• Honam Mathematical Journal
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• v.38 no.1
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• pp.25-37
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• 2016

In 1972, Andrews derived the basic analogue of Gauss's second summation theorem and Bailey's theorem by implementing basic analogue of Kummer's theorem into identity due to Jackson. Recently Lavoie et.al. derived many results closely related to Kummer's theorem, Gauss's second summation theorem and Bailey's theorem and also Rakha et. al. derive the basic analogues of results closely related Kummer's theorem. The aim of this paper is to derive basic analogues of results closely related Gauss's second summation theorem and Bailey's theorem. Some applications and limiting cases are also considered.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.875-880
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• 1995

Let $S_p(\alpha)$ denote the class of the Spirallike functions of order $\alpha, 0 < $\mid$\alpha$\mid$ < \frac{\pi}{2}$ Let $\Pi_N$ denote the subset of $S_p(\alpha)$ consisting of all products $z\Pi^N_{j=1}(1-u_j z)^{-mt_j}$ where $m = 1 + e^{-2i\alpha},$\mid$u_j$\mid$ = 1, t_j > 0$ for $j = 1, \cdots, N$ and $\sum^{N}_{j=1}{t_j = 1}$. In this paper we prove that extreme points of $S_p(\alpha)$ may be found which lie in $\Pi_N$ for some $N \geq 2$. We are let to conjecture that all exreme points of $S_p(\alpha)$ lie in $\Pi_N$ for somer $N \geq 1$ and that every such function is an extreme point.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1131-1138
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• 2010

In the present paper, we evaluate an analytic formula as a solution of Susceptible Infective (SI) model problem for communicable disease in which the daily contact rate (C(N)) is supposed to be varied linearly with population size N(t) that is large so that it is considered as a continuous variable of time t. Again, we introduce some Lie group of operators to make an extension of above analytic formula of the determin-istic epidemics model problem. Finally, we discuss some of its particular cases.

• Korean Journal of Mathematics
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• v.24 no.2
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• pp.139-168
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• 2016

In this work, we rst introduce a class of analytic functions involving the Dziok-Srivastava linear operator that generalizes the class of uniformly starlike functions with respect to symmetric points. We then establish the closure of certain well-known integral transforms under this analytic function class. This behaviour leads to various radius results for these integral transforms. Some of the interesting consequences of these results are outlined. Further, the lower bounds for the ratio between the functions f(z) in the class under discussion, their partial sums $f_m(z)$ and the corresponding derivative functions f'(z) and $f^{\prime}_m(z)$ are determined by using the coecient estimates.

• Structural Engineering and Mechanics
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• v.74 no.2
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• pp.215-225
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• 2020

Thin films easily wrinkle under compressive loading due to their small bending stiffness resulting from their tiny thickness. For a thin film deposited on a functionally graded substrate with non-uniform stiffness exponentially changes along the length span in this paper, the uniaxial wrinkling problem is solved analytically in terms of hyper-Bessel functions. For infinite, semi-infinite and finite length systems the wrinkling load and wrinkling wavenumber are determined and compared with those in literature. In comparison with a homogeneous substrate-bounded film in which the wrinkling pattern is uniform along the length span, for a functionally graded substrate-film system the wrinkles accumulate around the softer location of the functionally graded substrate. Therefore, the effective length of the film influenced by the wrinkles decreases, the amplitude of the wrinkles on softer regions of the functionally graded substrate grows and the wrinkling load of the functionally graded substrates with higher softening rate decreases more. The results of the current research are expected to be useful in science and technology of thin films and wrinkling of the structures especially living tissues.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.597-610
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• 2016

For a sufficiently adequate special case of the Dziok-Srivastava linear operator defined by means of the Hadamard product (or convolution) with Srivastava-Wright convolution operator, the authors investigate several mapping properties involving various subclasses of analytic and univalent functions, $G({\lambda},{\alpha})$ and $M({\lambda},{\alpha})$. Furthermore we discuss some inclusion relations for these subclasses to be in the classes of k-uniformly convex and k-starlike functions.

