• Journal of the Korean Vacuum Society
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• v.5 no.1
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• pp.67-72
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• 1996

$RU_{1-x}Ir_xO_2$ films were deposited on the quartz substrate by a spray pyrolysis method. The x-ray diffraction patterns showed that the structure of the $RU_{1-x}Ir_xO_2$ film was tetragonal and the lattice constant $a_o$ and $c_o$ were increased from 4.495 A to 4.058 A and from 3.092A to 3.156 A, respectively as the Ir composition varied from 0.0 to 1.0. The $RU_{1-x}Ir_xO_2$ film was metallic and the resistivity of the samples was increased from $7{\times}10^{-5}{\Omega}\textrm{cm}$ to $48{\times}10^{-5}{\Omega}\textrm{cm}$ with increasing the Ir x. The surface of the sample was slightly roughed, the grain size and the grain boundary width were increased as the Ir composition varied from 0.0 to 1.0.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.753-782
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• 2016

In this paper we deduce the number of representations of a positive integer n by each of the six triangular forms as $${\frac{1}{2}}x_1(x_1+1)+{\frac{3}{2}}x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\{\frac{1}{2}}x_1(x_1+1)+{\frac{1}{2}}x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\{\frac{1}{2}}x_1(x_1+1)+{\frac{1}{2}}x_2(x_2+1)+{\frac{1}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\x_1(x_1+1)+x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\x_1(x_1+1)+{\frac{3}{2}}x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+3x_4(x_4+1),\\{\frac{1}{2}}x_1(x_1+1)+{\frac{1}{2}}x_2(x_2+1)+3x_3(x_3+1)+3x_4(x_4+1).$$

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.455-466
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• 2008

In, [7], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\left\|{\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i{\left\|^2+{\sum\limits_{i=1}^{n}}\right\|}{x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}x_j}}\right\|^2}={\sum\limits_{i=1}^{n}}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\cdots},x_{n}{\in}V$. Let V,W be real vector spaces. It is shown that if a mapping $f:V{\rightarrow}W$ satisfies $$(0.1){\hspace{10}}nf{\left({\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i \right)}+{\sum\limits_{i=1}^{n}}f{\left({x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}}x_i}\right)}\\{\hspace{140}}={\sum\limits_{i=1}^{n}}f(x_i)$$ for all $x_1$, ${\dots}$, $x_{n}{\in}V$ $$(0.2){\hspace{10}}2f\(\frac{x+y}{2}\)+f\(\frac{x-y}{2} \)+f\(\frac{y}{2}-x\)\\{\hspace{185}}=f(x)+f(y)$$ for all $x,y{\in}V$. Furthermore, we prove the generalized Hyers-Ulam stability of the functional equation (0.2) in real Banach spaces.

• Analytical Science and Technology
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• v.13 no.2
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• pp.208-214
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• 2000

The formation and dissolution of hydroxides, carbonates and hydroxyapatite (HAp), which depend on the pH of solution, are important factor for the preparation of homogeneous and fine HAp, $Ca_{10-x}(HPO_4)_x(PO_4)_{6-x}(OH)_{2-x}(x=0)$, ceramic powder from the $Ca-PO_4-H_2O$ system. Since the solubility of each complex ion is a linear function of pH, the solubility diagram can be obtained by plotting the logarithmic molar concentrations calculated from the values of the equilibrium constants and solubility products for hydroxides, carbonates, and hydroxyapatite. The optimum pH condition for the formation of single phase $Ca_{10-x}(HPO_4)_x(PO_4)_{6-x}(OH)_{2-x}(x=0)$ powder in $Ca-PO_4-H_2O$ system at $25^{\circ}C$ was estimated as $10.5{\pm}0.5$ through the theoretical consideration. The HAp powder dried at $80^{\circ}C$ showed a fine agglomerated particles with a size of 75 nm. The HAp powder calcined at $1,000^{\circ}C$ consisted of nearly homogeneous particles with a size of 450 nm. Even though the dried HAp particles consisted of agglomeration, mechanical properties were superior due to fine microstructure after sintering.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.391-402
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• 2019

In this paper, I prove the stability of the following set-valued functional equation $$f(x+2y){\oplus}f(x-2y){\oplus}3f(2x){\oplus}f(-2x)\\{\hspace{100}}=4f(x+y){\oplus}4f(x-y){\oplus}10f(x)$$ by employing the direct method in the sense of Hyers and Ulam.

