• East Asian mathematical journal
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• v.36 no.3
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• pp.359-364
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• 2020

It is known that a 2-generator knot K has a cyclic Alexander module ℤ[t, t^―1]/(Δ(t)) where Δ(t) is the Alexander polynomial of K. In this paper we explicitly show how to reduce 2-generator Alexander modules to cyclic ones by using Chiswell, Glass and Wilsons presentations of 2-generator knot groups $$<\;x,\;y\;{\mid}\;(x^{{\alpha}_1})^{y^{{\gamma}_1}},\;{\cdots}\;,\;(x^{{\alpha}_k})^{y^{{\gamma}_k}}\;>$$ where a^b = bab^-1.

• International Journal of Computer Science & Network Security
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• v.21 no.6
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• pp.252-257
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• 2021

The application of the principle of trigeneration allows to simultaneously provide electricity to power electronic devices, as well as heat and cold to create the necessary microclimate of the premises and increase efficiency compared to separate cooling and heating systems. The use of Peltier thermoelectric modules (TEM) as part of trigenerative systems allows for smooth and precise control of the temperature regime, high manufacturability and reliability due to the absence of moving parts, resistance to shock and vibration, and small weight and size parameters of the system. One of the promising areas of improvement of trigenerative systems is their modeling and optimization based on the automatic control theory. A block diagram and functional model of an energy-saving trigenerative climate control system based on Peltier modules are developed, and the transfer functions of an open and closed system are obtained. The simulation of the transient characteristics of the system with varying parameters of the components is performed. The directions for improving the quality of transients in the climate control system are determined, as well as the prospects of the proposed methodology for modeling and analyzing control systems operating in substantially nonlinear modes.

• East Asian mathematical journal
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• v.30 no.3
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• pp.293-302
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• 2014

In this paper we provide a rigorous proof for the fact that there are exactly 8 connected Alexander quandles of order $2^5$ by combining properties of fixed point free automorphisms of finite abelian 2-groups and the classification of conjugacy classes of GL(5, 2). Furthermore we verify that six of the eight associated Alexander modules are simple, whereas the other two are semisimple.

• Korean Institute of Interior Design Journal
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• v.25 no.3
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• pp.31-39
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• 2016

This study is aimed to increase the possibility of using the Christopher Alexander's pattern language. The methodology of this study is (i) to analyze the pattern language by using the network analysis tool in order to understand the complicate network structure of the pattern language, and (ii) to apply the Alexander's method of using the pattern language by using the network analysis tool (Gephi) and to examine the feasibility of the network analysis tool as a tool for using the pattern language. Firstly, as a result of analysing the pattern language, (i) the pattern language classified by pattern number is distinguished by the patterns of towns, buildings and construction, among which the pattern of buildings plays a key function in the networks; (ii) the buildings functions a medium connecting between the towns and the construction; and (iii) the pattern language is divided into 6 sub-modules, through which the user can select a pattern. Secondly, the result of using the network analysis tool as a tool for using the pattern language (i) suggests the new method of using the pattern language by using the network analysis tool (Gephi); (ii) makes it possible to easily figure out the characteristics of the links between the patterns; and (iii) increases the completeness of the pattern language by making it easy to find out the sub-patterns in selecting a pattern.