• 한국학교수학회논문집
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• 제5권1호
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• pp.111-122
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• 2002

The purpose of this study was to examine high school second graders' understanding of the basic nature of logarithm, the major type of error they made about logarithmic function and the cause of such an error, and to seek ways to instruct it better. For that purpose, three research questions were posed: 1. Investigate how much high school students in their second year comprehend the nature of logarithm. 2. Analyze what type of error they make about logarithmic function. 3. Analyze the cause of their error according to the selected error models and how it could be taught more efficiently. The findings of this study were as below: First, the natural science students had a better understanding of the basic nature of logarithm than the academic students. What produced the widest gap between the two groups' understanding was applying the nature of logarithm to the given problems, and what caused the smallest gap was the definition of logarithm and the condition of base. Second, the academic students had a poorer understanding of the basic nature of logarithmic function graph and of applying the nature of logarithm to the given problems. Third, the natural science students didn't comprehend well the basic nature of logarithmic function graph, the nature of characteristics and mantissa. Fourth, for all the students from academic and natural science courses, the most common errors were caused by the poor understanding of theorem or nature of the ［E4] model. Fifth, the academic students made more frequent errors due to the unfamiliar signs of the ［El］ model, the imperfect understanding of theorem or nature of the ［E4］ model, and the technical part of the ［E6］ model. Sixth, the natural science students made more frequent errors because of the improper problem interpretation of the ［E2］ model and the logically improper inference of the ［E3］ model.

• 한국수학사학회지
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• 제27권6호
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• pp.409-419
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• 2014

In school mathematics, the logarithmic function is defined as the inverse function of an exponential function. And the natural logarithm is defined by the integral of the fractional function 1/x. But historically, Napier had already used the concept of logarithm in 1614 before the use of exponential function or integral. The calculation of the logarithm was a hard work. So mathematicians with arithmetic ability made the tables of values of logarithms and people used the tables for the estimation of data. In this paper, we first take a look at the mathematicians and mathematical principles related to the appearance and the developments of the logarithmic tables. And then we deal with the confusions between mathematicians, raised by the estimation data which were known as proportional parts or mean differences in common logarithmic tables.

• 한국공간구조학회논문집
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• 제18권1호
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• pp.77-84
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• 2018

The identification of damping ratios in buildings is a well-known problem and appears to be of important and crucial interest in the safety and serviceability design. When compared to an estimation of the stiffness, i.e. natural frequency, and mass, the damping ratio is the most difficult quantity to determine. Many previous studies have examined the characteristics of damping ratios from ambient vibration, but the measurement time is roughly within 2 hours. In this paper, characteristics of damping ratios and natural frequencies of 4 story RC building were investigated using long-term ambient vibration. Free vibrations were obtained using random decrement technique, and damping ratios were evaluated by the envelop function, continuous wavelet transform, and logarithmic decrement. It was found that although the natural frequencies show little variations with time, the damping ratios show some variations with time and the largest variations found in the damping ratios obtained from the continuous wavelet transform. The damping ratios from the envelop function showed the smallest mean and standard deviation. And the probability distribution of damping ratios seems to follow the logarithmic normal distribution.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1996년도 추계학술대회논문집; 한국과학기술회관, 8 Nov. 1996
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• pp.313-318
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• 1996

In this paper, a parametric study of the unbalance response and the stability is carried out to show the influence of seal parameters on the response of rotor. The seal parameters optimized are the seal clearance and the seal length. The minimum quantity of a Q factor in the critical speed and the maximum quantity of a logarithmic decreement in the operating speed, avoiding the reign of resonance, are the objective function. This paper describes a new approach to find a seal parameter of rotor system. The optimization method is used genetic algorithms, which are search algorithms based on the mechanics of natural selection and natural genetics. The results show the capability of this method and indicate that an optimal design of seals can improve the unbalance and the stability of rotor.

