• 한국수학사학회지
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• 제20권4호
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• pp.71-84
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• 2007

베르누이가 처음으로 자연수 k에 대하여 합 $S_n(k)=\sum_{{\iota}=1}^n\;{\iota}^k$에 관한 공식들을 유도하는 방법을 발견하였다([4]). 그 이후, 리만 제타함수와 관련된 베르누이 수와 오일러 수에 관한 성질들이 연구되어왔다. 최근에 김태균은 $\mathbb{Z}_p$상에서 p-진 q-적분과 관련된 확장된 q-베르누이 수와 q-오일러 수, 연속된 q-정수의 멱수의 합에 관한 성질들을 밝혔다. 본 논문에서는 연속된 q-정수의 멱수의 합에 관한 역사적 배경과 발달과정을 고찰하고, 오일러 및 베르누이 수와 관련된 리만 제타함수가 해석적 함수로써 값을 가지는 문제를 q-확장된 부분의 이론으로 연구되어온 q-오일러 제타함수에 대해 체계적으로 논의한다.

• IMMUNE NETWORK
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• 제2권2호
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• pp.72-78
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• 2002

Background: The precise mechanism by which CTLA-4 regulates T cell immune responses is still not fully understood. Previously we proposed that CTLA-4 could downregulate T cell function by modulating a signaling cascade initiated from the T cell receptor complex. The evidence for this notion comes from our findings that CTLA-4 associated with the T cell receptor zeta (TCR zeta) chain, and hence regulated TCR zeta phosphorylation by co-associated SHP-2 tyrosine phosphatase (1). In this report, we investigated whether any other signaling molecules could be involved in the CTLA-4 signaling pathway. Methods: We have taken biochemical approaches, such as immunoprecipitation followed by autoradiography or immunoblotting, to identify the molecules associated with CTLA-4. To perform these assays, we used activated primary T cells and ectopically transfected 293 cells. Various truncation mutants of CTLA-4 were used to map the interaction site on CTLA-4. Results: We found that in addition to TCR zeta and SHP-2, a recently cloned small adaptor molecule, SAP (SLAM-associated protein), was also able to associate with CTLA-4. We identified the domain of SAP association in CTLA-4 being a motif involving GVYVKM. This motif has been previously found to bind SHP-2 through its phosphorylated tyrosine interaction with SH-2 domain of SHP-2. Indeed, co-expression of SAP and SHP-2 reduced their binding to CTLA-4 significantly, suggesting that SAP and SHP-2 compete for the common binding site, GVYVKM. Thus, by blocking SHP-2 recruitment SAP could function as a negative regulator of CTLA-4. Conclusion: Taken together, our data suggest the existence of complicate signaling cascade in regulating CTLA-4 function, and further provide evidence that SAP can act either as a positive or negative regulator depending on the nature of the associating receptors.

• 한국결정성장학회지
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• 제15권6호
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• pp.239-243
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• 2005

The effect of pH and particle size on the dispersion stability of ultra-fine $BaTiO_3$ suspensions in aqueous medium have been investigated by means of zeta potential, sediment experiments, and powder properties (particle analysis, specific surface area) etc. Zeta potential as a function of pH for two particles of different size increases from -75 to +10 mV with decreasing pH from 8.5 to 1.4. The curve of zeta potential for small particle (150 nm) has slow slope than that of large particle (900nm), giving IEP (isoelectric point) value of pH=1.6 for small particle and pH=1.9 for large particle respectively, which means that it is more difficult to control zeta potential with pH fur small particle than large particle. The dispersion stability of $BaTiO_3$ particles in aqueous medium was found to be strongly related with the agglomeration of colloidal suspensions with time through the sedimentation behaviors of colloidal particles with time and pH value.

• 대한화장품학회지
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• 제33권2호
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• pp.105-110
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• 2007

제타전위를 이용하여 이산화티탄의 분산 안정성을 평가하고 이를 통하여 분산안정도 향상에 응용하고자 하였다. 본 연구에서는 제타전위와 관련된 전기이중층, 전기영동, 등전점 및 전기 침투에 대하여 설명하였으며 측정이론을 기술하였다. H-S equation을 이용하여 수계에 분산된 미립자 이산화티탄의 pH변화에 따른 제타전위 변화를 측정하였으며 제타전위는 pH $3.0{\sim}9.0$에서 음의 값으로 측정되었다. 제타전위 값은 pH값 상승에 따라 절대값이 증가하였으며 분산액의 pH 8.0과 9.0에서는 지속적으로 분산이 유지되었다. 이를 통하여 제타전위가 이산화티탄의 분산에 영향을 미치며 제타전위의 절대값 크기가 수계에서 이산화티탄의 분산안정도에 중요한 역할을 하는 것으로 생각된다.

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.611-623
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• 2020

In this paper, we define a q-analogue of the poly-Euler numbers and polynomials which is generalization of the poly Euler numbers and polynomials including q-analogue of polylogarithm function. We also give the relations between generalized poly-Euler polynomials. Furthermore, we introduce zeta fuctions of Arakawa-Kaneko type and talk their properties and the relation with q-analogue of poly-Euler polynomials.

• 호남수학학술지
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• 제38권4호
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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.

• East Asian mathematical journal
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• 제8권2호
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• pp.235-240
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• 1992

• East Asian mathematical journal
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• 제11권1호
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• pp.81-86
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• 1995

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1573-1581
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• 2010

we investigate the n-fold convolution of the uniform distributions. First, we are concerned with the explicit distribution function of the partial sum ${\zeta}_n$ when the random variables are independent and has identically uniform distribution, next, we determine the n-fold convolution distribution of ${\zeta}_n$ when the identically distributed condition is not satisfied.

• 대한수학회논문집
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• 제33권1호
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• pp.13-36
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• 2018

In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several quadratic and cubic Euler sums through zeta values and linear sums. Furthermore, some relationships between harmonic numbers and Stirling numbers of the first kind are established.