• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.89-99
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• 1992

In this paper we will prove some theorems on the period and the linear complexity of certain sequences in GF(q) which are generated by combining two sequences in a reasonable way. In fact these theorems are generalizations of the main result in [1]. A sequence of elements of GF(2) is called a binary sequence. In recent years considerable interest has been shown in the generation of binary sequences which have good properties. Such binary sequences play an important role in a stream cipher system.

• Proceedings of the KSRS Conference
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• v.2
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• pp.627-630
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• 2006

Sequential Pattern Mining is the mining approach which addresses the problem of discovering the existent maximal frequent sequences in a given databases. In the daily and scientific life, sequential data are available and used everywhere based on their representative forms as text, weather data, satellite data streams, business transactions, telecommunications records, experimental runs, DNA sequences, histories of medical records, etc. Discovering sequential patterns can assist user or scientist on predicting coming activities, interpreting recurring phenomena or extracting similarities. For the sake of that purpose, the core of sequential pattern mining is finding the frequent sequence which is contained frequently in all data sequences. Beside the discovery of frequent itemsets, sequential pattern mining requires the arrangement of those itemsets in sequences and the discovery of which of those are frequent. So before mining sequences, the main task is checking if one sequence is a subsequence of another sequence in the database. In this paper, we implement the subsequence matching method as the preprocessing step for sequential pattern mining. Matched sequences in our implementation are the normalized sequences as the form of number chain. The result which is given by this method is the review of matching information between input mapped sequences.

• Korean Journal of Remote Sensing
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• v.22 no.5
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• pp.457-462
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• 2006

Sequential Pattern Mining is the mining approach which addresses the problem of discovering the existent maximal frequent sequences in a given databases. In the daily and scientific life, sequential data are available and used everywhere based on their representative forms as text, weather data, satellite data streams, business transactions, telecommunications records, experimental runs, DNA sequences, histories of medical records, etc. Discovering sequential patterns can assist user or scientist on predicting coming activities, interpreting recurring phenomena or extracting similarities. For the sake of that purpose, the core of sequential pattern mining is finding the frequent sequence which is contained frequently in all data sequences. Beside the discovery of frequent itemsets, sequential pattern mining requires the arrangement of those itemsets in sequences and the discovery of which of those are frequent. So before mining sequences, the main task is checking if one sequence is a subsequence of another sequence in the database. In this paper, we implement the subsequence matching method as the preprocessing step for sequential pattern mining. Matched sequences in our implementation are the normalized sequences as the form of number chain. The result which is given by this method is the review of matching information between input mapped sequences.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1383-1392
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• 2020

Let H_n be the n-th harmonic number and let ν_n be its denominator. Shiu proved that there are infinitely many positive integers n with ν_n = ν_n+1. Recently, Wu and Chen proved that the set of positive integers n with ν_n = ν_n+1 has density one. They also proved that the same result is true for the denominators of alternating harmonic numbers. In this paper, we prove that the result is true for the denominators of 𝜀-harmonic numbers, where 𝜀 = {𝜀_i}^∞_i=1 is a pure recurring sequence with 𝜀_i ∈ {-1, 1}.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.1-16
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• 2019

Let a, b, P, and Q be real numbers with $PQ{\neq}0$ and $(a,b){\neq}(0,0)$. The Horadam sequence $\{W_n\}$ is defined by $W_0=a$, $W_1=b$ and $W_n=PW_{n-1}+QW_{n-2}$ for $n{\geq}2$. Let the sequence $\{X_n\}$ be defined by $X_n=W_{n+1}+QW_{n-1}$. In this study, we obtain some new identities between the Horadam sequence $\{W_n\}$ and the sequence $\{X_n\}$. By the help of these identities, we show that Diophantine equations such as $$x^2-Pxy-y^2={\pm}(b^2-Pab-a^2)(P^2+4),\\x^2-Pxy+y^2=-(b^2-Pab+a^2)(P^2-4),\\x^2-(P^2+4)y^2={\pm}4(b^2-Pab-a^2),$$ and $$x^2-(P^2-4)y^2=4(b^2-Pab+a^2)$$ have infinitely many integer solutions x and y, where a, b, and P are integers. Lastly, we make an application of the sequences $\{W_n\}$ and $\{X_n\}$ to trigonometric functions and get some new angle addition formulas such as $${\sin}\;r{\theta}\;{\sin}(m+n+r){\theta}={\sin}(m+r){\theta}\;{\sin}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},\\{\cos}\;r{\theta}\;{\cos}(m+n+r){\theta}={\cos}(m+r){\theta}\;{\cos}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},$$ and $${\cos}\;r{\theta}\;{\sin}(m+n){\theta}={\cos}(n+r){\theta}\;{\sin}\;m{\theta}+{\cos}(m-r){\theta}\;{\sin}\;n{\theta}$$.

• International Journal of Contents
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• v.14 no.4
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• pp.70-75
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• 2018

The purpose of this corpus-based study was to find 4-word lexical bundles in computer science research articles. As the demand for research articles (RAs) for international publication increases, the need for acquiring field-specific writing conventions for this academic genre has become a burning issue. Particularly, one area of burgeoning interest in the examination of rhetorical structures and linguistic features of RAs is the use of lexical bundles, the indispensable building blocks that make up an academic discourse. To illustrate, different academic discourses rely on distinctive repertoires of lexical bundles. Because lexical bundles are often acquired as a whole, the recurring multi-word sequences can be retrieved automatically to make written discourse more fluent and natural. Therefore, the proper use of rhetorical devices specific to a particular discipline can be a vital indicator of success within the discourse communities. Hence, to identify linguistic features that make up specific registers, this corpus-based study examines the types and usage frequency of lexical bundles in the discipline of CS, one of the most in-demand fields world over. Given that lexical bundles are empirically-derived formulaic multi-word units, identifying core lexical bundles used in RAs, they may provide insights into the specificity of particular CS text types. This will in turn provide empirical evidence of register specificity and technicality within the academic discourse of computer science. As in the results, pedagogical implications and suggestions for future research are discussed.

