Yoko Ohura

Direct method of solution for general boundary value problem of the Laplace equation

A general boundary value problem for two-dimensional Laplace equation in the domain enclosed by a piecewise smooth curve is considered. The Dirichlet and the Neumann data are prescribed on respective parts of the boundary, while there is the second part of the boundary on which no boundary data are given. There is the third part of the boundary on which the Robin condition is prescribed. This problem of finding unknown values along the whole boundary is ill posed. In this sense we call our problem an inverse boundary value problem. In order for a solution to be identified the inverse problem is reformulated in terms of a variational problem, which is then recast into primary and adjoint boundary value problems of the Laplace equation in its conventional form. A direct method for numerical solution of the inverse boundary value problem using the boundary element method is presented. This method proposes a non-iterative and unified treatment of conventional boundary value problem, the Cauchy problem, and under- or over-determined problems.

Direct numerical identification of boundary values in the Laplace equation

An inverse boundary value problem for the Laplace equation is considered. The Dirichlet and the Neumann data are prescribed on respective part of the boundary, while there is the second part of the boundary where no boundary data are given. There is the third part of the boundary where the Robin condition is prescribed. This ill-posed problem of finding unknown values along the whole boundary is reformulated in terms of the variational problem, which is then recast into primary and adjoint boundary value problems of the Laplace equation in conventional forms. A direct method for numerical solution of the boundary value problems using the boundary element method is presented.

Toward Learning Support for Decision Making: Utilization of Library and Lecture Data

Supporting students’ learning is very important for a university as an educational organization. It is highly expected to give supports individually according to each student’s situation such as his or her knowledge, study skills, learning history, preferences, etc. Due to the development of information and communications technology including Web and Internet, it becomes popular and easy to automatically collect data, and to analyze them and extract knowledge and information about the users’ behavior and preferences. For example, the net-companies, such as the ones proving e-commerce services, utilize the customers’ behavior data for extracting marketing information. Quite a lot of universities that provide institutional repository (IR) service try to analyze the log data in order to understand and evaluate what the service means for them. The data relating to library services are also useful for library marketing, which aims to provide better user, or patron, services and to improve management. In this paper, we discuss the importance of data analysis of the data relating to lecture data of university classes together with library data.

An Attempt on Effort-Achievement Analysis of Lecture Data for Effective Teaching

The eventual goal of the study in this paper is to find inspiring tips for effective teaching by analyzing lecture data. As a case study, we take a course in a junior college and investigate the relations between effort and achievement of the students. We take two types of data for measuring effort of students; attendance and homework. The former one is for representing the students’ “superficial” efforts and the latter for representing the students’ “intentional” efforts. We take the term-end examination score for measuring the student’s achievement. In this paper, we first try to find what kind of efforts the students put in terms of effort by comparing the attendance and the homework data. Then we investigate the relations between the efforts and achievement and try to find if the efforts of students really give good amount of influence to their achievements. As a result of the analysis we have found even with some amount of efforts, students learn just a little bit in achievement in terms of practically applicable skills. We need further investigation in order to give more clear influencing factor in effort-achievement analysis of lecture data.

Investigation of Students' Attitudes to Lectures with Text-Analysis of Questionnaires

The eventual goal of our study is to help teachers who give lectures in universities and other educational organizations with advising them as well as to help the attending students in order to maximize the learning performance of student. In order to achieve this goal we take the model-based approach. We construct students learning model at first, and then extract appropriate tips on teaching for teachers and on learning for students. In this paper, as an attempt in this approach, we analyze the text data which were obtained as answers to a term-end questionnaire in a course. Firstly we make a grouping of students based on a correspondence analysis of students and words from the answers to a question about the students achievement in taking the course. Then we compare these student groups in combination with other data such as examination scores as achievement, and attendance and homework scores as effort, as well as the features of words used in the answered texts. We have found that the students who have good achievement scores often give the comments from a wider view than what they actually learned in the class. On the other hand the students who give the comments using those terms which were taught in the class tends to have low achievement scores. The methods for in-depth analysis used in this paper are supposed to be appropriate tools for complementing the results from using the big data analysis methods and need to be developed more toward the future.

