• Bulletin of the Korean Chemical Society
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• 제21권10호
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• pp.969-972
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• 2000

[Fe II Fe III $BPLNP(OAc)_2](BPh_4)_2$ (1), a new model for the reduced form of the purple acid phosphatases, has been synthesized by using a dinucleating ligand, 2,6-bis[((2-pyridylmethyl)(6-methyl-2-pyridylmethyl)ami-no)methyl]-4-nitrophenol (HBPLNP) . Complex 1 has been studied by electronic spectral, NMR, EPR, SQUID, and electrochemical methods. Complex 1 exhibits two strong bands at 498 nm $(\varepsilon=$ 2.6 ${\times}10^3M-^1cm-^1)$ and 1363 nm $(\varepsilon=$ 5.7 ${\times}10^2M-^1cm-^1)$ in $CH_3CN.$ These are assigned to phenolate-to-FeIII and intervalence charge-transfer transitions, respectively. NMR spectrum of complex 1 exhibits sharp isotropically shifted resonances, which number is half of those expected for a valence-trapped species, indicating that electron transfer between FeⅡ and FeⅢ centers is faster than NMR time scale at room temperature. Complex 1 undergoes quasireversible one-electron redox processes. The $FeIII_2/FeIIFeIII$ and $FeIIFeIII/FeII_2$ redox couples are at 0.807 and 0.167 V ver-sus SCE, respectively. It has Kcomp = 5.9 ${\times}$10 1s(acetato) ligand combination sta-bilizes a mixed-valence FeIIFeIII complex in the air. Interestingly, complex 1 exhibits intense EPR signals at g = 8.56, 5.45, 4.30 corresponding to mononuclear high-spin FeⅢ species, which suggest a very weak magnetic coupling between the iron centers. Magnetic susceptibility study shows that there is a very weak antiferromag-netic coupling (J = $-0.78cm-^1$, H = $-2JS_1${\times}$S_2)$ between FeII and FeIII centers. Thus, we can suggest that complex 1 has a very weak antiferromagnetic coupling between the iron centers due to the electronic effect of the nitro group in the bridging phenolate ligand.

• 대한수학회논문집
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• 제18권1호
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• pp.117-126
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• 2003

Let {$X_{nk}$\mid$1\;{\leq}\;k\;{\leq}\;n,\;n\;{\geq}\;1$} be an array of row negatively associated (NA) random variables which satisfy $P($\mid$X_{nk}$\mid$\;>\;x)\;{\leq}\;P($\mid$X$\mid$\;>\;x)$. For weighed sums ${{\Sigma}_{k=1}}^{Tn}\;a_kX_{nk}$ indexed by random variables {$T_n$\mid$n\;{\geq}$1$}, we establish a general weak law of large numbers (WLLN) of the form $({{\Sigma}_{k=1}}^{Tn}\;a_kX_{nk}\;-\;v_{[nk]})\;/b_{[an]}$ under some suitable conditions, where $\{a_n$\mid$n\;\geq\;1\},\; \{b_n$\mid$n\;\geq\;1\}$ are sequences of constants with $a_n\;>\;0,\;0\;<\;b_n\;\rightarrow \;\infty,\;n\;{\geq}\;1$, and {$v_{an}$\mid$n\;{\geq}\;1$} is an array of random variables, and the symbol [x] denotes the greatest integer in x.

• 디지털콘텐츠학회 논문지
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• 제5권4호
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• pp.289-294
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• 2004

영상분석을 하기 위하여 이용되는 많은 방법들은 기본적으로 잘 알려진 여러 가지 수학적인 이론에 기초해 전개 된다. 예로써 영상을 이변 함수에 대응시켜 기존의 미분 또는 편미분을 통한 경도 및 에너지 함수를 이용하거나 미분기하학적 측면에서 접평면 및 곡률을 사용하는 등과 같이 전통의 수학적 기법댐들이 적용되기도 한다. 그러나 국소적 변화를 효과적으로 분석하기 위해 사용되는 이러한 수학적 이론은 대상을 표현하는 함수가 충분히 연속적으로 변화하는 매우 부드러운 함수임을 가정하는 데에서 시작하게 된다. 그러므로 실제 자연의 형상 또는 현상을 구현하는 함수에 알려진 수학적 이론을 직접적으로 대입하므로 야기되는 여러 가지 불량문제를 종종 접하게 된다. 이러한 문제를 해결하기 위한 한 방법으로 본 논문에서는 보다 효율적으로 계산되고 광범위하게 적용될 수 있는 약미분을 정의하고 이를 해석하고자 하였다.

