Language：Japanese  

J-GLOBAL

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Publishing type：Research paper (scientific journal)  

In this paper, we present a method to compose conformal mapping functions of arbitrary given simply connected domains which are bounded by the smooth boundary curves of finite length onto the unit disk as the standard domain. The Riemann mapping theorem tells that such domains are conformally equivalent and the mapping functions are uniquely determined under certain normalizing conditions. We here adopt a normalizing condition, in which the two lists of three distinct points are given on the boundary curves of the problem domain, and of the unit disk, as the normalizing points. The mapping functions are uniquely determined to map the points on the boundary onto the points on the unit circle. Our method is based on the method of numerical conformal mappings by the charge simulation method, which is provided to meet the different types of normalizing conditions. ©2014 International Information Institute.

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Publishing type：Research paper (scientific journal)   Publisher：Science and Engineering Publishing Company  

DOI： 10.14355/ijics.2014.03.007

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Academy Publisher  

In this paper, we propose an efficient search method for unstructured P2P networks. The method is based on the existing method called expanding ring in which the search area is gradually enlarged. In expanding ring, a large number of queries are forwarded unnecessarily because the same query is forwarded to the same node multiple times. We mitigate this problem by using temporary links. By conducting simulations, we demonstrate that the proposed method can spread search queries with fewer messages than existing methods. We also show that it is possible to search efficiently in various types of networks by using degree and cluster coefficient information obtained from the nodes through which a search query passes. © 2014 ACADEMY PUBLISHER.

DOI： 10.4304/jnw.9.7.1665-1673

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Language：Japanese   Publisher：The Japan Society for Industrial and Applied Mathematics  

In the conformal mapping of multiply connected domains, the following five canonical slit domains listed by Nehari (1952) are well known: the parallel, circular and radial slit domains, and the circle and circular ring with concentric circular slits. Before that, Koebe (1916) listed thirty-nine canonical slit domains. In this paper, using the charge simulation method, we propose a method of numerical conformal mappings onto their first thirteen canonical slit domains including the above five domains in a more general form. Numerical experiments show the effectiveness of our method. We examine also some problems in the computation of complex logarithmic function.

DOI： 10.11540/jsiamt.24.3_157

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Publishing type：Research paper (scientific journal)  

We present a numerical method for the conformal mapping of unbounded multiply connected domains exterior to closed Jordan curves onto the general spiral slit domain, which is a natural extension of the circular and radial slit domains. ©2013 International Information Institute.

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Language：Japanese   Publisher：一般社団法人情報処理学会  

The transformational group structure theory successfully explains how the different types of cognitive judgments of patterns such as similarity and goodness are performed by the concept of cognitive transformation groups and transformational group structures. However, it involves the difficulty that most pattern pairs or patterns can not be distinguished in similarity or goodness judgments as the number of elements of binary patterns increases. We here introduce the concept of quasi-transformational group structures with Hamming's distance, and show by experiments using linear binary patterns that the human cognitive system employs the quasi-transformational group structure in goodness judgments as well as in the similarity judgments.

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Language：English   Publishing type：Research paper (scientific journal)  

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The aim of this study is to propose an efficient broadcasting method considering node density and to conduct a comparative evaluation with existing methods. In our proposed method, broadcasting is carried out efficiently using positional information attached to messages at the time of broadcasting and not by periodically exchanging positional information or routing tables. We run a simulation considering the variation of node density and show that the proposed method excels other methods in overall performance. © 2013 ACADEMY PUBLISHER.

DOI： 10.4304/jnw.8.4.804-811

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER JAPAN KK  

We propose a numerical method for the conformalmapping of unbounded multiply connected domains exterior to closed Jordan curvesC1, . . . ,Cn onto a canonical linear slit domain, which is the entire plane with linear slits S 1, . . . , S n of angles θ 1, ⋯ , θ n arbitrarily assigned to the real axis, respectively. Ifθ1 = ⋯ =θn =θ then it is thewell-known parallel slit domain, which is important in the problem of potential flows past obstacles. In the method, we reduce the mapping problem to a boundary value problem for an analytic function, and approximate it by a linear combination of complex logarithmic functions based on the charge simulation method. Numerical examples show the effectiveness of our method. © The Author(s) 2012.

