• 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.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.503-507
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• 2006

Let X be a Tychonoff space and ${\sum}(X)$ the set of all the subrings of C(X) that contain $C^*(X)$. For any A(X) in ${\sum}(X)$ suppose $_{{\upsilon}A}X$ is the largest subspace of ${\beta}X$ containing X to which each function in A(X) can be extended continuously. Let us write A(X) ~ B(X) if and only if $_{{\upsilon}A}X=_{{\upsilon}B}X$, thereby defining an equivalence relation on ${\sum}(X)$. We have shown that an A(X) in ${\sum}(X)$ is isomorphic to C(Y ) for some space Y if and only if A(X) is the largest member of its equivalence class if and only if there exists a subspace T of ${\beta}X$ with the property that A(X)={$f{\in}C(X):f^*(p)$ is real for each $p$ in T}, $f^*$ being the unique continuous extension of $f$ in C(X) from ${\beta}X$ to $\mathbb{R}^*$, the one point compactification of $\mathbb{R}$. As a consequence it follows that if X is a realcompact space in which every $C^*$-embedded subset is closed, then C(X) is never isomorphic to any A(X) in ${\sum}(X)$ without being equal to it.

• Journal of KIISE:Databases
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• v.31 no.6
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• pp.664-674
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• 2004

The trajectory preservation property that stores only one trajectory in a leaf node is the most important feature of an index structure, such as the TB-tree for retrieving object's moving paths in the spatio-temporal space. It performs well in trajectory-related queries such as navigational queries and combined queries. But, the MBR of non-leaf nodes in the TB-tree have large amounts of dead space because trajectory preservation is achieved at the sacrifice of the spatial locality of trajectories. As dead space increases, the overlap between nodes also increases, and, thus, the classical range query cost increases. We present a new split policy and entry relocation policies, which have no deterioration of the performance for trajectory-related queries, for improving the performance of range queries. To maximally reduce the dead space of a non-leaf node's MBR, the Maximal Area Reduction (MAR) policy is used as a split policy for non-leaf nodes. The entry relocation policy induces entries in non-leaf nodes to exchange each other for the purpose of reducing dead spaces in these nodes. We propose two algorithms for the entry relocation policy, and evaluate the performance studies of new algorithms comparing to the TB-tree under a varying set of spatio-temporal queries.

• Journal of the Korean Geographical Society
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• v.48 no.2
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• pp.259-271
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• 2013

This paper addresses the efficient facility placements to adopt a super WiFi network, taking significant considerations as the next generation 'information highway'. Since the super WiFi has a wider geographic coverage by utilizing the white spaces of TV broadcasting which are empty and available frequencies for the wireless communications, it would play an important role in releasing digital divide of the internet access for low populated or mountainous areas. The purpose of this paper is to explore systematic and efficient spatial plans for the super WiFi. For doing this, we applied optimal location covering models to Gurye-gun, Jeonlanamdo. From the application, we presented optimal locations for super WiFi facilities and significant analytical results, such as the tradeoff between the number of facilities and coverage and marginal coverage for establishing super WiFi network. The results of this research would be usefully utilized for decision makers who wish to adopt a super WiFi, to extend wireless networks in a city or build a regional infrastructure of wireless facilities.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• v.9 no.1
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• pp.315-318
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• 2005

Recently, the advent of wireless communication and other handhold devices like Personal Digital Assistants and smart cards have made in implementation of cryptosystems a major issue. One important aspect of modern day ciphers is the scope for hardware sharing between the encryption and decryption algorithm. The cellular Automata which have been proposed as an alternative to linear feedback shift registers(LFSRs) can be programmed to perform the operations without using any dedicated hardware. But to generalize and analyze CA is not easy. In this paper, we characterizes uniform/hybird complemented group CA with rules 195/153/51 that divide the entire state space into smaller spaces of maximal equal lengths. This properties can be useful in constructing key agreement algorithm.

• Asian-Australasian Journal of Animal Sciences
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• v.14 no.2
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• pp.174-183
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• 2001

During the rapid phase of gonadal development of the freshwater teleost, the catfish (Silurus asotus), the influence of hCG upon the inducement of final oocyte maturation and spawning was investigated electrophoretically and ultrastructurally. The electrophoretic patterns obtained were different in the presence and absence of some of the major or minor zones, because of the hormone level in catfish. The vitellogenin of hormone-treated fish was stained more intensively than that of sham-treated fish. These proteins showed some minor or main bands of egg extracts which migrated at positions corresponding to molecular weights of approximately 90,000. However, the thickness of electrophoretic band in molecular weight for hCG-treated fish was slightly lower than that for saline control. It seemed the plasma protein with molecular weight of approximately 45,000 in hCG-treated fish disappeared. In contrast to the control fish, the ovaries in the catfish treated with hCG shows a marked ultrastructural change under the electron microscope. No dilated profiles were seen in the granulosa cells of the mature oocyte before ovulation. After germinal vesicle breakdown (GVBD), the zona radiata interna (ZRI) becomes more compact, and there is a loss of all the processes from the pore canals. There is a wide space between the vitelline membrane and zona radiata. Also, during final maturation, the microvillar processes from the oocyte are seen no longer to penetrate deeply into the extracellular spaces of the overlying granulosa cells, and the reticulate patterns of the zona radiata interna becomes occluded, giving the zona radiata a more solid appearance. It has been possible to initiate 100% oocyte maturation in yolk granules and follicles in vivo by treatment with hCG and a high water temperature ($27^{\circ}C$). In hCG-treated fish, the percentages of successful artificial fertilization and hatching were maximal at 15 h after a single injection. It seems clear that a long acting preparation containing hCG can be successfully used in prespawning fish to advance the final events of gonadal maturation and initiate spawning. Further studies are necessary to evaluate the potential of hCG to either stimulate or inhibit the reproductive development of fish at other stages of the seasonal reproductive cycle.