• Communications of the Korean Mathematical Society
• /
• v.26 no.1
• /
• pp.99-113
• /
• 2011

In this paper, we investigate the stability using shadowing property in Abelian metric group and the generalized Hyers-Ulam-Rassias stability in Banach spaces of a quadratic functional equation, $f(x_1+x_2+x_3+x_4)+f(-x_1+x_2-x_3+x_4)+f(-x_1+x_2+x_3)+f(-x_2+x_3+x_4)+f(-x_3+x_4+x_1)+f(-x_4+x_1+x_2)=5{\sum\limits_{i=1}^4}f(x_i)$. Also, we study the stability using the alternative fixed point theory of the functional equation in Banach spaces.

• Kyungpook Mathematical Journal
• /
• v.49 no.1
• /
• pp.1-6
• /
• 2009

Let B(X) denote the algebra of operators on a complex Banach space X, H(X) = {h ${\in}$ B(X) : h is hermitian}, and J(X) = {x ${\in}$ B(X) : x = $x_1$ + $ix_2$, $x_1$ and $x_2$ ${\in}$ H(X)}. Let ${\delta}_a$ ${\in}$ B(B(X)) denote the derivation ${\delta}_a$ = ax - xa. If J(X) is an algebra and ${\delta}_a^{-1}(0){\subseteq}{\delta}_{a^*}^{-1}(0)$ for some $a{\in}J(X)$, then ${\parallel}a{\parallel}{\leq}{\parallel}a-(x^*x-xx^*){\parallel}$ for all $x{\in}J(X){\cap}{\delta}_a^{-1}(0)$. The cases J(X) = B(H), the algebra of operators on a complex Hilbert space, and J(X) = $C_p$, the von Neumann-Schatten p-class, are considered.

• Korean Journal of Mathematics
• /
• v.20 no.4
• /
• pp.517-524
• /
• 2012

In this paper, we first show that for any space X, there is a Boolean subalgebra $\mathcal{G}(z_X)$ of R(X) containg $\mathcal{G}(X)$. Let X be a strongly zero-dimensional space such that $z_{\beta}^{-1}(X)$ is the minimal cloz-coevr of X, where ($E_{cc}({\beta}X)$, $z_{\beta}$) is the minimal cloz-cover of ${\beta}X$. We show that the minimal cloz-cover $E_{cc}(X)$ of X is a subspace of the Stone space $S(\mathcal{G}(z_X))$ of $\mathcal{G}(z_X)$ and that $E_{cc}(X)$ is a strongly zero-dimensional space if and only if ${\beta}E_{cc}(X)$ and $S(\mathcal{G}(z_X))$ are homeomorphic. Using these, we show that $E_{cc}(X)$ is a strongly zero-dimensional space and $\mathcal{G}(z_X)=\mathcal{G}(X)$ if and only if ${\beta}E_{cc}(X)=E_{cc}({\beta}X)$.

• Journal of Environmental Science International
• /
• v.23 no.3
• /
• pp.359-368
• /
• 2014

The aim of our research was to apply experimental design methodology in the optimization of N, N-Dimethyl-4-nitrosoaniline (RNO, which is indictor of OH radical formation) degradation using gas mixing-circulation plasma process. The reaction was mathematically described as a function of four independent variables [voltage ($X_1$), gas flow rate ($X_2$), liquid flow rate ($X_3$) and time ($X_4$)] being modeled by the use of the central composite design (CCD). RNO removal efficiency was evaluated using a second-order polynomial multiple regression model. Analysis of variance (ANOVA) showed a high coefficient of determination ($R^2$) value of 0.9111, thus ensuring a satisfactory adjustment of the second-order polynomial multiple regression model with the experimental data. The application of response surface methodology (RSM) yielded the following regression equation, which is an empirical relationship between the RNO removal efficiency and independent variables in a coded unit: RNO removal efficiency (%) = $77.71+10.04X_1+10.72X_2+1.78X_3+17.66X_4+5.91X_1X_2+3.64X_2X_3-8.72X_2X_4-7.80X{_1}^2-6.49X{_2}^2-5.67X{_4}^2$. Maximum RNO removal efficiency was predicted and experimentally validated. The optimum voltage, air flow rate, liquid flow rate and time were obtained for the highest desirability at 117.99 V, 4.88 L/min, 6.27 L/min and 24.65 min, respectively. Under optimal value of process parameters, high removal(> 97 %) was obtained for RNO.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 1996.05a
• /
• pp.185-188
• /
• 1996

The doped n-type $Al_{x}Ga_{1-x}Sb$ crystals were grown by the vertical Bridgman method at composition ratio x=0, x=0.1, x=02 respectively. The lattice constants of the $Al_{x}Ga_{1-x}Sb$ crystals were 6.096${\AA}$, 6.097${\AA}$, 6.106${\AA}$ at composition ratio respectively. The carrier concentration, the resistivity, and the carrier mobility measured by the Van der Pauw method at x-0 were n≡1 x $10^{17}$$cm^{-3}$, $\rho$≡0.15 ${\Omega}$-cm, ${\mu}$$_{n}$≡500 $\textrm{cm}^2$$V^{-1}$$sec^{-1}$ at 300K. The carrier concentration, the resistivity, and the carrier mobility measured by the Van der Pauw method at x=0.1 were n≡2.96 x $10^{15}$$cm^{-3}$, $\rho$≡103 $\textrm{cm}^2$$V^{-1}$$sec^{-1}$ at 300K.