DOI： 10.1007/s13160-012-0058-0

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Publishing type：Research paper (scientific journal)  

Seamless availability on applying to the problems of various types of simply and multiply connected domains is one of the key features of Amano's method of numerical conformal mappings. We studied the application of the method for a doubly connected rectangular domain with a slit and obtain an approximation of the conformal mapping function which maps the domain onto the canonical annular domain. In the method the charge simulation method of complex logarithmic functions are used. Therefore, the premapping technique is necessary to open the slit for placing the charges outside the problem domain. In addition, we need arrangement of the charges well adapted to the corner singularity of the rectangle. We show, by a numerical example, the effectiveness of the method and a simple application on image processing.

DOI： 10.11345/nctam.60.333

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Conformal mappings are familiar in science and engineering. Recently, the problem of multiply connected domains has attracted special interest. We here present a unified scheme for numerical conformal mappings of unbounded, multiply connected domains onto the parallel, circular and radial slit domains under two different conditions. These are canonical slit domains important in potential flow problems. We express the mapping functions in terms of an analytic function so that its real part is subject to a Dirichlet boundary condition, and have approximate mapping functions of simple form and high accuracy using the charge simulation method. Numerical examples show the effectiveness of our method. We also make a short survey of relevant works.

DOI： 10.11345/nctam.60.317

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It is possible to recover the original data from a certain amount of encoded data by using rateless codes, which are utilized for multicast streaming. In this paper, we propose an effective replication technique using rateless codes for unstructured P2P networks. More specifically, we propose a method to spread and find chunks generated from files efficiently. Through simulation experiments, we show that the proposed technique achieves high search success ratio and shortens the time required to obtain a file. © 2012 Academy Publisher.

DOI： 10.4304/jcm.7.4.349-356

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Language：Japanese   Publisher：Kyoto University  

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Other Link： http://hdl.handle.net/2433/170734

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

近年,非構造化P2Pネットワークにおいては様々な検索手法が提案されているが,一般に検索速度と通信負荷はトレードオフの関係にある.すなわち,目的ファイルを短時間で発見できる検索手法は,一般に通信負荷が高い.本論文では,Acquaintance Link,Light Floodという二つの既存手法を組み合わせることにより,検索速度向上と通信負荷軽減を同時に実現する手法を提案する.

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Language：Japanese  

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Publishing type：Research paper (scientific journal)  

DOI： 10.14495/jsiaml.2.53

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Language：Japanese   Publisher：情報処理学会  

Numerical conformal mappings are important in scientific computations. In this paper, we present a numerical method for the conformal mapping of unbounded multiply connected domains onto the canonical parallel slit domain, and then the collinear slit domain. We approximate a pair of harmonic functions by a linear combination of complex logarithmic functions based on the charge simulation method, and obtain a simple form of approximate mapping functions with high accuracy. Some numerical examples show the effectiveness of our method.

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Other Link： http://id.nii.ac.jp/1001/00067267/

Language：Japanese  

Numerical conformal mappings onto canonical slit domains are important in scientific computations. In this paper, using the charge simulation method, we present a numerical method for the conformal mapping of unbounded multiply connected domains onto a rectilinear slit domain, which is a generalization of the parallel slit domain well-known for potential flow problems. Simple numerical examples show the effectiveness of our method.

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Language：Japanese   Publisher：Kyoto University  

CiNii Books

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Other Link： http://hdl.handle.net/2433/140187

Language：Japanese   Publisher：情報処理学会  

The transformational group structure theory explains how different types of cognitive judgments of patterns such as similarity and goodness are performed, and predicts their ordinal relations by the concept of cognitive transformation groups and transformational group structures. Many experiments have supported this prediction. However, the theory involves the difficulty that most pattern pairs or patterns have the so called empty transformational group structure as the number of elements of binary patterns increases, and consequently that they can not be distinguished in similarity or goodness judgments. We here introduce the concept of Hamming's distance into the transformational group structure and define quasi-transformational group structures, and then show by experiments of similarity judgments of linear binary pattern pairs that the human cognitive system uses the quasi-transformational group structure in similarity judgments.

