• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1911-1916
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• 2003

Parameter set of an LPV system is divided into a number of subsets so that robust feedback gains may be designed for each subset of parameters. A concept of quasi-invariant set is introduced, which allows finite steps of delay in reentrance to the set. A feasible and positively invariant set with respect to a gain-scheduled state feedback control can be easily obtained from the quasi-invariant set. A receding horizon control strategy can be derived based on this feasible and invariant set.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.697-712
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• 1995

In the present article we consider multiparameter maximal averages and discover the crucial roles played by the number of parameters in their boundedness properties. The problem we shall deal with is initiated by Rubio de Francia [8] and will be in the spirit of an inductive extension to multiparameter cases, in which tools of our study rely on the theory of Harmonic Analysis on product spaces. Suppose that $d_\mu$ is a complex Borel measure supported on a compact subset S of $R^N$ having total mass one, $\smallint_S d_\mu = 1$.

• Journal of the Korean Mathematical Society
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• v.41 no.4
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• pp.737-746
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• 2004

In this paper, from the KKM theorem, we deduce almost fixed point theorems for convex-valued u.s.c. (or l.s.c.) multimaps satisfying certain conditions originated from Zima [19]. From these results, we obtain various fixed point theorems which extend a number of known results.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.287-293
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• 2010

It is well known that there is a residual subset J of the space of $C^1$-diffeomorphisms on a compact Riemannian manifold M such that the maps f $\mapsto$ chain recurrent set of f and f $\mapsto$ number of chain components of f are continuous on J. In this paper we get the flow version of the above results on diffeomorphisms.

• IE interfaces
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• v.16 no.spc
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• pp.132-137
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• 2003

We consider scheduling jobs on multipurpose machines where jobs can be processed by a subset of the machines operated in parallel with the objective of minimizing makespan. We apply LPT(Longest Processing Time first) algorithm and prove that its posterior worst-case performance ratio is at most $log_24m/(1+{\lambda})$, where \lambda is the number of machines eligible for processing the job with the latest completion time. In general, LPT is shown to always find a schedule with makespan at most $log_24m/3$ times optimum.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1995.10b
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• pp.218-223
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• 1995

A new design scheme of a binary decision tree is proposed. In this scheme a binary decision tree is constructed by using genetic algorithm and FCM algorithm. At each node optimal or near-optimal feature or feature subset among all the available features is selected based on fitness function in genetic algorithm which is inversely proportional to classification error, balance between cluster, number of feature used. The proposed design scheme is applied to the handwtitten alphabetic characters. Experimental results show the usefulness of the proposed scheme.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.435-440
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• 2006

Let G be a simple graph with vertex set V(G) and edge set E(G). A subset S of E(G) is called an edge cover of G if the subgraph induced by S is a spanning subgraph of G. The maximum number of edge covers which form a partition of E(G) is called edge covering chromatic number of G, denoted by X'c(G). It is known that for any graph G with minimum degree ${\delta},\;{\delta}-1{\le}X'c(G){\le}{\delta}$. If $X'c(G) ={\delta}$, then G is called a graph of CI class, otherwise G is called a graph of CII class. It is easy to prove that the problem of deciding whether a given graph is of CI class or CII class is NP-complete. In this paper, we consider the classification of nearly bipartite graph and give some sufficient conditions for a nearly bipartite graph to be of CI class.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.391-402
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• 2022

For a given graph G = (V, E), a dominating set is a subset V' of the vertex set V so that each vertex in V ＼ V' is adjacent to a vertex in V'. The minimum cardinality of a dominating set of G is called the domination number of G and is denoted by γ(G). For an integer k ≥ 1, the k-th power G^k of a graph G with V (G^k) = V (G) for which uv ∈ E(G^k) if and only if 1 ≤ d_G(u, v) ≤ k. Note that G² is the square graph of a graph G. In this paper, we obtain some tight bounds for the sum of the domination numbers of a graph and its square graph in terms of the order, order and size, and maximum degree of the graph G. Also, we characterize such extremal graphs.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.10
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• pp.5132-5148
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• 2017

Cyber attacks are evolving commensurate with recent developments in information security technology. Intrusion detection systems collect various types of data from computers and networks to detect security threats and analyze the attack information. The large amount of data examined make the large number of computations and low detection rates problematic. Feature selection is expected to improve the classification performance and provide faster and more cost-effective results. Despite the various feature selection studies conducted for intrusion detection systems, it is difficult to automate feature selection because it is based on the knowledge of security experts. This paper proposes a feature selection technique to overcome the performance problems of intrusion detection systems. Focusing on feature selection, the first phase of the proposed system aims at constructing a feature subset using a sequential forward floating search (SFFS) to downsize the dimension of the variables. The second phase constructs a classification model with the selected feature subset using a random forest classifier (RFC) and evaluates the classification accuracy. Experiments were conducted with the NSL-KDD dataset using SFFS-RF, and the results indicated that feature selection techniques are a necessary preprocessing step to improve the overall system performance in systems that handle large datasets. They also verified that SFFS-RF could be used for data classification. In conclusion, SFFS-RF could be the key to improving the classification model performance in machine learning.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.237-242
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• 1994

One of the most well-known geometric lattices is a partition lattice. Every upper interval of a partition lattice is a partition lattice. The whitney numbers of a partition lattices are the Stirling numbers, and the characteristic polynomial is a falling factorial. The set of partitions with a single non-trivial block containing a fixed element is a Boolean sublattice of modular elements, so the partition lattice is supersolvable in the sense of Stanley [6]. In this paper, we rephrase four results due to Heller[1] and Murty [4] in terms of matroids and give several characterizations of partition lattices. Our notation and terminology follow those in [8,9]. To clarify our terminology, let G, be a finte geometric lattice. If S is the set of points (or rank-one flats) in G, the lattice structure of G induces the structure of a (combinatorial) geometry, also denoted by G, on S. The size vertical bar G vertical bar of the geometry G is the number of points in G. Let T be subset of S. The deletion of T from G is the geometry on the point set S/T obtained by restricting G to the subset S/T. The contraction G/T of G by T is the geometry induced by the geometric lattice [cl(T), over ^1] on the set S' of all flats in G covering cl(T). (Here, cl(T) is the closure of T, and over ^ 1 is the maximum of the lattice G.) Thus, by definition, the contraction of a geometry is always a geometry. A geometry which can be obtained from G by deletions and contractions is called a minor of G.