• 대한수학회지
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• 제34권4호
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• pp.871-894
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• 1997

For a lifted nontrivial additive character $\lambda'$ and a multiplicative character $\chi$ of the finite field with $q^2$ elements, the 'Gauss' sums $\Sigma\lambda'$(tr $\omega$) over $\omega$ $\in$ SU(2n + 1, $q^2$) and $\Sigma\chi$(det $\omega$)$\lambda'$(tr $\omega$) over $\omega$ $\in$ U(2n + 1, $q^2$) are considered. We show that the first sum is a polynomial in q with coefficients involving certain new exponential sums and that the second one is a polynomial in q with coefficients involving powers of the usual twisted Kloosterman sums and the average (over all multiplicative characters of order dividing q-1) of the usual Gauss sums. As a consequence we can determine certain 'generalized Kloosterman sum over nonsingular Hermitian matrices' which were previously determined by J. H. Hodges only in the case that one of the two arguments is zero.

• 대한수학회지
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• 제47권5호
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• pp.947-965
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• 2010

The main purpose of this paper is using estimates for character sums and analytic methods to study the mean value involving the incomplete character sums, 2-th power mean of the inversion of Dirichlet L-function and general Kloosterman sums, and give four interesting asymptotic formulae for it.

• Korean Journal of Mathematics
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• 제23권4호
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• pp.571-590
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• 2015

Let a, b, q be integers with q > 0. The homogeneous Dedekind sum is dened by $$\Large S(a,b,q)={\sum_{r=1}^{q}}\(\({\frac{ar}{q}}\)\)\(\({\frac{br}{q}}\)\)$$, where $$\Large ((x))=\{x-[x]-{\frac{1}{2}},\text{ if x is not an integer},\\0,\hspace{75}\text{ if x is an integer.}$$ In this paper we study the mean value of S(a, b, q) by using mean value theorems of Dirichlet L-functions, and give some asymptotic formula.

• 대한수학회보
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• 제58권3호
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• pp.593-602
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• 2021

We use a kind of modified Hurwitz class numbers to express the number of representing a positive integer by some ternary quadratic forms such as the sum of three squares, and the Fourier coefficients of weight 2 modular forms of prime level with trivial character.

• 대한불안의학회지
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• 제12권1호
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• pp.13-20
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• 2016

Objective : The purpose of this study was to verify the differences of expressed character strengths graded as per the Korean Strength Scale, based on the type of work. Methods : A total of 2,444 conglomerate workers were classified into two groups: 1,356 office workers and 1,088 production workers. The subjects were examined through a web or mobile application based on the Korean Strength Scale. The Korean Strength Scale consists of a total of four top entries and 25 sub-items with appropriate validity. Results : The difference in the average score of sum of character strengths between the two groups was not significant. In the office worker group, character strengths such as love of learning, creativity, perspective, curiosity, facilitation, judgment and faith had significantly high scores. On the other hands, modesty, hope, gratitude, sincerity, magnanimity and self-regulation were high in the production worker group. The results remained unchanged in additional analysis of covariants as sex, age and education level, except for self-regulation and faith. Conclusion : Our results suggest significant differences in the character strengths between the two types of work; however, the average of sum of character strength score remains unchanged. These results may help to understand differences between work environments and thus help to establish a positive foundation.

• 대한수학회보
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• 제56권4호
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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 applied mathematics & informatics
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• 제31권1_2호
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• pp.119-130
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• 2013

In this paper, we obtain some generalized symmetry identities involving a unified class of polynomials related to the generalized Bernoulli, Euler and Genocchi polynomials of higher-order attached to a Dirichlet character. In particular, we prove a relation between a generalized X version of the power sum polynomials and this unified class of polynomials.

• 대한수학회보
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• 제49권6호
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• pp.1303-1310
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• 2012

Let $p$ > 2 be a prime, and let $k{\geq}1$ be an integer. Let ${\chi}$ be a Dirichlet character modulo $p$, and let $L(s,{\chi})$ be the Dirichlet L-function corresponding to ${\chi}$. In this paper we consider the mean values of $$\sum_{{\chi}\;mod\;p\\{\chi}(-1)=-1}{\chi}(2^k)|L(1,\chi)|^2$$.

• 지능정보연구
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• 제8권2호
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• pp.105-115
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• 2002

본 논문에서는 4 방향 윤곽선 추적 알고리즘(contour tracking algorithm)과 개선된 ART1을 이용한 영문 명함인식 방법을 제안한다. 영문 명함 영상에서 문자열 추출은 영상을 3배로 축소하여 수평 스미어링 기법(smearing method)과 4방향 윤곽선 추적 방법을 적용하여 문자열 후보 영역을 추출하고 수평 및 수직의 비율과 면적을 이용하여 문자열 영역과 비문자열 영역을 구분하였다. 추출된 문자열 영역에서 개별 문자 추출은 수평 스미링 기법과 윤곽선 추적 알고리즘을 이용하여 추출하였고 개별 문자들의 인식은 ART1 알고리즘을 개선하여 인식에 적용하였다. 본 논문에서 제안한 ARTI 알고리즘은 퍼지 합 접속 연산자를 이용하여 유사도를 동적으로 조정함으로써 기존의 ART1을 개선하였다. 추출 및 인식 실험 결과, 제안된 추출 및 인식 방법이 영문 명함 인식에서 효율적인 것을 확인하였다.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.295-303
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• 2007

In this paper we investigate the boundedness character of the positive solutions of the rational difference equation of the form $$x_{n+1}=\frac{a_0+{{\sum}^k_{j=1}}a_jx_{n-j+1}}{b_0+{{\sum}^k_{j=1}}b_jx_{n-j+1}},\;\;n=0,\;1,...$$ where $k{\in}N,\;and\;a_j,b_j,\;j=0,\;1,...,\;k $, are nonnegative numbers such that $b_0+{{\sum}^k_{j=1}}b_jx_{n-j+1}>0$ for every $n{\in}N{\cup}\{0\}$. In passing we confirm several conjectures recently posed in the paper: E. Camouzis, G. Ladas and E. P. Quinn, On third order rational difference equations(part 6), J. Differ. Equations Appl. 11(8)(2005), 759-777.