• 대한수학회보
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• 제27권2호
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• pp.157-164
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• 1990

The purpose of this paper is to consider the inhomogeneous initial value problem (Fig.) in a Banach space X, where Z is the generator of an exponentially bounded C-semigroup in X, f9t) : [0, T].rarw.X and x.mem.X. Davies-Pang [1] showed the corresponding homogeneous equation, this is, the equation with f(t).iden.0, has a unique solution depending continuoously on the initial value x.mem.CD(z) in the $C^{-1}$-graph norm on CD(Z) when T=.inf..

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.435-443
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• 2007

An important approach towards solving the scattered data problem is by using radial basis functions. However, for a large class of smooth basis functions such as Gaussians, the existing theories guarantee the interpolant to approximate well only for a very small class of very smooth approximate which is the so-called 'native' space. The approximands f need to be extremely smooth. Hence, the purpose of this paper is to study approximation by a scattered shifts of a radial basis functions. We provide error estimates on larger spaces, especially on the homogeneous Sobolev spaces.

• 충청수학회지
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• 제1권1호
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• pp.71-76
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• 1988

For each continuous convex function ${\phi}$ defined on an open convex subset $A_{\phi}$ of a Banach space X, if we define a positively homogeneous sublinear functional ${\sigma}_x$ on X by ${\sigma}_x(y)=\sup{\lbrace}f(y)\;:\;f{\in}{\partial}{\phi}(x){\rbrace}$, where ${\partial}{\phi}(x)$ is a subdifferential of ${\phi}$ at x, then we get the following characterization theorem of Gateaux differentiability (weak Asplund) sapce. THEOREM. For every ${\phi}$ above, $D_{\phi}={\lbrace}x{\in}A\;:\;\sup_{||u||=1}\;{\sigma}_x(u)+{\sigma}_x(-u)=0{\rbrace}$ contains dense (dense $G_{\delta}$) subset of $A_{\phi}$ if and only if X is a Gateaux differentiability (weak Asplund) space.

• 천문학회보
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• 제40권1호
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• pp.80.1-80.1
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• 2015

We present a study of outflows on 24 embedded young stellar objects selected from the source list of the Dust, Ice, and Gas in Time (DIGIT) Herschel key program. To study the relation between the CO outflows observed in low-J transitions and the properties of protostars more consistently with a homogeneous data set, we mapped the CO outflows of the selected targets in the J = 1-0 and J = 2-1 lines with two Korean telescopes (SRAO and TRAO). We compare CO outflow force ($F_{CO}$) with the bolometric luminosity, ($L_{bol}$) bolometric temperature, and the FIR molecular line luminosities of CO, $H_2O$, OH, and [O I] detected by the Herschel-PACS observations. We find that $F_{CO}$ of J = 1-0 is greater than that of 2-1 by a factor of ~ 2. The well known correlation between $F_{CO\;2-1}$ and $L_{bol}$ is not very evident in our sample as a whole, but they show a rather strong correlation when IRAM 04191+1522 is excluded. IRAM 04191+1522 has relatively high $F_{CO\;2-1}$ in spite of its low $L_{bol}$. This object is a well-known VeLLO, which is believed in the quiescent phase of the episodic mass accretion in the embedded stage. $L_{bol}$ traces a current accretion, but $F_{CO\;2-1}$ traces accretion happened long ago. Therefore, the low-$L_{bol}$ with the high-$F_{CO\;2-1}$ can be explained by the episodic accretion. $F_{CO\;2-1}$ shows little correlation with individual FIR line luminosities of CO, $H_2O$, OH, while [O I] and total FIR line luminosity seem to have correlations with $F_{CO\;2-1}$. This result is interpreted as the accretion energy deposits on species differently depending on shock properties, but the total FIR line luminosity sums the total accretion energy dispersed to different species.

• 대한수학회지
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• 제38권3호
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• pp.503-521
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• 2001

A change of Finsler metric L(x,y)longrightarrowL(x,y) is called a Randers change of L, if L(x,y) = L(x,y) +$\rho$(x,y), where $\rho$(x,y) = $\rho$(sub)i(x)y(sup)i is a 1-form on a smooth manifold M(sup)n. Let us consider the special Randers change of Finsler metric LlongrightarrowL = L + $\beta$ by $\beta$. On the basis of this special Randers change, the purpose of the present paper is devoted to studying the conditions for Finsler space F(sup)n which are transformed by a special Randers change of Finsler spaces F(sup)n with ($\alpha$,$\beta$)-metrics of Douglas type to be also of Douglas type, and vice versa.

