• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.2
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• pp.157-160
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• 2003

In this paper, we describe how to represent lower case hand-written English alphabets by a sequence of two to seven fuzzy sets. Each fuzzy set represents an arc segment of the character and each arc segment is assumed to be a part of an ellipse. The part of an ellipse is defined by five quantities; its short and long radii, its orientation angle, whether it is a part of the lower half or the upper half, and whether it is the full half or a part of a half. Hence, we use the Cartesian product of five fuzzy sets to represent each arc segment. We show that this representation is a translation, rotation, and scaling invariant and that it can be used to generate the hand-written English alphabets. The representation we describe is different from the one proposed earlier by the author and when compared with the previous representation, the one described in this paper simulates more closely the behavior of how one writes English characters.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.185-199
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• 2020

In this paper, we introduce the definitions of s_p-convergent sequence in fuzzy metric spaces and fuzzy normed spaces. We investigate relations of convergence, s_p-convergence, s_∞-convergence and st-convergence in fuzzy metric spaces and fuzzy normed spaces. We also study s_p-convergence, s_∞-convergence and st-convergence using the sub-sequence of convergent sequence in fuzzy metric spaces and fuzzy normed spaces. Stationary fuzzy normed spaces are defined and investigated. We finally define s_p-closed sets, s_∞-closed sets and st-closed sets in fuzzy metric spaces and fuzzy normed spaces and investigate relations of them.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.277-294
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• 2016

The aim of this paper is to present the classical sets of sequences and related matrix transformations with respect to the b-metric. Also, we introduce the relationships between these sets and their classical forms with corresponding properties including convergence and completeness. Further we determine the duals of the new spaces and characterize matrix transformations on them into the sets of b-bounded, b-convergent and b-null sequences.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.39-47
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• 2009

Pan, Shen and Woo [8] introduced the concept of the G-sequence of a map. We introduce the G'-sequence of a map, which is a dual concept of the G-sequence of a map. We obtain some sufficient conditions for the all sets in the G'-sequence of a map are groups, and for the exact G'-sequence of a map.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.899-908
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• 2017

We call a sequence $(T_n)_n$ of bounded operators on a Banach space X, BSC-Sequence if it is a Cauchy sequence in the strong operator topology and is uniformly bounded below. We determine conditions under which such sequences has a fixed point.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.32-35
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• 2003

In this paper, we describe how to represent lower case hand-written English alphabets by a sequence of two to seven fuzzy sets. Each fuzzy set represents an arc segment of the character and each arc segment is assumed to be a part of an ellipse. The part of an ellipse is defined by five quantities: its short and long radii, its orientation angle, whether it is a part of the lower half or the upper half and whether it is the full half or a part of a half. Hence, we use the Cartesian product of five fuzzy sets to represent each arc segment. We show that this representation is a translation, rotation, and scaling invariant and that it can be used to generate the hand-written English alphabets. The representation we describe is different from the one proposed earlier by the author and when compared with the previous representation, the one described in this paper simulates more closely the behavior of how one writes English characters.

• Mycobiology
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• v.42 no.1
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• pp.46-51
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• 2014

A degenerated strain of Pleurotus eryngii KNR2312 was isolated from a commercial farm. Random amplified polymorphic DNA analysis performed on the genomic DNA of the normal and degenerated strains of this species revealed differences in the DNA banding pattern. A unique DNA fragment (1.7 kbp), which appeared only in the degenerated strain, was isolated and sequenced. Comparing this sequence with the KNR2312 genomic sequence showed that the sequence of the degenerated strain comprised three DNA regions that originated from nine distinct scaffolds of the genomic sequence, suggesting that chromosome-level changes had occurred in the degenerated strain. Using the unique sequence, three sets of PCR primers were designed that targeted the full length, the 5' half, and the 3' half of the DNA. The primer sets P2-1 and P2-2 yielded 1.76 and 0.97 kbp PCR products, respectively, only in the case of the degenerated strain, whereas P2-3 generated a 0.8 kbp product in both the normal and the degenerated strains because its target region was intact in the normal strain as well. In the case of the P2-1 and P2-2 sets, the priming regions of the forward and reverse primers were located at distinct genomic scaffolds in the normal strain. These two primer sets specifically detected the degenerate strain of KNR2312 isolated from various mushrooms including 10 different strains of P. eryngii, four strains of P. ostreatus, and 11 other wild mushrooms.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.433-444
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• 2022

In the present paper, we introduce some new notions of Wijsman ${\mathcal{I}}$-statistical convergence with the use of Orlicz function, lacunary sequence and triple sequences of sets, and obtain some analogous results from the new definitions point of views.

• Research in Mathematical Education
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• v.8 no.4
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• pp.279-291
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• 2004

Mandelbrot sets and its generalizations have been extensively studied by using the Picard iterations. The purpose of this paper is to study superior Mandelbrot sets, a new class of Mandelbrot sets by introducing the Mann iterative procedure for polynomials Q$_{c}$(z) := z$^n$ + c. We generate some superior Mandelbrot sets for different values of n ($\geq$2) and these new figures are exciting and fascinating.g.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1623-1639
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• 2017

The generalized coGottlieb sets are not known to be groups in general. We study some conditions which make them groups. Moreover, there are actions on the generalized coGottlieb sets which are different from known actions up to now. We give related exact sequence of the generalized coGottlieb sets. Using them, we obtain certain results related to the maps which preserve generalized coGottlieb sets.