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Other Link： http://id.nii.ac.jp/1001/00009523/

Language：English   Publishing type：Research paper (scientific journal)   Publisher：INT INFORMATION INST  

We recently presented a method of numerical conformal mapping of multiply-connected domains onto some canonical slit domains, where we approximated a pair of harmonic functions by a linear combination of complex logarithmic functions. We here present a method of numerical conformal mapping onto the parallel slit domain subject to a different condition, and compute the coefficients of the Laurent expansion that appears in the well-known theorem of existence and uniqueness of the conformal mapping. A few examples show the effectiveness of the method.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：INT INFORMATION INST  

The transformational group structure theory predicts ordinal relations of similarity of pattern pairs and goodness of patterns by the concept of transformational group structures. The validity of the prediction should be confirmed by a statistical test, which needs a multiple comparison of many classes. We applied the paired t-test and Tukey's HSD method to experimental results on similarity judgment of binary square matrix pattern pairs to confirm the validity of the prediction.

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Language：Japanese   Publisher：Kyoto University  

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Other Link： http://hdl.handle.net/2433/81327

Language：Japanese   Publisher：一般社団法人情報処理学会  

An experiment of similarity judgment of linear binary pattern pairs shows that intra-pattern transformational group structures affect the easiness and the clearness of inter-pattern transformational group structures, which causes the difference of rated similarities.

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Language：Japanese   Publisher：一般社団法人情報処理学会  

The transformational group structure theory predicts ordinal relations of the similarity of pattern pairs by the concept of inter-pattern transformational group structures, which are defined by mutual transformability using cognitive transformation groups. Experimental results have supported this prediction. However, Gestalt psychology suggests that the inter-pattern transformational group structure, which is independent of spatial relations between the paired patterns, is unconsciously cognized under mutual interactions caused by the spatial relation. We here show by experiments of similarity judgments of linear binary pattern pairs presented left-and-right and top-and-bottom that the spatial relation between the paired patterns affects their similarlity through the easiness and the clearness of cognition of the inter-pattern transformational group structure. It should be noted that both the experimental results are compatible with the theoretical prediction.

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

The transformational group structure theory explains how different types of cognitive judgments of patterns such as similarity and goodness are performed, and predicts their ordinal relations by the concepts of transformational group structures using cognitive transformation groups. We briefly review the transformational group structure theory based on our recent works.

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Language：Japanese   Publisher：Ehime University  

The transformational group structure theory explains how different types of cognitive judgments of patterns such as similarity and goodness are performed, and predicts their ordinal relations by the concepts of cognitive transformation groups and transformational group structures. This paper is a brief review of the transformational group structure theory based on our recent works with a prospect of future developments.

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Other Link： https://opac1.lib.ehime-u.ac.jp/iyokan/TD00000963

Language：Japanese   Publisher：National Committee for IUTAM  

On computation of conformal mappings, the mapping functions between a given problem domain and its corresponding canonical domains are concerned.Usually, two different methods are used to obtain the mapping functions, which map the problem domain onto and from the canonical domains.Our method of the numerical conformal mappings by the charge simulation method is applicable to such problems in two directions and offers the both mapping functions in similar way.However, the method was not applicable to the problem with the canonical slit domains, which are important for the potential flow analysis of multiply connected domains.Here, we provide a solution to this difficulty, which improve the method and expand its bi-directional applicability to the problem with multiply connected domains.

DOI： 10.11345/japannctam.54.0.99.0

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Usually, on computation of conformal mappings, different methods are used to obtain the mapping functions of two directions between a problem domain and a canonical domain. Amano proposed a method based on the numerical conformal mappings by the charge simulation method, and it offers the both mapping functions of simply connected problem domains and the canonical domains like the unit disk. However, his method cannot be used to obtain the mapping function on the canonical slit domains, which are important for the potential flow analysis of multiply connected domains. Here, we provide a solution to this difficulty, and propose a new method which improves the method of numerical conformal mappings by the charge simulation method, and expands the bi-directional applicability to the problem of multiply connected domains.

DOI： 10.11345/nctam.54.357

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Language：Japanese   Publisher：一般社団法人情報処理学会  

In this paper, we propose a method of conformal mapping w = f (z) of an unbounded multiply-connected domain D subject to the condition f (∞) = ∞, where v is a given finite point in the problem domain. In the method, we reduce the mapping problem to a Dirichlet problem of a pair of conjugate harmonic functions and approximate them, using the charge simulation method, by a linear combination of complex logarithmic functions. The method can be applied to the analysis of a potential flow with a vortex pair past obstacles. A typical example shows the effectiveness of the method. Besides, the idea described here is applicable to some other comformal mappings which are important in potential flow problems.

