• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.183-194
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• 2009

In this paper, we considered the following four-point boundary value problem $\{{x"(t)+h(t)f(t,x(t),x'(t))=0,\;0<t<1\atop%20x'(0)=ax(\xi),\;x'(1)=bx(\eta)}\$. where $0\;<\;{\xi}\;<\;{\eta}\;<\;1,\;{\delta}\;=\;ab{\xi}\;-\;ab{\eta}\;+\;a\;-\;b\;<\;0,\;0\;<\;a\;<\;\frac{1}{\xi},\;0\;<\;b\;<\;\frac{1}{\eta}$. After the discussion of the Green function of the corresponding homogeneous system, we establish some criteria for the existence of positive solutions by using the generalized Leggett-William's fixed point theorem. The interesting point is the expression of the Green function, which is a difficulty for multi-point BVP.

• 대한수학회지
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• 제32권1호
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• pp.17-31
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• 1995

A Lorentzian para-Sasakian manifold M$(\varphi, \zeta, \eta, g)$ (abr. LPS-manifold) has been defined and studied in [9] and [10]. On the other hand, para-Sasakian (abr. PS)-manifolds are special semi-cosympletic manifolds (in the sense of [2]), that is, they are endowed with an almost cosympletic 2-form $\Omega$ such that $d^{2\eta}\Omega = \psi(d^\omega$ denotes the cohomological operator [6]), where the 3-form $\psi$ is the associated Lefebvre form of $\Omega$ ([8]). If $\eta$ is exact, $\psi$ is a $d^{2\eta}$-exact form, the manifold M is called an exact Ps-manifold. Clearly, any LPS-manifold is endowed with a semi-cosymplectic structure (abr. SC-structure).

• Bulletin of the Korean Chemical Society
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• 제4권1호
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• pp.36-41
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• 1983

An equation is derived which correlates the unperturbed dimensions $_0$ of polypeptides with the helical contents in the helix-coil transition region by using a simple model of a polypeptide chain. The model is a chain of connected balls which represent the repeating units, -CO-NH-CHR-, based on the fact that the repeating unit has a plane structure. The changing trend of the expansion factor ${\alpha}_{\eta}$ in the transition region is connected with the helical content $f_H$. The intrinsic viscosities [${\eta}$] of polypeptides are calculated from the unperturbed dimensions and the ${\alpha}_{\eta}$ factors. The above calculated results concerning $_0$ and [${\eta}$] are compared with other authors' theoretical and experimental results. From the comparison, we concluded that our theory explains better the chain dimensional behavior of polypeptides in the helix-coil transition region than others.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.1-23
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• 2007

The purpose of this paper is to develop a fairly large number of sets of global parametric sufficient optimality conditions under various generalized $({\theta},\;{\eta},\;{\rho})-V-invexity$ assumptions for a discrete minmax fractional programming problem involving arbitrary norms.

• 충청수학회지
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• 제13권1호
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• pp.139-144
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• 2000

The generalized noncommutative torus $T_{\rho}^d$ of rank m was defined in [2]. Assume that for the completely irrational noncommutative subtorus $A_{\rho}$ of rank m of $T_{\rho}^d$ there is no integer q > 1 such that $tr(K_0(A_{\rho}))=\frac{1}{q}{\cdot}tr(K_0(A_{\rho^{\prime}}))$ for $A_{\rho^{\prime}}$ a completely irrational noncommutative torus of rank m. All $C^*$-algebras ${\Gamma}({\eta})$ of sections of locally trivial $C^*$-algebra bundles ${\eta}$ over $M=\prod_{i=1}^{e}S^{2k_i}{\times}\prod_{i=1}^{s}S^{2n_i+1}$, $\prod_{i=1}^{s}\mathbb{PR}_{2n_i}$, or $\prod_{i=1}^{s}L_{k_i}(n_i)$ with fibres $T_{\rho}^d{\otimes}M_c(\mathbb{C})$ were constructed in [6, 7, 8]. We prove that ${\Gamma}({\eta}){\otimes}M_{p^{\infty}}$ is isomorphic to $C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C}){\otimes}M_{p^{\infty}}$ if and only if the set of prime factors of cd is a subset of the set of prime factors of p, that $\mathcal{O}_{2u}{\otimes}{\Gamma}({\eta})$ is isomorphic to $\mathcal{O}_{2u}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if and only if cd and 2u - 1 are relatively prime, and that $\mathcal{O}_{\infty}{\otimes}{\Gamma}({\eta})$ is not isomorphic to $\mathcal{O}_{\infty}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if cd > 1 when no non-trivial matrix algebra can be ${\Gamma}({\eta})$.

