수학사적 관점에서 오일러 및 베르누이 수와 리만 제타함수에 관한 탐구

김태균,장이채,Kim, Tae-Kyun,Jang, Lee-Chae 한국수학사학회 2007 Journal for history of mathematics Vol.20 No.4

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. J. Bernoulli first discovered the method which one can produce those formulae for the sum $S_n(k)=\sum_{{\iota}=1}^n\;{\iota}^k$ for any natural numbers k. After then, there has been increasing interest in Bernoulli and Euler numbers associated with Riemann zeta functions. Recently, Kim have been studied extended q-Bernoulli numbers and q-Euler numbers associated with p-adic q-integral on $\mathbb{Z}_p$, and sums of powers of consecutive q-integers, etc. In this paper, we investigate for the historical background and evolution process of the sums of powers of consecutive q-integers and discuss for Euler zeta functions subjects which are studying related to these areas in the recent.

사주와 성격검사의 공인(共因)에 관한 연구

김태균 공주대학교 동양학연구소 2000 초자연현상연구 Vol.7 No.-

본 연구는 四柱의 과학성을 확립하기 위한 과정에서 사주에서 본 개인의 성격과 과학적 연구 방법을 통해 형성된 KPDI 성격 진단 검사 사이의 共因 관계를 알아봄으로써 사주 성격 해석의 타당성을 입증하기 위한 탐색 연구이다. 연구 대상은 서울과 대구 소재 20세 이상 남녀 47명이었다. 연구 목적을 달성하기 위해 두 가지 검증 절차를 사용하였다. 먼저 양적 연구로서, KPDI의 요인들 중 사주의 성격 해석에서 양화가 가능한 8개 척도(주도성, 사교성, 자신감, 책임감, 사회화, 자기통제, 관용성, 지적효율성)를 선별하고, 사주를 KPDI의 조작적 정의에 맞춰 再 정의하여 이에 따라 사주 판단이 가능한 전문가(김태균)가 9점으로 평정하였다. 이 평정치와 KPDI T점수 사이의 상관관계를 산출하였다. 그 결과 각 하위 요인 간 상관관계는 부분적이기는 하지만 유의미한 관계가 나타났다. (사교성, 자신감, 자기통제 3개 요인에서 r=.252 ~.339) 특히 연령별 분석에서는 8개 측정 요인 중 사교성과 자신감은 매우 높은 관련성(최고 r=.814)을 보였다. 30대는 대부분의 요인에서 가장 높은 관련성을 보였고, 그 다음은 50대, 20대 순이었다. 두 번째 방법은 질적 분석을 포함한다. 성격은 성격을 구성하고 있다고 간주된 요인들 간의 조합에 의해 각기 독특한 양상을 드러낸다. 따라서 요인들의 개별 점수보다는 그 요인들의 조합에 의한 각 개인의 전체적 인상 또는 패턴이 더 중요하다. 이런 관점에서 질적 접근은 앞서 양적 접근 보다 더 중요한 의미를 갖는다고 볼 수 있다. 두 번째 검증 방법은 사주상의 성격과 KPDI 결과를 공동연구자가 각각 따로 해석하고 그 결과를 10인의 평정자들이 두 검사간의 일치 정도를 평정하였다. 그 결과 전체 연령에서 평균 6점 이상의 일치정도를 나타냈다. 결론적으로 사주의 성격 해석 방법은 KPDI 성격 진단 검사와 부분적이나마 유의미한 관련성이 있음을 알 수 있다. 그러므로 사주성격해석의 타당성을 입증하기 위한 지속적 연구의 필요성이 제기된다. This study has the purpose to prove the validity of a personality interpretation by Saju with common characteristics shared by KPDI’s Personality Diagnosis Inventory and Saju’s scientific approach. To do this job. we sampled 47 people older than 20 years old males and females in Seoul and Daegu and surveyed their Saju, employing the two approaches: the quantitative and the qualitative. First, for the quantitative, we selected 8 variables which could be compatibly measured within KPDI’s variables (dominance. sociability, self-respect, responsibility, socialization, self-control, tolerance, inteligent-efficacy.) With adjusted KPDI’s standard to Saju’s variables, the expert (Kim, Taegiun) reevaluated the results with 9 points. And, we compared Saju’s results with KPDI’s and induced their relativeness. As a result, the correlation in the lower parts of variables was partly but meaningfully related with each other (sociability, self-respect. and self-control indicate r=.252~.339). Especially, in the analysis of the level of age. the two varialbles (socialblity and self-respect) revealed high-scores in the relativeness (maximum r=.814): the thirties showed high relativeness in most of the varialbles followed by the fifties and twenties. Second, for the qualitative, Personality carried out its own aspects made by the combination of its elemental composition. The whole impression, therefore, could be considered more important than the individual point on each variable, in this respect, the qualitative approach had more meaningful than the quantitative. The qualitative was for co-researchers individually to interpret the personality from Saju and the result by KPDT. Finally, their consistency would be evaluated by 10 evaluators, in all age levels, however, the mean level of consistency was above 6 points. In conclusion. there was some meaningful relativeness in between Saju personality Interpretaion and KPDI personality Diagnosis Inventory. Therefore, It should suggest that we continue to study more about the validity of saju persaonalty Interpretation.

