• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.803-814
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• 2001

A projective Schur algebra associated with a partition of finite group G can be constructed explicitly by defining linear transformations of G. We will consider various linear transformations and count the number of equivalent classes in a finite group. Then we construct projective Schur algebra dimension is determined by the number of classes.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.24 no.5
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• pp.77-82
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• 2024

The test set of machine learning consists of the remaining data that did not participate as training data. It is quantitative division and it is setting aside a certain amount of data which has the same effect as random selection. However from a software testing perspective, test cases sufficient to catch errors are selected as a test set rather than a random selection. This is called the adequacy of the test case, and the higher the adequacy, the better the test case is selected. We want to examine whether the test cases used in machine learning are sufficient from this perspective by comparing them with the equivalence split method of software testing. If higher sufficiency is guaranteed when applying a software test design technique, that is, equivalence splitting, high effectiveness can be achieved with a small number of test sets. This reduces the size of the test set, thereby increasing the size of the training data set and ultimately securing more data to learn. It can be expected that more sophisticated models can be built with larger training data sets.

• The Transactions of the Korea Information Processing Society
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• v.5 no.10
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• pp.2627-2640
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• 1998

In this paper, we analyze the performance of the virtual cell system[1] for the transmission of IP datagrams in mobile computer communications. A virtual cell consistsof a group of physical cells shose base stationsl are implemented b recote bridges and interconnected via high speed datagram packet switched networks. Host mobility is supported at the data link layer using the distributed hierachical location information of mobile hosts. Given mobility and communication ptems among physical cells, the problem of deploying virtual cells is equivalent to the optimization cost for the entire system where interclster communication is more expesive than intracluster communication[2]. Once an iptimal partitionof disjoint clusters is obtained, we deploy the virtual cell system according to the topology of the optimal partition such that each virtual cell correspods to a cluser. To analyze the performance of the virtual cell system, we adopt a BCMP open multipel class queueing network model. In addition to mobility and communication patterns, among physical cells, the topology of the virtual cell system is used to determine service transition probabilities of the queueing network model. With various system parameters, we conduct interesting sensitivity analyses to determine network design tradeoffs. The first application of the proposed model is to determine an adequate network bandwidth for base station networking such that the networks would not become an bottleneck. We also evaluate the network vlilization and system response time due to various types of messages. For instance, when the mobile hosts begin moving fast, the migration rate will be increased. This results of the performance analysis provide a good evidence in demonsratc the sysem effciency under different assumptions of mobility and communication patterns.