• Journal of the Korean Statistical Society
• /
• 제17권1호
• /
• pp.46-55
• /
• 1988

Two-piece double exponential distribution (TPDE) with one piece $(X \leq 0)$ having the scale parameter $\theta_1$ while the other piece (X>0) having $\theta_2$ is considered here. Distribution of the sum of n-independent variables from such a distribution is obtained. Special cases of this distribution are also treated. Next, distribution of the ratio of two independent (TPDE) variables is derived. As an extension, distribution of $x_1/x_2x_3$ is expressed terms of hypergeometric functions. A small table gives the power of the test regarding double exponential against (TPDE).

• Journal of applied mathematics & informatics
• /
• 제39권1_2호
• /
• pp.83-91
• /
• 2021

In this paper, we introduce the concepts of q-cosine tangent polynomials and q-sine tangent polynomials. From these polynomials, we find some identities and properties by using q-numbers and q-trigonometric functions.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2007년도 심포지엄 논문집 정보 및 제어부문
• /
• pp.74-76
• /
• 2007

This paper presents the hardware design of a 32bit floating point based processor. The processor can perform nonlinear functions such as sinusoidal functions, exponential functions, and other nonlinear functions. Using the Taylor series and the Newton - Raphson method, nonlinear functions are approximated. The processor is actually embedded on an FPGA chip and tested. The numerical accuracy of the functions is compared with those computed by the MATLAB.

• 한국산학기술학회논문지
• /
• 제12권11호
• /
• pp.5347-5356
• /
• 2011

본 연구에서는 Lagrangian/Hermite 보간함수를 혼합정식화한 유한요소법과 다양한 전단변형함수로 역대칭 앵글-플라이 샌드위치판 모델을 비교하였다. 제시된 전단변형함수는 판의 상하면에서 전단응력이 0이 되는 다항식, 삼각함수, 쌍곡삼각함수 및 지수함수로 구성되어 있다. 모든 전단변형함수는 해석해(Analytical solution)와 비교하였으며, 합리적인 정확도를 갖는 것으로 예측되었다. 특히, 지수형태의 전단변형함수가 복합면재를 갖는 샌드위치판 해석에 있어서 상대적으로 가장 우수한 결과를 보였다.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2003년도 ICCAS
• /
• pp.2298-2303
• /
• 2003

In this paper, very simple methods based on the exponential analysis are presented by which transfer function models for processes can easily be obtained. These methods employ step responses or impulse responses of the processes. These can also give a more precise transfer function model compared to the well-known graphical methods. Transfer functions are determined based on Prony method, which is one of the oldest and the most representative methods in the exponential analysis. Here, the method is reformed and applied to obtain the so-called low-order transfer function with pure time delay from the data of the step response. The effectiveness of the proposed method is examined through several numerical examples and experiments of the 2-tank level control process.

• Korean Journal of Mathematics
• /
• 제8권1호
• /
• pp.73-86
• /
• 2000

We study the Sobolev spaces to the generalized Sobolev spaces $H^s_{\mathcal{G}}$ of exponential type based on the Silva space $\mathcal{G}$ and investigate its properties such as imbedding theorem and structure theorem. In fact, the imbedding theorem says that for $s$ > 0 $u{\in}H^s_{\mathcal{G}}$ can be analytically continued to the set {$z{\in}\mathbb{C}^n{\mid}{\mid}Im\;z{\mid}$ < $s$}. Also, the structure theorem means that for $s$ > 0 $u{\in}H^{-s}_{\mathcal{G}}$ is of the form $$u={\sum_{\alpha}\frac{s^{{|\alpha|}}}{{\alpha}!}D^{\alpha}g{\alpha}$$ where $g{\alpha}$'s are square integrable functions for ${\alpha}{\in}\mathbb{N}^n_0$. Moreover, we introduce a classes of symbols of exponential type and its associated pseudo-differential operators of exponential type, which naturally act on the generalized Sobolev spaces of exponential type. Finally, a generalized Bessel potential is defined and its properties are investigated.

• 응용통계연구
• /
• 제8권1호
• /
• pp.133-149
• /
• 1995

파워(>2)분산함수를 가진 자연지수계열군에 속하는 분포들의 확률밀도함수는 무한급수로 표현되기 때문에 분포들의 유용성에도 불구하고 취급하기가 매우 힘들다. 따라서 이 논문에서는 분포들에 대한 백분위수들의 표를 제시하고자 하였다. 확률밀도 함수의 형태때문에 계산하기 곤란했던 몇가지 백분위수들이 위 분포들이 가지는 확률적 성질들에 기인하여 구해지는 근사백분위수에 의해 상당히 잘 대체될 수 있음을 보여주었다.

• Journal of Forest and Environmental Science
• /
• 제28권2호
• /
• pp.63-67
• /
• 2012

Crown ratio is the ratio of live crown length to tree height. It is often used as an important predictor variable for tree growth equation. It indicates tree vigor and is a useful parameter in forest health assessment. The objective of the study was to develop crown ratio prediction models for Tectona grandis. Based on the data set from the temporary sample plots, several non linear equations including logistics, Chapman Richard and exponential functions were tested. These functions were evaluated in terms of coefficient of determination ($R^2$) and standard error of the estimate (SEE). The significance of the estimated parameters was also verified. Plot of residuals against estimated crown ratios were observed. Although the logistic model had the highest $R^2$ and the least SEE, Chapman-Richard and Exponential functions were observed to be more consistent in their predictive ability; and were therefore recommended for predicting crown ratio in the stand.

• Journal of applied mathematics & informatics
• /
• 제27권3_4호
• /
• pp.591-601
• /
• 2009

In the present paper, one new generalized 'useful' information generating function and two new relative 'useful' information generating functions have been defined with their particular and limiting cases. It is interesting to note that differentiations of these information generating functions at t=0 or t=1 give some known and unknown generalized measures of useful information and 'useful' relative information. The information generating functions facilitates to compute various measures and that has been illustrated by applying these information generating functions for Uniform, Geometric and Exponential probability distributions.

• 복합신소재구조학회 논문집
• /
• 제1권3호
• /
• pp.1-9
• /
• 2010

본 연구에서는 Lagrangian 및 Hermite 보간함수를 혼합정식화한 유한요소법과 다양한 전단변형함수로 등방성, 대칭 적층 및 샌드위치판 모델을 제시하였다. 제시된 전단변형이론은 판의 상하면에서 전단응력이 0이 되는 다항식, 삼각함수, 쌍곡삼각함수 및 지수함수로 구성되어 있다. 모든 전단변형함수는 해석해, 정해 및 기발표된 유한요소 결과치와 비교하였으며, 합리적인 정확도를 갖는 것으로 예측되었다. 특히, 지수형태의 전단변형함수(Karama et al. 2003; Aydogu 2009)가 적층 및 샌드위치판 해석에 있어서 상대적으로 가장 우수한 결과를 보였다.