• Nuclear Engineering and Technology
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• v.52 no.4
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• pp.819-826
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• 2020

The method of the Laplace transform has been used to obtain an analytical solution of the three-dimensional steady state advection diffusion equation for the airborne radionuclide release from any nuclear installation such as the power reactor in an area source. The present treatment takes into account the removal of the pollutants through the nuclear reaction. We assume that the pollutants are emitted as a constant rate from the area source. This physical consideration is achieved by assuming that the vertical eddy diffusivity coefficient should be a constant. The prevailing wind speed is a constant in 𝑥- direction and a linear function of the vertical height z. The present model calculations are compared with the other models and the available data of the atmospheric dispersion experiments that were carried out in the nuclear power plant of Angra dos Reis (Brazil). The results show that the present treatment performs well as the analytical dispersion model and there is a good agreement between the values computed by our model and the observed data.

• 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.

• Genomics & Informatics
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• v.5 no.1
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• pp.10-18
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• 2007

Numerous studies have reported that genes with similar expression patterns are co-regulated. From gene expression data, we have assumed that genes having similar expression pattern would share similar transcription factor binding sites (TFBSs). These function as the binding regions for transcription factors (TFs) and thereby regulate gene expression. In this context, various analysis tools have been developed. However, they have shortcomings in the combined analysis of expression patterns and significant TFBSs and in the functional analysis of target genes of significantly overrepresented putative regulators. In this study, we present a web-based A Functional Clustering Analysis Tool for Predicted Transcription Regulatory Elements and Gene Ontology Terms (FCAnalyzer). This system integrates microarray clustering data with similar expression patterns, and TFBS data in each cluster. FCAnalyzer is designed to perform two independent clustering procedures. The first process clusters gene expression profiles using the K-means clustering method, and the second process clusters predicted TFBSs in the upstream region of previously clustered genes using the hierarchical biclustering method for simultaneous grouping of genes and samples. This system offers retrieved information for predicted TFBSs in each cluster using $Match^{TM}$ in the TRANSFAC database. We used gene ontology term analysis for functional annotation of genes in the same cluster. We also provide the user with a combinatorial TFBS analysis of TFBS pairs. The enrichment of TFBS analysis and GO term analysis is statistically by the calculation of P values based on Fisher’s exact test, hypergeometric distribution and Bonferroni correction. FCAnalyzer is a web-based, user-friendly functional clustering analysis system that facilitates the transcriptional regulatory analysis of co-expressed genes. This system presents the analyses of clustered genes, significant TFBSs, significantly enriched TFBS combinations, their target genes and TFBS-TF pairs.

• Fisheries and Aquatic Sciences
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• v.25 no.5
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• pp.287-297
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• 2022

The objective of this study was to evaluate the probability of norovirus foodborne illness by raw oyster consumption. One hundred fifty-six oyster samples were collected to examine the norovirus prevalence. The oyster samples were inoculated with murine norovirus and stored at 4℃-25℃. A plaque assay determined norovirus titers. The norovirus titers were fitted with the Baranyi model to calculate shoulder period (h) and death rate (Log PFU/g/h). These kinetic parameters were fitted to a polynomial model as a function of temperature. Distribution temperature and time were surveyed, and consumption data were surveyed. A dose-response model was also searched through literature. The simulation model was prepared with these data in @RISK to estimate the probability of norovirus foodborne. One sample of 156 samples was norovirus positive. Thus, the initial contamination level was estimated by the Beta distribution (2, 156), and the level was -5.3 Log PFU/g. The developed predictive models showed that the norovirus titers decreased in oysters under the storage conditions simulated with the Uniform distribution (0.325, 1.643) for time and the Pert distribution (10, 18, 25) for temperature. Consumption ratio of raw oyster was 0.98%, and average consumption amount was 1.82 g, calculated by the Pert distribution [Pert {1.8200, 1.8200, 335.30, Truncate (0, 236.8)}]. ₁F₁ hypergeometric dose-response model [1 - (1 + 2.55 × 10^-3 × dose)^-0.086] was appropriate to evaluate dose-response. The simulation showed that the probability of norovirus foodborne illness by raw oyster consumption was 5.90 × 10^-10 per person per day. The annual socioeconomic cost of consuming raw oysters contaminated with norovirus was not very high.