• Bulletin of the Korean Chemical Society
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• v.18 no.11
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• pp.1210-1213
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• 1997

• Korean Journal of Food Science and Technology
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• v.30 no.2
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• pp.341-347
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• 1998

To develop simple and accurate analytical method for freezing time prediction of beef and tylose under various freezing conditions, freezing time (Y) was regressed against the reciprocal $(X_3)$ of difference of initial freezing point and freezing medium temperature, reciprocal $(X_4)$ of surface heat transfer coefficient, the initial temperature $(X_1)$ and thickness $(X_2)$ of samples which should cover most situations arising in frozen food industry. As results of the multiple regression analysis, equations were obtained as follows. $Y_{tylose}=3.45X_1+7642.84X_2+4642.67X_3+2946.89X_4-431.33\;(R^2=0.9568)$ and $Y_{beef}=0.68X_1+7568.98X_2+2430.78X_3+3293.26X_4-299.00\;(R^2=0.9897)$. These equations offered better results than Plank, Nagaoka and Pham's models, shown in satisfactory agreement with models of Cleland & Earle and Hung & Thompson when were compared to previous models, and the accuracy of its was very high as average absolute difference of about 10% in the difference between the fitted and experimental results. Also, thermal diffusivities of beef and tylose were measured as $4.43{\times}10^{-4}m^2/hr$ and $4.39{\times}10^{-4}m^2/hr$ at $6{\sim}7^{\circ}C$, $2.42{\times}10^{-3}m^2/hr$ and $3.32{\times}10^{-3}m^2/hr$ at $-10{\sim}-12^{\circ}C$. Initial freezing points of beef and tylose were $-1.2^{\circ}C\;and\;-0.6^{\circ}C$, respectively. Surface heat transfer coefficients were estimated $20.57\;W/m^2^{\circ}C$ with no-packing, $16.11\;W/m^2^{\circ}C$ with wrap packing and $13.07\;W/m^2^{\circ}C$ with Al-foil packing, and the cooling rate of immersion freezing method was about 10 times faster than that of air blast freezing method.

• Korean Journal of Materials Research
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• v.7 no.3
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• pp.218-223
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• 1997

At the aim of finding a Fehased amorphous alloy with a wide supercooled liquid region (${\Delta}T_{x}=T_{x}-T_{g}$) before crystallization, the changes in glass transition temperatudfI$T_{g}$ and crystallization temperature ($T_{x}$) by the dissolution of additional M elements were examined for the $Fe_{80}P_{10}C_{6}B_{4}$(x~6at%. M= transition metals) amorphous alloys. The ${\Delta}T_{x}$ value is 27K for the Fe,,,P,,,C,,R, alloy and increases to 40K for the addition of M=4at%Hf, 4at%Ta or 4at%Mo. The increase in ${\Delta}T_{x}$ is due to the increase of $T_{x}$ exceeding the degree in the increase in $T_{g}$. The $T_{g}$ and $T_{x}$ increase with decreasing electron concentration (e/a) from about 7 38 to 7.05. The decrease of e/a also implies the increase in the attractive bonding state between the M elements and other constitutent elements. It is therefore said that $T_{g}$ and $T_{x}$ increase kith increasing attractive bonding force.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.705-710
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• 2018

Let T(X) be the full transformation semigroup on a set X and ${\sigma}$ be an equivalence relation on X. Denote $$E(X,{\sigma})=\{{\alpha}{\in}T(X):{\forall}x,\;y{\in}X,\;(x,y){\in}{\sigma}\;\text{implies}\;x{\alpha}=y{\alpha}\}.$$. Then $E(X,{\sigma})$ is a subsemigroup of T(X). In this paper, we characterize two semigroups of type $E(X,{\sigma})$ when they are isomorphic.

• Journal of Korean Library and Information Science Society
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• v.30 no.1
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• pp.61-92
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• 1999

This study is to set up a formula of the staff size for university libraries in Korea. The methodology of this study applied the multiple regression analysis and the component ratio of professional staff versus nonprofessional staff. The results of this study are swrunarized as follows: (1) Number of librarians = 3.016 + 0.0l6xholdings(unit : 1000 vols) - 0.008volumesadded(unit : 100 vols) + 0.031 x graduate enrollments(unit : 10 persons) + 0.069 x undergraduate enrollments(unit : 100 persons) + 0.043 x library materials expenditure(unite: 10 million won). (2) Number of library staff = 4.638 + 0.024 x holdings(unit : 1000 vols) - 0.012 x volumes added(unit: 100 vols) + 0.017 x graduate enrollments(unit : 10 persons) + 0.106 x undergraduate enrollments(unit : 100 persons)+0.066xlibrary materials expenditure(unit : 10 million won).