• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.2095-2105
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• 2015

Given c, a positive integer, we set. $$M(f,c):=\frac{2}{{\phi}(f)}\sum_{{\chi}{\in}X^-_f}{\chi}(c)|L(1,{\chi})|^2$$, where $X^-_f$ is the set of the $\phi$(f)/2 odd Dirichlet characters mod f > 2, with gcd(f, c) = 1. We point out several mistakes in recently published papers and we give explicit closed formulas for the f's such that their prime divisors are all equal to ${\pm}1$ modulo c. As a Corollary, we obtain closed formulas for M(f, c) for c $\in$ {1, 2, 3, 4, 5, 6, 8, 10}. We also discuss the case of twisted quadratic moments for primitive characters.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.603-618
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• 2015

We derive three identities of symmetry in two variables and eight in three variables related to generalized twisted Bernoulli polynomials and generalized twisted power sums, both of which are twisted by unramified roots of unity. The case of ramified roots of unity was treated previously. The derivations of identities are based on the p-adic integral expression, with respect to a measure introduced by Koblitz, of the generating function for the generalized twisted Bernoulli polynomials and the quotient of p-adic integrals that can be expressed as the exponential generating function for the generalized twisted power sums.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.511-516
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• 2011

In this paper we prove a generalized symmetry relation between the generalized Euler polynomials and the generalized higher-order (attached to Dirichlet character) Euler polynomials. Indeed, we prove a relation between the power sum polynomials and the generalized higher-order Euler polynomials..

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.815-827
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• 2019

It is well known that the denominator of the Dedekind sum s(c, d) divides 2 gcd(d, 3)d and that no smaller denominator independent of c can be expected. In contrast, here we prove that we usually get a smaller denominator in S(H, d), the sum of the s(c, d)'s over all the c's in a subgroup H of order n > 1 in the multiplicative group $(\mathbb{Z}/d\mathbb{Z})^*$. First, we prove that for p > 3 a prime, the sum 2S(H, p) is a rational integer of the same parity as (p-1)/2. We give an application of this result to upper bounds on relative class numbers of imaginary abelian number fields of prime conductor. Finally, we give a general result on the denominator of S(H, d) for non necessarily prime d's. We show that its denominator is a divisor of some explicit divisor of 2d gcd(d, 3).

• Journal of Intelligence and Information Systems
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• v.27 no.3
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• pp.75-94
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• 2021

The low birth rate and shortened military service period are causing concerns about selecting excellent military officers. The Republic of Korea entered a low birth rate society in 1984 and an aged society in 2018 respectively, and is expected to be in a super-aged society in 2025. In addition, the troop-oriented military is changed as a state-of-the-art weapons-oriented military, and the reduction of the military service period was implemented in 2018 to ease the burden of military service for young people and play a role in the society early. Some observe that the application rate for military officers is falling due to a decrease of manpower resources and a preference for shortened mandatory military service over military officers. This requires further consideration of the policy of securing excellent military officers. Most of the related studies have used social scientists' methodologies, but this study applies the methodology of text mining suitable for large-scale documents analysis. This study extracts words of discriminative characteristics from the Republic of Korea Air Force Non-Commissioned Officer Applicant cover letters and analyzes the polarity of pass and fail. It consists of three steps in total. First, the application is divided into general and technical fields, and the words characterized in the cover letter are ordered according to the difference in the frequency ratio of each field. The greater the difference in the proportion of each application field, the field character is defined as 'more discriminative'. Based on this, we extract the top 50 words representing discriminative characteristics in general fields and the top 50 words representing discriminative characteristics in technology fields. Second, the number of appropriate topics in the overall cover letter is calculated through the LDA. It uses perplexity score and coherence score. Based on the appropriate number of topics, we then use LDA to generate topic and probability, and estimate which topic words of discriminative characteristic belong to. Subsequently, the keyword indicators of questions used to set the labeling candidate index, and the most appropriate index indicator is set as the label for the topic when considering the topic-specific word distribution. Third, using L-LDA, which sets the cover letter and label as pass and fail, we generate topics and probabilities for each field of pass and fail labels. Furthermore, we extract only words of discriminative characteristics that give labeled topics among generated topics and probabilities by pass and fail labels. Next, we extract the difference between the probability on the pass label and the probability on the fail label by word of the labeled discriminative characteristic. A positive figure can be seen as having the polarity of pass, and a negative figure can be seen as having the polarity of fail. This study is the first research to reflect the characteristics of cover letters of Republic of Korea Air Force non-commissioned officer applicants, not in the private sector. Moreover, these methodologies can apply text mining techniques for multiple documents, rather survey or interview methods, to reduce analysis time and increase reliability for the entire population. For this reason, the methodology proposed in the study is also applicable to other forms of multiple documents in the field of military personnel. This study shows that L-LDA is more suitable than LDA to extract discriminative characteristics of Republic of Korea Air Force Noncommissioned cover letters. Furthermore, this study proposes a methodology that uses a combination of LDA and L-LDA. Therefore, through the analysis of the results of the acquisition of non-commissioned Republic of Korea Air Force officers, we would like to provide information available for acquisition and promotional policies and propose a methodology available for research in the field of military manpower acquisition.