• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.873-882
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• 2022

In this paper, we construct the multiple (h, p, q)-Hurwitz-Euler eta function by generalizing the multiple Hurwitz-Euler eta function. We get some explicit formulas and properties of the higher-order (h, p, q)-Euler numbers and polynomials.

• East Asian mathematical journal
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• v.25 no.2
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• pp.159-169
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• 2009

In this paper, we introduce a generalized system of nonlinear relaxed co-coercive variational inclusions involving (A, ${\eta}$)-monotone map-pings in the framework of Hilbert spaces. Based on the generalized resol-vent operator technique associated with (A, ${\eta}$)-monotonicity, we consider the approximation solvability of solutions to the generalized system. Since (A, ${\eta}$)-monotonicity generalizes A-monotonicity and H-monotonicity, The results presented this paper improve and extend the corresponding results announced by many others.

• Journal of the Korean Chemical Society
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• v.35 no.4
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• pp.410-413
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• 1991

A tripledecker sandwichcomplex, bis(${\eta}^5$-cyclopentadienyl)-${\mu}$-(${\eta}^6$-2,3-dialkyl-1,4-dimethyl-1,4-dibora-2,5-cyclohexadiene)dicobalt 1 was synthesized as a starting material. By the reaction of compound 1 with the excess 3-hexyne two kinds of sandwichcomplexes, cyclopentadienyl(${\eta}^6$-2,3-dialkyl-1,4-dimethyl-1,4-dibora-2,5-cyclohexadiene)cobalt 2 and cyclopentadienyl(${\eta}^6$-hexaethyl benzene)cobalt 3 were separated. The complex 3 was decomposed during purifying at RT to give a cyclization product of 3-hexyne, hexaethyl benzene.

• Journal of Life Science
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• v.8 no.5
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• pp.492-496
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• 1998

Intact measurement of leaf water content was attempted using the transmission of beta radiation. Prior to the experiments, two tested plants, rice and soybean, were grown in 1/5000a wagner pot. The moisure ratio of plant leaves were measured with the beta radiation transmission method using a G-M detector and $^{99}$ Tc as the beta ray sou-rce. Beta radiation transmission showed a tendancy to increase with the passage of time after leaf cutting. However, it showed a tendancy to decrease with water supply for the lack of water. A positive correlation was found between the leaf water content and beta radiation transmission. The mutiple regression analysis about leaf water content was obtained that the coefficient of partial regression for beta radiation transmission was much higher(rice; -0.863, soybean; -0.904) than that for specific leaf area(rice; 0.007, soybean: 0.004).

• Korean Journal of Social Welfare
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• v.56 no.4
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• pp.215-238
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• 2004

The purpose of this paper is to examine the impact of conflict and nurturing factors for the divorced parent on the behavioral adaptation of their children. The participants in this study include 216 children in divorced families nationwide. Structural Equation Modeling with LISREL8 was used for statistical method. In order to achieve the purpose, researchers firstly tried to test a construct validity of conceptual variables(parental conflict, negative attitude of parental nurturing, child's belief about parental divorce, child's aggression and child's delinquence) by employing exploratory factor analysis(EFA) and confirmatory factor analysis(CFA). Result showed that all the five conceptual variables were discriminated. It was identified as the fit index of path structure was good(CFI=.955, NNFI=.947, RMSEA=.046). The specific result were as follows: 1. the parental conflict(${\xi}1$) was directly related to the negative attitude of parental nurturing(${\eta}1$) and the child's belief about parental divorce(${\eta}2$). 2. the parental conflict(${\xi}1$) was indirectly related to child's belief about parental divorce(${\eta}2$), the child's aggression(${\eta}3$) and delinquence(${\eta}4$). 3. the negative attitude of parental nurturing(${\eta}1$) was directly related to the child's belief about parental divorce(${\eta}2$). 4. the negative attitude of parental nurturing(${\eta}1$) was indirectly related to the child's aggression(${\eta}3$) and delinquence(${\eta}4$). Lastly, and, the child's belief about parental divorce(${\eta}2$) was directly related to the child's aggression(${\eta}3$) and delinquence(${\eta}4$). Researchers also identified the mediating effect of the parental nurturing between parental conflict and child's belief about parental divorce. On the basis of these results, this article provided some suggestions for promoting of children welfare.

