• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.85-107
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• 2007

In this paper, we develop a fairly large number of sets of global semiparametric sufficient efficiency conditions under various generalized (${\theta},{\eta},{\rho}$)-V-invexity assumptions for a multiobjective fractional programming problem involving arbitrary norms.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.27-41
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• 2019

We determine explicit formulas for the number of representations of a positive integer n by quaternary quadratic forms with coefficients 1, 2, 5 or 10. We use a modular forms approach.

• Bulletin of the Korean Chemical Society
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• v.15 no.11
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• pp.990-996
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• 1994

New ferrocene-based chelate amines, $Fe[C_5H_4CH(Me)NMe_2]_2\;(3), \;Fe[C_5H-3(CH(Me)NMe_2)(PPh_2)-1,2]_2\;(4),\;(C_5H_5)Fe(C_5H_3(CH_2NMe_2)(CH(CN)NMe_2-1,2)\;(6),\;and\;(C_5H_5)Fe(C_5H_3(CH_2NMe_2)(CH(Me)NMe_2-1,2)$ (7) have been prepared. The reaction and the coordination chemistry of 4 and other related compounds (S,R)-(1-N,N-dimethylaminoethyl)-2-dicyclohexylphosphino)ferrocene (CPFA) and 1,1'-bis-(diphenylphosphino)ferrocene (BPPF) with $Rh_2(OAc)_4(MeOH)_2$ were investigated. The reaction of the chiral ligand (S,R)-CPFA forms a complex of the type (${\eta}^1$-(S,R)-CPFA-P)$_2Rh_2(OAc)_4$ (8) in which the ligand is coordinated to both rhodium centers in a monodentate fashion through phosphorus. In contrast, the bisphosphine analogues such as BPPF and 4 afford chelate complexes of the type (${\eta}^2-PP)Rh_2(OAc)_4$ (9 & 10) where both ligands act as a chelate bidentate to a single rhodium atom. All these complexes were characterized by microanalytical and spectroscopic techniques. In one case, the structure of 8 was determined by X-ray crystallography. Crystals are monoclinic, space group C2 (No. 5), with a=26.389 (3), b=12.942 (1), c=11.825 (1) A, ${\beta}$=111.22(1)$^{\circ}$, V=3964.7 (8) $A^3$, Z=4, and $D_{calc}$=1.58 g $cm^{-3}$. Two Rh(II) centers are bridged by four $AcO^-$ groups in the ${\eta}^1$ : ${\eta}^1$ mode across a Rh-Rh single bond, and octahedral coordination at Rh(1) and Rh(1') is completed by axially coordinating (S,R)-CPFA and a briding $AcO^-$, respectively.

• Journal of the Korean Chemical Society
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• v.8 no.1
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• pp.20-24
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• 1964

The linear combination of bond orbitals method is used to investigate the reactivity of halomethanes in abstraction reactions by atoms. The activation energy is evaluated on the assumption that, in an activated complex, two electrons in a bond to be broken become completely isolated from the rest of the ${\sigma}$-electron systems. Such a model leads to an intuitively attractive concept that the interactions between the reactive bond and the neighboring bonds govern the reactivity of ${\sigma}$-electron systems. The resulting equation for the activation energy, ${\varepsilon},\;is:\;{\narepsilon}= ${\varepsilon}={\zeta}+$$${\sum}_{i=1}^3$${\eta}c-I,$ c-4 Here, subscript C-4 indicates the bond to be broken, while C-i represents the other three bonds surrounding the reactive bond; ξ is the activation energy of a hypothetical reaction of an isolated C-4 bond and an attacking atom; and ${\eta}$C-i,C-4 stems from the stabilizing interacting of C-4 bond with neighboring C-i bonds. A choie of η′s consistent with bond strength data simplifies the above equation to a form ${\varepsilon}={\zeta}\;+\;N{\eta}c$-H, C-4 where N denotes the number of C-H plus C-F bond in halomethanes. In agreement with this equation, experimental -values increase linearly with increasing N.