• Bulletin of the Korean Chemical Society
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• 제19권4호
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• pp.462-466
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• 1998

The homobimetallic anion, $({\eta}^5-MeCp)Mn(CO)_2Mn(CO)_5-M^+\; (M^+=Na^+, PPN^+$) was disrupted by $PR_3\;(R=C_6H_5,\;C_2H_5,\;OCH_3)$ in THF at various temperatures (r.t. ∼65℃) under the pseudo first order reaction conditions where excess of $PR_3$ was employed under a nitrogen atmosphere. For the reaction involving $PPN^+$ analog, Mn-Mn heterolytic cleavage occurred, leading to $PPN^+Mn(CO)_5^-\; and \;({\eta}^5-MeCp)Mn(CO)_2PR_3$ as products; however, in case of $Na^+\; analog,\; Na^+$ seems to play a novel counter ion effect on the disruption reaction by transferring one terminal CO from the $Mn(CO)_5$ moiety on to the $({\eta}^5-MeCp)Mn(CO)_2$ of the corresponding homobimetallic complex, eventually resulting in $Na^+Mn(CO)_4PR_3^-\;and\;({\eta}^5-MeCp)Mn(CO)_3$. This reaction is of overall first order with respect to [homobimetallic complex] with the activation parameters (ΔH≠=23.0±0.7 kcal/mol, ΔS≠= - 8.7±0.8 e.u. for $Na^+$ analog; ΔH≠=28.8±0.4 kcal/mol, ΔS≠=15.7±0.6 e.u. for $PPN^+$ analog reaction).

• 전기의세계
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• 제27권2호
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• pp.69-74
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• 1978

There have been a number of experimental or theorethical investigations of transport coefficient for electrons in the field of gas. In this paper the authors present the method by which Townsend first ionization doefficient (.alpha.) or attachment coefficient (.eta.) can be deduced easily and precisely by means of analyzing Townsend equation based on linealized least squares method. The apparent ionization coefficient (.alpha.-.eta.)/p have been analyzed from the experimental data by applying the new method above mentioned. And the values of (.alpha.-.eta.)/p in SF$_{6}$ as a function of E/p were agreement with the values measured by Bhalla et al. who analyzed th experimental pre-breakdown currents. In the same way (.alpha.-.eta.)/p in N$_{2}$O had a same tendency to that of Folkard et al.l.

• Journal of Communications and Networks
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• 제10권4호
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• pp.437-443
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• 2008

The randomized projective coordinate (RPC) method applied to a pairing computation algorithm is a good solution that provides an efficient countermeasure against side channel attacks. In this study, we investigate measures for increasing the efficiency of the RPC-based countermeasures and construct a method that provides an efficient RPC-based countermeasure against side channel attacks. We then apply our method to the well-known $\eta_T$ pairing algorithm over binary fields and obtain an RPC-based countermeasure for the $\eta_T$ pairing; our method is more efficient than the RPC method applied to the original $\eta_T$ pairing algorithm.

• Structural Engineering and Mechanics
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• 제17권5호
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• pp.691-706
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• 2004

The paper presents shear lag parameters for beam-to-column connections in steel box piers. Previous researches have analyzed beam-to-column connections in steel piers using a shear lag parameter ${\eta}_o$ obtained from a simple beam model, which is not based on a reasonable design assumption. Instead, the current paper proposes a cantilever beam model and has proved the effectiveness through theoretical and experimental studies. The paper examines the inaccuracy of the previous researches by estimating the effective width, the width-span length ratio L/b, and the sectional area ratio S of a cantilever beam. Two different shear lag parameters are defined using the cantilever model and the results are compared each other. The first type of shear lag parameter ${\eta}_c$ of a cantilever beam is derived using additional moments from various stress distribution functions while the other shear lag parameter ${\eta}_{eff}$ of a cantilever beam is defined based on the concept of the effective width. An evaluation method for shear lag stresses has been investigated by comparing analytical stresses with test results. Through the study, it could be observed that the shear lag parameter ${\eta}_{eff}$ agrees with ${\eta}_c$ obtained from the $2^{nd}$ order stress distribution function. Also, it could be observed that the shear lag parameter ${\eta}_c$ using the $4^{th}$ order stress distribution function almost converges to the upper bound of test results.

• 공업화학
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• 제3권1호
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• pp.88-99
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• 1992

광 전기분해시 양극으로 사용되는 산화티타늄 반도체 전극의 안정성을 증대시키고 효율향상을 위해서 순수한 티타늄 전극을 양극 산화법, 전기로 산화법, 불꽃 산화법으로 산화 피막을 제조하였으며 In을 Ti와 $TiO_2$소지에 전기도금을 한 후 전기로 산화법으로 혼합 산화물을 제조하였다. 또한 $Al_2O_3$ 와 NiO는 진공증착 방법을 이용하여 Ti 소지위에 증착시킨 후 전기로 산화법을 이용하여 혼합 산화물을 제조하였다. 에너지변환 효율(${\eta}$)은 인가전위에 따라서 다른 값을 갖는데 0.6V로 계산하여 보면 $1200^{\circ}C$의 불꽃으로 2분간 산화시킨 전극이 0.98%로 가장 큰 값을 가졌으며 양극 산화법으로 제조한 전극의 ${\eta}$는 0.14%로 작은 값을 보여 주었다. 한편 $800^{\circ}C$ 전기로에서 10분간 산화시킨 전극의 ${\eta}$는 0.57%로 띠간 에너지는 2.9eV로 나타났다. 한편 In을 Ti 및 $TiO_2$ 소지위에 전기도금시킨 전극의 ${\eta}$는 0.8%였으며 인가전위가 증가함에 따라서 ${\eta}$는 증가하였다. 그러나 $Al_2O_3$와 NiO를 Ti소지위에 진공증착시킨 전극의 ${\eta}$는 다른 전극들에 비해서 가장 낮은 값을 나타내었다.