• 전자공학회논문지A
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• 제33A권7호
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• pp.65-75
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• 1996

The probability distributio function (pdf) of transmitted symbols should be asymmectric for recovering the received data in the 3rd order blind equalizer system. In this paper, we hav edesigned the blind equalizer using symmetric-asymmetric (SA) and asymmetric-symmetric (AS) transforms for less computational complexities and robustness in the noisy environments. The method of SA and AS transform was peformed using natural logarithmic operation. This paper proves that the proposed in this paper can be performed as real time operation. This paper proves that the compression factor k has no effet on transmitted symbols. Also 3rd order equalization method proposed in this paper can be performed as real time operation. As a result of computer simulatio, the computational complexity of proposed algorithm is reduced to be an half of 4th order method and MSE is enhanced as 10dB at the case of 4-PAM and 15dB at the case of 8-PAM respectivley. Conclusively, we have found that 3rd order blind equalizer can be implemented when the pdf of transmitter is asymmetric.

• 통합자연과학논문집
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• 제7권4호
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• pp.273-277
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• 2014

In this article, we consider a singular and a degenerate elliptic operators in a divergence form. The singularities exist on a part of boundary, and comparable to the logarithmic distance function or its inverse. If we assume that the operator can be treated in a pointwise sense than distribution sense, with this operator we obtain a priori Harnack continuity near the boundary. In the proof we transform the singular elliptic operator to uniformly bounded elliptic operator with unbounded first order terms. We study this type of estimations considering a De Giorgi conjecture. In his conjecture, he proposed a certain ellipticity condition to guarantee a continuity of a solution.

• 한국컴퓨터정보학회논문지
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• 제16권10호
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• pp.101-109
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• 2011

리만의 제타함수 $\zeta(s)$는 주어진 수 x보다 작은 소수의 개수 $\pi$(x)를 구하는 해답으로 알려져 있으며, 소수정리에서 지금까지 리만의 제타 함수 이외에 $\frac{x}{lnx}$,Li(x)와 R(x)의 근사치 함수가 제안되었다. 여기서 $\pi$(x)와의 오차는 R(x) < Li(x) < $\frac{x}{lnx}$이다. 로그적분함수 Li(x) = $\int_{2}^{x}\frac{1}{lnt}dt$, ~ $\frac{x}{lnx}\sum\limits_{k=0}^{\infty}\frac{k!}{(lnx)^k}=\frac{x}{lnx}(1+\frac{1!}{(lnx)^1}+\frac{2!}{(lnx)^2}+\cdots)$ 이다. 본 논문은 $\pi$(x)는 유한급수��Li(x)로 표현됨을 보이며, 일반화된 $\sqrt{ax}{\pm}{\beta}$의 소수계량함수를 제안한다. 첫 번째로, $\pi$(x)는 $0{\leq}t{\leq}2k$의 유한급수인 $Li_3(x)=\frac{x}{lnx}(\sum\limits_{t=0}^{{\alpha}}\frac{k!}{(lnx)^k}{\pm}{\beta})$와 $Li_4(x)=\lfloor\frac{x}{lnx}(1+{\alpha}\frac{k!}{(lnx)^k}{\pm}{\beta})\rfloor$, $k\geq2$ 함수로 표현됨을 보였다. $Li_3$(x)는 $\pi(x){\simeq}Li_3(x)$가 되도록 ${\alpha}$ 값을 구하고 오차를 보정하는 ${\beta}$ 값을 갖도록 조정하였다. 이 결과 $x=10^k$에 대해 $Li_3(x)=Li_4(x)=\pi(x)$를 얻었다. 일반화된 함수로 $\pi(x)=\sqrt{{\alpha}x}{\pm}{\beta}$를 제안하였다. 제안된 $\pi(x)=\sqrt{{\alpha}x}{\pm}{\beta}$ 함수는 리만의 제타함수에 비해 소수를 월등히 계량할 수 있었다.

