• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.167-172
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• 1992

In this paper, we introduce $T_0$, $T_1$ and Hausdorff axioms in fibrewise convergence spaces as a generalization of fibrewise topological spaces and of convergence spaces. Furthermore we investigate some results about the fibrewise Hausdorff convergence space.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.303-319
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• 2021

In this paper, we introduce the concepts of Wijsman strongly p-lacunary summability of order 𝛼, Wijsman lacunary statistical convergence of order 𝛼 and Hausdorff lacunary statistical convergence of order 𝛼 for double set sequences. Also, we investigate some properties of these new concepts and examine the existence of some relationships between them. Furthermore, we study the relationships between these new concepts and some concepts in the literature.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.87-94
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• 2003

We use geometric properties of Gromov-Hausdorff-convergence to present a way to construct rough but natural invariants of metric geometry.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.189-193
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• 1998

In this paper we construct a sequence of spaces which has Gromov-Hausdorff limit such that a geodesic in the limit space is not realized as a limit of geodesics in the spaces of the sequence. This contrasts with the result of Grove and Petersen in [1] where they proved otherwise for Alexandrov spaces with common curvature bounds.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.35-43
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• 2011

In this paper we define the convergence of ${\delta}$-filters and study them. We show that ${\delta}$-filters on a Hausdorff space X converge at most one point in X. We also show that in a P-space X, ${\delta}$-filters on X converge at most one point in X if and only if X is a Hausdorff space.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.137-148
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• 2002

The notion of Interval Valued Fuzzy Sets (IVF sets) was introduced by T. K. Mondal. In this paper a notion of IVF filter is introduced and studied. A new notion of Hausdorffness, which can not be defined in crisp theory of filters, is defined on IVF filters and their properties are studied.

• Journal of information and communication convergence engineering
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• v.13 no.2
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• pp.74-80
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• 2015

In cognitive radios, spectrum sensing plays an important role in accurately detecting the presence or absence of a licensed user. However, the intervention of malicious users (MUs) degrades the performance of spectrum sensing. Such users manipulate the local results and send falsified data to the data fusion center; this process is called spectrum sensing data falsification (SSDF). Thus, MUs degrade the spectrum sensing performance and increase uncertainty issues. In this paper, we propose a method based on the Hausdorff distance and a similarity measure matrix to measure the difference between the normal user evidence and the malicious user evidence. In addition, we use the Dempster-Shafer theory to combine the sets of evidence from each normal user evidence. We compare the proposed method with the k-means and Jaccard distance methods for malicious user detection. Simulation results show that the proposed method is effective against an SSDF attack.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.1035-1049
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• 2023

Approximation of functions of Lipschitz and Zygmund classes have been considered by various researchers under different summability means. In the proposed study, we investigated an estimation of the order of convergence of a function associated with Hardy-Littlewood series in the weighted Zygmund class W(Z^(𝜔)_r)-class by applying Euler-Hausdorff summability means and subsequently established some (presumably new) results. Moreover, the results obtained here represent the generalization of several known results.

• Journal of the Institute of Convergence Signal Processing
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• v.7 no.1
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• pp.11-16
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• 2006

To manipulate large video databases, effective video indexing and retrieval are required. A large number of video indexing and retrieval algorithms have been presented for frame-w]so user query or video content query whereas a relatively few video sequence matching algorithms have been proposed for video sequence query. In this paper, we propose an efficient algorithm to extract key frames using color histograms and to match the video sequences using edge features. To effectively match video sequences with low computational load, we make use of the key frames extracted by the cumulative measure and the distance between key frames, and compare two sets of key frames using the modified Hausdorff distance. Experimental results with several real sequences show that the proposed video retrieval algorithm using color and edge features yields the higher accuracy and performance than conventional methods such as histogram difference, Euclidean metric, Battachaya distance, and directed divergence methods.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.765-782
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• 1998

The purpose of this paper is to give convergence theorems both for closed convex set valued and relative fuzzy valued martingales, and sub- and super- martingales. These kinds of martingales, sub- and super-martingales are the extension of classical real valued martingales, sub- and super-martingales. Here we compare two kinds of convergences, in the Hausdorff metric and in the Kuratowski-Mosco sense. We also introduce a new convergence for the fuzzy valued case in the graph sense and obtain convergence theorems.