• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.349-369
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• 2013

The present paper envisages the $q$-analogue of the exponential operators, determined by G. Dattoli and his collaborators for translation and diffusive operators which were utilized to establish analytical solutions of difference and integral equations. The generalization of their technique is expected to cover wide range of such utilization.

• 대한수학회보
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• 제35권1호
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• pp.45-52
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• 1998

In this paper, we establish the exponential formula for C-semigroup. If A is the generator of a C-semigroup S(t), then S(t) can be represented by exp(tA) in some sense.

• 충청수학회지
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• 제24권4호
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• pp.783-793
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• 2011

In this paper we introduce the concept of extended linear negative quadrant dependence and obtain some exponential inequalities, complete convergence and almost sure convergence for extended linear negative quadrant dependent random variables.

• 대한수학회논문집
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• 제34권2호
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• pp.383-390
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• 2019

In this paper, we discuss special polynomials involving exponential distribution, which is related to life testing. We derive some identities of special polynomials such as the symmetric property, recurrence formula and so on. In addition, we investigate explicit properties of special polynomials by using their derivative and integral.

• East Asian mathematical journal
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• 제39권1호
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• pp.87-92
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• 2023

In this paper, we study the nonlinear hyperbolic system with epsilon perturbation s_tt - div[c(x)∇s] + (ε - 1)s_t = |s|^γs. Under the conditions of c, γ and other assumptions, we prove the exponential behavior rates of the modified energy perturbation.

• 한국국방경영분석학회지
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• 제8권1호
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• pp.99-107
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• 1982

This paper is concerned with the optimality of exponential smoothing applied to the general IMA process with different moving average and differencing orders. Numerical experiments were performed for IMA(m,n) process with various combinations of m and n, and the corresponding forecast errors were compared. Results show that the higher differencing order is more critical to the optimality of exponential smoothing, i.e., the IMA process with the higher moving average order, forecasted by exponential smoothing, has comparatively smaller forecast error. If the difference between the differencing order and the moving average order becomes larger, the accuracy of forecast by exponential smoothing declines gradually.

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

• 한국지능시스템학회논문지
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• 제24권4호
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• pp.398-402
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• 2014

일반화된 삼각함수 퍼지집합은 삼각함수 퍼지수의 일반화이다. Zadeh([7])는 확률을 이용하여 퍼지이벤트에 대한 확률을 정의하였다. 우리는 정규분포와 지수분포를 각각 이용하여 실수 $\mathbb{R}$ 위에서 정규퍼지확률과 지수퍼지확률을 정의하고, 일반화된 삼각함수 퍼지집합에 대하여 정규퍼지확률과 지수퍼지확률을 계산하였다.

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

• Journal of the Korean Data and Information Science Society
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• 제18권2호
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• pp.553-560
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• 2007

In this paper, we consider two components system which lifetimes have Freund's bivariate exponential model with equal failure rates. We propose Bayesian multiple comparisons procedure for the failure rates of I Freund's bivariate exponential populations based on Dirichlet process priors(DPP). The family of DPP is applied in the form of baseline prior and likelihood combination to provide the comparisons. Computation of the posterior probabilities of all possible hypotheses are carried out through Markov Chain Monte Carlo(MCMC) method, namely, Gibbs sampling, due to the intractability of analytic evaluation. The whole process of multiple comparisons problem for the failure rates of bivariate exponential populations is illustrated through a numerical example.