On identifying Dirichlet condition for under-determined problem of the Laplace equation by BEM

The purpose of this paper is to present a numerical technique for the solution of an under-determined problem of the Laplace equation in two spatial dimensions. A resolution is sought for the problem in which the Dirichlet and Neumann data are, respectively, imposed on two disjoint parts of the boundary of the domain, so that the union of the two parts does not constitute the whole boundary. This under-determined boundary value problem can be regarded as a boundary inverse problem, in which the proper Dirichlet condition is to be identified for the rest of the boundary. The solution of this problem is not unique. The technique is based on the direct variational method, and a functional introduced is minimized by the method of the steepest descent. Since the functional is convex, the minimum is attained uniquely. The minimization problem is recast into successive primary and adjoint boundary value problems of the Laplace equation. The boundary element method is applied for numerical solution of the boundary value problems. Some empirical tricks are proposed for increasing the efficiency of the numerical method. A few simple examples show that the method yields a convergent solution which corresponds to the minimum of the functional.

Numerical solution of under-determined 2D laplace equation with internal information

Publisher Summary This chapter provides a numerical treatment concerning an underdetermined problem of the Laplace equation in two spatial dimensions. The Dirichlet and Neumann data are respectively imposed on two parts of the boundary of the domain. Besides, the values of the unknown function are specified at n distinct internal points. This new problem is regarded as a boundary inverse problem because the proper boundary conditions are to be identified for the rest of the boundary. The treatment is based on the direct variational method. A functional is minimized by the method of the steepest descent. The minimization problem is transformed into iterative primary and dual boundary value problems of the Laplace equation. In simple numerical examples, this chapter compares numerical solution containing internal information with the numerical solution not containing internal information. It is concluded that adding internal information can significantly improve the numerical solution.

Does Student’s Diligence to Study Relate to His/Her Academic Performance?

It is often pointed out that students’ academic performance becomes worse. Lack of professors’ teaching ability is often considered its major cause, and universities promote faculty development programs. According to our observation, however, the major cause is rather on student’s side, such as lack of motivation, diligence, and other attitudes toward learning. In this paper, we focus on diligence. Diligence is quite important for students to learn effectively. Among various kinds of diligence, we take two kinds of them into consideration; the length of answer text to a questionnaire, and the amount of submitted homework assignments. We investigate how these kinds of diligence of students relate each other, and how they relate to the examination score.

A Characterization of Student's Viewpoint to Learning and its Application to Learning Assistance Framework.

Due to the advancement of popularization of university education, it becomes more and more necessary for university staff to help students by enhancing their motivations to learn in addition to training study skills. We approach to this problem from lecture data analytics. We have been investigating students’ answer to a term-end retrospective questionnaire, and found students’ attitude in learning and their academic performance correlate significantly. On the basis of this finding, in this paper, we propose a framework for assisting students to improve their learning attitude. It consists of four participants; lecturer, assisting staff including librarian, data analysts, and learning assistance system built on top of learning management system. We discuss how the results of our previous studies can be utilized to assist students in this framework. Further, we introduce two indexes for measuring the weights of a student viewpoint between lecture and themselves, and between good points and bad points. These indexes show how a student’s viewpoint to the class is located in comparison with other students’ viewpoints.

A part-of-speech-based exploratory text mining of students’ looking-back evaluation

In our lectures at universities, we observe that the students’ attitudes affects a lot to their achievements. In order to prove this observation based on data, we have been investigating to find effective methods that extract students’ attitudes from lecture data; such as examination score as an index to student’s achievement, attendance and homework data for his/her effort, and answer texts of the term-end questionnaire as information source of attitude. In this chapter, we take another approach to investigate the influences of words used in the answer texts of students on their achievements. We use a machine learning method called Support Vector Machine (SVM), which is a tool to create a model for classifying the given data into two groups by positive and negative training sample data. We apply SVM to the answer texts for analyzing the influences of parts of speech of words to the student’s achievement. Even though adjectives and adverbs are the same in the sense that they modify nouns and verbs, we found that adverbs affects much more than adjectives, as a result. From our experiences so far, we believe that analysis of answers to the evaluations of students toward themselves and lectures are very useful source of finding the students’ attitudes to learning.