• The Mathematical Education
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• v.10 no.2
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• pp.4-8
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• 1972

We consider the class (equation omitted) of all k-degenerate graphs, for k a non-negative integer. The class (equation omitted) and (equation omitted) are exactly the classes of totally disconnected graphs and of forests, respectively; the classes (equation omitted) and (equation omitted) properly contain all outerplanar and planar graphs respectively. The advantage of this view point is that many of the known results for chromatic number and point arboricity have natural extensions, for all larger values of k. The purpose of this note is to show that a graph G is (P$^3$)-realizable if G is planar and 3-degenerate.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.485-506
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• 2015

Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the forbidden number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.8
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• pp.1239-1249
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• 1990

In this paper, using the neural network design techniques, an adaptive Mahalanobis distance classifier(AMDC) is designed. This classifier has three layers: input layer, internal layer and output layer. The connection from input layer to internal layer is fully connected, and that from internal to output layer has partial connection that might be thought as an Oring. If two ormore clusters of patterns of one class are laid apart in the feature space, the network adaptively generate the internal nodes, whhch are corresponding to the subclusters of that class. The number of the output nodes in just same as the number of the classes to classify, on the other hand, the number of the internal nodes is defined by the number of the subclusters, and can be optimized by itself. Using the method of making the subclasses, the different patterns that are of the same class can easily be distinguished from other classes. If additional training is needed after the completion of the traning, the AMDC does not have to repeat the trainging that has already done. To test the performance of the AMDC, the experiments of classifying 500 Hangeuls were done. In experiment, 20 print font sets of Hangeul characters(10,000 cahracters) were used for training, and with 3 sets(1,500 characters), the AMDC was tested for various initial variance \ulcornerand threshold \ulcorner and compared with other statistical or neural classifiers.

• Journal of the Korean Institute of Educational Facilities
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• v.16 no.6
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• pp.3-12
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• 2009

Reports on population movement(2000-2030) by the National Statistical Office show that the number of elementary school age population will be decreased by 1.4million from 2005 to 2020. It will effect both school size and the policies for school facilities, which have focused on downsizing class as the high standard of OECD nations. As the unfolding evidence is emerging that a number of schools and classes will be emptied out by 2030. This study aims at developing a objective and scientific device for estimate the number of students at future and evaluating the validity of school establishment. In doing so, it explores the relationship between the changing factors and the number of students. It proposes four factors such as the changes of population, the fertility rate, the number of apartment occupant and movement of population. As the result of the statistic analysis on the correlation coefficient, it finds out that the change of apartment occupant has a close correlation with the change in the number of student and has a deep effect on the establishment of school. Finally, it shows the construction of school according to urban developments during 1999-2008 in Incheon Metro-City. This study would help the authorities to expect the future number of student and to restrict overbuilding of surplus classes, finally the reasonable expenditure for school facilities.

• Structural Engineering and Mechanics
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• v.70 no.3
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• pp.367-380
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• 2019

The paper concerns topology and geometry optimization of statically determinate beams with arbitrary number of supports. The optimization problem is treated as a bi-criteria one, with the objectives of minimizing the absolute maximum bending moment and the maximum deflection for a uniform gravity load. The problem is formulated and solved using the Pareto optimality concept and the lexicographic ordering of the objectives. The non-dominated sorting genetic algorithm NSGA-II and the local search method are used for the optimization in the Pareto sense, whereas the genetic algorithm and the exhaustive search method for the lexicographic optimization. Trade-offs between objectives are examined and sets of Pareto-optimal solutions are provided for different topologies. Lexicographically optimal beams are found assuming that the maximum moment is a more important criterion. Exact formulas for locations and values of the maximum deflection are given for all lexicographically optimal beams of any topology and any number of supports. Topologies with lexicographically optimal geometries are classified into equivalence classes, and specific features of these classes are discussed. A qualitative principle of the division of topologies equivalent in terms of the maximum moment into topologies better and worse in terms of the maximum deflection is found.

• Proceedings of the Korean Society for Emotion and Sensibility Conference
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• 2001.05a
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• pp.131-135
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• 2001

Recently, Internet is used widely. Many Web sites, however, are not designed based on user's view. So, this research aimed at grasping the user needs and structure of Web site which user used easily. First, to grasp user needs, questionnaires about the motivation, the purpose and the evaluation items of Web page were done. As a result, we found the easiness for the user. Next, we made subjects operated test pages in which the number of classes and the amount of information were changed. We collected the quantitative data of the optimum number of classes, amount of information and retrieval time. As a result, there was a significant difference in each numerical value. The results of this research are available when constructing a web site. so, usability of Web site can be improved by them.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.181-193
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• 1997

The enumeration of various classes of paths in the real plane has an important implications in the area of combinatorics wit statistical applications. In 1887, D. Andre [3, pp. 21] first solved the famous ballot problem, formulated by Berttand [2], by using the well-known reflection principle which contributed tremendously to resolve the problems of enumeration of various classes of lattice paths in the plane. First, it is necessary to state the definition of NSEW-paths in the palne which will be employed throughout the paper. From [3, 10, 11], we can find results concerning many of the basics discussed in section 1 and 2.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1485-1495
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• 2019

The purpose of this paper is to compute the number of semistar operations of certain classes of finite dimensional $Pr{\ddot{u}}fer$ domains. We prove that ${\mid}SStar(R){\mid}={\mid}Star(R){\mid}+{\mid}Spec(R){\mid}+ {\mid}Idem(R){\mid}$ where Idem(R) is the set of all nonzero idempotent prime ideals of R if and only if R is a $Pr{\ddot{u}}fer$ domain with Y -graph spectrum, that is, R is a $Pr{\ddot{u}}fer$ domain with exactly two maximal ideals M and N and $Spec(R)=\{(0){\varsubsetneq}P_1{\varsubsetneq}{\cdots}{\varsubsetneq}P_{n-1}{\varsubsetneq}M,N{\mid}P_{n-1}{\varsubsetneq}N\}$. We also characterize non-local $Pr{\ddot{u}}fer$ domains R such that ${\mid}SStar(R){\mid}=7$, respectively ${\mid}SStar(R){\mid}=14$.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.25 no.5
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• pp.31-38
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• 2002

In this paper, we model a two-server queueing system with priority, to which we put a restriction on the number of servers for each customer class. customers are divided into two different classes. Class 1 customers have non-preemptive priority over class 2 customers. They are served by both servers when available but class 2 customers are served only by a designated server. We use a method of generating function depending on the state of servers. We find the generating function of the number of customers in queue, server utilization, mean queue length and mean waiting time for each class of customers.

• Industrial Engineering and Management Systems
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• v.13 no.4
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• pp.357-368
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• 2014

Since its birth in 1993, fuzzy time series have seen different classes of models designed and applied, such as fuzzy logic relation and rule-based models. These models have both advantages and disadvantages. The major drawbacks with these two classes of models are the difficulties encountered in identification and analysis of the model. Therefore, there is a strong need to explore new alternatives and this is the objective of this paper. By transforming a fuzzy number to a real number via integrating the inverse of the membership function, new autoregressive models can be developed to fit the observation values of a fuzzy time series. With the new models, the issues of model identification and parameter estimation can be addressed; and trends, seasonalities and multivariate fuzzy time series could also be modeled with ease. In addition, asymptotic behaviors of fuzzy time series can be inspected by means of characteristic equations.