• Kyungpook Mathematical Journal
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• v.14 no.2
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• pp.165-170
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• 1974

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.419-426
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• 2009

In expansion of function by special basis functions, properties of expansion kernel are very important. In the Fourier series, the series are expressed by the convolution with Dirichlet kernel. We investigate some of properties of kernel in wavelet expansions both in one and higher dimensions.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.537-546
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• 2010

Multiple discrete Hilbert type inequalities are established in the case of non-homogeneous kernel function by means of Laplace integral representation of associated Dirichlet series. Using newly derived integral expressions for the Mordell-Tornheim Zeta function a set of subsequent special cases, interesting by themselves, are obtained as corollaries of the main inequality.

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1599-1611
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• 2019

Let $m,n{\in}{\mathbb{N}}$. We represent the additive subgroups of the ring ${\mathbb{Z}}_m{\times}{\mathbb{Z}}_n$, which are also (unital) subrings, and deduce explicit formulas for $N^{(s)}(m,n)$ and $N^{(us)}(m,n)$, denoting the number of subrings of the ring ${\mathbb{Z}}_m{\times}{\mathbb{Z}}_n$ and its unital subrings, respectively. We show that the functions $(m,n){\mapsto}N^{u,s}(m,n)$ and $(m,n){\mapsto}N^{(us)}(m,n)$ are multiplicative, viewed as functions of two variables, and their Dirichlet series can be expressed in terms of the Riemann zeta function. We also establish an asymptotic formula for the sum $\sum_{m,n{\leq}x}N^{(s)}(m,n)$, the error term of which is closely related to the Dirichlet divisor problem.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1529-1547
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• 2021

In this series, we investigate the calculation of mean values of derivatives of Dirichlet L-functions in function fields using the analogue of the approximate functional equation and the Riemann Hypothesis for curves over finite fields. The present paper generalizes the results obtained in the first paper. For µ ≥ 1 an integer, we compute the mean value of the µ-th derivative of quadratic Dirichlet L-functions over the rational function field. We obtain the full polynomial in the asymptotic formulae for these mean values where we can see the arithmetic dependence of the lower order terms that appears in the asymptotic expansion.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.605-612
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• 2004

The Gibbs’ phenomenon for the classical Fourier series is known. This occurs for almost all series expansions. This phenomenon has been observed even in sampling series. In this paper, we show the existence of Gibbs phenomenon for trigonometric interpolating polynomial by a simple and different manner from the wok[4].

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.657-666
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• 2002

ThE Gibbs' phenomenon in the classical Fourier series is well-known. It is closely related with the kernel of the partial sum of the series. In fact, the Dirichlet kernel of the courier series is not positive. The poisson kernel of Cesaro summability is positive. As the consequence of the positiveness, the partial sum of Cesaro summability does not exhibit the Gibbs' phenomenon. Most kernels associated with wavelet expansions are not positive. So wavelet series is not free from the Gibbs' phenomenon. Because of the excessive oscillation of wavelets, we can not follow the techniques of the courier series to get rid of the unwanted quirk. Here we make a positive kernel For Meyer wavelets and as the result the associated summability method does not exhibit Gibbs' phenomenon for the corresponding series .

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.323-328
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• 2007

In this paper, we extend the result of Ram [3] and also study the $L^1$-convergence of the $r^{th}$ derivative of cosine series.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.849-856
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• 2016

General summation formula for sums involving ${\sigma}(n)/n$ is expressed with infinite series containing a Bessel function.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.10
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• pp.176-182
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• 2018

In order to understand and track the trends of construction safety accident, this study shows the topic trends in the construction safety accident with LDA(Latent Dirichlet Allocation)-based topic modeling method for data analytics. Especially, it performs to figure out the main issue of construction safety accident with unstructured data analysis based on the topic modeling rather than a variety of structured data analysis for preventing to safety accident in construction industry. To apply this methodology, I randomly collected to 540 news article data about construction accident from January 2017 to February 2018. Based on the unstructured data with the LDA-based topic modeling, I found the 10 topics and identified key issues through 10 keyword in each 10 topics. I forecasted the topic issue related to construction safety accident based on analysis of time-series trends about the news data from January 2017 to February 2018. With this method, this research gives a hint about ways of using unstructured news article data to anticipate safety policy and research field and to respond to construction accident safety issues in the future.