• Ocean Systems Engineering
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• 제8권1호
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• pp.41-55
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• 2018

Accidental oil and gas leak is a critical concern for the offshore industry because it can lead to severe consequences and as a result, it is imperative to evaluate the probabilities of occurrence of the consequences of the leakage in order to assess the risk. Event Tree Analysis (ETA) is a technique to identify the consequences that can result from the occurrence of a hazardous event. The probability of occurrence of the consequences is evaluated by the ETA, based on the failure probabilities of the sequential events. Conventional ETA deals with events with crisp failure probabilities. In offshore applications, it is often difficult to arrive at a single probability measure due to lack of data or imprecision in data. In such a scenario, fuzzy set theory can be applied to handle imprecision and data uncertainty. This paper presents fuzzy ETA (FETA) methodology to compute the probability of the outcomes initiated due to oil/gas leak in an actual offshore-onshore installation. Post FETA, sensitivity analysis by Fuzzy Weighted Index (FWI) method is performed to find the event that has the maximum contribution to the severe sequences. It is found that events of 'ignition', spreading of fire to 'equipment' and 'other areas' are the highest contributors to the severe consequences, followed by failure of 'leak detection' and 'fire detection' and 'fire water not being effective'. It is also found that the frequency of severe consequences that are catastrophic in nature obtained by ETA is one order less than that obtained by FETA, thereby implying that in ETA, the uncertainty does not propagate through the event tree. The ranking of severe sequences based on their probability, however, are identical in both ETA and FETA.

• Korean Journal of Mathematics
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• 제15권2호
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• pp.149-165
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• 2007

We investigate the existence of multiple nontrivial solutions $u(x,t)$ for a perturbation $b[({\xi}-{\eta}+2)^+-2]$ of the hyperbolic system with Dirichlet boundary condition $$(0.1)\;L{\xi}={\mu}[({\xi}-{\eta}+2)^+-2]\;in\;({-{\frac{{\pi}}{2}}},{\frac{{\pi}}{2}}){\times}\mathbb{R},\\L{\eta}={\nu}[({\xi}-{\eta}+2)^+-2]\;in\;({-{\frac{{\pi}}{2}}},{\frac{{\pi}}{2}}){\times}\mathbb{R},$$, where $u^+$=max{u,o}, ${\mu}$, ${\nu}$ are nonzero constants. Here L is the wave operator in $\mathbb{R}^2$ and the nonlinearity $({\mu}-{\nu})[({\xi}-{\eta}+2)^+-2]$ crosses the eigenvalues of the wave operator.

• 호남수학학술지
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• 제29권4호
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• pp.723-732
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• 2007

We investigate the existence of solutions u(x, t) for a perturbation b[$(\xi+\eta+1)^+-1$] of the hyperbolic system with Dirichlet boundary condition (0.1) = $L\xi-{\mu}[(\xi+\eta+1)^+-1]+f$ in $(-\frac{\pi}{2},\frac{\pi}{2}\;{\times})\;\mathbb{R}$, $L\eta={\nu}[(\xi+\eta+1)^+-1]+f$ in $(-\frac{\pi}{2},\frac{\pi}{2}\;{\times})\;\mathbb{R}$ where $u^+$ = max{u,0}, ${\mu},\nu$ are nonzero constants. Here $\xi,\eta$ are periodic functions.

• 대한수학회논문집
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• 제32권4호
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• pp.933-957
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• 2017

In this paper, we prove some existence results of solutions for a new class of generalized bi-quasi-variational-like inequalities (GBQVLI) for (${\eta}-h$)-quasi-pseudo-monotone type I and strongly (${\eta}-h$)-quasi-pseudo-monotone type I operators defined on non-compact sets in locally convex Hausdorff topological vector spaces. To obtain our results on GBQVLI for (${\eta}-h$)-quasi-pseudo-monotone type I and strongly (${\eta}-h$)-quasi-pseudo-monotone type I operators, we use Chowdhury and Tan's generalized version of Ky Fan's minimax inequality as the main tool.

• East Asian mathematical journal
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• 제28권1호
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• pp.37-47
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• 2012

In this paper, we study generalized implicit variational-like inclusions and $J^{\eta}$-proximal operator equations in Banach spaces. It is established that generalized implicit variational-like inclusions in real Banach spaces are equivalent to fixed point problems. We also establish relationship between generalized implicit variational-like inclusions and $J^{\eta}$-proximal operator equations. This equivalence is used to suggest a iterative algorithm for solving $J^{\eta}$-proximal operator equations.