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Language：Japanese   Publisher：Kyoto University  

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Other Link： http://hdl.handle.net/2433/25136

Language：Japanese   Publisher：Kyoto University  

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Other Link： http://hdl.handle.net/2433/25137

Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

We present here a simple method of numerical conformal mappings from bounded multiply connected domains onto the bounded canonical slit domains of Nehari, i.e., a disk with concentric circular slits, and an annulus with concentric circular slits. In this method, we express the mapping functions in terms of a pair of conjugate harmonic functions and approximate them, using the charge simulation method, by a linear combination of complex logarithmic functions. Some numerical examples show the effectiveness of the method. © 2003 Elsevier B.V. All rights reserved.

DOI： 10.1016/S0377-0427(03)00572-7

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Language：Japanese   Publisher：一般社団法人情報処理学会  

The transformational structure theory explains how different types of cognitive judgment of patterns such as similarity and goodness are performed, and predicts their ordinal relations by the concepts of cognitive tranformations and transformational structures. In this paper we propose a model of goodness judgments of linear binary patterns using the transformation groups. In the model, we define the transformational group structures of patterns by the four cognitive transformation groups, i.e., the identity, the mirror-image, the phase and the value-reversal transformation groups, and then predict their orders of goodness by the structures. Typical experiments and tests show the validity of the model.

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Language：Japanese   Publisher：Kyoto University  

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Other Link： http://hdl.handle.net/2433/43078

Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

We present here a fundamental solution method for two-dimensional viscous flow problems with obstacles in a two-dimensional periodic array. Our problem is mathematically a boundary value problem of the Stokes equations with periodic boundary conditions, to which it is difficult to give a good approximation by the ordinary fundamental solution method. We propose a fundamental solution method for our problem based on the periodic fundamental solution obtained by Hasimoto (J. Fluid Mech. 5 (1959) 317). In our method, the solution is approximated by using a linear combination of the periodic fundamental solutions. © 2002 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0377-0427(02)00720-3

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

In this paper, we propose a method of numerical conformal mappings from a domain with a curved slit onto the canonical slit domains. Our method is based on Amano's method, which uses the charge simulation method as a rapid solver for potential problems. Due to the potential solver, his method gives high accuracy in many cases. The basic idea of the preceding method is to provide an approximation of harmonic functions by a linear combination of the complex logarithmic functions, g(z)=∑j Qj log(z -ζj), where the singularity points ζj are placed outside the problem domain. However, there are some difficulties on applying it to the problem domain with corners on the boundary, and the problem domain without enough space to place the singularity points properly. The problem domain with a curved slit is a typical example of such a difficulty. A technique we provide here is based on use of the Joukowski transformation. It inherits all the good properties of the original method. We show the effectiveness of our proposal by some numerical examples. © 2002 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0377-0427(02)00722-7

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Language：English   Publisher：愛媛大学工学部  

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：KINOKUNIYA CO LTD  

We show that the linear system appearing in the invariant scheme of the charge simulation method is uniquely solvable when the scheme is applied to a two-dimensional Dirichlet problem for a disk, for an ellipse, and for an annulus with properly chosen charge points and collocation ones, which are extensions of the previous results due to Katsurada-Okamoto, Nishida, and Murota. We also prove the unique solvability in a ball of dimension > 3, which we believe is entirely new.

DOI： 10.1007/BF03167460

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

We present here a charge simulation method for problems of two-dimensional flows past obstacles in a two-dimensional periodic array. Our problem is mathematically a boundary value problem of the Stokes equation with periodic boundary conditions, to which it is difficult to give a good approximation by the ordinary charge simulation method. We propose a charge simulation method for our problem based on the periodic fundamental solution obtained by Hasimoto. In our method, the solution is approximated by using a linear combination of the periodic fundamental solutions.

