• 대한수학회지
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• 제47권6호
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• pp.1107-1122
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• 2010

In this paper, we shall use analytic methods to study the hybrid mean value involving the mixed two-term exponential sums C(m, n, r, $\chi$; q), and give several sharp asymptotic formulae.

• 한국통신학회논문지
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• 제27권6A호
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• pp.517-523
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• 2002

이 논문에서는 국소 최적 순위 검파기의 점수 함수의 합과 가중합의 완전한 골을 유도하였다. 순위통계량과 부호통계량에 바탕을 둔 검파기의 점근 성능 특성은 점수 함수의 합과 가 중합으로부터 얻어지기 때문에, 합과 가중합은 매우 중요하나, 이들을 구하기 위해서는 상당한 수학적 조작이 필요하다. 이 논문에서 다루어진 점수 함수는 순위통계량에 바탕을 둔 것들 뿐 아니라 절대값 순위통계량과 부호통계량에 바탕을 둔 것들을 포함한다. 따라서, 이 논문의 결과를 써서 여러 가지 잡음 모형에서 쓸모 있는 검 파기들의 점근 성능을 쉽게 구할 수 있다.

• 충청수학회지
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• 제27권1호
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• pp.1-8
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• 2014

Recently, q-Dedekind-type sums related to q-Euler polynomials was studied by Kim in [T. Kim, Note on q-Dedekind-type sums related to q-Euler polynomials, Glasgow Math. J. 54 (2012), 121-125]. It is aim of this paper to consider a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order Dedekind-type sums with weight related to modified q-Euler polynomials with weight by using Kim's p-adic q-integral.

• 대한수학회지
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• 제43권4호
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• pp.859-869
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• 2006

Let {$X,\;X_n;n\;{\geq}\;1$} be a sequence of ${\imath}.{\imath}.d.$ random variables which belong to the attraction of the normal law, and $X^{(1)}_n,...,X^{(n)}_n$ be an arrangement of $X_1,...,X_n$ in decreasing order of magnitude, i.e., $\|X^{(1)}_n\|{\geq}{\cdots}{\geq}\|X^{(n)}_n\|$. Suppose that {${\gamma}_n$} is a sequence of constants satisfying some mild conditions and d'($t_{nk}$) is an appropriate truncation level, where $n_k=[{\beta}^k]\;and\;{\beta}$ is any constant larger than one. Then we show that the conditionally trimmed sums obeys the self-normalized law of the iterated logarithm (LIL). Moreover, the self-normalized LIL for conditionally censored sums is also discussed.

• 대한수학회보
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• 제60권4호
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• pp.985-1001
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• 2023

Recently, Alzer and Choi [2] introduced and studied a set of the four linear Euler sums with parameters. These sums are parametric extensions of Flajolet and Salvy's four kinds of linear Euler sums [9]. In this paper, by using the method of residue computations, we will establish two explicit combined formulas involving two parametric linear Euler sums S⁺⁺_p,q (a, b) and S^+-_p,q (a, b) defined by Alzer and Choi, which can be expressed in terms of a linear combinations of products of trigonometric functions, digamma functions and Hurwitz zeta functions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권2호
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• pp.53-61
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• 2001

We introduce sums and joins of fuzzy finite state machines and investigate their algebraic structures.

• 대한수학회지
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• 제46권1호
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• pp.187-213
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• 2009

For a positive integer k and an arbitrary integer h, the classical Dedekind sums s(h,k) is defined by $$S(h,\;k)=\sum\limits_{j=1}^k\(\(\frac{j}{k}\)\)\(\(\frac{hj}{k}\)\),$$ where $$((x))=\{{x-[x]-\frac{1}{2},\;if\;x\;is\;not\;an\;integer; \atop \;0,\;\;\;\;\;\;\;\;\;\;if\;x\;is\;an\;integer.}\$$ J. B. Conrey et al proved that $$\sum\limits_{{h=1}\atop {(h,k)=1}}^k\;s^{2m}(h,\;k)=fm(k)\;\(\frac{k}{12}\)^{2m}+O\(\(k^{\frac{9}{5}}+k^{{2m-1}+\frac{1}{m+1}}\)\;\log^3k\).$$ For $m\;{\geq}\;2$, C. Jia reduced the error terms to $O(k^{2m-1})$. While for m = 1, W. Zhang showed $$\sum\limits_{{h=1}\atop {(h,k)=1}}^k\;s^2(h,\;k)=\frac{5}{144}k{\phi}(k)\prod_{p^{\alpha}{\parallel}k}\[\frac{\(1+\frac{1}{p}\)^2-\frac{1}{p^{3\alpha+1}}}{1+\frac{1}{p}+\frac{1}{p^2}}\]\;+\;O\(k\;{\exp}\;\(\frac{4{\log}k}{\log\log{k}}\)\).$$. In this paper we give some formulae on the mean value of the Dedekind sums and and Hardy sums, and generalize the above results.

• 대한수학회보
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• 제39권3호
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• pp.511-526
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• 2002

In this paper, we concern with SLLN for sums Of in-dependent random upper-semicontinuous fuzzy sets. We first give a generalization of SLLN for sums of independent and level-wise identically distributed random fuzzy sets, and establish a SLLN for sums of random fuzzy sets which is independent and compactly uniformly integrable in the strong sense. As a result, a SLLN for sums of independent and strongly tight random fuzzy sets is obtained.

• 대한수학회보
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• 제49권6호
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• pp.1327-1334
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• 2012

In this paper, using analytic method and the properties of the Legendre's symbol, we prove an exact calculating formula on the $2m$-th power mean value of the generalized quadratic Gauss sums for $m{\geq}2$. This solves a conjecture of He and Zhang [On the 2k-th power mean value of the generalized quadratic Gauss sums, Bull. Korean Math. Soc. 48 (2011), no. 1, 9-15].

• 대한수학회지
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• 제36권1호
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• pp.37-49
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• 1999

We derive the almost sure convergence for weighted sums of random variables which are either pairwise positive quadrant dependent or pairwise positive quadrant dependent or pairwise negative quadrant dependent and then apply this result to obtain the almost sure convergence of weighted averages. e also extend some results on the strong law of large numbers for pairwise independent identically distributed random variables established in Petrov to the weighted sums of pairwise negative quadrant dependent random variables.