• Korean Journal of Materials Research
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• v.2 no.5
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• pp.330-336
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• 1992

Four distinctive hot pressed and heat treated S${i_3}{N_4}$ceramics, S${i_3}{N_4}$-8%${Y_2}{O_3}$, S${i_3}{N_4}$-6% ${Y_2}{O_3}$-2% $A{l_2}{O_3}$, S${i_3}{N_4}$-4% ${Y_2}{O_3}$-3% $A{l_2}{O_3}$, 그리고 S${i_3}{N_4}$-1% MgO-1% Si$O_2$(in wt%), were prepared and characterized by X-ray diffraction, scanning electron microscopy, image analysis and mechanical tests. The fracture toughness of S${i_3}{N_4}$-8% ${Y_2}{O_3}$specimens containing large elongated grains showed the highest value of about 9.8MPa$m^{1/2}$. Two out of four S${i_3}{N_4}$, ceramics(S${i_3}{N_4}$-6% ${Y_2}{O_3}$-2% $A{l_2}{O_3}$and S${i_3}{N_4}$-4% ${Y_2}{O_3}$-3% $A{l_2}{O_3}$) heat treated at 200 $0^{\circ}C$retained the fracture strength of over 900MPa and fracture toughness of over 8.0MPa$m^{1/2}$. Large ${\beta}$-S${i_3}{N_4}$grains having a diameter larger than 1${\mu}$m appeared to contribute to increase in fracture toughness.

• 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.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.345-358
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• 2020

In this paper, we study the concepts of Wijsman lacunary invariant convergence, Wijsman lacunary invariant statistical convergence, Wijsman lacunary ${\mathcal{I}}_2$-invariant convergence (${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$), Wijsman lacunary ${\mathcal{I}}^*_2$-invariant convergence (${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$), Wijsman p-strongly lacunary invariant convergence ([W₂N_σθ]_p) of double sequence of sets and investigate the relationships among Wijsman lacunary invariant convergence, [W₂N_σθ]_p, ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$ and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$. Also, we introduce the concepts of ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence of sets.

• Journal of Animal Environmental Science
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• v.4 no.2
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• pp.183-191
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• 1998

This study was carried out to elucidate the correlation between Germination Index(G.I.) and CO2 emission for evaluation of the maturity of compost products. 13 compost samples was used for this experiment. The G.I. test was carried out on the basis of T-N 200ppm. As a result of this research, we found that CO2 emission method was good simple indicator for evaluation of maturity of compost materials, in spite of G.I. The obtain results are summarized as follows ; 1. The correlation value between the G.I. and the CO2 emission was R2 = 0.776. 2. The correlation value between EC(Electric Conductivity) and G.I. was R2 =0.7. 3. The equation calculated from G.I. and CO2 emission was G.I. = -16.7(InCO2) - 6.87. 4. From these results, we found the possibility of estimation for the value of G.I.(T-N 200ppm) from CO2 emission volume under specific condition.

• Korean Journal of Mathematics
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• v.19 no.1
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• pp.77-85
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• 2011

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 $n{\geq}2$ $${\sum_{i=1}^{n}}\left\|x_i-{\frac{1}{n}}{\sum_{j=1}^{n}}x_j \right\|^2={\sum_{i=1}^{n}}{\parallel}x_i{\parallel}^2-n\left\|{\frac{1}{n}}{\sum_{i=1}^{n}}x_i \right\|^2$$ holds for all $x_1$, ${\cdots}$, $x_n{\in}V$. Let V, W be real vector spaces. It is shown that if an even mapping $f:V{\rightarrow}W$ satisfies $$(0.1)\;{\sum_{i=1}^{2n}f}\(x_i-{\frac{1}{2n}}{\sum_{j=1}^{2n}}x_j\)={\sum_{i=1}^{2n}}f(x_i)-2nf\({\frac{1}{2n}}{\sum_{i=1}^{2n}}x_i\)$$ for all $x_1$, ${\cdots}$, $x_{2n}{\in}V$, then the even mapping $f:V{\rightarrow}W$ is quadratic. Furthermore, we prove the generalized Hyers-Ulam stability of the quadratic functional equation (0.1) in Banach spaces.