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Language：Japanese   Publisher：一般社団法人情報処理学会  

We extend the transformational group structure theory on similarity judgments of one dimensional elliptic patterns (linear binary patterns) to that of two-dimensional dot patterns (square binary matrix patterns). Specifically speaking, we define the transformational group structures of pattern pairs by the four cognitive transformation groups, i.e., the identity, the dihedral, the translation and the value-reversal transformation groups, and then predict their orders of similarity by the structures. Simple experiments and tests show the validity of the model.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：KINOKUNIYA CO LTD  

We propose a method of numerical conformal mapping of periodic structure domains onto periodic parallel slit domains. In the method presented here, the mapping problem is reduced to a Dirichlet one for a pair of conjugate harmonic functions with a periodic boundary condition. We modify the charge simulation method for solving periodic boundary value problem and apply it to our mapping problem. Some numerical examples show that our method is efficient. We also show an application of our method to the analysis of potential flow past obstacles in a periodic array.

DOI： 10.1007/BF03167456

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Language：Japanese   Publisher：一般社団法人情報処理学会  

We present a method of numerical conformal mapping of a bounded multiply-connected domain onto a circular annulus with concentric circular slits. In the method, we reduce the mapping problem to a Dirichlet one for a pair of conjugate harmonic functions and solve it using the charge simulation method, which yields an approximate mapping function expressed with a linear combination of complex logarithmic potentials. We also present continuous schemes for practical computations in order to avoid the discontinuities due to using the principal value of the complex logarithmic function. Numerical results for a typical problem show the effectiveness of our method. This paper completes a series of our studies on the numerical conformal mappings onto the standard slit domains of Nehari (1952).

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Language：Japanese   Publisher：愛媛大学工学部  

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Language：Japanese   Publisher：一般社団法人情報処理学会  

The transformational structure theory systematically explains how different types of cognitive judgments of patterns such as similarity and goodness are performed, and predicts their ordinal relations by the concepts of cognitive tranformations and transformational structures. In this paper we propose a mathematical model of similarity judgments of linear binary patterns based on the transformation groups. Transformational group structures of pattern pairs are first defined by the four cognitive transformation groups, i. e. , the identity, mirror-image, phase and reversal transformation groups, and then their orders of similarity are predicted by the structures. The final results are expressed by a Hasse diagram. Typical experiments and tests show the validity of the model.

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Language：English   Publisher：Kyoto University  

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Other Link： http://hdl.handle.net/2433/64895

Language：Japanese   Publisher：一般社団法人情報処理学会  

The parallel, circular and radial slit domains are the entire planes with parallel rectilinear slits, circular slits concentric to the origin and radial slits pointing at the orgin, respectively. We here present a simple method of numerical conformal mappings of an unbounded multiply-connected domain exterior to closed Jordan curves onto the parallel, circular and radial slit domains. These conformal mappings are familiar in science and engineering, and especially important in problems of two-dimensional potential flows around obstacles with vortices and point-sources or sinks together with a uniform flow. But, no systematic method of computation has been established. We reduce the problems of conformal mapping to the Dirichlet problem with a pair of conjugate harmonic functions and employ the charge simulation method, where the conjugate harmonic functions are approximated by a linear combination of complex logarithmic potentials. The problems are finally reduced to a set of linear equations with a same coefficient matrix. The approximate mapping functions are continuous and analytic using the principal value of logarithmic function, and invariant to the scaling of the coordinate system. The numerical method for simple, accurate approximate mapping functions was a missing link between theory and applications of the conformal mappings.

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Language：Japanese   Publisher：Information Processing Society of Japan (IPSJ)  

The transformational structure theory systematically explains how different types of cognitive judgments of patterns such as similarity and goodness are performed, and predicts their ordinal relations by the concepts of cognitive tranformations and transformational structures. We here present a mathematical model, the transformational group structure theory, of similarity judgments of linear binary patterns based on the transformational structure theory.

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Publishing type：Research paper (scientific journal)  

Recently, we proposed an integrated method for the problem of numerical conformal mappings of the unbounded multiply-connected domains onto the canonical slit domains of Nehari(l952). The problem is important in potential flow analysis. Our method which uses the charge simulation method offers not only highly accurate mapping functions, but also their analytical derivatives. This enables us to use various formulas for applications, which would be useful but lack easy numerical implementation. In this paper, as a simple example, we offer a Newton's iteration method for computing the stagnation points around obstacles placed in the uniform potential flow. The algorithm is simple, and as shown, the numerical experiments give high accuracy.