• Journal of the Korean Ceramic Society
• /
• v.34 no.7
• /
• pp.722-730
• /
• 1997

The nonstoichiometry (x) of UO2+x and (Er0.06U0.94)O2+x has been in-situ measure against oxygen activity (Po2) at elevated temperatures by a coulometric titration method. From the dependence of the oxygen excess (x) of UO2+x on Po2 at 1000℃, it has been concluded that (2Vo2Oia2Oib)〃〃and (2Vo2Oia2Oib)' clusters are prevailing at low oxygen partial pressure [log(Po2/atm) -10.6] and at high oxygen partial pressure [log(Po2/atm) -10.6], respectively. The nonstoichiometry is found to be reduced with the addition of Er, which is ascribed to the fact that the fixed-valent Er3+ reduces the oxidation capacities of UO2+x. The enthalpy of oxygen incorporation in (Er0.06li0.94)O2+x has been evaluated from the mean valences of U-ion as -180±70 kJ/mole.

• Journal of Korea Foundry Society
• /
• v.24 no.1
• /
• pp.40-44
• /
• 2004

The influence of Pd and Ag additions on the thermal stability, the glass forming ability (GFA) and mechanical property of $Zr_{55}Al_{10}Cu_{20}Ni_{10}Pb_{(5-x)}Ag_x$ (x = $0{\sim}5at%$) alloys obtained by melt spun and injection casting method have been investigated by using of X-ray diffraction, thermal analysis (DTA, DSC) and micro-Vickers hardness(Hv) testing. The thermal properties of melt-spun $Zr_{55}Al_{10}Cu_{20}Ni_{10}Pb_{(5-x)}Ag_x$ (x = $0{\sim}5at%$) alloys exhibit a supercooled liquid region(${\Delta}T_x$) exceeding 91 K before crystallization. The largest ${\Delta}T_x$ reaches as large as 126 K for the $Zr_{55}Al_{10}Cu_{20}Ni_{10}Pb_5$ alloy. The reduced glass transition temperature, $T_{rg}$ increased with increasing Ag content. The largest $T_{rg}$ is obtained for the $Zr_{55}Al_{10}Cu_{10}Ni_{10}Ag_5$ alloy. The $Zr_{55}Al_{10}Cu_{10}Ni_{10}Ag_5$ bulk amorphous alloy rod with 3 mm in diameter was fabricated by injection casting. Hv increased with increasing Ag content and the largest value was obtained for the $Zr_{55}Al_{10}Cu_{10}Ni_{10}Ag_5$ bulk amorphous alloy.

• Korean Journal of Applied Biomechanics
• /
• v.26 no.3
• /
• pp.265-272
• /
• 2016

Objective: The aim of this study was to analyze X-factor, triple X-factor, and the center of pressure (COP) according to the feel of golf driver swing. Method: For this research, 9 golfers from the Korea Professional Golfers' Association (age: $30.11{\pm}2.98yrs$, height: $178.00{\pm}8.42cm$, weight: $76.22{\pm}8.42kg$, experience: $10.06{\pm}3.11yrs$) were recruited to participate in the experiment. Twelve Motion Analysis Eagle-4 cameras were installed and an image analysis was conducted by using the NLT (non-linear transformation) method, and 2 units of Kistler type 5233A dynamometer were used to measure ground reaction force. The sampling ratio was set at 1000 Hz. The golfers each took 10 swings by using their own driver, and chose the best and worse feel from among 10 shots. A paired-sample t-test was used to analyze the results. Results: In regard to feel, no change in head speed, X-factor, and the triple X-factor's X-factor stretch, hip rise, and head swivel, was observed (p>.05). Regarding ground reaction force, a difference was observed between the top of the backswing (p<.05) and impact (p<.05) in the vertical force of the left foot. For COP, a difference was also observed between the mid backswing (p<.001), late backswing (p<.001), and top of the backswing (p<.05) for the right foot X-axis and Y-axis mid follow through (p<.01). Conclusion: It can be reasoned that, irrespective of feel, the head speed, X-factor and triple X-factor's X-factor stretch, hip rise and head swivel did not have an effect on drive distance for domestic golfers, and the vertical reaction force of the left foot and left-right movement span's pressure dispersal of the right foot had an increasing effect on drive distance.

• The Pure and Applied Mathematics
• /
• v.20 no.1
• /
• pp.71-78
• /
• 2013

Let X be a space and $2^X$(C(X);K(X);$C_K$(X)) denote the hyperspace of nonempty closed subsets(connected closed subsets, compact subsets, subcontinua) of X with the Vietoris topology. We investigate the relationships between the space X and its hyperspaces concerning the properties of connectedness im kleinen. We obtained the following : Let X be a locally compact Hausdorff space. Let $x{\in}X$. Then the following statements are equivalent: (1) X is connected im kleinen at $x$. (2) $2^X$ is arcwise connected im kleinen at {$x$}. (3) K(X) is arcwise connected im kleinen at {$x$}. (4) $C_K$(X) is arcwise connected im kleinen at {$x$}. (5) C(X) is arcwise connected im kleinen at {$x$}.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.5
• /
• pp.1369-1374
• /
• 2014

We show that the Diophantine equation $$aQ(x_1,x_2)+bQ(x_3,x_4)+cQ(x_5,x_6)=abc$$ has integral solutions for arbitrary positive integers a, b, c when Q(x, y) is a norm form for some imaginary quadratic fields.