• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.235-244
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• 2024

In this paper, we establish relations between the sets of strongly Cesàro summable sequences of complex numbers for modulus functions f and g satisfying various conditions. Furthermore, for some special modulus functions, we obtain relations between the sets of strongly Cesàro summable and statistically convergent sequences of complex numbers.

• Journal of Communications and Networks
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• v.14 no.3
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• pp.230-236
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• 2012

Based on the known binary sequence sets and Gray mapping, a new method for constructing quaternary sequence sets is presented and the resulting sequence sets' properties are investigated. As three direct applications of the proposed method, when we choose the binary aperiodic, periodic, and Z-complementary sequence sets as the known binary sequence sets, the resultant quaternary sequence sets are the quaternary aperiodic, periodic, and Z-complementary sequence sets, respectively. In comparison with themethod proposed by Jang et al., the new method can cope with either both the aperiodic and periodic cases or both even and odd lengths of sub-sequences, whereas the former is only fit for the periodic case with even length of sub-sequences. As a consequence, by both our and Jang et al.'s methods, an arbitrary binary aperiodic, periodic, or Z-complementary sequence set can be transformed into a quaternary one no matter its length of sub-sequences is odd or even. Finally, a table on the existing quaternary periodic complementary sequence sets is given as well.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.83-116
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• 2020

Let G be a finite group. By a sequence over G, we mean a finite unordered sequence of terms from G, where repetition is allowed, and we say that it is a product-one sequence if its terms can be ordered such that their product equals the identity element of G. The large Davenport constant D(G) is the maximal length of a minimal product-one sequence, that is, a product-one sequence which cannot be factored into two non-trivial product-one subsequences. We provide explicit characterizations of all minimal product-one sequences of length D(G) over dihedral and dicyclic groups. Based on these characterizations we study the unions of sets of lengths of the monoid of product-one sequences over these groups.

• 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 Information Technology and Architecture
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• v.9 no.1
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• pp.11-19
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• 2012

Generally, a suffix tree is an efficient data structure since it reveals the detailed internal structures of given sequences within linear time. However, it is difficult to implement a suffix tree for a large number of sequences because of memory size constraints. Therefore, in order to compare multi-mega base genomic sequence sets using suffix trees, there is a need to re-construct the suffix tree algorithms. We introduce a new method for constructing a suffix tree on secondary storage of a large number of sequences. Our algorithm divides three files, in a designated sequence, into parts, storing references to the locations of edges in hash tables. To execute experiments, we used 1,300,000 sequences around 300Mbyte in EST to generate a suffix tree on disk.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1057-1073
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• 2020

In this paper, we study some of the factorization aspects of rational multicyclic monoids, that is, additive submonoids of the nonnegative rational numbers generated by multiple geometric sequences. In particular, we provide a complete description of the rational multicyclic monoids M that are hereditarily atomic (i.e., every submonoid of M is atomic). Additionally, we show that the sets of lengths of certain rational multicyclic monoids are finite unions of multidimensional arithmetic progressions, while their unions satisfy the Structure Theorem for Unions of Sets of Lengths. Finally, we realize arithmetic progressions as the sets of distances of some additive submonoids of the nonnegative rational numbers.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.7
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• pp.525-530
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• 2004

A classifier was constructed by using a generalized regression neural network (GRU) and random generator (RG), which was applied to classify DNA sequences. Three data sets evaluated are eukaryotic and prokaryotic sequences (Data-I), eukaryotic sequences (Data-II), and prokaryotic sequences (Data-III). For each data set, the classifier performance was examined in terms of the total classification sensitivity (TCS), individual classification sensitivity (ICS), total prediction accuracy (TPA), and individual prediction accuracy (IPA). For a given spread, the RG played a role of generating a number of sets of spreads for gaussian functions in the pattern layer Compared to the GRNN, the RG-GRNN significantly improved the TCS by more than 50%, 60%, and 40% for Data-I, Data-II, and Data-III, respectively. The RG-GRNN also demonstrated improved TPA for all data types. In conclusion, the proposed RG-GRNN can effectively be used to classify a large, multivariable promoter sequences.

• Journal of Communications and Networks
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• v.12 no.4
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• pp.330-333
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• 2010

In this paper, using binary (N, M, L, $\epsilon$) low correlation zone (LCZ) sequence sets, we construct new quaternary LCZ sequence sets with parameters (2N, 2M, L, $2{\epsilon}$). Binary LCZ sequences for the construction should have period $N\;{\equiv}\;3$ mod 4, L|N, and the balance property. The proposed method corresponds to a quaternary extension of the extended construction of binary LCZ sequence sets proposed by Kim, Jang, No, and Chung [1].

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.1
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• pp.21-32
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• 2002

In this paper, for any prime q, new cyclic difference sets with Singer parameter equation omitted are constructed by using the q-ary sequences (d-homogeneous functions) of period $q_n$-1. When q is a power of 3, new cyclic difference sets with Singer parameter equation omitted are constructed from the ternary sequences of period $q_n$-1 with ideal autocorrealtion found by Helleseth, Kumar and Martinsen.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.515-525
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• 1998

In this paper we obtain a "compactness" result that asserts the existence, in certain sets of sequences, of a sequence which has a maximal reciprocal sum. We derive this result from a much more general theorem which will be proved by introducing a metric into the set of sequences and using a topological argument.