DOI： 10.11345/nctam.50.303

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Language：Japanese   Publisher：一般社団法人情報処理学会  

We present a method of numerical conformal mapping of multiply-connected domains with closed boundary Jordan curves onto the unit disk with concentric circular slits. It is a basic problem of conformal mapping of multiply-connected domains. If the domain is bounded by a single closed Jordan curve, the problem is identified as Riemann's mapping theorem. We reduce the mapping problem to a Dirichlet problem with a pair of conjugate harmonic functions and apply the charge simulation method, where the conjugate harmonic functions are approximated by a linear combination of complex logarithmic potentials. We here give an explicit form of approximate mapping function which is continuous using the pricipal value of logarithmic function.

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Language：English   Publisher：Kyoto University  

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Other Link： http://hdl.handle.net/2433/63951

Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER  

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER  

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The numerical schemes for computing the approximations have been recently proposed for interior and exterior conformal mappings by Inoue (1997). The theoretical base and the mathematical properties of the schemes are studied in this paper. The base depends on theorems in Henrici (1986) introduced from Symm's integral equations. The mathematical properties are as follows: (a) The constant terms in the schemes have a geometric meaning. (b) The schemes are dual with respect to interior and exterior mappings. (c) The schemes are invariant under scaling of the domains.

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Language：Japanese   Publisher：Information Processing Society of Japan (IPSJ)  

In this note, we present a method of approximating the real function f(x)analytic on a bounded closed interval by applying the charge simulation method and the Joukowski transformation.

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Language：Japanese   Publisher：National Committee for IUTAM  

Conformal mappings are familiar in science and engineering. However, exact mapping functions are not known except for a limited class of domains. Therefore, numerical conformal mappings have been studied for a long time. Recently, the problem of multiply connected domains has attracted special interest. In the conformal mapping of multiply connected domains, a standard domain such as the unit disk for simply connected domains does not exist, and canonical domains with slits of various shapes are used. In this report, we show that approximate mapping functions of simple form and high accuracy are obtained for conformal mappings of given problem domains onto the canonical slit domains, where we express analytic functions by a linear combination of complex logarithmic functions. It is important also in the viewpoint of applications of numerical conformal mappings.

DOI： 10.11345/japannctam.60.0.106.0

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Language：Japanese   Publisher：National Committee for IUTAM  

Seamless availability on applying to the problems of various types of simply and multiply connected domains is one of the key features of Amano's method of numerical conformal mappings.We studied the application of the method for a doubly connected rectangular domain with a slit and obtain an approximation of the conformal mapping function which maps the domain onto the canonical annular domain. In the method the charge simulation method of complex logarithmic charges is used. Therefore, the premap technique is necessary to open the slit for placing the charges outside the problem domain. In addition, we need arrangement of the charges well adapted to the corner singularity of the rectangle.We'll show, by some numerical examples, the effectiveness of the method and a small application on image processing.

DOI： 10.11345/japannctam.60.0.108.0

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An experiment of similarity judgment of linear binary pattern pairs shows that intra-pattern transformational group structures affect the easiness and the clearness of inter-pattern transformational group structures, which causes the difference of rated similarities.

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Other Link： http://id.nii.ac.jp/1001/00067770/

Language：Japanese   Publisher：Information Processing Society of Japan (IPSJ)  

The transformational group structure theory predicts ordinal relations of the similarity of pattern pairs by the concept of inter-pattern transformational group structures, which are defined by mutual transformability using cognitive transformation groups. Experimental results have supported this prediction. However, Gestalt psychology suggests that the inter-pattern transformational group structure, which is independent of spatial relations between the paired patterns, is unconsciously cognized under mutual interactions caused by the spatial relation. We here show by experiments of similarity judgments of linear binary pattern pairs presented left-and-right and top-and-bottom that the spatial relation between the paired patterns affects their similarlity through the easiness and the clearness of cognition of the inter-pattern transformational group structure. It should be noted that both the experimental results are compatible with the theoretical prediction.

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Other Link： http://id.nii.ac.jp/1001/00010285/

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Language：Japanese   Publisher：Forum on Information Technology  

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In this paper, we propose a method of conformal mapping w = f (z) of an unbounded multiply-connected domain D subject to the condition f (∞) = ∞, where v is a given finite point in the problem domain. In the method, we reduce the mapping problem to a Dirichlet problem of a pair of conjugate harmonic functions and approximate them, using the charge simulation method, by a linear combination of complex logarithmic functions. The method can be applied to the analysis of a potential flow with a vortex pair past obstacles. A typical example shows the effectiveness of the method. Besides, the idea described here is applicable to some other comformal mappings which are important in potential flow problems.

