• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.105-116
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• 2021

Information systems and decision rules with imprecision and uncertainty in data analysis are studied in complete residuated lattices. In this paper, we introduce the notions of distance spaces, Alexandrov pretopology (precotopology) and join-meet (meet-join) operators in complete co-residuated lattices. We investigate their relations and properties. Moreover, we give their examples.

• Kyungpook Mathematical Journal
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• v.9 no.1_2
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• pp.59-62
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• 1969

• Bulletin of the Korean Mathematical Society
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• v.11 no.2
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• pp.69-72
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• 1974

• East Asian mathematical journal
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• v.13 no.1
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• pp.123-130
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• 1997

• Journal of the Korean Mathematical Society
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• v.25 no.1
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• pp.11-23
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• 1988

• Journal of the Korean Mathematical Society
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• v.10 no.2
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• pp.77-80
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• 1973

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1121-1137
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• 2007

There are 7 types of 4-dimensional solvable Lie groups of the form ${\mathbb{R}^3}\;{\times}_{\varphi}\;{\mathbb{R}}$ which are unimodular and of type (R). They will have left. invariant Riemannian metrics with maximal symmetries. Among them, three nilpotent groups $({\mathbb{R}^4},\;Nil^3\;{\times}\;{\mathbb{R}\;and\;Nil^4)$ are well known to have lattices. All the compact forms modeled on the remaining four solvable groups $Sol^3\;{\times}\;{\mathbb{R}},\;Sol_0^4,\;Sol_0^'4\;and\;Sol_{\lambda}^4$ are characterized: (1) $Sol^3\;{\times}\;{\mathbb{R}}$ has lattices. For each lattice, there are infra-solvmanifolds with holonomy groups 1, ${\mathbb{Z}}_2\;or\;{\mathbb{Z}}_4$. (2) Only some of $Sol_{\lambda}^4$, called $Sol_{m,n}^4$, have lattices with no non-trivial infra-solvmanifolds. (3) $Sol_0^{'4}$ does not have a lattice nor a compact form. (4) $Sol_0^4$ does not have a lattice, but has infinitely many compact forms. Thus the first Bieberbach theorem fails on $Sol_0^4$. This is the lowest dimensional such example. None of these compact forms has non-trivial infra-solvmanifolds.

• Korean Journal of Crystallography
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• v.17 no.1
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• pp.1-5
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• 2006

After the definition of the basis vectors of the two-dimensional direct and reciprocal lattices, various interrelations between them are derived, and additionally how to calculate $\vec{d^*}(hk)//direction\;of\;(hk),\;d(hk)=1/d^*(hk),\;[uv]$, planes belonging to a direction [uv], areas and interplanar spacing of 2-dimensional low different lattices are shown.

• The Transactions of the Korea Information Processing Society
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• v.3 no.7
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• pp.1822-1833
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• 1996

As the size and complexity of networks increase, it is difficult to manage the whole network using single network manager, thus it is more resonable to manage the network using several network managers distributed on the network. Security interoperability should be supported among network management systems (NMSs)that use different management policies. In this paper, an algorithm that makes it posible to take a role into a role lattices is suggested to provide security interoperability among NMSs that have their own role lattices. In addition, security constraints are proposed to maintain the confidentiality and integrity of information by dynamically modifying the access rights of roles as the state of a system changes. Also, the security constraints are expressed using ECA rules in this paper.

• Journal of Ocean Engineering and Technology
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• v.2 no.2
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• pp.130-137
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• 1988

This thesis introduced that character of a treatment technique for a mading synthetic resin Hifiow-Ring. The material system of packings make an experiment air$NH_{3}$/air$H_{2}SO_{4}$, $SO_{2}$-air/NaOH, $NH_{3}$-air/$/H_{2}SO_{4}$ under general conditions. Lattices packing compared with conventional packings was proved low pressure loss and high separation efficiency for high loading per trans unit. And an inflow materal tested for absorption and rectification, it made an experiment under a range regular temperature, low energy and small amount of money. That made possible in simple equation, volume material tranfer coefficient$\beta_{L}$ . a by absorption or $\beta_{V}$ .a calculated in all range loading. The peculiarity pressure loss $\Delta\;P/NUT_{ov}$ for Hiflow-ring contributed to a fall cost of energy, a grade number of a vacuum rectification and absorption calculation.