A note on degenerate central factorial polynomials of the second kind

김태균,장관우,김태균 장전수학회 2019 Advanced Studies in Contemporary Mathematics Vol.29 No.1

In a recent work, the degenerate central factorial numbers of the second kind were introduced. In this paper, we study the degenerate central factorial polynomials of the second kind and give some identities for these polynomials associated with special numbers and polynomials.

[OPINION] “현장에 도움될 수 있는 실용 중심의 연구에 집중할 것” : 김태균 한국전력공사 전력연구원장

김태균,배성수 대한전기협회 2020 전기저널 Vol.- No.526

SYMMETRIC IDENTITIES OF DEGENERATE BERNOULLI POLYNOMIALS

김태균 장전수학회 2015 Proceedings of the Jangjeon mathematical society Vol.18 No.4

We investigate some identities and properties of symmetry for degenerate Brenoulli polynomials which are derived from the p-adic invari- ant integral on Zp.

A STUDY ON THE q-EULER NUMBERS AND THE FERMIONIC q-INTEGRAL OF THE PRODUCT OF SEVERAL TYPE q-BERNSTEIN POLYNOMIALS ON Zp

김태균 장전수학회 2013 Advanced Studies in Contemporary Mathematics Vol.23 No.1

In this paper, we investigate some properties between q-Bernstein polynomials and q-Euler numbers by using fermionic p-adic q-integrals on Zp. From these properties, we derive some interesting identities related to the q-Euler numbers.

On the k-dimensional generalization of q-Bernstein polynomials

김태균,최종성,김영희 장전수학회 2011 Proceedings of the Jangjeon mathematical society Vol.14 No.2

Recently, the q-Bernstein polynomials are constructed in [5]. In this paper, we propose the k-dimensional generalizations of the q-Bernstein polynomi-als.

SYMMETRIC IDENTITIES FOR q-EULER POLYNOMIALS UNDER THE FOURTH DIHEDRAL GROUP

김태균,J. J. Seo 장전수학회 2015 Proceedings of the Jangjeon mathematical society Vol.18 No.2

Recently, Some identities of symmetry for Carlitz's q-Bernoulli polynomials under the fourth Dihedral group D4 were introduced in [10]. In this paper, we give some new identities of symmetry for the Carlitz's type q-Euler polynomials under the fourth Dihedral group D4 which are derived from the fermionic p-adic q-integral on Zp.

Economic Damage Assessment of Coastal Development using Dynamic Bioeconomic Model

김태균 한국항해항만학회 2012 한국항해항만학회지 Vol.36 No.9

This article analyzes the interdependency between nonrenewable marine sand resources and renewable fishery resources by the developed dynamic bioeconomic model. The developed bioeconomic model is applied to a case study of efficient sustainable management for marine sand mining, which adversely affects a valuable blue crab fishery and its habitat in Korea. The socially-efficient extraction plan for marine sand and the time-variant environmental external costs to society in terms of diminished harvest rate of blue crab are determined. To take into account long-term effects from destroyed fishery habitat, a Beverton-Holt age structure model is integrated into the bioeconomic model. The illustrative results reveal that the efficient sand extraction plan is dynamically constrained by the stock size of the blue crab fishery over time. Thus, the dynamic environmental external cost is more realistic resource policy option than the classical fixed external cost for determining socially optimal extraction plans. Additionally, the economic value of bottom habitat, which supports the on- and off-site commercial blue crab fishery is estimated. The empirical results are interpreted with emphasis on guidelines for management policy for marine sand mining.

Continuous Improvements of a Clinical Pathway Increased Its Feasibility and Improved Care Providers’ Perception in TKA

김태균,장문종,김석진,송영동,김세경 대한슬관절학회 2014 대한슬관절학회지 Vol.26 No.4

purpose: We aimed to determine 1) whether dropout rate decreased and 2) whether health care providers’ perceptions were changed with continued improvements of contents of clinical pathway (CP) for total knee arthroplasty (TKA).materials and methods: This retrospective study included two separate analyses of patients and health care providers. In the analysis of patients, dropout rates and reasons were evaluated in two cohorts of patients who underwent TKA with CP applied at two different time periods (384 patients from 2009 to 2010 and 242 patients from 2012 to 2013). Contents of CP were continuously improved during the 3-year interval. Self-administered questionnaire surveys targeted to health care providers were carried out twice (2010 and 2013) and compared. results: Dropout rate decreased from 19.1% in the first time period to 10.4% in the second time period. Although overall satisfaction of care providers was high at both time-points, doctors had more favorable perceptions than nurses; most positive changes of perception were noted in nurses. The health care providers’ perceptions for potential concerns of CP were improved while the perceptions for potential benefits and satisfaction were maintained. conclusions: Continuously improved CP has increased feasibility for TKA patients and reduced health care providers’ concern about its value. We propose that CP can be implemented and actively used to improve the outcomes and efficacy of patient care for TKA, regardless of the rotation of care providers.