We consider the evolution equations F-t = -(H-l)(alpha)nu, where 0 < <alpha> < 1, <nu> is the unit outer normal vector and H-1 is the harmonic mean curvature defined by H-1 = ((K-1(-1) + K-2(-1))/2)(-1) In this paper, we prove the nonuniqueness of their strictly convex self similar solutions for some 0 < <alpha> < 1. This result implies that there are non-spherical self similar solutions.

In this paper, we proposed a numerical method for estimating blow-up rate of blow-up solutions for a class of nonlinear evolution equations which have a scaling invariance. To use this scaling invariance we adopt the rescaling algorithm to the problems and numerically estimate the blow-up rates. Applying the method to several examples, we examine the effectiveness of the method.

In this paper, our aim has been to develop a research information relation visualization system (ResearchView) that can be applied to replace attribute graph grammar, which is used as the semantic rule of the Research Information Relation Graph (RIRG). This paper describes a text notation method of the attribute graph grammar which can be interpreted by computer and the development of a source-code generator for automatic generation of a ResearchView upon its input.

We introduce "the steepest ascent method" and "the steepest descent method" to more effectively detects ridges and valleys in terrain maps, respectively. First, we propose algorithms by our methods. Next, we detect ridges and valleys in the entire Japan to compare our methods with the discrete Laplace transform method and show various advantages for our methods. And then, we claim that our algorithms can get sharper ridge and valley lines than the discrete Laplace transform method and makes it possible to generate terrain maps detected ridges and valleys in a huge area such as the entire Japan.

The game of Go has a graph theoretical structure. Connected stones and enclosed regions are very worthful. On the other hand, we need to recalcurate groups of connected stones at each change of connectedness. BW Graph model gives us one of clear representations of features of positions with connectednesses and its recursions. By using recursions of positions, we can return from a given position to a previous position. In this paper, we focus on two moves, nakate and takefu. Nakate and takefu change connectednesses of intersections. We make static formulations of nakate and takefu moves by using the BW graph model.

This paper introduces a ridge detection algorithm from terrain maps represented by homogenous triangular dissections. This paper also introduces a data format of the triangular dissections and a concept of processing system.

In order to display 3D terrain map effectively, detections of features on maps are very important. In this paper, we discuss a method for detection of ridges. It is known in the previous work that the steepest ascent method is effective for a ridge detection on terrain map represented by rectangular dissections. We will introduce the steepest ascent method in triangular dissections generated by homogeneous rectangular dissections.

The game of Go is an ancient board game. In this game, players aim to capture the stones of their opponent by enclosing them. One possible condition for a stone is described as "safe". A safe stone can never be captured. This has been represented with a static determination by Benson [1]. In this paper, we analyze this determination mathematically, using the BW graph model that was introduced by Sato et al. [2][3][4][5]. As the result, we propose a new representation that reduces the required number of backtracking searches.

We deal with data structures and algorithms for bundles of binary images represented by raster data. In this paper, a bundle with images is called a multiple layer image. Our purpose is to introduce algorithms for rotation of objects included in multiple layer binary images. In addition, we will provide both of rotation and translation in a binary image at the same time.

This paper considers a multiple 3D object. In this paper, each 3D object in a multiple 3D object is dealt as a single rectangular solid dissection (a 3D world), and a multiple 3D object are dealt as a multiple rectangular solid dissection. This paper introduces a 40 degree grid graph called "a 5 times octgrid" for a model of a multiple 3D object dealt as a multiple rectangular solid dissection. This paper also provides projection, translation and rotation algorithms of specified 3D objects in multiple 3D object systems with a 40 degree grid graph model.

The game of Go is a zero-sum game by two players with perfect information. The game of Go has a graph theoretical structure and tactics. BW graph model is a mathematical model for the game of Go, and represents postions and games graph theoretically. This model uses degrees of intersections on the board. In this paper, we formulate a pattern of stones, shicho. By our result, we can represent shicho states and determine these results statically.

Heterogeneous rectangular dissections are frequently used in information processing such as multiple paged books in spread sheet languages and multi-layer image data. In previous studies, a hexadecimal grid graph model was proposed for multi-layer rectangular dissections and certain algorithms were provided.
In this paper, we propose a 16-ary list structure to implement their algorithms for the hexadecimal grid graph model. The list structure has limited number of fields in a record, so the computation time is low.
Furthermore, it has one record for each node in the given hexadecimal grid, and 48 fields for each record. We also show a data format of the whole structure of the list.

In sharing information for the research support at university laboratories, not only the research documents including references, seminar documents, research data, and articles but also the context information including the process of the research activities that have been conducted and the relations between the research documents are important. In this study, both research documents and context information are called "research information". This research information can be effectively managed and shared in a visual manner on the system. In collecting research information, the members' workload must be reduced as much as possible. In addition, to better share research information, it should be able to be visualized quickly without stress. Therefore, this paper describes a research information collection and sharing method developed by introducing attribute graph grammar. Specifically, this paper presents a research information collection method that can deal with various research activities and reduce members' workload for collecting information by introducing a research information relations graph (RIRG) and generating RIRG based on the production of the attribute graph grammar. In addition, this paper describes a method for effectively drawing RIRG by using a semantic rule of the attribute graph grammar. Finally, this paper introduces a research information collection and sharing support system (Research View) using this method.

