• Honam Mathematical Journal
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• v.30 no.3
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• pp.443-468
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• 2008

We give a theorem of existence of six nontrivial solutions of the nonlinear Hamiltonian system $\.{z}$ = $J(H_z(t,z))$. For the proof of the theorem we use the critical point theory induced from the limit relative category of the torus with three holes and the finite dimensional reduction method.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.589-598
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• 2010

Generalizing normally quasi-ordered spaces, we introduce a concept of regularly quasi-ordered spaces and study their categorical properties. We obtain well behaved reflective subcategories of the category Rqos of regularly quasi-ordered spaces and continuous isotones, namely the full subcategory of Rqos determined by $T_0$-objects among others, and this result can be extended to that in the category Nqos of normally quasi-ordered spaces and continuous isotones.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.387-391
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• 2004

Let A be Noetherian ring, a= (${\tau}_1..., \tau_n$ an ideal of A and $C_{A}$ be category of A-modules and A-homomorphisms. We show that the connected left sequences of covariant functors ${limH_i(K.(t^t,-))}_{i\geq0}$ and ${lim{{Tor^A}_i}(\frac{A}{a^f}-)}_{i\geq0}$ are isomorphic from $C_A$ to itself, where $\tau^t\;=\;{{\tau_^t}_1$, ㆍㆍㆍ${\tau^t}_n$.

• Proceedings of the KIEE Conference
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• summer
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• pp.354-356
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• 2004

This paper is the transient analysis for choosing the optimal SCR ratings of AC3 utilization category testing equipment(AC3 TE) used for electrical durability test for magnetic switch according to IEC60947-4 Annex B by utilizing EMTP -ATPDraw. Magnetic contactor closes and opens the motor load with ON/OFF switch of electronic contactor. It is also used for protecting and controlling the load. Magnetic contactor detects the over-current flow in the load with a over-current relay and disconnects the load by opening its control power. The key cost of AC3 TE is the SCR ratings. The more decreases SCR ratings, the more decreased the cost is, but it is impossible to ensure the reliability. On the other hand, the more increases SCR ratings, the more increased the cost is. Thereupon, in this paper after the testing circuit is simulated by using EMTP-ATPDraw the SCR ratings will be applied in order to guarantee the testing reliability of PT&T(Power Testing and Technology institute in LG Industrial Systems Co.,Ltd.).

• Journal of Korean Society of Environmental Engineers
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• v.36 no.3
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• pp.162-171
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• 2014

In this study, the uncertainty analysis of present land pollutant load estimation with simplified land category in TMDLs was performed and the enhanced method for land pollutant load estimation with level II land cover consisting of 23 categories was suggested, which was verified by L-THIA model. For land TP load estimation in Jinwi stream basin, the result of comparison between existing method with simplified land category (Scenario 1) and enhanced method with level II land cover (Scenario 2) showed high uncertainty in existing method. TP loads estimated by Scenario 2 for land covers included in the site land category were in the range of 3.45 to 56.69 kg/day, in which TP loads differed by sixteen times as much among them. For application of scenario 2 to TMDLs, Land TP loads were estimated by matching level II land cover to 28 land categories in serial cadastral map (Scenario 3). In order to verify accuracy of TP load estimation by scenario 3, the simulation result of L-THIA was compared with that and the difference between the two was as little as 10%. The result of this study is expected to be used as primary data for accurate estimation of land pollutant load in TMDLs.

• The Mathematical Education
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• v.16 no.2
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• pp.22-26
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• 1978

It is shown that a map having an extension to an open map between the Alex-androff base compactifications of its domain and range has a unique such extension. J.S. Wasileski has introduced the Alexandroff base compactifications of Hausdorff spaces endowed with Alexandroff bases. We introduce a definition of morphism between such spaces to obtain a category which we denote by ABC. We prove that the Alexandroff base compactification on objects can be extended to a functor on ABC and that the compact objects give an epireflective subcategory of ABC. For each topological space X there exists a completely regular space $\alpha$X and a surjective continuous function $\alpha$$_{x}$ : Xlongrightarrow$\alpha$X such that for each completely regular space Z and g$\in$C (X, Z) there exists a unique g$\in$C($\alpha$X, 2) with g=g$^{\circ}$$\beta$$_{x}$. Such a pair ($\alpha$$_{x}$, $\alpha$X) is called a completely regularization of X. Let TOP be the category of topological spaces and continuous functions and let CREG be the category of completely regular spaces and continuous functions. The functor $\alpha$ : TOPlongrightarrowCREG is a completely regular reflection functor. For each topological space X there exists a compact Hausdorff space $\beta$X and a dense continuous function $\beta$x : Xlongrightarrow$\beta$X such that for each compact Hausdorff space K and g$\in$C (X, K) there exists a uniqueg$\in$C($\beta$X, K) with g=g$^{\circ}$$\beta$$_{x}$. Such a pair ($\beta$$_{x}$, $\beta$X) is called a Stone-Cech compactification of X. Let COMPT$_2$ be the category of compact Hausdorff spaces and continuous functions. The functor $\beta$ : TOPlongrightarrowCOMPT$_2$ is a compact reflection functor. For each topological space X there exists a realcompact space (equation omitted) and a dense continuous function (equation omitted) such that for each realcompact space Z and g$\in$C(X, 2) there exists a unique g$\in$C (equation omitted) with g=g$^{\circ}$(equation omitted). Such a pair (equation omitted) is called a Hewitt's realcompactification of X. Let RCOM be the category of realcompact spaces and continuous functions. The functor (equation omitted) : TOPlongrightarrowRCOM is a realcompact refection functor. In [2], D. Harris established the existence of a category of spaces and maps on which the Wallman compactification is an epirefiective functor. H. L. Bentley and S. A. Naimpally [1] generalized the result of Harris concerning the functorial properties of the Wallman compactification of a T$_1$-space. J. S. Wasileski [5] constructed a new compactification called Alexandroff base compactification. In order to fix our notations and for the sake of convenience. we begin with recalling reflection and Alexandroff base compactification.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.199-209
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• 2005

