• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.123-135
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• 2008

This study analysed the schemata which are requisite to understand and prove examples of mathematical induction, and examined students' construction of the schemata. We verified that the construction of implication-valued function schema and modus ponens schema needs function schema and proposition-valued function schema, and needs synthetic coordination for successive mathematical induction schema. Given this background, we establish $1{\sim}4$ levels for students' understanding of the mathematical induction. Further, we analysed cognitive difficulties of students who studying mathematical induction in connection with these understanding levels.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1274-1276
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• 1993

We have designed a multiple-valued fuzzy Approximate Analogical-Reseaning system (AARS). The system uses a similarity measure of fuzzy sets and a threshold of similarity ST to determine whether a rule should be fired, with a Modification Function inferred from the Similarity Measure to deduce a consequent. Multiple-valued basic fuzzy blocks are used to construct the system. A description of the system is presented to illustrate the operation of the schema. The results of simulations show that the system can perform about 3.5 x 106 inferences per second. Finally, we compare the system with Yamakawa's chip which is based on the Compositional Rule of Inference (CRI) with Mamdani's implication.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.449-449
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• 2000

Many researchers have studied architectures for non-Neumann's computers because of escaping its bottleneck. To avoid the bottleneck, a neuron-based computer has been developed. The computer has only neurons and their connections, which are constructed of the learning. But still it has information processing facilities, and at the same time, it is like as a simplified brain to make inference; it is called "neuron-computer". No instructions are considered in any neural network usually; however, to complete complex processing on restricted computing resources, the processing must be reduced to primitive actions. Therefore, we introduce the instructions to the neuron-computer, in which the most important function is implications. There is an implication represented by binary-operators, but general implications for multi-value or fuzzy logics can't be done. Therefore, we need to use Lukasiewicz' operator at least. We investigated a neuron-computer having instructions for general implications. If we use the computer, the effective inferences base on multi-value logic is executed rapidly in a small logical unit.

• The Korean Journal of Financial Management
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• v.22 no.1
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• pp.147-179
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• 2005

It is frequently said that mortgage-backed securities (MBS) of different security designs are issued in an attempt to meet the varying needs and expectations of investors. If this is true indeed, MBS of complicated risk-return characteristics are likely to be priced higher than MBS of simple risk-return characteristics we. We test this implication by establishing a recombining binomial interest rate prepayment model with a burnout effect embedded. More specifically, we compare the relative values (utilities) of a pass-through and a PAC- Support collateralized mortgage obligation(CMO), and theoretically show why and how the CMO is more highly valued than is the pass-through. The model is established such that mortgage prepayment is a function of the current value of, and the past path of, the mort-gage market rate. Since we work on not the total value of the two MBS but the value of each tranche of either MBS, the test results could be robust to slightly different versions of similar tests, which may be done in the future.