Rectangular dissections are commonly used for tabular forms such as spreadsheets, raster data in computer graphics, and so forth and we need processing for cells of data represented by rectangular dissections. In this paper, we deal with data structures and algorithms for rectangular dissections or raster data with heterogeneous parts. In particular, we would like to introduce an algorithm to subdivide and homogenize rectangular dissections with heterogeneous parts represented by octgrids.

Copyright © 2015 by The International Society for Computers and Their Applications (ISCA). It is very important to reduce the number of cells in raster data such as 2D image and so forth. In this paper, we deal with the "octgrid" model which is an octal degree grid graph model. The "octgrid" model is suitable for raster data with heterogeneous parts and can be used to reduce the number of cells in raster data. In this paper, we investigate change ratio of the number of cells when some regions are rotated in 2D images. In addition we describe that the change ratios by the "octgrid" model are less than ones by the quadtree.

We consider the connectedness in the game of Go. This game has a graph theoretical structure and the connectedness of the stones is very important to evaluate positions. In this paper, we construct the mathematical model which represents the connectedness of the stones and the relationship between blocks and null intersections. We propose the recursion of extended liberties to evaluate positions analytically.

It is important to sharpen features such as ridges for effective displaying of 3D terrain maps. This paper deals with a ridge detection method. In previous works, the steepest ascent method is known as a ridge detection method. In this paper, we will improve the steepest ascent method in triangular dissections.

This paper deals with a data structure that models time-continous 4D objects. We propose a 64-degree grid graphs by dimension hightening of tetraicosa-grids. Algorithm used for resolution reduction is also introduced. Fortheremore, 64-degree grid is compared to 16-ary trees with respect to effectiveness and efficiency.

We discuss triangulations for terrain maps represented by raster data. In this paper, we propose an algorithm to generate triangular dissections with elevation values from terrain maps represented by homogeneous raster data.

The game of Go has a graph theoretical structure. "BW graph model" gives one of clear representations of features of positions with degrees. The degrees of intersections are very important to evaluate positions. In this paper, we introduce the applications of the mathematical model "BW graph model".

To share information more effectively in a laboratory, this study develops a method to collect and visualize research documents as well as research activities efficiently without exception. First, this paper introduces a research information relation graph that reflects research activities that obtain information. Furthermore, this paper makes research activities modeled as productions that help to generate the graph and defines the graph grammar, which generates a research information relation graph, by using the production. It is expected that conducting research in accordance with this grammar can reduce the burden of laboratory members in making research information graphs and make information sharing easy by visualizing both research documents and the context information. Customizing the graph grammar in accordance with a particular scenario and applying this method to various scenarios can make it easy to realize a system for collecting and sharing research information in different research fields.

In order to efficiently share research information on research supports, in a university laboratory, not only the research documents but also context information is important. The context information shows details of research activities where each document is generated and the relation between documents. Therefore, to visually share and to visually manage this information on a system is effective. In the case of workflow, because research information including context information has been collected by making rules, the user's burden will be reduced. However, because research activities are various according to the field and the researchers, there is a problem that the relevant information cannot be collected by the existing workflow. On the other hand, research information sharing, in general, is difficult because of the time complexity of graph drawing on constraints is large. Therefore, the system requirement for visualizing research information is to draw it in time without stress. To solve these problems, this study has developed the research information collecting and sharing methods based on the attribute graph grammar. Concretely, at first, the research information related graph (RIRG) has been newly introduced. By generating the RIRG with the production of the attribute graph grammar, the burden reduction of the collection work, corresponding to various research activities, can be expected. Then, the problem on the collecting side is solved. Moreover, an efficient drawing of RIRG can be expected by using the semantic rule of the attribute graph grammar. Then, the problem on the sharing side is solved.

In order to efficiently share research information in a laboratory, we develop a method to accumulate and presented efficiently without omission research information along with the research activities. First, this research introduced the "research information relation graph" (which expresses the research information accompanied by research activities, and its relation). And we define a graph grammar for deriving Research Information Relation Graph that reflected the production to research activities. By advancing research activities in accordance with this grammar, it can be expected that reference of research information and those relations with research activities are visually understood, and information sharing becomes easy. In addition, it is believed that by customizing the graph grammar, the present method is applicable in various situations.

we deal with data structures and algorithms suitable for the displaying of multiple binary raster images. Multiple images are dealt as a multiple layer image. In this paper, we introduce three algorithms for operation of images represented by hexadeci-grid as multiple layer images and show some examples for our introduced alghrithms.

Takeo Yaku et al proposed octal degree heterogeneous grid graphs, called octgrids[4, 6], that represent heterogeneous rectangular dissections such as spreadsheet. Meanwhile, because octgrid is very complex, it would be difficult to create octgrid application systems if you manipulate the octgrid directly. Therefore, we represent octgrid by an XML notation, and represent the octgrid on an SQL database system by storing each node of octgrid in SQL table. It will be easier to manipulate the octgrid because you can manipulate it by SQL commands. In this paper, we deal with editing for spreadsheet based on octgrids and SQL database system. Copyright ISCA, CAINE 2014.

