• 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.

• 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.

• 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.

• Korean Journal of Materials Research
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• v.10 no.9
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• pp.612-618
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• 2000

The WC/WC grain boundary structure and intergranular segregation in WC-Co and WC-VC-Co cemented carbides were investigated by high-resolution transmission electron microscopy and energy dispersive X-ray spectroscopy in order to elucidate whether contiguous boundaries were present or not at the atomic level. Some grain boundaries were separated by liquid phase, while others were contiguous at the atomic level. Cobalt was found to be segregated to WC/WC grain boundaries in WC-Co. Cobalt and vanadium were co-segregated to grain boundaries in WC-VC-Co. The segregation width in both materials was about 6 nm. These results suggest that the vanadium present in contiguous boundaries acts as an effective barrier to the migration of boundaries during sintering and annealing. This could explain the grain growth inhibiting mechanism of VC added to WC-Co.

• Investigative Magnetic Resonance Imaging
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• v.18 no.3
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• pp.232-243
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• 2014

Purpose : To evaluate the incidence of secondary contiguous or non-contiguous subchondral bone impactions (SBI) in subaxial cervical spinal injury and associated primary injury patterns. Materials and Methods: A retrospective review of computed tomography, magnetic resonance imaging, and medical records was carried out for 47 patients who had sustained a subaxial cervical spinal injury. Presence, number, level, and sites of secondary contiguous or non-contiguous SBI were recorded. To evaluate primary injury patterns, the level and number of primary injury sites of subaxial cervical spine injury, injury morphology, anterior/posterior discoligamentous complex (ADC/PDC) injury, posterior ligamentous complex (PLC) injury, spinal cord injury, and mechanism of injury (MOI) were analyzed. Differences in primary injury pattern of subaxial cervical spine injury and MOI between patients with and without SBI, and between contiguous or non-contiguous SBI were analyzed using the Mann-Whitney U test, Pearson's chi square test and Fisher's exact test. Results: Eighteen patients (18/47, 38.29%) had developed contiguous (n=9) or non-contiguous (n=9) SBI, most commonly involving T3 (15/47, 31.91%) and 3 levels (6/18, 33.33%). All SBIs had developed near the anterosuperior region of the body and the superior endplate and were the result of a high-impact MOI. SBIs were statistically significant in association with injury morphology and PLC injury (P=0.001, P=0.009, respectively) at the primary injury site. Non-contiguous SBI was more frequently accompanied by upper cervical spinal injuries in association with PDC injuries, as opposed to contiguous SBI, with statistical significance (P=0.009), while no other statistically significant differences were found. Conclusion: Secondary SBIs are common and probably associated with subaxial cervical spinal injuries with high energy compressive flexion forces.

• Honam Mathematical Journal
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• v.40 no.1
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• pp.163-186
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• 2018

The objective of this paper is to present 87 recurrence relations for the Jacobi polynomials $P_n^{({\alpha},{\beta})}(x)$. The results presented here most of which are presumably new are obtained with the help of Gauss's fifteen contiguous function relations and some other identities recently recorded in the literature.

• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.255-259
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• 2006

In 1994, Lavoie et al. have obtained twenty tree interesting results closely related to the classical Dixon's theorem on the sum of a $_3F_2$ by making a systematic use of some known relations among contiguous functions. We aim at showing that these results can be derived by using the same technique developed by Bailey with the help of Gauss's summation theorem and generalized Kummer's theorem obtained by Lavoie et al..

• Journal of the Korean Institute of Telematics and Electronics
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• v.15 no.6
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• pp.79-86
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• 1978

The characteristics of contiguous pulse trains of stopped FM signals with binary phase coding, to be used as radar signals, were investigated. For this purpose, the general expressions for the spectra and the ambiguity functions of this class of signals were first obtained; these expressions were then compute6 and plotted by the use of computer for various coding scheme. The results show that alternate phase coding provides the best time resolution and the corresponding ambiguity functon has a configuration of "be6 of spikes" in the whole time-velocity plane.ity plane.