• Journal of Astronomy and Space Sciences
• /
• v.9 no.1
• /
• pp.11-29
• /
• 1992

In 1963, Toomre built up classes of mass models for the highly flattened galaxies which have free parameters n, $a_n$ and $C_n$. In order to keep the universal dimension, we adopt parameters $b_n({C_n}^2={a_n}^{2n}+^2{b_n}^2/(n-1)!)$ insteal of $C_n$. Series of the normalized Toomre's mass models (G = $V_{max}$ =$R_{max}$ = 1, n = 1 to 7) are derived and the normalized parameters $a_n$ and $b_n$ are determined by the iteration method. Replacing parameters $a_n$ and $b_n$ to ${a_n}^l(=a_nr_{max})$ and ${b_n}^l(=b_n\cdotV_{max}/r_{max})$, we can get the generalization of Toomre's mass model.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2000.07a
• /
• pp.726-729
• /
• 2000

Though L $a_{1+x}$S $r_{2-x}$M $n_2$ $O_{7}$ n=2 R-P phases have been well known to have CMR effect, it was generally believed that n=1 phase was insulating. But recently monolayered perovskite $Ca_{2-x}$L $n_{x}$Mn $O_4$phase has been reported to show magnetoresistance. In this study, layered perovskite $Ca_{2-x}$L $n_{x}$Mn $O_4$ (x=0, 0.5, Ln=Pr, Nd, Sm, Gd) phases were synthesized by solid state reaction and their structures were refined by Rietveld method. The space groups of $Ca_2$Mn $O_4$, N $d_{0.5}$C $a_{1.5}$Mn $O_4$phases were refined as C2cb and Fmmm, respectively.y.ely.y.y.y.y.y.y.

• Korea-Australia Rheology Journal
• /
• v.16 no.2
• /
• pp.91-99
• /
• 2004

For the Rouse chain composed of infinite number of beads (continuous limit), conformational changes during the creep and creep recovery processes was recently analyzed to reveal the interplay among all Rouse eigenmodes under the constant stress condition (Watanabe and Inoue, Rheol. Acta, 2004). For completeness of the analysis of the Rouse model, this paper analyzes the conformational changes of the discrete Rouse chain having a finite number of beads (N = 3 and 4). The analysis demonstrates that the chain of finite N exhibits the affine deformation on imposition/removal of the stress and this deformation gives the instantaneous component of the recoverable compliance, $J_{R}$(0) = 1/(N-l)v $k_{B}$T with v and $k_{B}$ being the chain number density and Boltzmann constant, respectively. (This component vanishes for N\longrightarrow$\infty$.) For N = 2, it is known that the chain has only one internal eigenmode so that the affinely deformed conformation at the onset of the creep process does not change with time t and $J_{R}$(t) coincides with $J_{R}$(0) at any t (no transient increase of $J_{R}$(t)). However, for N$\geq$3, the chain has N-l eigenmodes (N-l$\geq$2), and this coincidence vanishes. For this case, the chain conformation changes with t to the non-affine conformation under steady flow, and this change is governed by the interplay of the Rouse eigenmodes (under the constant stress condition). This conformational change gives the non-instantaneous increase of $J_{R}$(t) with t, as also noted in the continuous limit (N\longrightarrow$\infty$).X>).TEX>).X>).

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.10 no.3
• /
• pp.242-246
• /
• 2010

It is well-known that the space $E^n$ of fuzzy numbers(i.e., normal, upper-semicontinuous, compact-supported and convex fuzzy subsets)in the n-dimensional Euclidean space $R^n$ is separable but not complete with respect to the $L_p$-metric. In this paper, we introduce the space $F_p(R^n)$ that is separable and complete with respect to the $L_p$-metric. This will be accomplished by assuming p-th mean bounded condition instead of compact-supported condition and by removing convex condition.

• Journal of The Korean Society of Grassland and Forage Science
• /
• v.20 no.4
• /
• pp.285-294
• /
• 2000

To investigate the effect of Mycorrhiza (Glomus intradics) and Rhizobium inoculation on the N, P utilization and growth response of Alfalfa (Medicago saliva L.) and Perennial ryegrass (Lolium perenne L.) in mixed sward, four treatments (non-inoculation, Control; Mycorrhiza inoculation: M; Rhizobium inoculation, R and Mycorrhiza and Rhizobium inoculation, M+R) were applied. The associated analyses were canied out on the early vegetative growth stage (DAS 56, 56 days after seeding) and on the early flowering stage (DAS 126). The decreased rate of total N and P content in soil, with advancing plant growth, was relatively higher in the M and M + R treatment than control. The content of availabie phosphorus in soil at DAS 126 increased by about 34 and 38 % in M and M+R treatment compared to control (189.2 mg PzOskg DM), while non-significant changes was observed in R treatment. Total N uptake and P uptake in the control at DAS 126 were 44.71 and 3.52 mglplant in mixed sward, respectively. About 71, 98 and 197 % of increases in total N uptake and 70, 72 and 11 1 % of increases in total P uptake were estimated in M, R and M+R treatment. Comparing to control, total dry matter yield significantly increased by 27, 33 and 53 %, and crude protein yield also by 78, 83 and 204 %, respectively, in M, R and M+R treatment. The present data indicated that mycorrhiza orland rhizobium inoculation improved N, P utilization of both alfalfa and perennial ryegrass plants, and consequently increased total yield (especially by dual inoculation, M+R). (Key words : Alfalfa, Perennial ryegrass, Mycorrhiza, Rhizobium, N and P Utilization, Growth, Yield)