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Other Link： http://id.nii.ac.jp/1001/00010897/

Language：Japanese   Publisher：National Committee for IUTAM  

We propose a method of numerical conformal mappings of unbounded multiply-connected domains, and apply the method to ploblems of potential flow past obstacles caused by a pair of vortexes or a pair of point source and sink. A typical example shows the effectiveness of our method.

DOI： 10.11345/japannctam.53.0.163.0

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Publisher：National Committee for IUTAM  

We propose a method of numerical conformal mappings of unbounded multiply-connected domains, and apply the method to ploblems of potential flow past obstacles caused by a pair of vortexes or a pair of point source and sink. A typical example shows the effectiveness of our method.

DOI： 10.11345/japannctam.53.0.163.0

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Language：Japanese   Publisher：Information Processing Society of Japan (IPSJ)  

The transformational structure theory explains how different types of cognitive judgment of patterns such as similarity and goodness are performed, and predicts their ordinal relations by the concepts of cognitive tranformations and transformational structures. In this paper we propose a model of goodness judgments of linear binary patterns using the transformation groups. In the model, we define the transformational group structures of patterns by the four cognitive transformation groups, i.e., the identity, the mirror-image, the phase and the value-reversal transformation groups, and then predict their orders of goodness by the structures. Typical experiments and tests show the validity of the model.

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Other Link： http://id.nii.ac.jp/1001/00011180/

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We extend the transformational group structure theory on similarity judgments of one dimensional elliptic patterns (linear binary patterns) to that of two-dimensional dot patterns (square binary matrix patterns). Specifically speaking, we define the transformational group structures of pattern pairs by the four cognitive transformation groups, i.e., the identity, the dihedral, the translation and the value-reversal transformation groups, and then predict their orders of similarity by the structures. Simple experiments and tests show the validity of the model.

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Other Link： http://id.nii.ac.jp/1001/00011420/

Language：Japanese   Publisher：Information Processing Society of Japan (IPSJ)  

We present a method of numerical conformal mapping of a bounded multiply-connected domain onto a circular annulus with concentric circular slits. In the method, we reduce the mapping problem to a Dirichlet one for a pair of conjugate harmonic functions and solve it using the charge simulation method, which yields an approximate mapping function expressed with a linear combination of complex logarithmic potentials. We also present continuous schemes for practical computations in order to avoid the discontinuities due to using the principal value of the complex logarithmic function. Numerical results for a typical problem show the effectiveness of our method. This paper completes a series of our studies on the numerical conformal mappings onto the standard slit domains of Nehari (1952).

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Other Link： http://id.nii.ac.jp/1001/00011649/

Language：Japanese   Publisher：Information Processing Society of Japan (IPSJ)  

The transformational structure theory systematically explains how different types of cognitive judgments of patterns such as similarity and goodness are performed, and predicts their ordinal relations by the concepts of cognitive tranformations and transformational structures. In this paper we propose a mathematical model of similarity judgments of linear binary patterns based on the transformation groups. Transformational group structures of pattern pairs are first defined by the four cognitive transformation groups, i. e. , the identity, mirror-image, phase and reversal transformation groups, and then their orders of similarity are predicted by the structures. The final results are expressed by a Hasse diagram. Typical experiments and tests show the validity of the model.

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Other Link： http://id.nii.ac.jp/1001/00011834/

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The parallel, circular and radial slit domains are the entire planes with parallel rectilinear slits, circular slits concentric to the origin and radial slits pointing at the orgin, respectively. We here present a simple method of numerical conformal mappings of an unbounded multiply-connected domain exterior to closed Jordan curves onto the parallel, circular and radial slit domains. These conformal mappings are familiar in science and engineering, and especially important in problems of two-dimensional potential flows around obstacles with vortices and point-sources or sinks together with a uniform flow. But, no systematic method of computation has been established. We reduce the problems of conformal mapping to the Dirichlet problem with a pair of conjugate harmonic functions and employ the charge simulation method, where the conjugate harmonic functions are approximated by a linear combination of complex logarithmic potentials. The problems are finally reduced to a set of linear equations with a same coefficient matrix. The approximate mapping functions are continuous and analytic using the principal value of logarithmic function, and invariant to the scaling of the coordinate system. The numerical method for simple, accurate approximate mapping functions was a missing link between theory and applications of the conformal mappings.