• 한국결정학회지
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• 제16권2호
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• pp.107-127
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• 2005

Five Cu(II) compounds were obtained from different copper salts with btp ligands, and their structures were determined by X-ray crystallography. The structure of coordination polymer 2 contains btp-bridged tetranuclear Cu(II) units weakly connected by nitrate ions, and the structure of a discrete Cu(II) molecule 1 contains acetates and btp ligands. With perchlorate anions, two btp ligands bridge Cu(II) ions to form a double zigzag chain 3, while a single zigzag chain 4 is created with sulfate anions. The reaction of $Cu(NO_{3})_{2}$ containing $NH_{4}PF_{6}$ with btp ligands also produced a polymeric compound 5 containing $Cu(H_{2}O)_{2}^{2+}$ and $Cu(NO_{3})_{2}$ units alternatively bridged by btp ligands with H-bonds between copper bonded water and nitrate oxygen atoms. Five Zn(II) compounds were obtained from different zinc salts with btp ligands, and the structures of polymeric compounds (6, 7 and 8) and monomeric compounds (9 and 10) were determined by X-ray crystallography. With nitrate, chloride and bromide anions, btp ligands bridge Zn(II) ions to form polymeric compounds (6, 7 and 8), but btp ligands coordinate to a Zn(II) ion to form monomeric complexes (9 and 10) with $PF_{6}^{-}$ and perchlorate anions. Four silver salts and btp ligands produced two kinds of structures, dinuclear 20-membered rings and one-dimensional zigzag chain depending on different anions. For $ClO_{4}^{-}$ and OTf anions, weak interactions between Ag(I) and anions make dinuclear 20-membered rings construct polymeric compounds (11 and 13). For $PF_{6}^{-}$ anion, there are also weak interactions between Ag(I) and $F(PF_{6}^{-})(12)$, but they do not construct a polymeric compound. For $O_{2}CCF_{3}^{-}$ anion, btp ligands bridge Ag(I) atoms to make one-dimensional zigzag chain (14), and there are also interactions between Ag(I) and anions.

• 한국소음진동공학회논문집
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• 제25권12호
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• pp.866-873
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• 2015

The transverse vibration of the deploying beam from rigid hub was analyzed by simulation and experiment. The linear governing equation of the deploying beam was obtained using the Euler-Bernoulli beam theory. To discretize the governing equation, the Galerkin method was used. After transforming the governing equation into the weak form, the weak form was discretized. The discretized equation was expressed by the matrix-vector form, and then the Newmark method was applied to simulate. To consider the damping effect of the beam, we conducted the modal test with various beam length. The mass proportional damping was selected by the relation of the first and second damping ratio. The proportional damping coefficient was calculated using the acquired natural frequency and damping ratio through the modal test. The experiment was set up to measure the transverse vibration of the deploying beam. The fixed beam at the carriage of the linear actuator was moved by moving the carriage. The transverse vibration of the deploying beam was observed by the Eulerian description near the hub. The deploying or retraction motion of the beam had the constant velocity and the velocity profile with acceleration and deceleration. We compared the transverse vibration results by the simulation and experiment. The observed response by the Eulerian description were analyzed.

