"Interdisciplinary information sciences","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70252843","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}
{"title":"On Explicit Construction of Simplex t -designs","authors":"M. S. Baladram","doi":"10.4036/IIS.2018.S.02","DOIUrl":"https://doi.org/10.4036/IIS.2018.S.02","url":null,"abstract":"","PeriodicalId":91087,"journal":{"name":"Interdisciplinary information sciences","volume":"24 1","pages":"181-184"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4036/IIS.2018.S.02","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70252366","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}
Harada (1971) argued some forty five years ago that the Japanese phenomenon called ‘‘Nominative/Genitive Conversion’’ (NGC) was undergoing a syntactic change, which was detected as idiolectal variations. Synchronically, Miyagawa (2011) argues that the NGC is not a free alternation but that more stative predicates are more likely to accept a Genitive subject. However, no one has ever proposed an argument that bridges the synchronic preference for ‘‘stativity’’ of the NGC and its diachronic syntactic change, which is characterized as ‘‘stativization.’’ In this article, we will show that the diachronic syntactic change has been in progress at least for the last 100 years. It will be shown that the semantic ‘‘stativization’’ is an epiphenomenon of the syntactic microparametric change which we refer to as ‘‘clause shrinking,’’ or a change in the syntactic size of the Genitive Subject Clause (GSC) from CP to TP to vP to VP/AP. Moreover, we will explain how such a drastic language change have actually influenced language acquisition for children who were born in different time periods, by integrating Kayne’s (2000) microparametric syntax, Snyder’s (2017) theory of competition between incompatible constructions, Lightfoot and Westergard’s (2009) micro-cue analysis of language acquisition, Manzini and Wexler’s (1987) Subset Principle, and Bošković (1997) Minimal Structure Principle.
{"title":"Diachronic Syntactic Change and Language Acquisition: A View from Nominative/Genitive Conversion in Japanese","authors":"Yoshiki Ogawa","doi":"10.4036/IIS.2018.R.01","DOIUrl":"https://doi.org/10.4036/IIS.2018.R.01","url":null,"abstract":"Harada (1971) argued some forty five years ago that the Japanese phenomenon called ‘‘Nominative/Genitive Conversion’’ (NGC) was undergoing a syntactic change, which was detected as idiolectal variations. Synchronically, Miyagawa (2011) argues that the NGC is not a free alternation but that more stative predicates are more likely to accept a Genitive subject. However, no one has ever proposed an argument that bridges the synchronic preference for ‘‘stativity’’ of the NGC and its diachronic syntactic change, which is characterized as ‘‘stativization.’’ In this article, we will show that the diachronic syntactic change has been in progress at least for the last 100 years. It will be shown that the semantic ‘‘stativization’’ is an epiphenomenon of the syntactic microparametric change which we refer to as ‘‘clause shrinking,’’ or a change in the syntactic size of the Genitive Subject Clause (GSC) from CP to TP to vP to VP/AP. Moreover, we will explain how such a drastic language change have actually influenced language acquisition for children who were born in different time periods, by integrating Kayne’s (2000) microparametric syntax, Snyder’s (2017) theory of competition between incompatible constructions, Lightfoot and Westergard’s (2009) micro-cue analysis of language acquisition, Manzini and Wexler’s (1987) Subset Principle, and Bošković (1997) Minimal Structure Principle.","PeriodicalId":91087,"journal":{"name":"Interdisciplinary information sciences","volume":"24 1","pages":"91-179"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70252220","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}
In this talk, I will give an introductory talk on the homogenization for fully nonlinear PDEs. To prove “homogenization” in a periodic setting, it is well-known that the cell problem, which is a kind of nonlinear eigenvalue problems, plays an important role. In the talk, I will show some of basic arguments in Lions-Papanicolaou-Varadhan (1987), and Evans (1992) and prove the homogenization in a periodic setting by using a perturbed test function method introduced in Evans (1989) as a starting point. In the second half of the talk, I will show some of recent development in Davini-FathiIturriaga-Zavidovique (2016), Mitake-Tran (2017) on the selection problem appearing in the cell problem. These results did not currently have a clear application to homogenization, but may have potential. I finally refer to a lecture note [6] on this direction. [1] A. Davini, A. Fathi, R. Iturriaga, M. Zavidovique, Convergence of the solutions of the discounted equation, Invent. Math. 206 (1) (2016) 29-55. [2] L. C. Evans, The perturbed test function method for viscosity solutions of nonlinear PDE, Proc. Roy. Soc. Edinburgh Sect. A 111 (1989), no. 3-4, 359-375. [3] L. C. Evans, Periodic homogenisation of certain fully nonlinear partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A 120 (1992), no. 3-4, 245-265. [4] P.-L. Lions, G. Papanicolaou, S. R. S. Varadhan, Homogenization of Hamilton-Jacobi equations, unpublished work (1987). [5] H. Mitake, H. V. Tran, Selection problems for a discount degenerate viscous Hamilton-Jacobi equation, Adv. Math. 306 (2017), 684-703. [6] N. Q. Le, H. Mitake and H. V. Tran, Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampere equations, to appear in Lecture Notes in Mathematics, Springer.