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Other Link： http://id.nii.ac.jp/1001/00012042/

Language：Japanese   Publisher：愛媛大学工学部  

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We present a method of numerical conformal mapping of multiply-connected domains with closed boundary Jordan curves onto the unit disk with concentric circular slits. It is a basic problem of conformal mapping of multiply-connected domains. If the domain is bounded by a single closed Jordan curve, the problem is identified as Riemann's mapping theorem. We reduce the mapping problem to a Dirichlet problem with a pair of conjugate harmonic functions and apply the charge simulation method, where the conjugate harmonic functions are approximated by a linear combination of complex logarithmic potentials. We here give an explicit form of approximate mapping function which is continuous using the pricipal value of logarithmic function.

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Other Link： http://id.nii.ac.jp/1001/00012341/

Language：Japanese   Publisher：愛媛大学工学部  

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Event date： 2020.9

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Event date： 2019.12

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Event date： 2019.12

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Event date： 2019.12

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We propose a method of numerical conformal mappings of unbounded multiply-connected domains, and apply the method to ploblems of potential flow past obstacles caused by a pair of vortexes or a pair of point source and sink. A typical example shows the effectiveness of our method.

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変換群構造説では，人（認知系）は提示されたパターンに対していくつかの変換群（認知的変換群）を施し，相互変換可能性や不変性によってその構造（変換群構造）を認知し，この認知された変換群構造に基づいてパターン対の類似性判断やパターンの良さ判断を行うと考える．実験はその妥当性を支持している．しかし，パターンを構成する2値要素の数の増加とともに空変換群構造（相互変換可能性や不変性を持たないことを意味する）の占める割合が急増し，大多数のパターン対の類似度やパターンの良さが区別できなくなるという困難があった．この論文では，変換群構造にハミング距離の概念を導入して准変換群構造を定義し，線形2値パターン対の類似性判断の実験を行って，認知系が准変換群構造を認知して類似性判断を行っていると考えられることを示す．The transformational group structure theory explains how different types of cognitive judgments of patterns such as similarity and goodness are performed, and predicts their ordinal relations by the concept of cognitive transformation groups and transformational group structures. Many experiments have supported this prediction. However, the theory involves the difficulty that most pattern pairs or patterns have the so called empty transformational group structure as the number of elements of binary patterns increases, and consequently that they can not be distinguished in similarity or goodness judgments. We here introduce the concept of Hamming's distance into the transformational group structure and define quasi-transformational group structures, and then show by experiments of similarity judgments of linear binary pattern pairs that the human cognitive system uses the quasi-transformational group structure in similarity judgments.

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近年,非構造化P2Pネットワークにおいては様々な検索手法が提案されているが,一般に検索速度と通信負荷はトレードオフの関係にある.すなわち,目的ファイルを短時間で発見できる検索手法は,一般に通信負荷が高い.本論文では,Acquaintance Link,Light Floodという二つの既存手法を組み合わせることにより,検索速度向上と通信負荷軽減を同時に実現する手法を提案する.

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Seamless availability on applying to the problems of various types of simply and multiply connected domains is one of the key features of Amano's method of numerical conformal mappings.We studied the application of the method for a doubly connected rectangular domain with a slit and obtain an approximation of the conformal mapping function which maps the domain onto the canonical annular domain. In the method the charge simulation method of complex logarithmic charges is used. Therefore, the premap technique is necessary to open the slit for placing the charges outside the problem domain. In addition, we need arrangement of the charges well adapted to the corner singularity of the rectangle.We'll show, by some numerical examples, the effectiveness of the method and a small application on image processing.

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Conformal mappings are familiar in science and engineering. However, exact mapping functions are not known except for a limited class of domains. Therefore, numerical conformal mappings have been studied for a long time. Recently, the problem of multiply connected domains has attracted special interest. In the conformal mapping of multiply connected domains, a standard domain such as the unit disk for simply connected domains does not exist, and canonical domains with slits of various shapes are used. In this report, we show that approximate mapping functions of simple form and high accuracy are obtained for conformal mappings of given problem domains onto the canonical slit domains, where we express analytic functions by a linear combination of complex logarithmic functions. It is important also in the viewpoint of applications of numerical conformal mappings.

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