• Journal of the Korean Chemical Society
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• v.35 no.4
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• pp.301-307
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• 1991

The solubilities of the n-propyl iodide in nitrobenzene and m-xylene have been measured at 8$^{\circ}$, 15$^{\circ}$ and 25$^{\circ}C$ in the presence and the absence of gallium iodide. When gallium iodide does not exist in the system, the solubility of n-propyl iodide in m-xylene is greater than in nitrobenzene, indicating a stronger interaction of n-propyl iodide with m-xylene than that with nitrobenzene. It could be thought that n-propyl iodide forms unstable complex with gallium iodide in the presence of gaillium iodide in the system. This complex has been assumed in various ways and evaluated, that instability constant (K value) is relatively certain under the assumption of 1:1 complex, n-C$_3H_7I{\cdot}GaI_3$. Therefore, the complex would form the following equilibrium in the solution: n-C$_3H_7{\cdot}GaI _3{\rightleftharpoons}n-C_3H_7I+1/2Ga_2I_6$ the instability of the complex of n-propyl iodide with gallium iodide is compared with similar complexes of gallium iodide with methyl iodide. The changes of enthalpy, free energy and entropy for the dissociation of the complex are also calculated.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2007.06a
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• pp.333-334
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• 2007

This paper describes the characteristics of poly (polycrystalline) 3C-SiC grown on SiOz and AlN substrates, respectively. The crystalline quality of poly 3C-SiC was improved from resulting in decrease of FWHM (full width half maximum) of XRD by increasing the growth temperature. The minimum growth temperature of poly 3C-SiC was $1100^{\circ}C$. The surface chemical composition and the electron mobility of poly 3C-SiC grown on each substrate were investigated by XPS and Hall Effect, respectively. The chemical compositions of surface of poly 3C-SiC films grown on $SiO_2$ and AlN were not different. However, their electron mobilities were $7.65\;cm^2/V.s$ and $14.8\;cm^2/V.s$, respectively. Therefore, since the electron mobility of poly 3C-SiC films grown on AlN buffer layer was two times higher than that of 3C-SiC/$SiO_2$, a AlN film is a suitable material, as buffer layer, for the growth of poly 3C-SiC thin films with excellent properties for M/NEMS applications.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.813-830
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• 2022

The generating functions of the divisor function σ_s(n) = Σ_0<d|n d^s are quasimodular forms. In this paper, we find the basis of the space of quasimodular forms of weight 6 on Γ₀(10) consisting of Eisenstein series and η-quotients. Then we evaluate the convolution sum Σ_ak+bl+cm=n σ(k)σ(l)σ(m) with lcm(a, b, c) = 10 and Σ_al+bm=n lσ(l)σ(m) and Σ_al+bm=n σ₃(l)σ(m) with lcm(a, b) = 10.

• Journal of the Korean Mathematical Society
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• v.8 no.1
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• pp.25-30
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• 1971

Put ($$^*$$) $$G[x,y]={\sum}\limits^{p+q=n}_{p,q=0}[-n]_{p+q}c_{p,q}x^py^q$$, where $[{\lambda}]_m$ is the Pocbhammer symbol and the $c_{p,q}$ are arbitrary constants. Making use of the specialized forms of some of his earlier results (see [8] and [9] the author derives here bilateral generating functions of the type ($$^{**}$$) $${\sum}\limits^{\infty}_{n=0}{\frac{[\lambda]_n}{n!}}_2F_1[\array{{\rho}-n,\;{\alpha};\\{\lambda}+{\rho};}x]\;G[y,z]t^n$$ where ${\alpha}$, ${\rho}$ and ${\lambda}$ are arbitrary complex numbers. In particular, it is shown that when G[y, z] is a double hypergeometric polynomial, the right-band member of ($^{**}$) belongs to a class of general triple hypergeometric functions introduced by the author [7]. An interesting special case of ($^{**}$) when ${\rho}=-m,\;m$ being a nonnegative integer, yields a class of bilateral generating functions for the Jacobi polynomials $\{P_n{^{{\alpha},{\beta}}}(x)\}$ in the form ($$^{***}$$) $${\sum\limits^{\infty}_{n=0}}\(\array{m+n\\n}\)P{^{({\alpha}-n,{\beta}-n)}_{m+n}(x)\;G[y,z]{\frac{t^n}{n!}}$$, which provides a unification of several known results. Further extensions of ($^{**}$) and ($^{***}$) with G[y, z] replaced by an analogous multiple sum $H\[y_1,{\cdots},y_m\]$ are also discussed.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.287-290
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• 2001

Let X$_1$, X$_2$, … be a sequence of independent and identically distributed random variables with continuous cumulative distribution function F(x). X(sub)j is an upper record value of this sequence if X(sub)j > max {X$_1$, X$_2$, …, X(sub)j-1}. We define u(n) = min {j│j > u(n-1), X(sub)j > X(sub)u(n-1), n $\geq$ 2} with u(1) = 1. Then F(x) = 1 - e(sup)-x/c, x > 0 if and only if E[X(sub)n(n+1) - X(sub)u(n)│X(sub)u(m) = y] = c or E[X(sub)u(n+2) - X(sub)u(n)│X(sub)u(m) = y] = 2c, n $\geq$ m+1.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.52 no.3
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• pp.256-267
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• 2019