在这次演讲中，我将对全非线性偏微分方程的均质化进行介绍。为了证明周期条件下的“均匀性”，众所周知，单元问题作为一种非线性特征值问题起着重要的作用。在演讲中，我将展示Lions-Papanicolaou-Varadhan(1987)和Evans(1992)中的一些基本论点，并使用Evans(1989)中引入的摄动测试函数方法作为起点，证明周期设置中的均匀化。在演讲的后半部分，我将展示Davini-FathiIturriaga-Zavidovique (2016)， Mitake-Tran(2017)关于细胞问题中出现的选择问题的一些最新进展。这些结果目前还没有明确的应用于均质化，但可能有潜力。关于这个方向，我最后参考了讲义b[6]。[10]张建军，张建军，张建军，张建军，张建军，张建军，张建军，张建军，张建军。数学。206(1)(2016)29-55。[10]李志强，张志强，非线性PDE黏度解的微扰测试函数法，工程力学与工程学报。Soc。爱丁堡教派，第111(1989)号。3 - 4, 359 - 375。[10]李志强，一类全非线性偏微分方程的周期均匀化，吉林大学学报。Soc。爱丁堡教派A 120(1992)，编号。3 - 4, 245 - 265。[4] p.l.。Lions, G. Papanicolaou, S. R. S. Varadhan, Hamilton-Jacobi方程的均匀化，未发表的作品(1987)。[10]陈宏伟，陈宏伟，张建军，一种基于线性回归的Hamilton-Jacobi方程求解方法，数学学报，36(2017)，684- 783。[1]李n . Q.，三竹和陈宏伟，Hamilton-Jacobi方程和线性化Monge-Ampere方程的动力学和几何方面，出现在数学讲义中，[10]。
{"title":"On Cell Problems for Nonlinear PDES and Its Application to Homogenization","authors":"Hiroyoshi Mitake","doi":"10.4036/IIS.2018.A.02","DOIUrl":"https://doi.org/10.4036/IIS.2018.A.02","url":null,"abstract":"In this talk, I will give an introductory talk on the homogenization for fully nonlinear PDEs. To prove “homogenization” in a periodic setting, it is well-known that the cell problem, which is a kind of nonlinear eigenvalue problems, plays an important role. In the talk, I will show some of basic arguments in Lions-Papanicolaou-Varadhan (1987), and Evans (1992) and prove the homogenization in a periodic setting by using a perturbed test function method introduced in Evans (1989) as a starting point. In the second half of the talk, I will show some of recent development in Davini-FathiIturriaga-Zavidovique (2016), Mitake-Tran (2017) on the selection problem appearing in the cell problem. These results did not currently have a clear application to homogenization, but may have potential. I finally refer to a lecture note [6] on this direction. [1] A. Davini, A. Fathi, R. Iturriaga, M. Zavidovique, Convergence of the solutions of the discounted equation, Invent. Math. 206 (1) (2016) 29-55. [2] L. C. Evans, The perturbed test function method for viscosity solutions of nonlinear PDE, Proc. Roy. Soc. Edinburgh Sect. A 111 (1989), no. 3-4, 359-375. [3] L. C. Evans, Periodic homogenisation of certain fully nonlinear partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A 120 (1992), no. 3-4, 245-265. [4] P.-L. Lions, G. Papanicolaou, S. R. S. Varadhan, Homogenization of Hamilton-Jacobi equations, unpublished work (1987). [5] H. Mitake, H. V. Tran, Selection problems for a discount degenerate viscous Hamilton-Jacobi equation, Adv. Math. 306 (2017), 684-703. [6] N. Q. Le, H. Mitake and H. V. Tran, Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampere equations, to appear in Lecture Notes in Mathematics, Springer.","PeriodicalId":91087,"journal":{"name":"Interdisciplinary information sciences","volume":"24 1","pages":"49-58"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70252210","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}
Fixed points of the self-power map over a finite field have been studied in cryptology as a special case of modular exponentiation. In this note, we define an elliptic-curve version of the self-power map, enumerate the number of curves that contain at least one fixed point, and give its upper and lower bounds. Our result is a partial solution to the open question raised by Glebsky and Shparlinski in 2010.