• 대한수학회논문집
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• 제34권1호
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• pp.185-202
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• 2019

In this paper, we investigate many types of stability, like (uniform stability, exponential stability and h-stability) of the first order dynamic equations of the form $$\{u^{\Delta}(t)=Au(t)+f(t),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ and $$\{u^{\Delta}(t)=Au(t)+f(t,u),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ in terms of the stability of the homogeneous equation $$\{u^{\Delta}(t)=Au(t),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ where f is rd-continuous in $t{\in}{\mathbb{T}}$ and with values in a Banach space X, with f(t, 0) = 0, and A is the generator of a $C_0$-semigroup $\{T(t):t{\in}{\mathbb{T}}\}{\subset}L(X)$, the space of all bounded linear operators from X into itself. Here D(A) is the domain of A and ${\mathbb{T}}{\subseteq}{\mathbb{R}}^{{\geq}0}$ is a time scale which is an additive semigroup with property that $a-b{\in}{\mathbb{T}}$ for any $a,b{\in}{\mathbb{T}}$ such that a > b. Finally, we give illustrative examples.

• Bulletin of the Korean Chemical Society
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• 제33권7호
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• pp.2315-2319
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• 2012

To improve the performance of $LiFePO_4F$, a novel sol-gel process is developed. For comparison, ceramic process is also implemented. From X-ray diffraction results we know that each sample adopts a triclinic $P{\bar{1}}$ space group, and they are isostructural with amblygonite and tavorite. The scanning electron microscope images show that the homogeneous grains with the dimension of 300-500 nm is obtained by the sol-gel process; meanwhile the sample particles obtained by ceramic process are as big as 1000-3000 nm. By galvanostatic tests and at electrochemical impedance spectroscopy method, the sample obtained by sol-gel process presents better electrochemical properties than the one obtained by ceramic process.

• 한국수자원학회논문집
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• 제36권6호
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• pp.1035-1046
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• 2003

TOPMODEL의 지하수면길이 분포에 대한 예측능력을 평가하기 위해 2개 기본가정과 지하수면깊이에 대한 지배방정식을 검증하였다. 검증에는 토양두께가 얇은 급경사 사면의 수문관측과 토양조사 자료를 이용하였다. 조사사면에서 지하수면반응과 토양의 수리적 특성은 지형경사와 평행하는 수리경사, 지하수면깊이에 지수함수적으로 감소하는 투수량계수 등과 같은 TOPMODEL의 기본가정과 일치하였다 토양의 투수량계수감소율(f)과 토성은 지표부터 깊이 0.3m까지 사면전체에서 공간적으로 균질하지만, 토성과 f의 수직적인 변화로 깊이 0.3m 아래부터 공간적으로 불균질한 특성을 보인다. 조사사면에서 TOPMODEL의 지배방정식은 f값이 공간적로 균질한 깊이의 지하수면깊이 분포를 예측하는데 적용할 수 있는 것으로 나타났다.

• 한국우주과학회:학술대회논문집(한국우주과학회보)
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• 한국우주과학회 1992년도 한국우주과학회보 제1권1호
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• pp.12-12
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• 1992

Results from the Earth Radiation Budget Experiment (ERBE) will help interpret the data from the operational satellite system. However, a major problem exists because a follow-on experiment to ERBE is not planned until the late 1990`s. Meanwhile, it will be necessary to provide OLR estimates from the operational satellite system. Since 1973the outgoing long wave radiation(OLR) data have been obtained by the 10#m window radiance(AVHRR) estimation technique from he observation NOAA operational satellites. However, those data have not been universall if accepted because they are estimated from the radiance in but one narrow spectral regiou. However , this type of technique has not been exploited for use with data from the ]fIRS multispectral radiometer. Since the radiance data measured by HIRS contains more: information on atmospheric variables than the AVHRR, it is a potentially better instrument for operational estimates of the OLR In this study, results from model are better flux estimates than the AVHRR, The technique is then tested by comparing simultalleous AVHRR and HIRS OLR estimations with a radiation model flux calculation froml homogeneous atmospheric scenes at the regions of desert and subtropic ocean.

• 대한수학회논문집
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• 제35권2호
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• pp.371-399
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• 2020

Let P_s := 𝔽₂[x₁, x₂, …, x_s] = ⊕_n⩾0(P_s)_n be the polynomial algebra viewed as a graded left module over the mod 2 Steenrod algebra, ${\mathfrak{A}}$. The grading is by the degree of the homogeneous terms (P_s)_n of degree n in the variables x₁, x₂, …, x_s of grading 1. We are interested in the hit problem, set up by F. P. Peterson, of finding a minimal system of generators for ${\mathfrak{A}}$-module P_s. Equivalently, we want to find a basis for the 𝔽₂-graded vector space ${\mathbb{F}}_2{\otimes}_{\mathfrak{A}}$ P_s. In this paper, we study the hit problem in the case s = 5 and the degree n = 5(2^t - 1) + 6 · 2^t with t an arbitrary positive integer.