• Korean Journal of Mathematics
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• 제19권3호
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• pp.331-342
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• 2011

We consider the multiplicity of the solutions for a class of a system of critical growth beam equations with periodic condition on t and Dirichlet boundary condition $$\{u_{tt}+u_{xxxx}=av+\frac{2{\alpha}}{{\alpha}+{\beta}}u_{+}^{{\alpha}-1}v_{+}^{\beta}+s{\phi}_{00}\;\;in\;(-\frac{\pi}{2},\;\frac{\pi}{2}){\times}R,\\u_{tt}+v_{xxxx}=bu+\frac{2{\alpha}}{{\alpha}+{\beta}}u_{+}^{\alpha}v_{+}^{{\beta}-1}+t{\phi}_{00}\;\;in\;(-\frac{\pi}{2},\;\frac{\pi}{2}){\times}R,$$ where ${\alpha}$, ${\beta}$ > 1 are real constants, $u_+=max\{u,0\}$, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_00=1$ of the eigenvalue problem $u_{tt}+u_{xxxx}={\lambda}_{mn}u$. We show that the system has a positive solution under suitable conditions on the matrix $A=\(\array{0&a\\b&0}\)$, s > 0, t > 0, and next show that the system has another solution for the same conditions on A by the linking arguments.

• 공업화학
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• 제17권6호
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• pp.625-632
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• 2006

임계 마이셀 농도의 온도 의존성을 통계 역학적으로 고찰하였다. 본 논문에서 논의된 단순하고 소박한 모델은 임계 마이셀 농도(CMC)가 온도에 대해서 ln CMC= A+BT+C/T+D ln T와 같이 변함을 말해준다. 여기에서 T는 온도이고 A, B, C, D는 마이셀을 이루는 계면활성제 분자의 성질에 의존하는 상수이다. 모델에서 얻어진 식은, 온도에 따른 CMC 측정 자료를 잘 맞춤하는 것으로 평가된, 기존의 Muller와 Lim의 식을 결합한 형태이다. 그러므로 본 논문에서 제안된 CMC의 온도 의존성에 대한 모델은 Muller와 Lim의 식에 대한 이론적인 토대를 제공한다.

• Structural Engineering and Mechanics
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• 제23권1호
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• pp.15-27
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• 2006

A locally varying temperature field or a mixture of two or more different materials can cause local variation of elasticity properties of a beam. In this paper, a new Euler-Bernoulli beam element with varying Young's modulus along its longitudinal axis is presented. The influence of axial forces according to the linearized 2nd order beam theory is considered, as well. The stiffness matrix of this element contains the transfer constants which depend on Young's modulus variation and on axial forces. Occurrence of the polynomial variation of Young's modulus has been assumed. Such approach can be also used for smooth local variation of Young's modulus. The critical loads of the straight slender columns were studied using the new beam element. The influence of position of the local Young's modulus variation and its type (such as linear, quadratic, etc.) on the critical load value and rate of convergence was investigated. The obtained results based on the new beam element were compared with ANSYS solutions, where the number of elements gradually increased. Our results show significant influence of the locally varying Young's modulus on the critical load value and the convergence rate.

• 한국안전학회지
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• 제9권3호
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• pp.13-21
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• 1994

Effects of tensile and compression residual stresses in the welded SS41 and A17075-76 on fatigue crack propagation behavior are investigated when a crack propagates from residual stresses region. We propose the fatigue crack growth equation on tensile and compression residual stresses in welded metal. The results obtained in this experimental study are summarized as follows . 1 ) A fatigue crack growth equation which applied fatigue fracture behavior of the welded metal is proposed. (equation omitted) where, $\alpha$, $\beta$, ${\gamma}$ and $\delta$ are constants, and R$_{eff}$ is effective stress ratio [R$_{eff}$=(Kmin+Kres)/(Kmax+Kres)], Kcf is critical fatigue stress intensity factor. The constants are obtained from nonlinear least square method. The relation between crack length and number of cycles obtained by integrating the fatigue crack growth rate equation is in agreement with the experimental data. 2) The experimental results confirmed that the cause of crack extension and retardation by residual stresses has relation to the phenomenon of crack closure. 3) The relaxing trend of residual stresses by the crack propagation was greater In case of compressive residual stress than that of tensile residual stress in the welded metal.tal.