• 한국수학교육학회지시리즈A:수학교육
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• 제37권1호
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• pp.87-99
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• 1998

Mathematics education is very important in future because mathematics is the basis of every study, for example, natural and social science, etc. Our nation wide curriculum has been revised six times since 1948. In 1992, the sixth revision was enforced and we are using the revised textbook now. This study aims at helping of continuous investigation for educational curriculum and textbook, and aims at efficient teaching by preventing unnecessary repetition and excessive gap in real field by analyzing the articulation of Analytics part in school textbook from elementary to high school. This thesis consists of the followings. 1.Investigation of the principles and natures of articulation along with curriculum course and notice the articulation based on the analysing tools. 2.Importance of learning functions. 3.To get the propriety, formation of 8 judging group and classification of content materials in function chapters by the judges based on the analyzing tools. 4.Analysis of presentation method and terminologies in the first concepts, suggestion teaching method to reduce gap and help of understanding on first concepts in the study of function. As a result 'development' consists of 55.8% of the total and it is higher than 'duplication' and 'gap'. To be specific in periods, between elementary school and middle school 'development' takes 64.5% and this shows an acceptable articulation in the period. While 39.4% of 'gap' in articulation between middle school and high school looks high compared with 'gap' between the previous periods. The item suggested with the 'gap' is the 'definition of function', 'value of function', 'parallel translation', 'exponential and logarithmic function'. It is observed that these materials is suddenly appeared in high school.

• 대한한방내과학회지
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• 제29권1호
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• pp.1-11
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• 2008

Objectives : Essential hyperhidrosis is a socially and occupationally disabling disorder. There are many suggestions that hyperhidrosis is associated with the autonomic nervous system. This study was designed to investigate the autonomic nerve system the patients with hyperhidrosis. Methods : 348 palmar and plantar hyperhidrosis patients and 20 systemic hyperhidrosis patients in the ambulatory care were investigated. All patients were inspected at the first medical examination, using the PSA of HRV. HRV was measured for 5 minutes after 5 minutes' bed rest. We checked the frequency domain analysis of HRV (i.e. TP, VLF, LF, HF and LF/HF) which were transformed into natural logarithm of patients against the standard measures of the HRV components. Then, we compared the means of patients with means and highest values of in the normal range of Koreans 1) between the patients with palmar and plantar hyperhidrosis and the healthy controls and 2) between the patients with the systemic hyperhidrosis and healthy controls, by the frequency domain analysis of heart rate variability (HRV), respectively. We then compared the results between 1) and 2). Results : The values of natural logarithmic measures of LF/HF ratio in the patients with palmar and plantar hyperhidrosis we examined were significantly higher than the values of healthy controls, but those in the patients with systemic hyperhidrosis were not higher. Conclusion : This study suggests that the autonomic nervous function did not simply increase but that the balance between sympathetic and parasympathetic nervous function did matter in patients with palmar and plantar hyperhidrosis. This balance included that the sympathetic nervous function aggravated comparatively with parasympathetic nervous function. On the other hand, we couldn't find any significance of the patients with the systemic hyperhidrosis as for the autonomic nervous function.

• 대한한방내과학회지
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• 제27권4호
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• pp.822-826
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• 2006

Objectives : Essential hyperhidrosis is a socially and occupationally disabling disorder. There are many suggestions that hyperhidrosis is associated with the autonomic nervous system, especiallythe sympathetic system. This study was designed to investigate the autonomic nerve system in patients with essential hyperhidrosis and healthy controls by the frequency domain analysis of heart rate variability (HRV). Methods : 17 head-hyperhidrosis patients in the ambulatory care were investigated. All were inspected at the first medical examination. using the PSA of HRV. HRV was measured for minutes after 5 minutes bed rest. We checked the frequency domain analysis of HRV (i.e. TP, VLF, LF, HF) which were transformed into natural logarithm of patients against the standard measures of the HRV components. Then we compared the values of patients with means of normal Korean subjects. Results : The values of natural logarithmic measure of HRV (LnTP, LnHF, LnLF, LnVLF) of patients With head-hyperhidrosis we examined were $6.85{\pm}1.61$, $4.93{\pm}$2.00, $5.40{\pm}1.83$, and $6.13{\pm}1.37$, respectively. None of these values were higher than means of normal subjects. Conclusions : This study suggests that the function of the autonomic nervous system does not increase in patients with head-hyperhidrosis.