Earticle

본 연구에서는 실수 e의 다양한 의미와 맥락을 살펴보고, 실수 e에 대한 예비교사들의 이해 정도를 조사하였다. 이를 위해 실수 e에 대한 역사적 발생과 수학적 의미를 살펴보았으며, 이 결과를 바탕으로 검사지를 개발하여 예비교사 28명에게 적용하였으며, 그 중 8명에게 반성 및 탐구 활동을 수행하였다. 실수 e에 대한 예비교사들의 이해를 분석한 결과는 다음과 같다. 상당수의 예비교사들이 실수 e의 형식적 정의와 그 표현과의 관계를 인식하지 못하였으며, 실수 e의 표현을 극한 표현에 편중되어 이해하고 있었다. 실수 e의 무리수 속성과 작도 불가능성에 대해 적절한 판단을 내렸으나, 그 근거에서는 다소 미흡한 면모를 드러내었다. 또한 실수 e의 연속 복리 맥락과 지수함수 맥락에는 높은 이해도를 나타낸 반면에, 기하적 맥락과 자연로그 맥락을 미흡하게 이해하고 있음을 확인하였다. 향후 예비교사 프로그램의 개선 방향으로, 예비교사들에게 실수 e의 다양한 표현과 속성, 맥락에 대한 학습기회를 제공하고, 실수 e의 다양한 측면이 잘 조직된 관계망 속에서 통합 지도될 필요가 있음을 제시하였다.

The purpose of this study is to analyze the concept of the real number e and to investigate the understanding of pre-service teachers about the real number e. 28 pre-service teachers were asked to take a test based on the various ideas of the real number e and 8 pre-service teachers were interviewed. The results of this study are as follows. First, a large number of pre-service teachers couldn't recognize relation between the formal definition and the representations of the real number e. Secondly, pre-service teachers judged appropriately for the irrationality and the construction impossibility of the real number e, but they couldn't provide reasonable evidence. Lastly, pre-service teachers understood the continuous compounding context and exponential function context of the real number e, but they had a difficulty in understanding the geometric context and natural logarithm context of the real number e.

In collecting and analyzing information about recent research papers, authors, and journals with their citation and indices, we noticed that in many cases such indices fail to reflect reality and are incapable to distinguish between different authors in some cases while they clearly have different research profiles. There are many research papers that can be found in literature that discussed the behavior and limitations of the current citation or publication indices. Most of them referred to the sensitivity problem and the fact that most indices neglect some publications during index calculation. These two problems are the most important limitations that may judge index fairness. In this paper, we proposed new indices; MIExp-Index using exponential function and MIArea-Index using the concept of the area under curve (AUC) in order to enhance the sensitivity and thus the fairness of index assessment. To demonstrate our two novel indices, data of real and hypothetical authors were used to demonstrate these two approaches. The results showed that both of the proposed indices are very sensitive for each single citation that the paper receives after being published. In addition, the two indices consider all authors’ publications, even the new ones, into account.

Beam-to-column connections are very important in steel structure buildings, and have direct effect on safety and economic efficiencies of the buildings. Especially, they have rigidity and ductility that are necessary for behavior and stress transmission of buildings. Furthermore, they are also needed carry strength and strain with easy construction. The design and analysis of steel structure connections are generally considered to consist of rigid, semi-rigid or pin joint. Deformation characteristic of H-shaped beams with newly T-stub connections is investigated for the effect of these joints on inelastic behavior of the beams in this paper. This research applies the model of exponential function based on the equations of equilibrium and compatibility equations at the location of bolts. The prying action reducing both the ultimate load capacity and the fatigue of the bolts are not considered in this study. The elasto-plastic behavior has been studied through various models with parameters of the length of T-flange, distance of bolts and the diameter of bolts. The results indicated that the distance of bolts has a great effect on the ultimate strength and deformation capacity of T-stub connections. The presented method may be a useful tool for the design of T-stub connections.

In this paper, we introduce some algebraic, rational and polynomial upper bounds of the exponential function on the interval [0,1). And then we compare the acuteness of these bounds.