{"title":"On the Fixed Points of an Elliptic-Curve Version of Self-Power Map","authors":"Hiroki Shizuya","doi":"10.4036/IIS.2018.S.01","DOIUrl":"https://doi.org/10.4036/IIS.2018.S.01","url":null,"abstract":"Fixed points of the self-power map over a finite field have been studied in cryptology as a special case of modular exponentiation. In this note, we define an elliptic-curve version of the self-power map, enumerate the number of curves that contain at least one fixed point, and give its upper and lower bounds. Our result is a partial solution to the open question raised by Glebsky and Shparlinski in 2010.","PeriodicalId":91087,"journal":{"name":"Interdisciplinary information sciences","volume":"24 1","pages":"87-90"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70252291","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}
Confidentiality is a fundamental duty of a physician to maintain a safe medical system. The authors are law researchers and medical researchers. We planned interdisciplinary workshops including both legal and medical viewpoints. Encouraging medical students to understand the importance of confidentiality and its exceptions, we studied others’ academic fields together over eight years, and established a fixed style of scenario-based group discussions. As a unique characteristic of this project, it includes actual students of law and other fields as facilitators to encourage mobility and circulation among disciplines. The workshop has continued since 2009, once a year. Results of student evaluations show their enhanced understanding of confidentiality as a core value of safety and sustainable medical systems. Other teaching purposes have mostly succeeded. Facilitators regard this workshop as a good opportunity to explore interdisciplinary studies as well. That interest maintains and reinforces the close relationship between these disciplines of study. Therefore, the authors conclude that this innovative workshop is very effective.
{"title":"Interdisciplinary Education for Physician's Confidentiality by Interdisciplinary Collaboration of Medical and Law Researchers","authors":"Ryoju Hamada, Junichi Kameoka, Yoshinari Kanaya, Yutaka Kagaya","doi":"10.4036/IIS.2017.R.02","DOIUrl":"https://doi.org/10.4036/IIS.2017.R.02","url":null,"abstract":"Confidentiality is a fundamental duty of a physician to maintain a safe medical system. The authors are law researchers and medical researchers. We planned interdisciplinary workshops including both legal and medical viewpoints. Encouraging medical students to understand the importance of confidentiality and its exceptions, we studied others’ academic fields together over eight years, and established a fixed style of scenario-based group discussions. As a unique characteristic of this project, it includes actual students of law and other fields as facilitators to encourage mobility and circulation among disciplines. The workshop has continued since 2009, once a year. Results of student evaluations show their enhanced understanding of confidentiality as a core value of safety and sustainable medical systems. Other teaching purposes have mostly succeeded. Facilitators regard this workshop as a good opportunity to explore interdisciplinary studies as well. That interest maintains and reinforces the close relationship between these disciplines of study. Therefore, the authors conclude that this innovative workshop is very effective.","PeriodicalId":91087,"journal":{"name":"Interdisciplinary information sciences","volume":"23 1","pages":"145-162"},"PeriodicalIF":0.0,"publicationDate":"2017-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43023876","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}
In this paper we study the asymptotic behavior of second-order uniformly elliptic operators on weighted Riemannian manifolds. They naturally emerge when studying spectral properties of the Laplace-Beltrami operator on families of manifolds with rapidly oscillating metrics. We appeal to the notion of H-convergence introduced by Murat and Tartar. In our main result we establish an H-compactness result that applies to elliptic operators with measurable, uniformly elliptic coefficients on weighted Riemannian manifolds. We further discuss the special case of ``locally periodic'' coefficients and study the asymptotic spectral behavior of compact submanifolds of $mathbb R^n$ with rapidly oscillating geometry.
