• Structural Engineering and Mechanics
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• 제20권6호
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• pp.713-726
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• 2005

Based on the improved first order Taylor interval expansion, a new interval analysis method for the static or dynamic response of the structures with interval parameters is presented. In the improved first order Taylor interval expansion, the first order derivative terms of the function are also considered to be intervals. Combining the improved first order Taylor series expansion and the interval extension of function, the new interval analysis method is derived. The present method is implemented for a continuous beam and a frame structure. The numerical results show that the method is more accurate than the one based on the conventional first order Taylor expansion.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1165-1176
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• 2009

This paper is concerned with the interval oscillation of the second order nonlinear ordinary differential equation (r(t)|y'(t)|$^{{\alpha}-1}$ y'(t))'+p(t)|y'(t)|$^{{\alpha}-1}$ y'(t)+q(t)f(y(t))g(y'(t))=0. By constructing ageneralized Riccati transformation and using the method of averaging techniques, we establish some interval oscillation criteria when f(y) is not differetiable but satisfies the condition $\frac{f(y)}{|y|^{{\alpha}-1}y}$ ${\geq}{\mu}_0$ > 0 for $y{\neq}0$.

• Structural Engineering and Mechanics
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• 제12권6호
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• pp.669-684
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• 2001

A new method for solving the uncertain eigenvalue problems of the structures with interval parameters, interval finite element method based on the element, is presented in this paper. The calculations are done on the element basis, hence, the efforts are greatly reduced. In order to illustrate the accuracy of the method, a continuous beam system is given, the results obtained by it are compared with those obtained by Chen and Qiu (1994); in order to demonstrate that the proposed method provides safe bounds for the eigenfrequencies, an undamping spring-mass system, in which the exact interval bounds are known, is given, the results obtained by it are compared with those obtained by Qiu et al. (1999), where the exact interval bounds are given. The numerical results show that the proposed method is effective for estimating the eigenvalue bounds of structures with interval parameters.

• Journal of applied mathematics & informatics
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• 제33권1_2호
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• pp.61-76
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• 2015

In this paper, a fifth order extension of Potra's third order iterative method is proposed for solving nonlinear equations. A convergence theorem along with the error bounds is established. The method takes three functions and one derivative evaluations giving its efficiency index equals to 1.495. Some numerical examples are also solved and the results obtained are compared with some other existing fifth order methods. Next, the interval extension of both third and fifth order Potra's method are developed by using the concepts of interval analysis. Convergence analysis of these methods are discussed to establish their third and fifth orders respectively. A number of numerical examples are worked out using INTLAB in order to demonstrate the efficacy of the methods. The results of the proposed methods are compared with the results of the interval Newton method.

• Communications for Statistical Applications and Methods
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• 제13권1호
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• pp.125-134
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• 2006

This study confirms that the regression model of endpoint of interval outputs is not identical with that of the other endpoint of interval outputs in interval regression models proposed by Tanaka et al. (1987) and constructs interval regression models using the best regression model given by variable selection. Also, this paper suggests a method to minimize the sum of lengths of a symmetric difference among observed and predicted interval outputs in order to estimate interval regression coefficients in the proposed model. Some examples show that the interval regression model proposed in this study is more accuracy than that introduced by Inuiguchi et al. (2001).

• Journal of the Korean Statistical Society
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• 제24권2호
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• pp.551-562
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• 1995

We consider the iterated bootstrap method in regression model with heterogeneous error variances. The iterated wild bootstrap confidence intervla of the mean response is considered. It is shown that the iterated wild bootstrap confidence interval has coverage error of order $n^{-1}$ wheresa percentile method interval has an error of order $n^{-1/2}$. The simulation results reveal that the iterated bootstrap method calibrates the coverage error of percentile method interval successfully even for the small sample size.

• 한국지능시스템학회논문지
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• 제22권5호
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• pp.646-655
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• 2012

First, we prove a number of results about interval-valued fuzzy groups involving the notions of interval-valued fuzzy cosets and interval-valued fuzzy normal subgroups which are analogs of important results from group theory. Also, we introduce analogs of some group-theoretic concepts such as characteristic subgroup, normalizer and abelian groups. Secondly, we prove that if A is an interval-valued fuzzy subgroup of a group G such that the index of A is the smallest prime dividing the order of G, then A is an interval-valued fuzzy normal subgroup. Finally, we show that there is a one-to-one correspondence the interval-valued fuzzy cosets of an interval-valued fuzzy subgroup A of a group G and the cosets of a certain subgroup H of G.

• 한국전자통신학회논문지
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• 제5권5호
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• pp.435-443
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• 2010

확률적 특성을 가지는 시스템의 시험을 위해서는 시험 입력을 일정 횟수만큼 반복하여 제공하고 관찰된 데이터를 기반으로 판정이 내려져야 한다. 구간 추정 기법을 이용하여 관찰된 데이터로부터 확률 값이 올바른지 여부를 판단할 수 있으며, 이 때 적절한 신뢰구간의 선택은 시험의 품질을 결정하는 중요한 요인이 된다. 본 논문에서는 다양한 크기의 표본에 대해 대표적인 구간 추정 기법인 Wald 신뢰구간과 Agresti-Coull 신뢰구간을 비교 분석한다. 각 신뢰구간이 확률 값 시험에 사용되었을 경우 올바른 구현 제품이 시험을 통과할 확률과 잘못된 구현제품이 시험을 통과하지 못할 확률을 기반으로 비교 분석을 수행하며, 확률 값이 올바른지를 판단하기 위한 양측검정뿐만 아니라 확률 값이 기준 확률 이상인지 여부를 판단하기 위한 단측검정을 사용하는 경우에 대해서도 비교 분석을 수행한다. 비교 분석 결과 양측검정의 경우 Agresti-Coull 신뢰구간을 사용할 것을 추천하며, 단측검정의 경우 큰 크기의 표본에 대해서는 Agresti-Coull 신뢰구간을, 적은 크기의 표본에 대해서는 Wald 신뢰구간 또는 Agresti-Coull 신뢰구간을 선택적으로 사용할 것을 추천한다.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2002년도 ITC-CSCC -3
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• pp.1792-1795
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• 2002

In this paper we investigated effects of the presentation time interval on a subjective evaluation test of loudness. We carried out paired comparison experiments of pure tones loudness with changing the time interval of the comparison. As the results, two characteristic effects were obtained. The difference limen of the loudness was almost proportional to the time interval in below 10 s and was almost the same value of 1.5 dB in above 10 s. On the other hand, the effect of the presentation order was smallest at the time interval of about 5 s.

• Earthquakes and Structures
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• 제7권6호
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• pp.1061-1070
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• 2014

An iterative hybrid structural dynamic reliability prediction model has been developed under multiple-time interval loads with and without consideration of stochastic structural strength degradation. Firstly, multiple-time interval loads have been substituted by the equivalent interval load. The equivalent interval load and structural strength are assumed as random variables. For structural reliability problem with random and interval variables, the interval variables can be converted to uniformly distributed random variables. Secondly, structural reliability with interval and stochastic variables is computed iteratively using the first order second moment method according to the stress-strength interference theory. Finally, the proposed method is verified by three examples which show that the method is practicable, rational and gives accurate prediction.