• Korean Journal of Mathematics
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• v.17 no.3
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• pp.283-291
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• 2009

We investigate the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+g_1(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}),\\{\eta}_t=-L{\eta}+g_2(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}).\end{array}$$ We show the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system when the nonlinearity $g^{\prime}_1,\;g^{\prime}_2$ are bounded and $3g^{\prime}_1(-{\infty})+g^{\prime}_2(-{\infty})<{\lambda}_1,\;{\lambda}_n<3g^{\prime}_1(+{\infty})+g^{\prime}_2(+{\infty})<{\lambda}_{n+1}$.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.553-564
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• 2008

We have a concern with the existence of solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+{\mu}g(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,2{\pi}),\\{\eta}_t=-L{\eta}+{\nu}g(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,2{\pi})\end{array}.$$ We prove the uniqueness theorem when the nonlinearity does not cross eigenvalues. We also investigate multiple solutions (${\xi}(x,t),\;{\eta}(x,t)$) for perturbations of the parabolic system with Dirichlet boundary condition when the nonlinearity f' is bounded and $f^{\prime}(-{\infty})<{\lambda}_1,{\lambda}_n<(3{\mu}+{\nu})f^{\prime}(+{\infty})<{\lambda}_{n+1}$.

• Proceedings of the Korea Crystallographic Association Conference
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• 2001.05a
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• pp.16-16
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• 2001

• Bulletin of the Korean Chemical Society
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• v.26 no.9
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• pp.1359-1365
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• 2005

A series of new chiral [iminophosphoranyl]ferrocenes, {${\eta}^5-C_5H_4-(PPh_2=N-2,6-R_2-C_6H_3)$}Fe{${\eta}^5-C_5H_3-1-PPh^2-2-CH(Me)NMe_2$} (1: R = Me, $^iPr$), {${\eta}^5{-C_5H_4-(PPh_2=N-2,6-R_2}^1-C_6H_3)$}Fe{${\eta}^5-C_5H_3-1-(PPh_2=N-2,6-R_2-C_6H_3)-2-CH(Me)R_2$} (2: $R^1\;=\;Me,\;^iPr;\;R^2\;=\;NMe_2$, OMe), and $({\eta}^5-C_5H_5)Fe${${\eta}^5-C_5H_4-1-PR_2-2-CH(Me)N=PPh_3$} (3:R = Ph, $C_6H_{11}$) have been prepared from the reaction of [1,1'-diphenylphosphino-2-(N,N-dimethylamino) ethyl]ferrocene with arylazides (1 & 2) and the reaction of phosphine dichlorides ($R_3PCl_{2}$) with [1,1'-diphenylphosphino-2-aminoethyl]ferrocene (3), respectively. They form palladium complexes of the type $[Pd(C_3H_5)(L)]BF_4$ (4-6: L = 1-3), where the ligand (L) adopts an ${\eta}^2-N,N\;(2)\;or\;{\eta}^2$-P,N (3) as expected. In the case of 1, a potential terdentate, an ${\eta}^2$-P,N mode is realized with the exclusion of the –=NAr group from the coordination sphere. Complexes 4-6 were employed as catalysts for allylic alkylation of 1,3-diphenylallyl acetate leading to an almost stoichiometric product yield with modest enantiomeric excess (up to 74% ee). Rh(I)-complexes incorporating 1-3 were also prepared in situ for allylic alkylation of cinnamyl acetate as a probe for both regio- and enantioselectivities of the reaction. The reaction exhibited high regiocontrol in favor of a linear achiral isomer regardless of the ligand employed.

• Bulletin of the Korean Chemical Society
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• v.15 no.5
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• pp.379-386
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• 1994

Reactions of 1',2-bis(diphenylphosphino)-l-(N,N-dimethylaminomethyl)ferrocene (FcNPP) with $M(CO)_6$ (M=Cr, Mo, W) in the presence of TMNO (Trimethylamine oxide) in a stoichiometric ratio of 1 : 1.5 : 3.5 produced a series of Gp 6 metal carbonyl derivatives with a variety of coordination modes: M(CO)$_4({\eta}^2$-FcNPP-P,P) (M=Cr, Mo, W), $M(CO)_5({\eta}^1-FcNPP-P) (M=Mo, W)\;,\; M_2(CO)_9({\eta}^1\;,\;{\eta}^2-FcNPP-P,P,N) (M=Cr, Mo)\;,\;M_2(CO)_{10}({\eta}^1\;,\;{\eta}^1-FcNPP-P,P) (M=Cr, Mo, W)\;, and\;W(CO)_4({\eta}^2-FcNPP(O)-P,N)$. All these complexes were characterized by microanalytical and spectroscopic techniques. In one case, the structure of W(CO)$_4({\eta}^2$-FcNPP(O)-P,N) was determined by X-ray crystallography. Crystals are monocinic, space group P$2_{1/C}$, with a=10.147(2), b=19.902(3), c=19.821(4) ${\AA},\;{\beta}=96.88(2)^{\circ},\;V=3974(l){\AA}^3$, Z=4, and $D_{calc}=1.64 g cm^{-3}$. The geometry around the central tungsten metal is a distorted octahedron, with the nitrogen and phosphorus atoms being cis to each other. Some of these complexes exhibited catalytic activities in the allylic oxidation and epoxidation of cholesterly acetate. Other oxidation products were also formed with the different chemical yields and product distribution depending upon the ligand and the central metal.