• 대한화장품학회지
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• 제13권1호
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• pp.45-71
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• 1987

${\beta}$-Carotene has been known as an effective quenching agent of singlet oxygen and the carotenoid pigments in general are expected to protect cells against photosensitized oxidations. We are determined the quenching rate constants of several Ketocarotenoids including capsanthin, capsanthin diester, astaxanthin and fucoxanthin, and the relative quenching actiyities against singlet oxygen were compared with those of ${\beta}$-carotene and reported carotenoids. Nevertheless the ketocarotenoids exhibited lower quenching rate constants than ${\beta}$-carotene, they showed more pronounced protective activitives than ${\beta}$-carotene against photohemlysis induced by singlet oxygen. Among the ketocarotenoids investigated, fucoxanthin indicated a significant protective activity for the cell. The results suggested that. 1) 1O2 may be alikely initiator of photohemolysis, but this reaction is followed by slow dark reactions involving secondary reactive species. 2) For protection of RBC against photodynamic action with carotenoids, carotenoids having functional groups such as -C=0 and -OH groups are most efficient. This suggests that partition of carotenoids between the buck and the mombrane and/or their specific binding to membrane proteins are more critical for the photo-protection by carotenoids than is a diffusional quenching of 1O2.

• 한국정밀공학회지
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• 제8권2호
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• pp.27-35
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• 1991

We propose the crack growth rate equation which applied over three regions (threshold region, stable region, unstable region) of fatigue crack propagation. Constant stress amplitude fatigue tests are conducted for four materials under three stress ratios of R=0.05, R=0.2 and R=0.4. Materials which have different mechanical properties i.e. stainless steel, low carbon steel, medium carbon steel and aluminum alloy are used. The fatigue crack growth rate equation is given by $da/dN={\beta} (1-R)^{\delta}\({\DELTA}K-{\DELTA}K_t)^{\alpha} / (K_{cf}-K_{max})$${\alpha}, {\beta}$ , and ${\delta}$ are constants, and ${\Delta}K_t$ is stress intensity factor range at low ${\Delta}K$ region. The constants are obtained from nonlinear least square method. $K_{ef}$is critical fatigue stress intensity factor. The relation between half crack length and number of cycles obtained by integrating the crack growth rate equation is in agreement with the experimental data. It is also experimented with constant maximum stress and decreasing stress ratios, and the fatigue growth rate of each material is in accord with the proposed equation.

• 한국환경과학회지
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• 제17권5호
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• pp.509-516
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• 2008

New functional surfactant, N,N-dimethyl-N-dodecyl-N-(2-methyl benzimidazoyl) ammonium chloride(DDBAC) having benzimidazole(BI) functional group have been synthesized and the critical micellar concentration of DDBAC measured by surface tentiometry and electric conductivity method was $8.9{\times}10^{-4}M$. Micellar effects in DDBAC functional surfactant solution on the hydrolysis of p-nitrophenylacetate(p-NPA), p-nitro-phenylpropionate(p-NPP) and p-nitrophenylvalerate(p-NPV) were observed with change of various pH (Tris-buffer). The pseudo first rate constants of hydrolysis of p-NPA, p-NPP and p-NPV in optimum concentration of DDBAC solution increase to about 160, 280 and 600 times, respectively, as compared with those of aqueous solution at pH 8.00(Tris-buffer). It is considered that benzimidazole functional moiety accelerates the reaction rates of hydrolysis because they act as nucleophile or general base. In optimum concentration of DDBAC solution, the rate constants of hydrolysis of p-NPP and p-NPV increase to about 1.5 and 3.0 times, respectively, as compared with that of p-NPA. It means that the more the carbon numbers of alkyl group of substrates, the larger the binding constants between DDBAC micelle and substrates are. To know the hydrolysis mechanism of p-NPCE(p-NPA, p-NPP and p-NPV), the deuterium kinetic isotope effects were measured in $D_2O$ solutions. Consequently the pseudo first order rate constant ratios in $H_2O$ and $D_2O$ solution, $k_{H_2O}/k_{D_2O}$, were about $2.8{\sim}3.0$ range. It means that the mechanism of hydrolysis were proceeded by nucleophile and general base attack in approximately same value.