• Applied Chemistry for Engineering
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• v.26 no.3
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• pp.377-380
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• 2015

In this paper, we have investigated the optimization of $I_2$ recovery process from $NH_4I$ solution, which is generated as by-product during the amination reaction of p-diiodobenzene (PDIB) for p-phenylenediamine (PPD) synthesis. The recovered $I_2$ is then recycled as a raw material for PDIB synthesis. We have employed a cation exchange resin to recover $I_2$ from $NH_4I$ sample solution, and determined the breakthrough point and exchange capacity from the breakthrough curve. Furthermore, we have suggested optimum conditions of our $I_2$ recovery process by measuring the purity and yield of recovered $I_2$ with respect to the concentrations of $NH_4I$ and oxidant ($H_2O_2$) solutions, the oxidation time, and the temperature of drying process. Finally, the yield and purity as high as 94.96% and 96.65%, respectively were obtained by reusing the residual solution still containing unrecovered iodide ions.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.685-691
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• 2008

Given operators $X_i$ and $Y_i$ (i = 1, 2, ${\cdots}$, n) acting on a Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A acting on $\mathcal{H}$ such that $AX_i$ = $Y_i$ for i= 1, 2, ${\cdots}$, n. In this article, if the range of $X_k$ is dense in H for a certain k in {1, 2, ${\cdots}$, n), then the following are equivalent: (1) There exists a self-adjoint operator A in $\mathcal{B}(\mathcal{H})$ stich that $AX_i$ = $Y_i$ for I = 1, 2, ${\cdots}$, n. (2) $sup\{{\frac{{\parallel}{\sum}^n_{i=1}Y_if_i{\parallel}}{{\parallel}{\sum}^n_{i=1}X_if_i{\parallel}}:f_i{\in}H}\}$ < ${\infty}$ and < $X_kf,Y_kg$ >=< $Y_kf,X_kg$> for all f, g in $\mathcal{H}$.

• Korean Journal of Crystallography
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• v.1 no.2
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• pp.76-83
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• 1990

The structures of dehydrated fully Ca2+ _exchanged zeolite A (a: 12.2a3(2) A and of its iodine sorption complex (a=12.258(2) A) have been determined by single-crystal X-ray diffraction methods in the cubic space group. Pm3m at 21(1)℃.the structures were refined to final R(weighted) indices of 0.081 with 206 reflections and 0.084 with 173 reflections, respectively for which I>3 w (I). In each structure. six divalent cations are located on three different theefold axes associated with 6-ring oxygens. Dehydrated Ca2+_A sorbs ca. 6.0 diiodine molecules per unit cell at 80℃(vapor pressure of I: is ca. 14.3 Torr). Each iodine molecule makes a close approach. along its ahs to framework oxygen atom with I-I distance of 2.71(2) A, I-O distance of 3.32(3) k. and I-I-0=180℃. The result indicates that diiodine molecule forms charge transfer complex with framework oxygen.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.221-231
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• 1995

Let $Z_1, Z_2, \ldots, Z_l$ be random set functions or intergrals. Then it is possible to discuss their products. In the case of random integrals, $Z_i$ is a random set function indexed y a family, $G_i$ say, of real valued functions g on $S_i$ for which the integrals $Z_i(g) = \smallint gdZ_i$ are well defined. If $g_i = \in g_i (i = 1, 2, \ldots, l) and g_1 \otimes \cdots \otimes g_l$ denotes the tensor product $g(s) = g_1(s_1)g_2(s_2) \cdots g_l(s_l) for s = (s_1, s_2, \ldots, s_l) and s_i \in S_i$, then we can defined $Z(g) = (Z_1 \times Z_2 \times \cdots \times Z_l)(g) = Z_1(g_1)Z_2(g_2) \cdots Z_l(g_l)$.

• ETRI Journal
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• v.23 no.4
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• pp.151-157
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• 2001

Spectroscopic and thermal analysis indicates that tellurite glasses doped with $B_2O_3$ and $GeO_2$ are promising candidate host materials for wide-band erbium doped fiber amplifier (EDFA) with a high 980 nm pump efficiency. In this study, we measured the thermal stabilities and the emission cross-sections for $Er^{3+}:^{4}I_{13/2}\;{\to}\;^{4}I_{15/2}$ transition in this tellurite glass system. We also determined the Judd-Ofelt parameters and calculated the radiative transition rates and the multiphonon relaxation rates in this glass system. The 15 mol% substitution of $B_2O_3$ for $TeO_2$ in the $Er^{3+}-doped\;75TeO_2-20ZnO-5K_2O$ glass raised the multiphonon relaxation rate for $^4I_{11/2}\;{\to}\;^4I_{13/2}$ transition from 4960 $s^{-1}$ to 24700 $s^{-1}$, but shortened the lifetime of the $^4I_{13/2}$ level by 14 % and reduced the emission cross-section for the $^4I_{13/2}\;{\to}\;^4I_{15/2}$ transition by 11%. The 15 mol% $GeO_2$ substitution in the same glass system also reduced the emission cross-section but increased the lifetime by 7%. However, the multiphonon relaxation rate for $^4I_{11/2}{\to}^4I_{13/2}$ transition was raised merely by 1000 $s^{-1}$. Therefore, a mixed substitution of $B_2O_3$ and $GeO_2$ for $TeO_2$ was concluded to be suitable for the 980 nm pump efficiency and the fluorescence efficiency of $^4I_{13/2}{\to}^4I_{15/2}$ transition in $Er^{3+}-doped$ tellurite glasses.