• Journal of the Chungcheong Mathematical Society
• /
• v.12 no.1
• /
• pp.125-131
• /
• 1999

We obtain some sufficient conditions for oscillation of the neutral difference equation with positive and negative coefficients $${\Delta}(x_n-cx_{n-m})+px_{n-k}-qx_{n-l}=0$$, where ${\Delta}$ denotes the forward difference operator, m, k, l, are nonnegative integers, and $c{\in}[0,1),p,q{\in}\mathbb{R}^+$.

• Communications of the Korean Mathematical Society
• /
• v.12 no.3
• /
• pp.797-812
• /
• 1997

For analytic functions we give an expression for the kernel $K_n$ of the remainder terms for the Gauss-Radau and the Gauss-Lobatto rules with end points of multiplicity r and prove the convergence of the kernel we obtained. The error bound are obtained for the type $$\mid$R_n(f)$\mid$ \leq \frac{1}{\pi}l(\Gamma) max_{z \in \Gamma} $\mid$K_n(z)$\mid$ max_{z \in \Gamma} $\mid$f(z)$\mid$$, where $l(\Gamma)$ denotes the length of contour $\Gamma$.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.2001-2011
• /
• 2017

In 1997, H. Li [12] proposed a conjecture: if $M^n(n{\geqslant}3)$ is a complete spacelike hypersurface in de Sitter space $S^{n+1}_1(1)$ with constant normalized scalar curvature R satisfying $\frac{n-2}{n}{\leqslant}R{\leqslant}1$, then is $M^n$ totally umbilical? Recently, F. E. C. Camargo et al. ([5]) partially proved the conjecture. In this paper, from a different viewpoint, we study closed convex spacelike hypersurface $M^n$ in locally symmetric Lorentz space $L^{n+1}_1$ and also prove that $M^n$ is totally umbilical if the square of length of second fundamental form of the closed convex spacelike hypersurface $M^n$ is constant, i.e., Theorem 1. On the other hand, we obtain that if the sectional curvature of the closed convex spacelike hypersurface $M^n$ in locally symmetric Lorentz space $L^{n+1}_1$ satisfies $K(M^n)$ > 0, then $M^n$ is totally umbilical, i.e., Theorem 2.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.1
• /
• pp.165-167
• /
• 2005

Let M = (R, +, $\cdot$, <, ... ) be an o-minimal expansion of the standard structure R = (R, +, $\cdot$, >) of the field of real numbers. We prove that if 2 $\le$ r < $\infty$, then every n-dimensional definable $C^r$ manifold is definably $C^r$ imbeddable into $R^{2n+l}$. Moreover we prove that if 1 < s < r < $\infty$, then every definable $C^s$ manifold admits a unique definable $C^r$ manifold structure up to definable $C^r$ diffeomorphism.

• Journal of The Korean Society of Agricultural Engineers
• /
• v.52 no.1
• /
• pp.1-11
• /
• 2010

Generation and transportation of runoff and pollutant loads within watershed generated eutrophication at Daecheong reservoir. To improve water quality at Daecheong reservoir, the best management practices should be developed and applied at upper watersheds for water quality improvement at downstream areas. In this study, two small watersheds of upper Daecheong reservoir were selected. The Long-Term Hydrologic Impact Assessment (L-THIA) model has been widely used for the estimation of the direct runoff worldwide. To apply the L-THIA ArcView GIS model was evaluated for direct runoff and water quality estimation at small watershed. And the Web-based Hydrograph Analysis Tool (WHAT) was used for direct runoff separating from total flow. As a result, the $R^2$ (Coefficient of determination) value and Nash-Sutcliffe coefficient value for direct runoff comparison at An-nae watershed were 0.81 and 0.71, respectively. And the $R^2$ value and Nash-Sutcliffe coefficient value at Wol-oe were 0.95 and 0.93. The $R^2$ value of BOD, TOC, T-N and T-P at An-nae watershed were BOD 0.94, TOC 0.81, T-N 0.94 and T-P 0.89. And the $R^2$ value of BOD, TOC, T-N and T-P at Wol-oe watershed were BOD 0.80, TOC 0.93, T-N 0.86 and T-P 0.65. The result that estimated pollutant loadings using the L-THIA ArcView GIS model reflected well the measured pollutant loadings except for T-P in Wol-oe watershed. With L-THIA ArcView GIS model, the direct runoff and non-point pollutant (NPS) loadings in the watershed could be analyzed through simple input data such as daily rainfall, land uses, and hydrologic soil group.