Styrofoam beads, which are relatively inexpensive and can provide a large specific surface area, were tested as filter media. Styrofoam beads with a diameter of $3{\pm}0.5mm$ were used; the specific surface area of the beads was $1,034m^2{\cdot}m^{-3}$. Five independent recirculating culture systems were used in the experiment. Each system consisted of one culture tank and three trickling bio-filters. Using the systems, nitrification efficiency was evaluated with respect to hydraulic loading rate (HLR) and carbon/nitrogen (C/N) ratio. The lowest ammonia and nitrogen concentrations were $0.84mg{\cdot}L^{-1}$ and $1.30mg{\cdot}L^{-1}$, respectively, observed at an HLR of $50.9m^3{\cdot}m^{-2}{\cdot}h^{-1}$. Nitrification efficiency in the culture tank was highest at a C/N ratio of 0, with ammonia and nitrite nitrogen concentrations of $0.32mg{\cdot}L^{-1}$ and $0.90mg{\cdot}L^{-1}$, respectively. Ammonia and nitrite nitrogen concentrations in the culture tank abruptly changed at C/N ratios ${\geq}3$.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2000.07a
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• pp.444-447
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• 2000

The spinel L $i_{1-x}$ M $n_2$ $O_4$has been synthesized by the solid-state reaction. L $i_{l-x}$M $n_2$ $O_4$which includes a mixture of LiOH . $H_2O$ and Mn $O_2$prepared by preliminary heating at 35$0^{\circ}C$ for 12hr. L $i_{l-x}$M $n_2$ $O_4$fired at temperature range from 75$0^{\circ}C$ for 48hr. The structure and the electrochemical characteristics of spinel to L $i_{1-x}$ M $n_2$ $O_4$which is fabricated by changing sintering condition from starting materials are investigated. The cyclic voltammetric measurement was performed using 3 electrode cells. Electrode specific capacity and cycle life behavior were tested in a 3.0~4.2V range at a constant current density of 0.45mA/c $m^2$. To improve the cycle performance of spinel L $i_{l-x}$M $n_2$ $O_4$as the cathode of 4V class lithium secondary batteries, spinel phases L $i_{1-x}$ M $n_2$ $O_4$were Prepared at various lithium. The results showed that discharge capacity of L $i_{l-x}$M $n_2$ $O_4$varied at lithium quantity decrease with increasing lithium add quantity. The discharge capacities of L $i_{0.925}$M $n_2$ $O_4$and LiM $n_2$ $O_4$revealed 108 and 117mAh/g, respectively.spectively.y.

• Polymer(Korea)
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• v.24 no.4
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• pp.445-452
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• 2000

The copolymerization of ethylene (E) and norbornene (N) was examined by using various metallocene catalysts and modified-MAO(MMAO) cocatalyst. For $C_2$-symmetry catalysts such as rac-Et(Ind)$_2$ZrC $l_2$, M $e_2$Si(Ind)$_2$ZrC $l_2$, M $e_2$Si(Cp)$_2$ZrC $l_2$ and Cs-symmetrical iPr(FluCp)ZrC $l_2$ as well as CGC and di-bridged zirconocene, the effects of catalyst structure and [N]/[E] feed ratio on catalyst activity, thermal property and [N] content of copolymer (COC) was investigated. For rac-Et(Ind)$_2$ZrC $l_2$ catalyst of a constant [N]/[E] feed ratio, the appropriate conditions of [Al]/[Zr] mole ratio, polymerization temperature and cocatalyst structure were found to be 3000, 4$0^{\circ}C$, MMAO cocatalyst, respectively. As [N]/[E] feed ratio increased, the incorporation of norbornene to copolymer increased while, the activity of catalyst decreased except for iPr(FluCp)ZrC $l_2$ With consideration of catalyst activity as well as N content, it was found that rac-Et(Ind)$_2$ZrC $l_2$/MMAO system exhibited relatively high activity and controllable $T_{g}$. Monomer reactivity ratio was determined by Kelen-Tudos method..

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.39-46
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• 1997

Given to be the $m^{th}$ correlation coefficient of the Rudin-Shapiro polynomials of degrees $2^n-1$, $$\mid$a_m$\mid$ \leq C(2^n)^{\frac{3}{4}}$ and there exists $\kappa \neq 0$ such that $$\mid$a_{\kappa}$\mid$ ＞D(2^n)^{0.73}$ (C and D are universal constants). Here we show that the 0.73 is optimal in the upper vound case.

• The Pure and Applied Mathematics
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• v.16 no.3
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• pp.283-296
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• 2009

Let f(x) = $x^n\;+\;a$ be a binomial polynomial in Z[x] and $f_m(x)$ be the m-th iterate of f(x). In this work we study a necessary condition to be the Galois group of $f_m(x)$ is isomorphic to a wreath product group $[C_n]^m$ where $C_n$ is a cyclic group of order n.