• 대한화학회지
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• 제46권3호
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• pp.213-218
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• 2002

(${\eta}^5$-Cyclopentadienyl)(${\eta}^6$-1,2,3,4-tetramethyl-1,4-dibora-2,5-cyclohexadiene)Ni(5)는 cyclopentadienyl (carbonyl)-nickel dimer와 1,2,3,4-tetramethyl-1,4-dibora-2-cyclohexene (1)을 반응시켜서 주생성물로 얻었다. Di-allyl nickel과 2,3-diethyl-1,4-dimethyl-1,4-dibora-2-cyclohexene (2)을 -20$^{\circ}C$에서 반응시켜서 bis[${\eta}^6$-2,3-dimethyl-1,4-diethoxy-1,4-dibora-2,5-cyclohexadiene]nickel (6) 착화합물을 15% 수율로 생성하였다. 그리고 야-allyl nickel과 2,3-dimethyl-1,4-diethoxy-1,4-dibora-2-cyclohexene (3)을 역시 -20$^{\circ}C$에서 반응시켜서 22% 수율로 bis[${\eta}^6$-2,3-dimethyl-1,4-diethoxy-1,4-dibora-2,5-cyclohexadiene] nickel (7)을 생성하였다. 이들 double-decker 착화합물들은 불안정하여 분리하기 어려웠으며, NMR, MS, 원소분석 등으로 확인하였다.

• 폴리머
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• 제34권5호
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• pp.415-423
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• 2010

고검화도(98%이상)의 폴리(비닐 알코올)(PVA)를 디메틸설폭사이드(DMSO) 용매에 녹인 뒤 PVA 준희박 용액 대에서 농도 $C{\simeq}0.14\;g/mL$까지 점성도를 측정하였으며, 이 시스템을 매트릭스로 하여 폴리스티렌(PS) 라텍스 입자의 확산운동 지연을 동적 광산란법으로 조사하였다. PVA/DMSO계의 점성도를 고유점성도 $[{\eta}]$로 스케일된 환산농도 $C[{\eta}]$에 대하여 도시하였을 때 C$[{\eta}]$ >2에서는 분자량 의존성이 강하게 나타났으며, 그 원인은 PVA 용액 내에 존재하는 불균일 영역때문인 것으로 추정하였다. 그러나 매트릭스 내에서 탐침입자의 확산운동은 모든 측정농도에서 단일모드로 관찰되었고, 용액상 및 용매상에서의 확산계수의 비인 D/Do를 $C[{\eta}]$로 도시할 때 전체 농도 범위에서 분자량 의존성은 전혀 나타나지 않았으나 신장지수함수의 적용 한계는 C$[{\eta}]$ >2.5인 것으로 관찰되었다.

• 대한화학회지
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• 제36권2호
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• pp.305-310
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• 1992

Cobalt 금속 중심으로 cyclopentadienyl을 ${\pi}$-착물로 결합하고, 또 oxime 화합물을 리간드로 하는 cobalt oxime sandwich형 착물을 합성하기 위하여 본 연구를 수행하였다. Cyclopentadienyl-cobalt 부분을 도입하기 위해, (${\eta}^5$-Cyclopentadienyl)bis(ethylene)cobalt (Jonas 시약), (η5-cyclopentadienyl)di(carbonyl)cobalt, 그리고 bis(${\eta}^5$-cyclopentadienyl)cobalt (cobaltocene)의 착물이 사용되었고, oxime을 각각 여러 가지 조건에서 반응시켰다. 그 중에서 Jonas 시약과 dienemonooxime인 2,4-hexadienealdoxime만이 반응되었으며, 그 생성물은 예상을 벗어난 (${\eta}^5$-cyclopentadienyl)(2,4-hexadienenitrile)cobalt [VII]로 밝혀졌다. 이 화합물의 구조는 NMR, mass spectrometer, IR 원소분석기를 통해 확인되었다.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2008년 영문 학술대회
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• pp.378-382
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• 2008

A 50 N monopropellant thruster being developed for attitude control in a variety of aerospace application systems is described in this paper. Ninety percent hydrogen peroxide was selected as a propellant, since it is much less hazardous than hydrazine. A scaled down thruster with aluminum oxide loaded with the platinum in the reaction chamber was tested to determine propellant decomposition onto a catalyst. A scaled up 50 N thruster, with a catalyst bed of 3 cm in diameter and 4 cm in length, was evaluated by decomposition efficiency based on temperature, ${\eta}_T$, efficiency of characteristic velocity, ${\eta}_{C^*}$, and measurement of thrust. The performance of a 50 N thruster was 40.5 Newton in thrust, about 100 % in ${\eta}_T$, and 98 % in ${\eta}_{C^*}$, and 125 sec in specific impulse at sea level.

• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.101-123
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• 2019

In this paper, we consider a system of nonlinear variational type inclusions involving ($H,{\varphi},{\eta}$)-monotone operators in real Banach spaces. Further, we define a proximal operator associated with an ($H,{\varphi},{\eta}$)-monotone operator and show that it is single valued and Lipschitz continuous. Using proximal point operator techniques, we prove the existence and uniqueness of a solution and suggest an iterative algorithm for the system of nonlinear variational type inclusions. Furthermore, we discuss the convergence of the iterative sequences generated by the algorithms.