This paper proposes an algorithm that solves the node-to-set disjoint paths problem in an n-Möbius cube in polynomial-order time of n. It also gives a proof of correctness of the algorithm as well as estimating the time complexity, O(n4), and the maximum path length, 2n-1. A computer experiment is conducted for n=1,2,...,31 to measure the average performance of the algorithm. The results show that the average time complexity is gradually approaching to O(n3) and that the maximum path lengths cannot be attained easily over the range of n in the experiment.

Conceptual data modeling is an important activity in database design. However, it is difficult for novice learners to master its skills. In the conceptual data modeling, learners are required to detect and correct errors of their artifacts by themselves because modeling tools do not assist these activities. We call such activities self checking, which is also an important process. However, the previous research did not focus on it and/or the data collection of self checks. The data collection of self checks is difficult because self checking is an internal activity and self checks are not usually expressed. Therefore, we developed a method to help learners express their self checks by reflecting on their artifact making processes. In addition, we developed a system, KIfU3, which implements this method. We conducted an evaluation experiment and showed the effectiveness of the method. From the experimental results, we found out that (1) the novice learners conduct self checks during their conceptual data modeling tasks; (2) it is difficult for them to detect errors in their artifacts; (3) they cannot necessarily correct the errors even if they could identify them; and (4) there is no relationship between the numbers of self checks by the learners and the quality of their artifacts.

Vocabulary acquisition based on the traditional pen-and-paper approach is outdated, and has been superseded by the multimedia-supported approach. In a multimedia-supported foreign language learning environment, a learning material comprised of a still-image, a text, and the corresponding sound data is considered to be the most effective way to memorize a noun. However, extraction of an appropriate still image for a noun has always been a challenging and time-consuming process for learners. Learners' burden would be reduced if a system could extract an appropriate image for representing a noun. Therefore, the present study purposed to extract an appropriate image for each noun in order to assist foreign language learners in acquisition of foreign vocabulary. This study presumed that, a learning material created with the help of an appropriate image would be more effective in recalling memory compared to the one created with an inappropriate image. As the first step to finding appropriate images for nouns, concrete nouns have been considered as the subject of investigation. Therefore, this study, at first proposed a definition of an appropriate image for a concrete noun. After that, an image re-ranking algorithm has been designed and implemented that is able to extract an appropriate image from a finite set of corresponding images for each concrete noun. Finally, immediate-after, short- and long-term learning effects of those images with regard to learners' memory retention rates have been examined by conducting immediate-after, delayed and extended delayed posttests. The experimental result revealed that participants in the experimental group significantly outperformed the control group in their long-term memory retention, while no significant differences have been observed in immediate-after and in short-term memory retention. This result indicates that our algorithm could extract images that have a higher learning effect. Furthermore, this paper briefly discusses an on-demand learning system that has been developed to assist foreign language learners in creation of vocabulary learning materials.

We developed a system called DELTA that supports the students' use of backward chaining (BC) to prove the congruence of two triangles. DELTA is designed as an interactive learning environment and supports the use of BC by providing hints and a function to automatically check the proofs inputted by the students. DELTA also has coloring, marking, and highlighting functions to support students' attempts to prove the congruence of two triangles. We evaluated the efficacy of DELTA with 36 students in the second grade of a junior high school in Japan. We found that (1) the mean number of problems, which the experimental group (EG) completely solved, was statistically higher than that of the control group on the post-test; (2) the EG effectively used the BC strategy to solve problems; and (3) the students' attempt to use both the forward chaining strategy and the BC strategy led to solving the problems completely.

The design of a liner decorrelating detector for multi-processing gain code-division multiple-access (MPG-CDMA) systems is proposed, and its performance is discussed. As the result, the performance improvement by this detector is confirmed. Also, it is found that that the degrees of the noise enhancement depend on the processing gains of the signals.