• Bulletin of the Korean Chemical Society
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• v.2 no.4
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• pp.142-147
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• 1981

A blend polymeric system composed of poly(methyl methacrylate) (PMMA or PM) and polystyrene (PS) dissolved in chloroform was rheologically studied. The viscosities ${\eta}_{bl}$ of the blend system with various blending ratios ${\chi}$ changing from zero (pure PS solution) to unity (pure PMMA solution) were measured at $25{\circ}C$ as a function of shear rates ${\dot{s}}$ by using a Couette type viscometer. ${\eta}_{bl}$ at a given ${\dot{s}}$ decreased exponentially with ${\chi}$ reaching asymptotic constant value of ${\eta}_{bl}$ ; ${\eta}_{bl}$ at a given ${\chi}$ is greater at a smaller ${\dot{s}}$. These results are explained by using Ree-Erying's theory of viscosity, ${\eta}_{bl}=(x_1{\beta}_1/{\alpha}_1)_{b}_1＋ (x_2{\beta}_2/{\alpha}_2)_{bl}[sinh^{-1}{\beta}_2(bl) {\dot{s}}]/{\beta}_2(bl){\dot{s}}$. The Gibbs activation energy ${\Delta}G_i^\neq$(i = 2 for non-Newtonian units) entering into the intrinsic relaxation time ${\beta}$ is represented by a linear combination ${\Delta}G_i^\neq(bl) ={\chi}{\Delta}G_i^{\neq}_{iPM}+(1-{\chi}){\Delta}G_i^{\neq}_{iPS}$;the intrinsic shear modulus$[[\alpha}_i]^{-1}$ is also represented by $[{\alpha}_i(bl)]^{-1}={\chi}[{\alpha}_{iPM}]^{-1}+(1-{\chi})[{\alpha}_{iPS}]^{-1}$ and the fraction of area on a shear surface occupied by the ith flow units $x_i(bl)$ is similarly represented, i.e., $x_i(bl) = {\chi}x_{iPM}+(1-{\chi})x_{iPS}$. By using these ideas the Ree-Eyring equation was rewritten which explained the experimental results satisfactorily.

• Korean Journal of Soil Science and Fertilizer
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• v.29 no.1
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• pp.34-43
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• 1996

Determining the actual evapotranspiration(ETa) of a crop, and appropriate water management of the crop based on the ETa are very important For increasing the yield. The present study aimed at determining ETa and crop coefficient of sesame growing under different climatic conditions with the transparent thin polyethylene film mulch(0.03 mm thick) and without this mulch. Bottomless cylindrical lysimeters(105cm in diameter, 120cm in height, protruded 20 cm above the soil surface) were installed on the field of sandy loam "Bonyang series" soil with a moderate drainage. The determination of ETa was performed by measuring each component of a model equation, $ETa=(R+I)-\{Ro+(D1+D2)\}+C{\pm}{\Delta}S$. Sesame, cv. "Ansan" was sown in two rows with the spacing of $50{\times}15cm$ on May 10 in 1991 and 1992. The mulching covers 80% of the soil surface. Sesame consumed the water of 139.0 mm(1.53 mm/day) and 171.2 mm(1.59 mm/day) in ETa without the film mulch, but that of 132.6 mm(1.46 mm/day) and 199.8 mm(1.85 mm/day) with its mulching through both years of 1991 and 1992, respectively. The ETa's accounted for 52 and 69% of the potential evapotranspiration(ETp) in the mulched crop, and 54 and 59% of ETp in the non-mulched crop 1991 through 1992, respectively. Its ETa's were much more and their gap between the mulching and non-mulching treatment was larger in 1992 than in 1991 as a result of the better climatic condition of 1992.