{"title":"H-Compactness of Elliptic Operators on Weighted Riemannian Manifolds","authors":"H. Hoppe, J. Masamune, S. Neukamm","doi":"10.4036/iis.2019.b.03","DOIUrl":"https://doi.org/10.4036/iis.2019.b.03","url":null,"abstract":"In this paper we study the asymptotic behavior of second-order uniformly elliptic operators on weighted Riemannian manifolds. They naturally emerge when studying spectral properties of the Laplace-Beltrami operator on families of manifolds with rapidly oscillating metrics. We appeal to the notion of H-convergence introduced by Murat and Tartar. In our main result we establish an H-compactness result that applies to elliptic operators with measurable, uniformly elliptic coefficients on weighted Riemannian manifolds. We further discuss the special case of ``locally periodic'' coefficients and study the asymptotic spectral behavior of compact submanifolds of $mathbb R^n$ with rapidly oscillating geometry.","PeriodicalId":91087,"journal":{"name":"Interdisciplinary information sciences","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46340090","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}
I. Crimaldi, Michela Del Vicario, G. Morrison, Walter Quattrociocchi, M. Riccaboni
We present a new network model accounting for multidimensional assortativity. Each node is characterized by a number of features and the probability of a link between two nodes depends on common features. We do not fix a priori the total number of possible features. The bipartite network of the nodes and the features evolves according to a stochastic dynamics that depends on three parameters that respectively regulate the preferential attachment in the transmission of the features to the nodes, the number of new features per node, and the power-law behavior of the total number of observed features. Our model also takes into account a mechanism of triadic closure. We provide theoretical results and statistical estimators for the parameters of the model. We validate our approach by means of simulations and an empirical analysis of a network of scientific collaborations.
{"title":"Modeling Networks with a Growing Feature-Structure","authors":"I. Crimaldi, Michela Del Vicario, G. Morrison, Walter Quattrociocchi, M. Riccaboni","doi":"10.4036/IIS.2017.R.01","DOIUrl":"https://doi.org/10.4036/IIS.2017.R.01","url":null,"abstract":"We present a new network model accounting for multidimensional assortativity. Each node is characterized by a number of features and the probability of a link between two nodes depends on common features. We do not fix a priori the total number of possible features. The bipartite network of the nodes and the features evolves according to a stochastic dynamics that depends on \u0000three parameters that respectively regulate the preferential attachment in the transmission of the features to the nodes, the number of new features per node, and the power-law behavior of the total number of observed features. \u0000Our model also takes into account a mechanism of triadic closure. We provide theoretical results and statistical estimators for the parameters of the model. \u0000We validate our approach by means of simulations and an empirical analysis of a network of scientific collaborations.","PeriodicalId":91087,"journal":{"name":"Interdisciplinary information sciences","volume":"23 1","pages":"127-144"},"PeriodicalIF":0.0,"publicationDate":"2017-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46008041","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}
Based on the similarity between telegraph equation for transmission lines and Klein–Gordon equation, we have related a distributed element model in electrical engineering to a discrete-time quantum walk through Dirac equation. As a result, we have constructed a discrete transmission line model for a discrete-time quantum walk, and it enables us understanding the characteristics of quantum walks as those of the transmission line.
{"title":"A Discrete Transmission Line Model for Discrete-time Quantum Walks","authors":"Y. Fukushima, T. Wada","doi":"10.4036/IIS.2017.A.11","DOIUrl":"https://doi.org/10.4036/IIS.2017.A.11","url":null,"abstract":"Based on the similarity between telegraph equation for transmission lines and Klein–Gordon equation, we have related a distributed element model in electrical engineering to a discrete-time quantum walk through Dirac equation. As a result, we have constructed a discrete transmission line model for a discrete-time quantum walk, and it enables us understanding the characteristics of quantum walks as those of the transmission line.","PeriodicalId":91087,"journal":{"name":"Interdisciplinary information sciences","volume":"23 1","pages":"87-93"},"PeriodicalIF":0.0,"publicationDate":"2017-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41765893","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}
{"title":"Periodicity of the Discrete-time Quantum Walk on a Finite Graph","authors":"Y. Higuchi, N. Konno, I. Sato, E. Segawa","doi":"10.4036/IIS.2017.A.10","DOIUrl":"https://doi.org/10.4036/IIS.2017.A.10","url":null,"abstract":"","PeriodicalId":91087,"journal":{"name":"Interdisciplinary information sciences","volume":"23 1","pages":"75-86"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4036/IIS.2017.A.10","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70252589","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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