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.

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.

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.

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

김태균,배성수 대한전기협회 2020 전기저널 Vol.- No.526

마취 단계별 뇌파의 특성에 관한 연구

김태균,홍정민,백승완,박종덕,전계록 대한마취통증의학회 2006 Korean Journal of Anesthesiology Vol.50 No.2

Background: Bispectrum and bicoherence analysis that is the frequency domain methods of EEG analysis was examined to elucidate the correlation with the depth of anesthesia. Methods: 25 patients under the gynecological surgery were studied. EEG was surveyed by PhysioLab 400. Analysis of EEG was done according to the progress of anesthesia, normal state before anesthesia, before incision of skin, operation 1, operation 2, awake and post-anesthesia. EEG is applied to filtering of signal, base line correction, linear detrend removal to get more reliable analysis. The appearance rate of bispectrum peaks are calculated by bispectrum operation. And bicoherences are calculated by bispectrum and power spectrum of AR model. Results: In awaking state of patient in pre-anesthesia and post anesthesia, appearance rate of bispectral coupling was observed that a strong appearance rate was represented in all area (0-35 Hz). During the anesthesia, the low frequency area (3-15 Hz) revealed a strong appearance. Also the 2D map of a appearance rate is divided into four sections for more objectivity. Of four sections Bipara#4 is considered that the best parameter which showed progress of anesthesia (P < 0.01). In bicoherence study, in awake state which patient is in pre-anesthesia and post anesthesia, appearance rate of bicoherence value was observed that a strong appearance rate was represented in high frequency range (15-30 Hz). However, under the anesthesia of patients, the low frequency area (0-10 Hz) revealed a strong appearance. And, of four sections Bicpara#2 and Bicpara#4 are considered that the best parameter which showed progress of anesthesia effectively (P < 0.01). Conclusions: The analysis of the peak appearance of bispectrum and bicoherence is useful monitoring for the depth of anesthesia. (Korean J Anesthesiol 2006; 50: 132~9)

Synergism between rocuronium and cisatracurium: comparison of the Minto and Greco interaction models

김태균,전소은,권재영,김해규 대한마취통증의학회 2016 Korean Journal of Anesthesiology Vol.69 No.4

Background: This study was conducted to investigate the pharmacodynamic interaction between rocuronium and cisatracurium using the response surface model, which is not subject to the limitations of traditional isobolographic analysis. Methods: One hundred and twenty patients were randomly allocated to receive one of the fifteen predefined combinations of rocuronium and cisatracurium. To study single drugs, cisatracurium 0.2, 0.15, or 0.1 mg/kg or rocuronium 0.8, 0.6 or 0.4 mg/kg doses were administered alone. To study the pharmacodynamic interaction, drugs were applied in three types of combination ratio, i.e., half dose of each drug alone, 75% of each single dose of rocuronium and 25% of each single dose of cisatracurium, and vice versa. Train-of-four (TOF) ratio and T1% (first twitch of the TOF presented as percentage compared to the initial T1) were used as pharmacodynamic endpoints, and the Greco and Minto models were used as surface interaction models. Results: The interaction term α of the Greco model for TOF ratio and T1% measurements showed synergism with values of 0.977 and 1.12, respectively. Application of the Minto model resulted in U50 (θ) values (normalized unit of concentration that produces 50% of the maximal effect in the 0 < θ < 1 region) less than 1 for both TOF ratio and T1% measurements, indicating that rocuronium and cisatracurium exhibit synergism. Conclusions: Response surface modeling of the interaction between rocuronium and cisatracurium, based on considerations of their effects on muscle relaxation as measured by TOF ratio and T1%, indicated that the two drugs show considerable synergism.

More about the basic assumptions of t-test: normality and sample size

김태균,박재홍 대한마취통증의학회 2019 Korean Journal of Anesthesiology Vol.72 No.4

Most parametric tests start with the basic assumption on the distribution of populations. The conditions required to conduct the t-test include the measured values in ratio scale or interval scale, simple random extraction, normal distribution of data, appropriate sample size, and homogeneity of variance. The normality test is a kind of hypothesis test which has Type I and II errors, similar to the other hypothesis tests. It means that the sample size must influence the power of the normality test and its reliability. It is hard to find an established sample size for satisfying the power of the normality test. In the current article, the relationships between normality, power, and sample size were discussed. As the sample size decreased in the normality test, sufficient power was not guaranteed even with the same significance level. In the independent t-test, the change in power according to sample size and sample size ratio between groups was observed. When the sample size of one group was fixed and that of another group increased, power increased to some extent. However, it was not more efficient than increasing the sample sizes of both groups equally. To ensure the power in the normality test, sufficient sample size is required. The power is maximized when the sample size ratio between two groups is 1 : 1.

Understanding one-way ANOVA using conceptual figures

김태균 대한마취통증의학회 2017 Korean Journal of Anesthesiology Vol.70 No.1

Analysis of variance (ANOVA) is one of the most frequently used statistical methods in medical research. The need for ANOVA arises from the error of alpha level inflation, which increases Type 1 error probability (false positive) and is caused by multiple comparisons. ANOVA uses the statistic F, which is the ratio of between and within group variances. The main interest of analysis is focused on the differences of group means; however, ANOVA focuses on the difference of variances. The illustrated figures would serve as a suitable guide to understand how ANOVA determines the mean difference problems by using between and within group variance differences.

전통 곶감의 수출시장 소비자 선호분석

김태균,조재환 한국유통학회 2001 한국유통학회 학술대회 발표논문집 Vol.- No.-

Modular Multilevel Converter(MMC)의 고조파 저감을 위한 모듈레이션 방식의 비교

김태균,여상민,박정수,최종윤 대한전기학회 2012 대한전기학회 학술대회 논문집 Vol.2012 No.7