• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.619-621
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• 2009

We exhibit an example that the scaling property of Hausdorff measure on $\mathbb{R}^{\infty}$ does not hold.

• Journal of The Korean Society of Agricultural Engineers
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• v.48 no.1
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• pp.41-48
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• 2006

In the evaluation of rural amenities, its properties are related with social, cultural, and environmental elements. In this study, Information Measure Model (IMM) and Cultural Property Priority Assessment Model (CPPAM) were developed adapting information measure model with text based surveying data. To apply developed model not only general properties but also specific surveyed data, Specific Information Gathering and Utilizing System (SIGUS) was constructed using the data in Dusan World encyclopedia. IMM shows priorities of cultural property by information in national-designated cultural properties. And CPPAM applied in surveying data in 2004 by Rural Resources Development Institute.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.28B no.10
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• pp.761-770
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• 1991

This paper suggests a measure constraint locus for characterization of the performance of a subtask for a redundant robot. The measure constraint locus are the loci of points satisfying the necessary constraint for optimality of measure in the joint configuration space. To uniquely obtain an inverse kinematic solution, one must consider both measure constraint locus and self-motion manifolds which are set of homogeneous solutions. Using measure constraint locus for maniqulability measure, the invertible workspace without singularities and the topological property of the configuration space for linding equilibrium configurations are analyzed. We discuss some limitations based on the topological arguments of measure constraint locus, of the inverse kinematic algorithm for a cyclic task. And the inverse kinematic algorithm using global maxima on self-motion manifolds is proposed and its property is studied.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.935-955
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• 2020

In this paper we present a measurable version of the Smale's spectral decomposition theorem for homeomorphisms on compact metric spaces. More precisely, we prove that if a homeomorphism f on a compact metric space X is invariantly measure expanding on its chain recurrent set CR(f) and has the eventually shadowing property on CR(f), then f has the spectral decomposition. Moreover we show that f is invariantly measure expanding on X if and only if its restriction on CR(f) is invariantly measure expanding. Using this, we characterize the measure expanding diffeomorphisms on compact smooth manifolds via the notion of Ω-stability.

• The Mathematical Education
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• v.6 no.2
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• pp.1-9
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• 1968

In mathematics, a definition must have authentic reasons to be defined so. On defining geometric figures, there must be adequencies in sequel and consistency in the concepts of figures, though the dimensions of them are different. So we can avoid complicated thoughts from the study of geometric property. From the texts of SMSG, UICSM and others, we can find easily that the same concepts are not kept up on defining some figures such as ray and segment on a line, angle and polygon on a plane, and polyhedral angle and polyhedron on a 3-dimensionl space. And the measure of angle is not well-defined on basis of measure theory. Moreover, the concepts for interior, exterior, and frontier of each figure used in these texts are different from those of general topology and algebraic topology. To avoid such absurdness, I myself made new terms and their definitions, such as 'gan' instead of angle, 'polygonal region' instead of polygon, and 'polyhedral solid' instead of polyhedron, where each new figure contains its interior. The scope of this work is hmited to the fundamental idea, and it merely has dealt with on the concepts of measure, dimension, and topological property. In this case, the measure of a figure is a set function of it, so the concepts of measure is coincided with that of measure theory, and we can deduce the topological property for it from abstract stage. It also presents appropriate concepts required in much clearer fashion than traditional method.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.71-80
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• 2002

We give a formulation of the large deviation property for rescalings of random measures on the d-dimensional Euclidean space R$^{d}$ . The approach is global in the sense that the objects are Radon measures on R$^{d}$ and the dual objects are the continuous functions with compact support. This is applied to the cluster random measures with Poisson centers, a large class of random measures that includes the Poisson processes.

• Journal of Korea Society of Digital Industry and Information Management
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• v.6 no.4
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• pp.11-20
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• 2010

Ontology is important role in semantic web to construct and query semantic data. Because of dynamic characteristic of ontology, P2P environment is considered for ontology processing in web environment. For efficient processing of ontology in P2P environment, clustering of peers should be considered. When new peer is added to the network, cluster allocation problem of the new peer is important for system efficiency. For clustering of peers with similar chateristics, similarlity measure method of ontology in added peer with ontologies in other clusters is needed. In this paper, we propose similarity measure techniques of ontologies for clustering of peers. Similarity measure method in this paper considered ontology's strucural characteristics like schema, class, property. Results of experiments show that ontologies of similar topics, class, property can be allocated to the same cluster.

• Communications for Statistical Applications and Methods
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• v.31 no.4
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• pp.459-466
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• 2024

Multivariate regular variation is a popular framework of multivariate extreme value analysis. However, a suitable parametric model needs to be introduced for efficient estimation of its spectral measure. In such a view, elliptical distributions have been employed for deriving such models. On the other hand, the second order behavior of multivariate regular variation has to be specified for investigating the property of the estimator. This paper derives such a behavior by imposing a widely adopted second order regular variation condition on the representation of elliptical distributions. As result, the second order variation for the convergence to spectral measure is characterized by a signed measure with a regular varying index. Moreover, it leads to the asymptotic bias of the estimator. For demonstration, multivariate t-distribution is considered.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.241-246
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• 2013

Choi [1] identified and characterized the limiting diffusion of this diploid model by defining discrete generator for the rescaled Markov chain. In this note, we define the operator of projection $S_t$ on limiting diffusion and new measure $dQ=S_tdP$. We show the martingale property on this operator and measure. Also we conclude that the martingale problem for diffusion operator of projection is well-posed.

• Journal of Korean Society for Quality Management
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• v.44 no.3
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• pp.527-540
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• 2016

Purpose: The purpose of this study was to propose contrast metric which is based on the human visual perception and thus it can be used to improve the quality of digital images in many applications. Methods: Previous literatures are surveyed, and then the proposed method is modeled based on Human Visual System(HVS) such as multiscale property of the contrast sensitivity function (CSF), contrast constancy property (suprathreshold), color channel property. Furthermore, experiments using digital images are shown to prove the effectiveness of the method. Results: The results of this study are as follows; regarding the proposed contrast measure of complex images, it was found by experiments that HVS follows relatively well compared to the previous contrast measurement. Conclusion: This study shows the effectiveness on how to measure the contrast of complex images which follows human perception better than other methods.