• East Asian mathematical journal
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• v.34 no.5
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• pp.643-649
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• 2018

Let M be a connected n-dimensional submanifold of a Euclidean space $E^{n+k}$ equipped with the induced metric and ${\Delta}$ its Laplacian. If the position vector x of M is decomposed as a sum of three vectors $x=x_1+x_2+x_0$ where two vectors $x_1$ and $x_2$ are non-constant eigenvectors of the Laplacian, i.e., ${\Delta}x_i={\lambda}_ix_i$, i = 1, 2 (${\lambda}_i{\in}R$) and $x_0$ is a constant vector, then, M is called a 2-type submanifold. In this paper we proved that a connected 2-type hypersurface M in $E^{n+1}$ whose postion vector x satisfies ${\langle}{\Delta}x,x-x_0{\rangle}=c$ for a constant c, where ${\langle}$, ${\rangle}$ is the usual inner product in $E^{n+1}$, is of null 2-type and has constant mean curvature and scalar curvature.

• The Pure and Applied Mathematics
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• v.23 no.3
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• pp.247-263
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• 2016

Let $M_{1}f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}f(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_{2}f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$. Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_{1}f(x,y),t){\geq}N({\rho}M_{2}f(x,y),t)$ where ρ is a fixed real number with |ρ| < 1, and (0.2) $N(M_{2}f(x,y),t){\geq}N({\rho}M_{1}f(x,y),t)$ where ρ is a fixed real number with |ρ| < $\frac{1}{2}$.

• The Korean Journal of Ceramics
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• v.4 no.2
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• pp.78-82
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• 1998

The oxygen nonstoichiometry (x) of UO$_{2+x}$ and $(Ce_yU_{1-y})O_{2+x}$ (y=0.05, 0.25) has been measured as a function of oxygen activity (a02) at 100$0^{\circ}C$ by a solid state coulometri titration technique. The results for UO$_{2+x}$ are in a good agreement with literature data and the ao2-dependence of the nonstoichimetry has been well explained with (2:2:2) cluster model. The equilibrium oxygen activity of $(Ce_yU_{1-y})O_{2+x}$ increases with Ce-content (y) for given nonstoichiometry (x), which is ascribed to the fact that Ce is present as Ce$^{3+}\; and\; Ce^{4+}$, and, therefore, the addition of Ce reduces the oxidation capacity of UO$_{2+x}$. From the oxygen activity dependence of x in $(Ce_yU_{1-y})O_{2+x}$ the defect structure of $(Ce_yU_{1-y})O_{2+x}$ is discussed.

• Journal of the Korean Society of Clothing and Textiles
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• v.9 no.1
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• pp.17-27
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• 1985

In order to investigate the warmth retaining properties of fabrics some characteristics such as thickness. porosity, packing density, thermal conductivity, moisture regain and air permeability were measured and experimental results were analysed statistically to relate the warmth retaining properties with those characteristics. From the analysis, the following results were obtained. 1. When the warmth retaining properties of fabrics (Y) are dependent variable and thickness ($x_1$), porosity ($x_2$), packing density ($x_3$), thermal conductivity ($x_4$), moisture regain ($x_5$) and air permeability ($x_6$) are independent variables, the regression equation of warmth retaining properties can be represented as follows. 1) Y= 1.6005+46.817$x_1$, (R=0.9487) 2)Y=-1.4187+26.5072$x_1$+0.2055$x_2$(R=0.9704) 3) Y= -3.6908+17.4482$x_1$+0.1782$x_2$+28.3243$x_3$ (R=0.9756) 4) Y=0.9202+16.9553$x_1$+0. 1167$x_2$+30.3577$x_3$+1.8884$x_4$ (R=0.9792) 5) Y=0.9353+17.2266$x_1$+0.1177$x_2$+28.9821$x_3$-1.8302$x_4$+0.0151$x_5$ (R=0.9792) 6) Y=0.7583+17.2343$x_1$+0.1196$x_2$+28.8830$x_3$-1.8336$x_4$+0.0187$x_5$0.0004$x_5$ (R=0.9792) 2. The warmth retaining properties of fabrics are merely affected by adding thermal conductivity, moisture regain and multiple regression equation which contains thickness, porosity and packing density as variables. Therefore the multiple regression which contains thickness, porosity and packing density as variables Y=-3.6908+17.4482$x_1$+0.1782$x_2$+28.3243$x_3$ is highly practical.