In this paper, for each natural number n, we construct a polynomial $p_n$(x) of degree n so that $p_n(x)\;\leq\;p_{n+1}(x)\;\leq\;e^x$ for $x\;\geq\;-1$. These polynomials are optimal in the sense that if p(x) is a polynomial of degree n with $p_{n-l}(x)\;\leq\;p(x)\;\leq\;e^x$, then $p(x)\;\leq\;p_n(x)$.

In this note, an alternative proof and extensions are provided for the following conclusions in [6, Theorem 1 and Theorem 3]: The functions $\frac1{x^2}-\frac{e^{-x}}{(1-e^{-x})^2}\;and\;\frac1{t}-\frac1{e^t-1}$ are decreasing in (0, ${\infty}$) and the function $\frac{t}{e^{at}-e^{(a-1)t}}$ for a $a{\in}\mathbb{R}\;and\;t\;{\in}\;(0,\;{\infty})$ is logarithmically concave.

In this note, an alternative proof and extensions are provided for the following conclusions in [6, Theorem 1 and Theorem 3]: The functions $\frac1{x^2}-\frac{e^{-x}}{(1-e^{-x})^2}\;and\;\frac1{t}-\frac1{e^t-1}$ are decreasing in (0, ${\infty}$) and the function $\frac{t}{e^{at}-e^{(a-1)t}}$ for a $a{\in}\mathbb{R}\;and\;t\;{\in}\;(0,\;{\infty})$ is logarithmically concave.

This paper studies the exponential stability of linear time-varying (LTV) systems using the recent proposed integral function. By showing the properties of the integral function and applying the Bellman-Gronwall Lemma, a sufficient and necessary condition for the exponential stability of LTV systems is derived. Furthermore, the exponential decay rate of the system trajectories can be obtained by computing the radii of convergence of integral function. The algorithm for computing the integral function is also developed and two classical examples are given to illustrate the proposed approach.

In this article, we discuss the reflective function which can be represented by three exponential matrixes and apply the results to studying the existence of periodic solutions of these systems. The obtained conclusions extend and improve the foregoing results.

In this paper, we give a solving approach based on a logarithmic-exponential multiplier penalty function for the constrained minimization problem. It is proved exact in the sense that the local optimizers of a nonlinear problem are precisely the local optimizers of the logarithmic-exponential multiplier penalty problem.

In this paper we have proposed a new loss function, namely, non-linear exponential(NLINEX) loss function, which is quite asymmetric in nature. We obtained the Bayes estimator under exponential(LINEX) and squared error(SE) loss functions. Moreover, a numerical comparison among the Bayes estimators of power function distribution under SE, LINEX, and NLINEX loss function have been made.

In this paper, we develop the reference and the matching priors for the reliability function of two-parameter exponential distribution. We derive the reference priors and the matching prior, and prove the propriety of joint posterior distribution under the general prior including the reference priors and the matching prior. Through the sim-ulation study, we show that the proposed reference priors match the target coverage probabilities in a frequentist sense.

We propose several estimators of the reliability function R of the two-parameter exponential distribution, and then compare those estimator in terms of the mean square error (MSE) through Monte Carlo method. We also consider the parametric bootstrap estimation. Using the parametric bootstrap estimator, we obtain the bootstrap confidence intervals for reliability function and compare the proposed bootstrap confidence intervals in terms of the length and the coverage probability through Monte Carlo method.

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be independent and identically distributed random variables having common exponential density with unknown mean ${\mu}$. In the sequential confidence interval estimation for the exponential hazard rate ${\theta}=1/{\mu}$, when the loss function is strictly convex, the following stopping rule is proposed with the half length d of prescribed confidence interval $I_n$ for the parameter ${\theta}$; ${\tau}$ = smallest integer n such that $n{\geq}z^2_{{\alpha}/2}\hat{\theta}^2/d^2+2$, where $\hat{\theta}=(n-1)\bar{X}{_n}^{-1}/n$ is the minimum risk estimator for ${\theta}$ and $z_{{\alpha}/2}$ is defined by $P({\mid}Z{\mid}{\leq}{\alpha}/2)=1-{\alpha}({\alpha}{\in}(0,1))$ Z ~ N(0, 1). For the confidence intervals $I_n$ which is required to satisfy $P({\theta}{\in}I_n){\geq}1-{\alpha}$. These estimated intervals $I_{\tau}$ have the asymptotic consistency of the sequential procedure; $$\lim_{d{\rightarrow}0}P({\theta}{\in}I_{\tau})=1-{\alpha}$$, where ${\alpha}{\in}(0,1)$ is given.

