• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.65-94
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• 2016

In 1812, Gauss obtained fifteen contiguous functions relations. Later on, 1847, Henie gave their q-analogue. Recently, good progress has been done in finding more contiguous functions relations by employing results due to Gauss. In 1999, Cho et al. have obtained 24 new and interesting contiguous functions relations with the help of Gauss's 15 contiguous relations. In fact, such type of 72 relations exists and therefore the rest 48 contiguous functions relations have very recently been obtained by Rakha et al.. Thus, the paper is in continuation of the paper [16] published in Computer & Mathematics with Applications 61 (2011), 620.629. In this paper, first we obtained 15 q-contiguous functions relations due to Henie by following a different method and then with the help of these 15 q-contiguous functions relations, we obtain 72 new and interesting q-contiguous functions relations. These q-contiguous functions relations have wide applications.

• Honam Mathematical Journal
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• v.21 no.1
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• pp.49-56
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• 1999

The object of this note is to provide various methods for proving two results contiguous to Kummer's second theorem by using the classical Gauss's summation theorem and contiguous relations.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.231-239
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• 2008

We obtain a necessary and sufficient condition for the existence of Mendelsohn triple systems excluding contiguous units with ${\lambda}$ = 1. Also, we obtain the spectrum for cyclic such systems.

• International Journal of Contents
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• v.3 no.2
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• pp.18-24
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• 2007

Biological sequences such as DNA and amino acid sequences typically contain a large number of items. They have contiguous sequences that ordinarily consist of more than hundreds of frequent items. In biological sequences analysis(BSA), a frequent contiguous sequence search is one of the most important operations. Many studies have been done for mining sequential patterns efficiently. Most of the existing methods for mining sequential patterns are based on the Apriori algorithm. In particular, the prefixSpan algorithm is one of the most efficient sequential pattern mining schemes based on the Apriori algorithm. However, since the algorithm expands the sequential patterns from frequent patterns with length-1, it is not suitable for biological datasets with long frequent contiguous sequences. In recent years, the MacosVSpan algorithm was proposed based on the idea of the prefixSpan algorithm to significantly reduce its recursive process. However, the algorithm is still inefficient for mining frequent contiguous sequences from long biological data sequences. In this paper, we propose an efficient method to mine maximal frequent contiguous sequences in large biological data sequences by constructing the spanning tree with a fixed length. To verify the superiority of the proposed method, we perform experiments in various environments. The experiments show that the proposed method is much more efficient than MacosVSpan in terms of retrieval performance.

• Genomics & Informatics
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• v.18 no.2
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• pp.15.1-15.6
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• 2020

Named entity recognition tools are used to identify mentions of biomedical entities in free text and are essential components of high-quality information retrieval and extraction systems. Without good entity recognition, methods will mislabel searched text and will miss important information or identify spurious text that will frustrate users. Most tools do not capture non-contiguous entities which are separate spans of text that together refer to an entity, e.g., the entity "type 1 diabetes" in the phrase "type 1 and type 2 diabetes." This type is commonly found in biomedical texts, especially in lists, where multiple biomedical entities are named in shortened form to avoid repeating words. Most text annotation systems, that enable users to view and edit entity annotations, do not support non-contiguous entities. Therefore, experts cannot even visualize non-contiguous entities, let alone annotate them to build valuable datasets for machine learning methods. To combat this problem and as part of the BLAH6 hackathon, we extended the TextAE platform to allow visualization and annotation of non-contiguous entities. This enables users to add new subspans to existing entities by selecting additional text. We integrate this new functionality with TextAE's existing editing functionality to allow easy changes to entity annotation and editing of relation annotations involving non-contiguous entities, with importing and exporting to the PubAnnotation format. Finally, we roughly quantify the problem across the entire accessible biomedical literature to highlight that there are a substantial number of non-contiguous entities that appear in lists that would be missed by most text mining systems.

• Genomics & Informatics
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• v.10 no.1
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• pp.51-57
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• 2012

Mining interesting patterns from DNA sequences is one of the most challenging tasks in bioinformatics and computational biology. Maximal contiguous frequent patterns are preferable for expressing the function and structure of DNA sequences and hence can capture the common data characteristics among related sequences. Biologists are interested in finding frequent orderly arrangements of motifs that are responsible for similar expression of a group of genes. In order to reduce mining time and complexity, however, most existing sequence mining algorithms either focus on finding short DNA sequences or require explicit specification of sequence lengths in advance. The challenge is to find longer sequences without specifying sequence lengths in advance. In this paper, we propose an efficient approach to mining maximal contiguous frequent patterns from large DNA sequence datasets. The experimental results show that our proposed approach is memory-efficient and mines maximal contiguous frequent patterns within a reasonable time.

• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.291-302
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• 2009

Contiguous relations for hypergeometric series contain an enormous amount of hidden information. Applications of contiguous relations range from the evaluation of hypergeometric series to the derivation of summation and transformation formulas for such series. In this paper, a general formula joining three Gauss functions of the form $_2F_1$[$a_1$, $a_2$; $a_3$; z] with arbitrary integer shifts is presented. Our analysis depends on using shifted operators attached to the three parameters $a_1$, $a_2$ and $a_3$. We also, discussed the existence condition of our formula.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.637-651
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• 2017

Very recently, Mubeen, et al. [6] have obtained fifteen contiguous function relations for k-hypergeometric functions with one parameter by the same technique developed by Gauss. The aim of this paper is to obtain seventy-two new and interesting contiguous function relations for k-hypergeometric functions with two parameters. Obviously, for $k{\rightarrow}1$ we recover the results obtained by Cho, et al. [2] and Rakha, et al. [8].

• Journal of the Korean Institute of Telematics and Electronics A
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• v.30A no.5
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• pp.36-44
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• 1993

In this paper, a simple design method is represented for a contiguous-band waveguide manifold diplexer which employs a half-wavelength line at the input port of the singly terminated bandpass filterand has resonant-slot coupled E-plane T-junctions. This design method is based on the fact that the input impedance characteristics of the singly terminated bandpass filter are approximately unchanged when a resonant slot and a half-wavelength line at the input port of the filter are employed. This design method is also applicable to the design of the multiplexer. A contiguous-band waveguide manifold diplexer using the post coupled cavity filters is designed, constructed, and tested. The computed and experimental results show the validity of the theory.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.395-403
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• 2005

The authors aim mainly at giving fifteen three-term contiguous relations for the basic hypergeometric series $series\;_2{\phi}_1$ corresponding to Gauss's contiguous relations for the hypergeometric series $series\;_2F_1$ given in Rainville([6], p.71). They also apply them to obtain two summation formulas closely related to a known q-analogue of Kummer's theorem.