• Honam Mathematical Journal
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• v.42 no.3
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• pp.449-460
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• 2020

In this paper, we investigate the stability of the additive-cubic functional equations f(x+ky)+f(x-ky)-k² f(x+y)-k² f(x-y)+(k²-1)f(x) - (k²-1)f(-x) = 0, f(x+ky)-f(ky-x)-k² f(x+y)+k² f(y-x)+2(k²-1)f(x)= 0, f(kx+y)+f(kx-y)-kf(x+y)-kf(x-y)-2f(kx)+2kf(x)= 0 by using the fixed point theory in the sense of L. Cădariu and V. Radu.

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

• Journal of the Korean Magnetics Society
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• v.10 no.5
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• pp.220-224
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• 2000

Ultra-fine $Co_{1+x}$F $e_{2-}$2x/ $Ti_{x}$ $O_4$ferrite powders have been prepared by the sol-gel method. The crystallographic and magnetic properties of the sample have been investigated by means of x-ray diffraction, Mossbauer spetroscopy and vibrating sample magnetometry. The formation of nano crystallized particles is confirmed. The x-ray diffractions of all samples with various compositions clearly indicate the presence of spinel structure. The Mossbauer spectra could be fitted as the superposition of two sextets due to F $e^{3+}$ A-site and B-site. The IS and QS values nearly constant with substituted Co-Ti contents, whereas $H_{hf}$ of B-site decreases with increasing Co-Ti substitution in $Co_{1+x}$F $e_{2-}$2x/ $Ti_{x}$ $O_4$. The magnetic behaviour of powders shows that the saturation magnetization and the coercivity decrease with increasing x in $Co_{1+x}$F $e_{2-}$2x/ $Ti_{x}$ $O_4$.$.X>.

• Journal of the Korean Magnetics Society
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• v.10 no.3
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• pp.106-111
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• 2000

The magnetic thin films can be prepared without vacuum process and under the low temperature (<100 $^{\circ}C$) by ferrite plating. We have performed ferrite plating of M $n_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$(x=0.00~0.08) films and N $i_{x}$Z $n_{0.22}$F $e_{*}$2.78-x/ $O_4$(x=0.00~0.15) films on cover glass at the substrate temperature 90 $^{\circ}C$. The crystal structure of the samples has been identified as a single phase of polycrystal spinel structure by x-ray diffraction technique. The lattice constant in the M $n_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$films increases but in the N $i_{x}$Z $n_{0.22}$F $e_{*}$2.78-x/ $O_4$films decrease with the composition parameter, x. The saturation magnetization in the M $n_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$films does not greatly change, in agreement with observations on bulk samples.k samples.k samples.

• Journal of the Korean Ceramic Society
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• v.13 no.3
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• pp.13-20
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• 1976

The magnetic properties, especially the magnetostriction, of ferroxplana $Zn_{1-x}$$M_X$Y(x=0.0, 0.2, 0.4, 0.6) were investigated at room temperature. In general, the Curie temperature and the permeability of ferroxplana $Zn_{1-X}$$Mn_X$Y increased while the amount of the other phase decrease with increased concentration of dopant $Mn^{2+} for $Zn^{2+}. The magnetostriction constnats K1, K2, K3 and K4 for ZnY were ＋0.3, -5.0, -4.3 and $-4.8{\times}$$10^{-6} while that for 4Zn^0.8$ $Mn^0.2$Y were ＋2.5, -5.4, -6.0 and $-3.4{\times}10^{-6}$, respectively.

• Journal of the Korean GEO-environmental Society
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• v.12 no.4
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• pp.25-31
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• 2011

In this study, the experimental design methodology was applied to optimize 1,4-dioxane treatment in E-beam process. Main factor was mathematically described as a function of parameters 1,4-dioxane removal efficiencies(%), TOC removal efficiencies(%) modeled by the use of the central composite design(CCD) method among the response surface methodology(RSM). Concentration of 1,4-dioxane is designated as "$x_1$" and Irradiation intensity is designated as "$x_2$". The regression equation in coded unit between the 1,4-dioxane concentration and removal efficiencies(%) was $y=71.00-10.85x_1+20.67x_2+{1.53x_1}^2-{7.92x_2}^2-1.23x_1x_2$. The regression equation in coded unit between the 1,4-dioxane concentration and TOC removal efficiencies(%) was $y=44.48-13.25x_1+9.54x_2+{5.43x_1}^2-{1.35x_2}^2+4.45x_1x_2$. The model predictions agreed well with the experimentally observed results $R^2$(Adj) over 90%. Toxicity test using algae Pseudokirchneriella Subcapitata showed that the inhibition was reduced according to increasing an E-beam irradiation.