Early in the development of the software reliability model, it was assumed that the operating environment of the software was used in the same or similar field environment as the test environment. However, they may also be used in many different locations that may differ from the environment in which they were developed and tested. And also, in general, software systems are known to degrade performance and increase failure rate as their service life increases. Therefore, efforts have been made to expand the exponential distribution assuming a constant failure rate. In this paper, we propose a new software reliability model with the generalized exponential (GE) fault detection rate function considering the uncertainty of operation environments based on a non-homogeneous Poisson process (NHPP). We examine the goodness-of-fit of a new NHPP software reliability model and other existing models based on dataset. As a result of comparison of goodness-of-fit, it can be confirmed that the new proposed model is significantly better by showing that all the criteria of the new proposed model are the lowest compared to other models. In addition, the results for the sensitivity analysis show that the parameters of a new NHPP software reliability model affect the mean value function.

This paper studies the exponential stability of continuous-time planar piecewise-linear systems (PPLS). By introducing a novel conception of integral function of PPLS and showing its properties, a sufficient and necessary condition for the exponential stability is derived. Furthermore, the exponential growth rate of system trajectories can be obtained accurately by computing the convergence radius of integral function. The algorithm for computing the integral function is developed and two examples are given to demonstrate the proposed approach.

표본조사에서는 추정의 정확성 및 정밀성 향상을 위해 흔히 층화추출법을 사용하며 층 내에서는 동일한 표본 가중치를 이용하여 표본을 추출한다. 그러나 실제 응답률은 관심변수 값에 영향을 받을 수 있기 때문에 주어진 동일한 가중치는 응답률을 반영하여 보정되어야 한다. 또한 관심변수가 연속형 보조변수와 선형 관계가 있고 보조변수를 기준으로 층이 나누어진 경우에는 층 내에서 동일한 가중치를 사용하는 것 보다 층을 세분화한 후 얻어진 가중치를 사용하는 것이 효과적일 수 있다. 본 연구에서는 응답률이 관심변수 자료 값의 지수함수이고, 관심변수가 보조변수와 선형 관계가 있을 때 정보적 표본설계 기법을 이용하여 추정의 정확성과 정밀성을 높이는 방법을 제안하였다. 또한 모의실험을 통하여 제안된 방법의 우수성을 확인하였다.

A stratified sampling method is generally used with a sample selected using the same sample weight in each stratum in order to improve the accuracy of the sampling survey estimation. However, the weight should be adjusted to reflect the response rate if the response rate is affected by the value of the variable of interest. It may be also more effective to adjust the weights by subdividing the stratum rather than using the same weight if the variable of interest has a linear relationship with the continuous auxiliary variables. In this study, we propose a method to increase the accuracy of estimation using an informative sampling design technique when the response rate is an exponential function of the variable of interest and the variable of interest has a linear relationship with the auxiliary variable. Simulation results show the superiority of the proposed method.

본 논문은 시스템의 출력 신호가 복소지수함수의 형태인 경우 시스템을 추정하고 이를 이용한 제어에 관한 논문이다. 제안한 방법은 시스템의 출력 신호가 복소지수함수의 형태라면 이산푸리에변환을 통하여 중요모드에서의 첨두주파수와 제동계수를 추정하고, 이를 이용하여 시스템의 전달함수를 2차의 표준형 전달함수를 이용하여 간단하게 추정한다. 그리고 제어기는 이 추정한 전달함수를 이용하여 사용자가 원하는 응답을 나타내도록 설계하였다. DC모터의 위치제어 시스템의 실험을 통하여 제안한 방법의 타당성과 효율성을 검증하였다.