• 한국전자파학회논문지
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• 제19권9호
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• pp.1020-1027
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• 2008

본 논문에서는 드루드 모형(Drude model) 특성을 가지는 메타 물질의 굴절각 및 임계각을 해석적으로 분석하였다. 메타 물질 슬래브(slab)에서의 전자기파의 반사 및 투과 특성을 해석하기 위해 메타 물질에서 적용된 드루드 모형에서는 30 GHz에서 각각 -1의 값을 갖는 유전율, 투자율을 사용하였다. 해석 결과로부터 드루드 모형에서 물리 상수(physical constant)의 부호가 주파수에 따라 연속적으로 변하기 때문에 주파수 대역별로 굴절각과 임계각이 각각 서로 다른 특성을 갖는다는 사실을 유도하였다. 본 논문에서 유도한 메타 물질의 주파수에 따른 굴절각 및 임계각 특성은 메타 물질의 주파수와 물리 상수간의 특성과 같은 전자기적 특성을 이해하고, 메타물질과 유전체간 다층 결합의 전파 특성 해석, 레이돔에 적용 가능한 신소재 메타 물질, 전기적 초소형 안테나와 같은 다양한 전자기파 응용에 유용하게 사용할 수 있다.

• Advances in nano research
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• 제8권1호
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• pp.59-68
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• 2020

In the present study, buckling analysis of sandwich composite (carbon nanotube reinforced composite and fiber reinforced composite) Euler-Bernoulli beam in two configurations (core and layers material), three laminates (combination of different angles) and two models (relative thickness of core according to peripheral layers) using differential quadrature method (DQM) is studied. Also, the effects of porosity coefficient and different types of porosity distribution on critical buckling load are discussed. Using sandwich beam, it shows a considerable enhancement in the critical buckling load when compared to ordinary composite. Actually, resistance against buckling in sandwich beam is between two to four times more. It is also showed the critical buckling loads of laminate 1 and 3 are significantly larger than the results of laminate 2. When Configuration 2 is used, the critical buckling load rises about 3 percent in laminate 1 and 3 compared to the results of configuration 1. The amount of enhancement for laminate 3 is about 17 percent. It is also demonstrated that the influence of the core height (thickness) in the case of lower carbon volume fractions is ignorable. Even though, when volume fraction of fiber increases, differences grow smoothly. It should be noticed the amount of decline has inverse relationship with the beam aspect ratio. Among three porosity patterns investigated, beam with the distribution of porosity Type 2 (downward parabolic) has the maximum critical buckling load. At the end, the first three modes of buckling will be demonstrated to investigate the effect of spring constants.

• 한국수산과학회지
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• 제29권1호
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• pp.92-96
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• 1996

CM-chitin의 고유특성 및 유동특성을 밝혀 효과적으로 식품산업에 이용하기 위하여 CM-chitin 수용액의 유동특성 중 임계농도와 유동방정식을 조사하였다. 물에서 CM-chitin의 환원농도는 2.5이었으며, 이 때의 임계농도는 $0.8\%(w/v)$이었다. 즉 $0.8\%$ 이하의 농도에서는 분자사슬간 상호작용이 일어나지 않았으며, $0.8\%$ 이상에서 상호작용이 일어나는 것으로 나타났다. $0.5\%$ CM-chitin 용액은 전단속도가 증가하여도 점도는 일정하게 유지되는 뉴우튼 유체의 특성을 보였으며, $1.0\%$ 용액은 전단속도가 증가하면 점도가 낮아지는 의가소성 유체의 특성을 보였다. $3.0\%$ CM-chitin 수용액의 유동상수 $\eta_\infty,\;\eta_0,\;\beta$, n은 각각 $0.0908(\fallingdotseq0.1)cp$, 770cp, 0.81, 0.36이었다. 따라서 $3.0\%$ CM-chitin 수용액의 유동방정식은 $\eta=0.1+\{{770/(1+0.81D^{0.36})\}$으로 나타낼 수 있다.