• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.321-330
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• 2002

We apply an Intermediate Problem Method to compute eigenvalues of an anharmonic oscillator. The method produces lower bounds to the eigenvalues while the Rayleigh-Ritz method yields upper bounds. We show the convergence rate of the Intermediate Problem Method is the same as the rate of the Rayleigh-Ritz method.

• Journal of the Korean Statistical Society
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• 제23권1호
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• pp.187-198
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• 1994

We derive a new Cramer-Rao type lower bound for the reciprocal of the density height of the median-unbiased estimators which improves most of the previous lower bounds and is attainable under much weaker conditions. We also identify useful necessary and sufficient condition for the attainability of the lower bound which is considerably weaker than those for the mean-unbiased estimators. It is shown that these lower bounds are attained not only for the family of continuous distributions with monotone likelihood ratio (MLR) property but also for the location and scale families with strong unimodal property.

• 한국통신학회논문지
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• 제37권2B호
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• pp.87-96
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• 2012

본 논문에서는 2-홉 릴레이 시스템에서 릴레이 노드와 목적지 노드가 모두 임의의 수를 갖는 간섭원들의 영향을 받는 상황을 고려한다. 특히 릴레이 채널과 액세스 채널, 그리고 간섭 채널들이 모두 레일리 페이딩을 겪는다고 가정할 때, 증폭-후-전달(amplify-and-forward: AF) 릴레이 시스템의 불능 확률에 대한 정확한 수식을 도출하고, 나아가 불능 확률의 상한 식(upper bound)과 하한 식(lower bound)을 도출한다. 또한 도출된 불능 확률의 상한 식과 하한 식을 이용하여 AF 릴레이 시스템의 비트 오류율 성능에 대한 상한 식과 하한 식을 도출한다. 그리고 도출된 AF 릴레이 시스템의 불능 확률과 비트 오류율 성능에 대한 상한 식과 하한 식의 정확도를 모의실험을 통해 확인한다.

• Geomechanics and Engineering
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• 제11권4호
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• pp.587-605
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• 2016

This study aimed to develop upper and lower bounds to predict the tunnel support pressure under the pile tip during the circular tunnel excavation. Most previous studies on the upper and lower bound methods were carried out for the single ground structures, e.g., retaining wall, foundation, ground anchor and tunnel, in the homogeneous ground conditions, since the pile-soil-tunnel interaction problem is very complicated and sophisticated to solve using those bound methods. Therefore, in the lower bound approach two appropriate stress fields were proposed for single pile and tunnel respectively, and then they were superimposed. In addition, based on the superimposition several failure mechanisms were proposed for the upper bound solution. Finally, these upper bound mechanisms were examined by shear strain data from the laboratory model test and numerical analysis using finite element method.

• Communications for Statistical Applications and Methods
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• 제14권1호
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• pp.147-153
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• 2007

In this note, we obtained results related to multiparameter discrete exponential families on considering lattice or semi-lattice in place of N (Natural numbers) in view of Cacoullos-type inequalities via the same arguments in Papathanasiou (1990, 1993).

• 한국통계학회:학술대회논문집
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• 한국통계학회 2000년도 추계학술발표회 논문집
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• pp.109-113
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• 2000

We consider the probability that the total population of a Jackson network exceeds a given large value. By using the relation to the stationary distribution, we derive upper and lower bounds on this probability. These bounds imply the stronger logarithmic limit than that in Glasserman and Kou(1995) when several nodes have the same maximal load.

• Journal of the Korean Data and Information Science Society
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• 제11권1호
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• pp.31-35
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• 2000

We shall give upper and lower bounds of the odds ratio of an event by a slight condition of the conditional probability of events.

• Nuclear Engineering and Technology
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• 제32권6호
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• pp.618-635
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• 2000

A total of 17 experimental data for the onset of slugging, which is assumed to be the precursor of the condensation-induced waterhammer (CIWH), have been obtained for various How rates of water Incorporating the most recent correlations of interfacial heat transfer and friction factor developed for a circular geometry and using an improved criterion of transition from stratified to a slug flow, two existing analytical models to predict lower and upper bounds for CIWH have been upgraded. Applicability of the present as well as existing CIWH models has been tested by comparison with two sets of CIWH data. The result of this comparison shows that the applicability of the present as well as existing models is reasonably good. Based on the present models for CIWH, a computer code entitled as“KAIST-CIWH”has been developed and sample guide charts to find CIWH free regions for a given combination of major flow parameters in a long horizontal pipe have been presented along with the results of parametric studies of major parameters (D, P, $T_{f,in}$, and L/D) on the critical inlet water flow rate（$W_{f,in}_crit$ for both lower and upper bounds. In addition, two simple formulas for lower and upper bounds that can be used in an emergency for quick results have been presented.

• Communications for Statistical Applications and Methods
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• 제21권3호
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• pp.201-212
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• 2014

We provide a simple basic method to find bounds for higher order moments of unimodal distributions in terms of lower order moments when the random variable takes value in a given finite real interval. The bounds for moments in terms of the geometric mean of the distribution are also derived. Both continuous and discrete cases are considered. The bounds for the ratio and difference of moments are obtained. The special cases provide refinements of several well-known inequalities, such as Kantorovich inequality and Krasnosel'skii and Krein inequality.

• Communications for Statistical Applications and Methods
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• 제11권3호
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• pp.455-463
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• 2004

In this paper, we derive sharp upper and lower expectation bounds on the extreme order statistics from possibly dependent random variables whose marginal distributions are only known. The marginal distributions of the considered random variables may not be the same and the expectation bounds are completely determined by the marginal distributions only.