• The Mathematical Education
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• v.42 no.3
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• pp.353-368
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• 2003

Analogy, based on a similarity, is to infer the properties of the similar object from properties of an object. It can be a very useful thinking tool for learning mathematical patterns and laws, noticing on relational properties among various situations. The purpose of this study, when manipulating hint condition, figure and table conditions and the amount of original learning by using algebra word problems, is to verify the effects of analogical transfer in solving equivalent, isomorphic and similar problems according to the similarity of source problems and target ones. Five study questions were set up for the above purpose. It was 354 first grade students of S and G middle schools in Seoul that were experimented for this study. The data was processed by MANOVA analysis of statistical program, SPSS 10.0. The results of this studies would indicate that most of the students would be poor at solving isomorphic and similar problems in the performance of analogical transfer according to the similarity of source and target problems. Hints, figure and table conditions did not facilitate the analogical transfer. Merely, on the condition that amount of teaming was increased, analogical transfer of the students was facilitated. Therefore, it is necessary to have students do much more analogical problem-solving experience to improve their analogical reasoning ability through the instruction program development in the educational fields.

• Journal of the Korean Geographical Society
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• v.39 no.4
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• pp.562-584
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• 2004

This paper intends to identify the structure of homogeneous regions and functional regions in Seoul based on B.J.L. Berry's ‘general field theory of spatial behavior’. The structure of homogeneous regions by using socio-economic variables can explain how the structural elements of the city are arranged. It can be ssid that Seoul has shifted towards more complicated and differentiated features in terms of homogeneous regions. The different patterns are found between the northern part to Han River where old torn areas are located and the southern part to Han River where newly urbanized areas are located. Usually, the concentric pattern and the sectoral pattern coexist, which is enhanced moving from CBD to the outskirt area. The distribution of different social classes shows irregular pattern similar to the variation of living environment. The social gap is expected to be more widening between new towns and old towns. The analysis of spatial movement pattern shows no clear hierarchical order because of current shifts towards both multi-nuclear pattern and spatial dispersion. The functional regions show duplicated structure overlapping their boundaries each other. The ‘general field theory of spatial behavior’ strongly suggests that spatial interactions among sub-areas in the city are differentiated from the basic characteristics and function of each sub-area. The attributes of homogeneous regions and functional regions are interrelated in the characteristics of isomorphic nature.

• Resources Recycling
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• v.32 no.3
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• pp.9-17
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• 2023

Efforts are currently underway to develop a method for efficiently recovering lithium from the cathode material of waste lithium iron phosphate batteries (LFP). The successful application of lithium battery recycling can address the regional ubiquity and price volatility of lithium resources, while also mitigating the environmental impact associated with both waste battery material and lithium production processes. The isomorphic substitution leaching process was used to recover lithium from spent lithium iron phosphate batteries. Lithium was leached by the isomorphic substitution of Fe²⁺ in LFP using a relatively inexpensive ferric chloride etching solution as a leaching agent. In the study, the leaching rate of lithium was compared using the ferric chloride etching solution at various multiples of the LFP molar ratio: 0.7, 1.0, 1.3, and 1.6 times. The highest lithium leaching rate was shown at about 98% when using 1.3 times the LFP molar ratio. Subsequently, to eliminate Fe, the leachate was treated with NaOH. The Fe-free solution was then used to synthesize lithium carbonate, and the harvested powder was characterized and validated. The surface shape and crystal phase were analyzed using SEM and XRD analysis, and impurities and purity were confirmed using ICP analysis.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.771-778
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• 2005

In this paper we shall give some group properties derived from the characteristic ring-module $_X(M)$, using the fact that $_X(M)_H$ is a conjugate to $_X(M)_{Ha}$ when M is an invertible right R-module. Also we shall prove that_X(M)$ is group-isomorphic to TR and some normal subgroup properties if M is invertible and R is commutative.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.495-504
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• 2010

This paper continues a line investigation in [1]. Let A be a K-algebra and M an A/K-bimodule. In [5] Hamaguchi gave a necessary and sufficient condition for gDer(A, M) to be isomorphic to BDer(A, M). The main aim of this paper is to establish similar relationships for generalized ($\sigma$, $\tau$)-derivations.

• Honam Mathematical Journal
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• v.4 no.1
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• pp.167-172
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• 1982

Let A be a Banach $^{\ast}$-algebra and C(t) be a closed $^{\ast}$-subalgebra of A gengerated by $t{\in}A$. A is locally $B^{\ast}$-equivalent [$B^{\ast}$-equivalent] if C(t) [A] for every hermitian element t is $^{\ast}$-isomorphic to some $B^{\ast}$-algebra. It was proved that the locally $B^{\ast}$-equivalent algebras with some conditions is $B^{\ast}$-equivalent by B. A. Barnes. In this paper, we obtain the some conditions for a locally $B^{\ast}$-equivalent algebra to be $B^{\ast}$-equivalent.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.199-210
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• 2007

Given a field K and a finite group G, it is a very interesting problem, although very difficult, to find all Galois extensions over K whose Galois group is isomorphic to G. In this paper, we prepare a theoretical background to study this type of problem when G is the Mathieu group $M_{24}$ and K is a field of characteristic two.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1169-1183
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• 2015

We describe generalized Cayley graphs of rectangular groups, so that we obtain (1) an equivalent condition for two Cayley graphs of a rectangular group to be isomorphic to each other, (2) a necessary and sufficient condition for a generalized Cayley graph of a rectangular group to be (strong) connected, (3) a necessary and sufficient condition for the colour-preserving automorphism group of such a graph to be vertex-transitive, and (4) a sufficient condition for the automorphism group of such a graph to be vertex-transitive.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.6
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• pp.838-842
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• 2007

In this paper, we define that a fuzzy convergence approach limit and a fuzzy approach Chuchy structure on X. And we investigate the relations between the category CAP and the category FCAP. And we show that the categories $FCAP_{RC}$ and $uFACHY_{cpl}$ are isomorphic.

• The Pure and Applied Mathematics
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• v.7 no.2
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• pp.71-78
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• 2000

Any Hausdoroff space on a set which has at least two points a regular closed Boolean algebra different from the indiscrete regular closed Boolean algebra as indiscrete space. The Sierpinski space and the space with finite complement topology on any infinite set etc. do the same. However, there is $T_{0}$ space which does the same with Hausdorpff space as above. The regular closed Boolean algebra in a topological space is isomorphic to that algebra in the space with its open extension topology.