• Bulletin of the Korean Chemical Society
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• v.14 no.1
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• pp.137-143
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• 1993

The tetranuclear heterometallic complex CpMo$Os_3(CO)_{10}({\mu]-H)2[{\mu}3-{\eta}^2-C(O)CH_2Tol]\;(1,\;Cp={\eta}^5-C_5H_5,\;Tol=p-C_6H_4Me)$ has been examined by variable-temperature $^{13}$C-NMR spectroscopy and by a full three-dimensional X-ray structual analysis. Complex 1 crystallizes in the orthorhombic space group Pna2$_1$ with a = 12.960(1) ${\AA}$, b = 11.255(l) ${\AA}$, c = 38.569(10)${\AA}$, V = 5626(2) ${\AA}^3$ and ${\rho}$(calcd) = 2.71 gcm$^{-3}$ for Z = 8 and molecular weight 1146.9. Diffraction data were collectedon a CAD4 diffractometer, and the structure was refined to $R_F$ = 9.7% and $R_{W^F}$ = 9.9% for 2530 data (MoK${\alpha}$ radiation). There are two essentially equivalent molecules in the crystallographic asymmetric unit. The tetranuclear molecule contains a triangulated rhomboidal arrangement of metal atoms with Os(2) and Mo at the two bridgehead positions. The metal framework is planar; the dihedral angle between Os(l)-Os(2)-Mo and Os(3)-Os(2)-Mo planes is 180$^{\circ}$. A triply bridging (${\mu}_3,\;{\eta}^2$) acyl ligand lies above the Os(l)-Os(2)-Mo plane; the oxygen atom spans the two bridgehead positions, while the carbon atom spans one bridgehead position and an acute apical position. The molecular architecture is completed by an ${\eta}^5$-cyclopentadienyl ligand and a semi-triply bridging carbonyl ligand on the molybdenum atom, and nine terminal carbonyl ligands-four on Os(3), three on Os(l), and two on Os(2). The two hydride ligands are inferred to occupy the Os(l)-Os(2) and Mo-Os(3) edges from structural and NMR data.

• Analytical Science and Technology
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• v.15 no.6
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• pp.550-555
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• 2002

The oxidation mechanism of boratabenzene was studied. As a model compound the ferrocene analogue (${\eta}^6$-1-Methylboratabenzene)(${\eta}^5$-Pentamethylcyclopentadiennyl)iron 3 was chosen. The complex underwent irreversible oxidation in the presence of ortho proton on the ring and a methyl group on the boron atom in methanol medium. Chemical oxidations with $Hg(OAc)_2$, $HgSO_4$, $Cu(OH)_2$, $AgCF_3SO_3$ or $FeCl_3$ in MeOH gave, via a transition state [3], at first the derivates 6 and 7, which were converted to each 8 and 9.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2005.05a
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• pp.92-95
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• 2005

The silver photodoping effect in amorphous AsGeSeS chalcogenide thin films for holographic recording has been investigated using a HeNe laser ($\lambda$=632.8 nm). The chalcogenide films prepared in this work were thinner in comparison with the penetration depth of recording light ($d_p$=1.66 mm). The variation of the diffraction efficiency $(\eta)$ in amorphous chalcogende films exhibits a tendency, independently of the Ag photodoping. That is, n increases relatively rapidly at the beginning of the recording process, reaches the maximum $({\eta}_{max})$ and slowly decreases. In addition, the value of ${\eta}_{max}$ depends strongly on chalcogenide film thickness(d) and its peak among the films with d = 40, 80, 150, 300, and 633 nm is observed at d = 150 nm (approximately 1/2n), where n is refractive index of the chalcogenide (n=2.0). The ${\eta}$ is largely enhanced by Ag photodoping into the chalcogenides. In particular, the value of hmax in a bilayer of 10-nm-thick Ag/150-nm-thick AsGeSeS film is about 1.6%, which corresponds to ~20 times in comparison with that of the AsGeSeS film (without Ag).

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.371-376
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• 2002

The aim of this paper is to study the condition of η-concavity. We will give examples of η-functions in Hilbert spaces on two different domains.