In this work, the heterogeneous rectangular dissections that represent multi-resolution images of raster data are considered. Specifically, heterogeneous rectangular dissections are changed to triangular dissections in order to provide more effective feature extraction. We propose a method of generating triangular dissections that maintains "octgrid" properties and have developed a list structure suitable for extracting image features (ridges, valleys, etc.) from terrain maps. We propose a detailed list structure called "H12Code" and present examples of feature extraction using H12Code lists.

Tabular forms are commonly used in software. Those tabular forms are represented as rectangular dissections. In rectangular dissections, ruled line oriented operations such as cell merge, line and column operations are often used. With respect to ruled line oriented operations, 8k-ary grid graphs have been introduced as models of rectangular dissections that provide fast algorithms. This paper surveys octal and hexa-decimal grid graph models of rectangular dissections. First, octal grids, called octgrids, for single layer rectangular dissections and related algorithms are introduced. Next, hexa-decimal grid graphs for multiple layer rectangular dissections, called hexadeci-grids, and related algorithms are introduced. Furthermore, tetraicosa-grid graphs for rectangular solid dissections for CG applications, called tetraicosa-grids and related algorithms are introduced. © 2014 Springer-Verlag Berlin Heidelberg.

We model multiple layer binary images with hexadecimal grid graphs. Then, we propose algorithms for translations of multiple layer binary images. We discuss that the modeling and algorithms may provide ease of system development for translations of multiple layer images. Furthermore, we show a concept of implementation.

We deal with a data structure which is suitable for expression of the binary images. In general, binary images are expressed in raster data or rectangular dissections. In this paper, we describe that it is possible to reduce effectively the number of nodes in raster data represented by "octgrid" which is a type of octal grid graphs to handle heterogeneous rectangular dissections. Precisely, we propose algorithms to reduce the resolution of binary images represented by "octgrid". Furthermore, we compare by examples our method with the Hilbert scanning, and show that our method reduces the rectangular number by less than 50% than the Hilbert scanning does, in several examples.

We deal with the "octgrid" model which is a data structure for raster data such as 2D images, spread sheets and so forth. The "octgrid" model is an octal degree grid graph model and is able to handle various raster data with heterogeneous parts. In this paper, we consider change ratio of the number of cells when regions are shifted in a 2D image represented by raster data with heterogeneous parts. We propose two algorithms for translation of regions in 2D images represented by the "octgrid" model to compare change rates of the number of cells with ones by quadtree. And then, we describe that our algorithms by the "octgrid" model keep the number of cells by some examples when some regions are shifted in an image.

We consider hexadeci-grids as a model of multiply layered heterogeneous tabular forms, which are generalization of the octgrid model. We introduce column deletion and multiple row deletion algorithms on the hexadeci-grid model. © 2012 Authors.

We deal with ridge detection methods from digital elevation map (DEM) data. As ridge detection methods, the O (N) -time steepest ascent method and the O (N) -time discrete Lap lace transform (D.L.T.) method are known, where N is the number of cells. However, the D.L.T. method is too blurry to form ridge lines. In this paper, we introduce a 12 neighbor D.L.T. method which is a modification of the 4 neighbor D.L.T. method. And we also introduce another ridge detection method by the classification of local shapes around each cell. We can consider 32 patterns for ridges or valleys. Furthermore, we compare and evaluate their ridge detection methods in a certain area. We note that our two methods provide blurry terrain maps, but it require only O (N) -time for N cells, in comparison with the steepest ascent method. © 2012 IEEE.

We propose a new method to detect ridges from digital elevation map (DEM) data. We call it "the steepest ascent method" which is based on steepest ascent lines obtained by selecting the maximum inclined direction from eight neighbors. Then ridge lines are extracted by their steepest ascent lines on a surface. In this paper it is shown that our method is able to detect ridge lines sharply. Besides we claim that our algorithm is simple and suitable for huge area such as the entire area of Japan. Finally, we give the ridge detected terrain map of the entire area of Japan and Korea by applying "the steepest ascent method".

We deal with a formalization of financial statements. In order to formalize financial statements, we have to specify the spatial order of items, and specify calculation methods. In this paper, we construct a context sensitive graph grammar to specify the order of items of financial statement. Furthermore we also append attribute rules to the context-sensitive graph grammar to specify calculation methods

We discuss tabular forms. It is known in the previous studies that the "octgrid" is a data structure for single layer tabular forms with ruled line preserving algorithms. And the "hexadeci-grid" is known as a data structure for multiply layered tabular forms which is a generalization of the "octgrid". Our purpose of this paper is to propose a new algorithm based on the "hexadeci-grid" model for editing tabular forms.

We propose combined algorithms such as a multiple row deletion algorithm based on octgrid graph model for a heterogeneous table.

In this paper we report on WBT content for geography and geology using VRML. We also propose an idea of WBT content for local area study that has not yet been implemented and discuss its effect from the viewpoint of knowledge management.