• The Pure and Applied Mathematics
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• v.14 no.1 s.35
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• pp.37-48
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• 2007

In this paper, we introduce and study a class of generalized multivalued quasivariational inclusions for fuzzy mappings, and establish its equivalence with a class of fuzzy fixed-point problems by using the resolvent operator technique. We suggest a new iterative algorithm for the generalized multivalued quasivariational inclusions. Further, we establish a few existence results of solutions for the generalized multivalued quasivariational inclusions involving $F_r$-relaxed Lipschitz and $F_r$-strongly monotone mappings, and discuss the convergence criteria for the algorithm.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.10
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• pp.1294-1299
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• 2000

The combustion characteristics have been investigated to develop the 50 kW-class gas turbine combustor. The combustor design program was developed and applied to design this combustor. The combustion air which has the temperature of 45, 200, $300^{\circ}C$ were supplied to combustor for elucidating the effect of inlet air temperature on CO, NOx emissions and flame temperature. The exit temperature and NO were increased and CO was decreased with increasing inlet air temperature. Also, the effect of equivalence ratio was considered to verify the combustor performance. The emissions of CO and NO with inlet air temperature can be analyzed qualitatively by measuring the temperature inside the combustor. The combustion performance with fuel schedule was evaluated to get the informations of the starting and part loading process of gas turbine. The combustion was stable above the equivalence ratio of 0.18. The pattern factor which is the important parameter of combustor performance was satisfied with the design criterion. Consequently the combustor was proved to meet the performance goal required for the target gas turbine system.

• 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 the Korea Institute of Information Security & Cryptology
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• v.6 no.4
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• pp.97-106
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• 1996

In this paper, we define an equivalence relation on the group of all permutations over the finite field GF($2^n$) and show each equivalence class has common cryptographic properties. And, we classify all exponent permutations over GF($2^7$) and GF($2^8$). Then, three applications of our results are described. We suggest a method for designing $n\;{\times}\;2n$ S(ubstitution)-boxes by the concatenation of two exponent permutations over GF($2^n$) and study the differential and linear resistance of them. And we can easily indicate that the conjecture of Beth in Eurocrypt '93 is wrong, and discuss the security of S-box in LOKI encryption algorithm.

• The Transactions of the Korea Information Processing Society
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• v.7 no.12
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• pp.3874-3884
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• 2000

An information retrieval system has to retrieve all and only documents which are relevant to a user query, even if index terms and query terms are not matched exactly. However, term mismatches between index terms and qucry terms have been a serious obstacle to the enhancement of retrieval performance. In this paper, we discuss automatic term normalization between words in text corpora and their application to a Korean information retrieval system. We perform two types of term normalizations to alleviate semantic term mismatches: equivalence class and co-occurrence cluster. First, transliterations, spelling errors, and synonyms are normalized into equivalence classes bv using contextual similarity. Second, context-based terms are normalized by using a combination of mutual information and word context to establish word similarities. Next, unsupervised clustering is done by using K-means algorithm and co-occurrence clusters are identified. In this paper, these normalized term products are used in the query expansion to alleviate semantic tem1 mismatches. In other words, we utilize two kinds of tcrm normalizations, equivalence class and co-occurrence cluster, to expand user's queries with new tcrms, in an attempt to make user's queries more comprehensive (adding transliterations) or more specific (adding spc'Cializationsl. For query expansion, we employ two complementary methods: term suggestion and term relevance feedback. The experimental results show that our proposed system can alleviatl' semantic term mismatches and can also provide the appropriate similarity measurements. As a result, we know that our system can improve the rctrieval efficiency of the information retrieval system.

