• Management Science and Financial Engineering
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• v.10 no.2
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• pp.103-118
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• 2004

$\epsilon$-sensitivity analysis is a kind of methods for performing sensitivity analysis for linear programming. Its main advantage is that it can be directly applied for interior-point methods with a little computation. Although $\epsilon$-sensitivity analysis was proposed several years ago, there have been no studies on its relationship with other sensitivity analysis methods. In this paper, we discuss the relationship between $\epsilon$-sensitivity analysis and sensitivity analysis using an optimal basis. First. we present a property of $\epsilon$-sensitivity analysis, from which we derive a simplified formula for finding the characteristic region of $\epsilon$-sensitivity analysis. Next, using the simplified formula, we examine the relationship between $\epsilon$-sensitivity analysis and sensitivity analysis using optimal basis when an $\epsilon$-optimal solution is sufficiently close to an optimal extreme solution. We show that under primal nondegeneracy or dual non degeneracy of an optimal extreme solution, the characteristic region of $\epsilon$-sensitivity analysis converges to that of sensitivity analysis using an optimal basis. However, for the case of both primal and dual degeneracy, we present an example in which the characteristic region of $\epsilon$-sensitivity analysis is different from that of sensitivity analysis using an optimal basis.

• Proceedings of the Korean Information Science Society Conference
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• 2008.06c
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• pp.289-294
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• 2008

어떤 자연언어 문서가 전달하려는 의미는 그 텍스트의 성격에 따라 아주 명확할 수도(예: 뉴스 문서), 아주 불분명할 수도 있다(예: 시). 이 연구는 이러한 '의미의 명확성(semantic transparency)'을 정량적으로 측정할 수 있다고 가정하고, 이 의미의 명확성을 판단하는 데에 단어들의 연쇄(word association)의 확률통계적 성질들이 어떻게 기능하는지에 대해 논한다. 이를 위해 특정 단어가 연쇄체를 형성하면서 발생하는 neighboring frequency와 degeneracy를 중심으로 Markov chain Monte Carlo scheme을 적용하여 의미망('Semantic Hypernetwork')으로 학습시킨 후 문서의 구성 단어들과 그 집합들 간의 연결 상태를 파악하였다. 우리는 의미적으로 그 표상이 분명하게 나뉘는 문서들(뉴스와 시)을 대상으로 이 모델이 어떻게 이들의 의미적 명확성을 분류하는지 분석하였다. Neighboring frequency와 degeneracy, 이 두 속성이 언어구조에서의 의미망 기억과 학습 탐색 기제에 유의한 기질로서 제안될 수 있다. 본 연구의 주요 결과로 1) 텍스트의 의미론적 투명성을 구별하는 통계적 증거와, 2) 문서의 의미구조에 대한 새로운 기질 발견, 3) 기존의 문서의 카테고리 별 분류와는 다른 방식의 분류 방식 제안을 들 수 있다.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.2
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• pp.109.2-109.2
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• 2012

Current microlensing follow-up observations focus on high-magnification events because of the high efficiency of planet detection. However, central perturbations of high-magnification events caused by a planet can also be produced by a very close or a very wide binary companion, and the two kinds of central perturbations are not generally distinguished without time consuming detailed modeling (a planet-binary degeneracy). Hence, it is important to resolve the planet-binary degeneracy that occurs in high-magnification events. In this paper, we investigate caustic-crossing high-magnification events caused by a planet and a wide binary companion. From this study, we find that because of the different magnification excess patterns inside the central caustics induced by the planet and the binary companion, the light curves of the caustic-crossing planetary-lensing events exhibit a feature that is discriminated from those of the caustic-crossing binary-lensing events, and the feature can be used to immediately distinguish between the planetary and binary companions.

• The Bulletin of The Korean Astronomical Society
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• v.45 no.1
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• pp.42.4-43
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• 2020

The hydrogen-rich envelope mass of a dying massive star is the key factor that determines the type and properties of the resulting supernova. Emulating wind-driven mass loss of single stars with the MESA(Modules for Experiments in Stellar Astrophysics) stellar evolution code, we made a grid of models for a large parameter space of initial mass (12 M⊙ to 30M⊙), metallicity (solar, LMC and SMC), hydrogen envelope mass (0.01M⊙ to 10M⊙) for progenitor stars in their final step of evolution. Our results suggest the final luminosity of the progenitor is largely determined by the initial mass, which means there is luminosity degeneracy for stars with the same initial mass but with different hydrogen-rich envelope masses. Since we can break this degeneracy by correcting luminosity with surface gravity (spectroscopic HR diagram), we can infer the exact mass property of an observed progenitor. The surface temperature drastically varies near the envelope mass of ~0.1M⊙ and surface temperature of ~10000 K, where the demarcation between the hydrogen-rich envelope and the helium core lies, which explains the rarity of 'white' supergiants. There also exists a discontinuity in the chemical composition of the progenitor envelope around this critical hydrogen-rich envelope mass of ~0.1 M⊙, which can be tested in future observations of "flash spectroscopy" of supernovae.

• Transactions of Materials Processing
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• v.11 no.2
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• pp.179-186
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• 2002

In the finite element analysis of metal forming Processes using general Lagrangian formulation, element nodes in the mesh move and elements are distorted as the material is deformed. The excessive degeneracy of mesh interrupts finite element analysis and thus increases the error of plastic deformation energy, In this study, a remeshing scheme using so-called mesh compression method is proposed to effectively analyze the flash which is generated usually in hot forging processes. In order to verify the effectiveness of the method, several examples are tested in two-dimensional and three-dimensional problems.

• Korean Management Science Review
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• v.16 no.1
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• pp.1-9
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• 1999

The purpose of this paper is to develope efficient techniques for implementing the dual simplex method. In this paper we proposed one artificial row technique to get an initial dual feasible basic solution, a dual steepest-edge method coupled with a dropping row selection rule, and an anti-degeneracy technique which resembles the EXPAND procedure for the primal simplex method. The efficiency of the above techniques is shown by experiments. Finally, the dual simplex method is shown to be superior to the primal simplex method when it is used in the integer programming.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1183-1197
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• 2006

Let X be a smooth, closed, connected spin 4-manifold with $b_1(X)=0$ and signature ${\sigma}-(X)$. In this paper we use Seiberg-Witten theory to prove that if X admits a spin alternating $A_4$ action, then $b^+_2(X)$ ${\geq}$ |${\sigma}{(X)}$|/8+3 under some non-degeneracy conditions.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.763-769
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• 2014

In this paper, we illustrate a counter example for the converse of a certain conjecture proposed by De Giorgi. De Giorgi suggested a series of conjectures, in which a certain integral condition for singularity or degeneracy of an elliptic operator is satisfied, the solutions are continuous. We construct some singular elliptic operators and solutions such that the integral condition does not hold, but the solutions are continuous.

• Journal of the military operations research society of Korea
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• v.9 no.2
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• pp.57-60
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• 1983

We show that the complexity of Simplex Method for Linear Programming problem is equivalent to the complexity of finding just an adjacent basic feasible solution if exists. Therefore a simplex type method which resolves degeneracy in polynomial time with respect to the size of the given linear programming problem can solve the general linear programming problem in polynomial steps.

• Communications for Statistical Applications and Methods
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• v.17 no.2
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• pp.223-229
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• 2010

We consider the asymptotic results of the variance ratio statistic when the underlying processes have moving average(MA) unit roots. This degenerate situation of zero spectral density near the origin cause the limit of the variance ratio to become zero. Its asymptotic behaviors are different from non-degenerating case, where the convergence rate of the variance ratio statistic is formally derived.