• Journal of Plant Biotechnology
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• v.49 no.1
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• pp.39-45
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• 2022

Conserved domains are defined as recurring units in molecular evolution and are commonly used to interpret the molecular function and biochemical structure of proteins. Herein, the ADP-glucose pyrophosphorylase (AGPase) amino acid sequences of three species of the Ipomoea genus [Ipomoea trifida, I. triloba, and I. batatas (L.) Lam. (sweetpotato)] were identified to investigate their physicochemical and biochemical characteristics. The molecular weight, isoelectric point, instability index, and grand average of hyropathy markedly differed among the three species. The aliphatic index values of sweetpotato AGPase proteins were higher in the small subunit than in the large subunit. The AGPase proteins from sweetpotato were found to contain an LbH_G1P_AT_C domain in the C-terminal region and various domains (NTP_transferase, ADP_Glucose_PP, or Glyco_tranf_GTA) in the N-terminal region. Conversely, most of its two relatives (I. trifida and I. triloba) were found to only contain the NTP_transferase domain in the N-terminal region. These findings suggested that these conserved domains were species-specific and related to the subunit types of AGPase proteins. The study may enable research on the AGPase-related specific characteristics of sweetpotatoes that do not exist in the other two species, such as starch metabolism and tuberization mechanism.

• Asia Pacific Journal of Corpus Research
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• v.4 no.2
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• pp.1-39
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• 2023

Recent research in usage-based Second Language Acquisition has provided new insights into second language (L2) learners' development of formulaic language (Wulff, 2019). The current study examines the use of phrase-frames, which are recurring sequences of words including one or more variable slots (e.g., it is * that), in written and oral production data from Asian learners of English across four proficiency levels (beginner, low-intermediate, high-intermediate, advanced) and native English speakers. The variability, predictability, and discourse functions of the most frequent 4-word phrase-frames from the written essay and spoken dialogue sub-corpora of the International Corpus Network of Asian Learners of English (ICNALE) were analyzed and then compared across groups and modes. The results revealed that while learners' phrase-frames in writing became more variable and unpredictable as proficiency increased, no clear developmental patterns were found in speaking, although all groups used more fixed and predictable phrase-frames than the reference group. Further, no developmental trajectories in the functions of the most frequent phrase-frames were found in both modes. Additionally, lower-level learners and the reference group used more variable phrase-frames in speaking, whereas advanced-level learners showed more variability in writing. This study contributes to a better understanding of the development of L2 phraseological competence.

• Proceedings of the Korean Society for Bioinformatics Conference
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• 2001.10a
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• pp.61-86
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• 2001

All cancers are caused by abnormalities in DNA sequence. Throughout life, the DNA in human cells is exposed to mutagens and suffers mistakes in replication, resulting in progressive, subtle changes in the DNA sequence in each cell. Since the development of conventional and molecular cytogenetic methods to the analysis of chromosomal aberrations in cancers, more than 1,800 recurring chromosomal breakpoints have been identified. These breakpoints and regions of nonrandom copy number changes typically point to the location of genes involved in cancer initiation and progression. With the introduction of molecular cytogenetic methodologies based on fluorescence in situ hybridization (FISH), namely, comparative genomic hybridization (CGH) and multicolor FISH (m-FISH) in carcinomas become susceptible to analysis. Conventional CGH has been widely applied for the detection of genomic imbalances in tumor cells, and used normal metaphase chromosomes as targets for the mapping of copy number changes. However, this limits the mapping of such imbalances to the resolution limit of metaphase chromosomes (usually 10 to 20 Mb). Efforts to increase this resolution have led to the "new"concept of genomic DNA chip (1 to 2 Mb), whereby the chromosomal target is replaced with cloned DNA immobilized on such as glass slides. The resulting resolution then depends on the size of the immobilized DNA fragments. We have completed the first draft of its Korean Genome Project. The project proceeded by end sequencing inserts from a library of 96,768 bacterial artificial chromosomes (BACs) containing genomic DNA fragments from Korean ethnicity. The sequenced BAC ends were then compared to the Human Genome Project′s publicly available sequence database and aligned according to known cancer gene sequences. These BAC clones were biotinylated by nick translation, hybridized to cytogenetic preparations of metaphase cells, and detected with fluorescein-conjugated avidin. Only locations of unique or low-copy Portions of the clone are identified, because high-copy interspersed repetitive sequences in the probe were suppressed by the addition of unlabelled Cotl DNA. Banding patterns were produced using DAPI. By this means, every BAC fragment has been matched to its appropriate chromosomal location. We have placed 86 (156 BAC clones) cytogenetically defined landmarks to help with the characterization of known cancer genes. Microarray techniques would be applied in CGH by replacement of metaphase chromosome to arrayed BAC confirming in oncogene and tumor suppressor gene: and an array BAC clones from the collection is used to perform a genome-wide scan for segmental aneuploidy by array-CGH. Therefore, the genomic DNA chip (arrayed BAC) will be undoubtedly provide accurate diagnosis of deletions, duplication, insertions and rearrangements of genomic material related to various human phenotypes, including neoplasias. And our tumor markers based on genetic abnormalities of cancer would be identified and contribute to the screening of the stage of cancers and/or hereditary diseases