• The KIPS Transactions:PartD
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• v.10D no.5
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• pp.859-872
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• 2003

Class hierarchies often constitute the backbone of object-oriented software. Their quality is therefore quite crucial. Building class hierarchies with good qualify is a very important and common tasks on the object oriented software development, but such hierarchies are not so easy to build. Moreover, the class hierarchy structure under construction is frequently restructured and refined until it becomes suitable for the requirement on the iterative and incremental development lifecycle. Therefore, there has been renewal of interest in all methodologies and tools to assist the object oriented developers in this task. In this paper, we define a set of quantitative metrics which provide a wav of capturing features of a rough estimation of complexity of class hierarchy structure. In addition to, we suggest a set of algorithms that transform a original class hierarchy structure into reorganized one based on the proposed metrics for class hierarchy structure. Furthermore, we also prove that each algorithm is "object-preserving". That is, we prove that the set of objects are never changed before and after applying the algorithm on a class hierarchy. The technique presented in this paper can be used as a guidelines of the construction, restructuring and refinement of class hierarchies. Moreover, the proposed set of algorithms based on metrics can be helpful for developers as an useful instrument for the object-oriented software development.velopment.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.285-295
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• 2013

In this study I examine the definitions of terms related to ratio and rate from 5, 6, 7th revised elementary school math textbooks to discuss the improvements and the remained problems in 2007 curriculum textbook. Next, I make the alternative definitions of the terms, 'biyoul', the value of 'bi', and 'baekboonyul' by re-establishing the relations between them. Finally, I point out that those problems are intrinsic to the attempt of the textbook to introduce the terms related to ratio with little consideration for the mathematical meaning of ratio as a equivalence class.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.809-823
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• 2020

Let C[0, T] denote the space of continuous, real-valued functions on the interval [0, T] and let C₀[0, T] be the space of functions x in C[0, T] with x(0) = 0. In this paper, we introduce a Banach algebra ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ on C[0, T] and its equivalent space ${\bar{\mathcal{F}}}({\mathcal{H}}) $, a space of transforms of equivalence classes of measures, which generalizes Fresnel class 𝓕(𝓗), where 𝓗 is an appropriate real separable Hilbert space of functions on [0, T]. We also investigate their properties and derive an isomorphism between ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ and ${\bar{\mathcal{F}}}({\mathcal{H}}) $. When C[0, T] is replaced by C₀[0, T], ${\bar{\mathcal{F}}}({\mathcal{H}}) $ and ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ reduce to 𝓕(𝓗) and Cameron-Storvick's Banach algebra 𝓢, respectively, which is the space of generalized Fourier-Stieltjes transforms of the complex-valued, finite Borel measures on L²[0, T].

• Journal of the Korean Statistical Society
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• v.34 no.2
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• pp.141-151
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• 2005

Under the assumption that the three-level factors are quantitative, the linear effects are taken more attention than the quadratic effects of the interaction terms. Webb (1971) presented some small incomplete factorial designs that are mixed two- and three-level designs with 20 or fewer runs. The designs provided the estimating linear-by-linear components of interactions between the three-level factors; moreover, they could also offer estimation of interactions that interest the experiments. Webb used ad hoc methods to find these plans; hence, there was still no unified structure to those experiments. In this paper, we develop the methods to construct the $2^{n}3^3$ and $2^{1}3^3$ designs. The designs constructed by these methods not only supply orthogonal estimates of all the main effects but also permit estimation of all the two-factor interactions not involving the quadratic effects. Furthermore, the designs we find are nearly orthogonal.

• East Asian mathematical journal
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• v.24 no.2
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• pp.177-186
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• 2008

In this paper, we introduce and study a new class of system of parametric general quasivariational-like inequalities. Using $\eta$-subdifferential and $\eta$-proximal mappings of proper functionals in Hilbert spaces, we prove the equivalence between the system of parametric general quasivariational-like inequalities and a xed point problem and construct two iterative algorithms. A few existence and uniqueness results as well as the sensitivity analysis of solutions are also established for the system of parametric general quasivariational-like inequalities, and some convergence results of iterative sequence generated by the algorithms are proved. Our results extend a few known results in the literature.