An ideal space is ${\cal{I}}-resolvable$ if it has two disjoint ${\cal{I}}-dense$ subsets. We answer the question: If X is ${\cal{I}}-resolvable$, then is X (${\cal{I}}\;{\cup}\;{\cal{N}$)-resolvable?, posed by Dontchev, Ganster and Rose. We give three generalizations of the well known Banach Category Theorem and deduce the Banach category Theorem as a corollary. Characterizations of completely codense ideals and ${\cal{I}-locally$ closed sets are given and their properties are discussed.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.1-17
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• 2016

Let $\mathcal{W}$ be an additive full subcategory of the category R-Mod of left R-modules. We provide a method to construct a proper ${\mathcal{W}}^H_C$-resolution (resp. coproper ${\mathcal{W}}^T_C$-coresolution) of one term in a short exact sequence in R-Mod from those of the other two terms. By using these constructions, we introduce and study the stability of the Gorenstein categories ${\mathcal{G}}_C({\mathcal{W}}{\mathcal{W}}^T_C)$ and ${\mathcal{G}}_C({\mathcal{W}}^H_C{\mathcal{W}})$ with respect to a semidualizing bimodule C, and investigate the 2-out-of-3 property of these categories of a short exact sequence by using these constructions. Also we prove how they are related to the Gorenstein categories ${\mathcal{G}}((R{\ltimes}C){\otimes}_R{\mathcal{W}})_C$ and ${\mathcal{G}}(Hom_R(R{\ltimes}C,{\mathcal{W}}))_C$ over $R{\ltimes}C$.

• Journal of Korean Society of Water and Wastewater
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• v.21 no.2
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• pp.165-175
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• 2007

Performance indicators haven't been used for the assessment of the wastewater treatment facility or management in Korea yet, therefore they are going to be important parts in wastewater utilities because they are used to understand present situation and to compare one with other wastewater utilities. In this study, we used performance indicators to assess the condition of wastewater utilities and they were divided into four categories (A, B, C, and D). A category represented the condition of the planning & construction and composed of wastewater supply, disaster defence and employees. B category represented maintenance of wastewater utilities and were composed of manhole, sewer, and technical employees. C category showed the operation efficiency of wastewater utilities and D category represented the environmental load. To analyze the situation of wastewater utilities overall, cluster analysis was performed using four categori' es indicators. And CCC (Cubic Clustering Criterion) and R-square were used to decide the proper number of clusters, and wastewater utilities of 48 cities were divided into 5 groups(I, II, III, IV, and V groups). Each cluster was analyzed by average and standard deviation to understand the situation of wastewater utilities. A group analysis showed that IV and V clusters were insufficient, B group showed that I and IV groups were insufficient, C group showed all clusters are above average, and D group was also like C group.

• Korean Parent-Child Health Journal
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• v.16 no.1
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• pp.17-26
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• 2013

Purpose: This study was to examine the mother's knowledge of premature development and rearing and their education needs in order to provide information to develop an education program for premature mothers. Methods: The study participants was 73 mothers of premature infants. Knowledge on premature infant's development and rearing was measured by measurement tools developed by previous research. The education needs about development and rearing were measured by self-report questionnaire. The data were analyzed using descriptive statistics, t-Test, ANOVA using SPSS 20.0. Results: The score of knowledge on development was 59.3 out of 100. The category of knowledge on language development was rated the highest, and motor development category was the lowest. The score of knowledge on rearing was 77.8 out of 100. The knowledge on bathing category was rated the highest and defecation category was the lowest. The growth education needs for premature infant development was the highest education needs of premature infant development. The method for developmental improvement was the highest education needs of premature infant rearing. Conclusion: The results showed that premature infant mothers have less knowledge on premature development than premature rearing, also mothers were interested in development and there were many needs on premature infant's development.