• 터널과지하공간
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• 제3권2호
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• pp.132-141
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• 1993

Laboratory and field tests were performed to find out the effectiveness of ground improvement by grouting for an urban subway tunnel that was excavated in weak rock by the NATM. Field measurements were carried out to monitor the behavior of rock mass around the tunnel and to ensure the validity of the current design of the distance form the measuring points to the tunnel face. The final converged displacement and the peroid were predicted using the gamma function. It was found that the ground improvement in terms of reduced permeability and increased stength in the self-supportability of the excavation face enabled the NATM applied in poor gorund. As the result of applying the gamma function to the predicting of displacement, the final displacement including the preceding one and the converged period could be approximately predicted at the early excavation stage.

• 대한수학회보
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• 제48권6호
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• pp.1169-1182
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• 2011

In this paper we study the existence of non-trivial weak solutions of the Neumann problem for quasilinear elliptic equations in the form $$-div(h(x){\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+b(x){\mid}u{\mid}^{p-2}u=f(x,\;u),\;p{\geq}2$$ in an unbounded domain ${\Omega}{\subset}\mathbb{R}^N$, $N{\geq}3$, with sufficiently smooth bounded boundary ${\partial}{\Omega}$, where $h(x){\in}L_{loc}^1(\overline{\Omega})$, $\overline{\Omega}={\Omega}{\cup}{\partial}{\Omega}$, $h(x){\geq}1$ for all $x{\in}{\Omega}$. The proof of main results rely essentially on the arguments of variational method.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2003년도 춘계학술대회 논문집
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• pp.78-81
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• 2003

Polishing Processes are widely used in the glass, optical, die and semiconductor industry and are conventionally carried out using abrasive slurry and a polishing pad. But abrasive slurry process has a weak point that is high cost of handling of used slurry and hard controllability of slurry. Recently, some researches have attempted to solve these problems and one method is the development of a fixed abrasive pad. FAP has a couple of advantages including clean environment, lower CoC, easy controllability and higher form accuracy. But FAP also has a weak point that is need of dressing because of glazing and loading. The paper introduces the basic concept and fabrication technique of FAP using hydrophilic polymers with swelling characteristics in water and explains the self-conditioning phenomenon. Experimental results demonstrate to achieve nano surface roughness of soda lime glass for optical application

• Steel and Composite Structures
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• 제24권5호
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• pp.523-536
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• 2017

A layerwise (LW) formulation based on the Galerkin method is presented to investigate the three-dimensional stress state in long sandwich plate which is subjected to tension force and pure bending moment. Based on the Galerkin method and the LW discretization approach, the equilibrium equations of elasticity for the long plate are written in the weak form and discretized through the thickness of the plate. The discretized equations are written in terms of displacement components of the numerical layers. The governing equations of the plate are solved analytically for the free edge boundary conditions. The distribution of stress state especially the 3D stress state in the vicinity of the edges of the sandwich plate which is subjected to tension and pure bending is studied. In order to increase the accuracy, the out of plane stresses are obtained by integrating the equilibrium equations of elasticity. The convergence and accuracy of the predictions are studied and various numerical results are presented for distribution of the in-plane and out of plane stresses in symmetric and un-symmetric sandwich plates.

• 대한수학회논문집
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• 제9권2호
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• pp.419-421
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• 1994

Recently Hong and Oh [5] provided a fairly general weak law for arrays in the following form: Let {(X/sub ni/, l ≤ i ≤ k/sub n/), n ≥ l}, k/sub n/ → ∞ as n → ∞, be an array of random variables on (Ω, F, P) and set F/sub nj/ = σ{X/sub ni/, 1 ≤ i ≤ j}, 1 ≤ j ≤ k/sub n/, n ≥ 1, and F/sub n0/ = {ø, Ω}, n ≥ 1. Suppose that (equation omitted) aP { X/sub ni/ /sup p/ ＞ a} → 0 as a → ∞ uniformly in n for some 0 < p < 2. Then S/sub n//(equation omitted) → 0 in probability as n → ∞ where S/sub n/ = (equation omitted)(X/sub ni/ - E(X/sib ni/I( X/sub ni/ /sub p/ ≤ k/sub n/) F/sub n,i-l/)). In this note, we will prove the following result under the same domination condition of Hong and Oh [5].(omitted)