• 대한수학회지
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• 제50권2호
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• pp.275-306
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• 2013

For two positive integers $m$ and $n$, let $\mathcal{P}_n$ be the open convex cone in $\mathbb{R}^{n(n+1)/2}$ consisting of positive definite $n{\times}n$ real symmetric matrices and let $\mathbb{R}^{(m,n)}$ be the set of all $m{\times}n$ real matrices. In this paper, we investigate differential operators on the non-reductive homogeneous space $\mathcal{P}_n{\times}\mathbb{R}^{(m,n)}$ that are invariant under the natural action of the semidirect product group $GL(n,\mathbb{R}){\times}\mathbb{R}^{(m,n)}$ on the Minkowski-Euclid space $\mathcal{P}_n{\times}\mathbb{R}^{(m,n)}$. These invariant differential operators play an important role in the theory of automorphic forms on $GL(n,\mathbb{R}){\times}\mathbb{R}^{(m,n)}$ generalizing that of automorphic forms on $GL(n,\mathbb{R})$.

• Journal of Astronomy and Space Sciences
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• 제25권2호
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• pp.87-100
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• 2008

소백산 천문대의 61cm 망원경에 부착된 bvri CCD 측광 시스템으로 근접쌍성 V523 Cas를 2003년 1월에 4일 밤을 관측하여 792점의 CCD 영상을 얻었다. 이 영상 내에 있는 17개의 BVRI 표준성을 이용하여 소백산 천문대의 bvri 측광계와 Johnson-Cousins의 BVRI 측광계 사이의 변환 관계를 V=v-0.0689(B-V)+0.0063, B-V=1.3197(b-v)-0.1733, V-R=0.9210(v-r)-0.1309, R-I=0.8892(r-i)-0.1055와 같이 구하였다. 이 식을 이용하여 근접쌍성 V523 Cas 근처에 있는 57개 별들의 표준 V등급과 색지수(B-V, V-R, R-I)를 결정하였다.

• 대한수학회보
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• 제61권4호
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• pp.959-968
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• 2024

Suppose f belongs to the Bloch space with f(0) = 0. For 0 < r < 1 and 0 < p < ∞, we show that $$M_p(r,\,f)\,=\,({\frac{1}{2\pi}}{\int_{0}^{2\pi}}\,{\mid}f(re^{it}){\mid}^pdt)^{1/p}\,{\leq}\,({\frac{{\Gamma}(\frac{p}{2}+1)}{{\Gamma}(\frac{p}{2}+1-k)}})^{1/p}\,{\rho}{\mathcal{B}}(log\frac{1}{1-r^2})^{1/2},$$ where ρʙ(f) = sup_z∈ⅅ(1 - |z|²)|f'(z)| and k is the integer satisfying 0 < p - 2k ≤ 2. Moreover, we prove that for 0 < r < 1 and p > 1, $${\parallel}f_r{\parallel}_{B_q}\,{\leq}\,r\,{\rho}{\mathcal{B}}(f)(\frac{1}{(1-r^2)(q-1)})^{1/q},$$ where f_r(z) = f(rz) and ||·||ʙ_q is the Besov seminorm given by ║f║ʙ_q = (∫_𝔻 |f'(z)|^q(1-|z|²)^q-2dA(z)). These results improve previous results of Clunie and MacGregor.

• 대한수학회논문집
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• 제12권2호
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• pp.293-303
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• 1997

The existence theorem for the operator valued function space integral has been studied, when the wave function was in $L_1(R)$ class and the potential energy function was represented as a double integra [4]. Johnson and Lapidus established the existence theorem for the operator valued function space integral, when the wave function was in $L_2(R)$ class and the potential energy function was represented as an integral involving a Borel measure [9]. In this paper, we establish the existence theorem for the operator valued function we establish the existence theorem for the operator valued function space integral as an operator from $L_1(R)$ to $L_\infty(R)$ for certain potential energy functions which involve double integrals with some Borel measures.

• East Asian mathematical journal
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• 제36권3호
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• pp.389-415
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• 2020

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (𝜙, ξ, η, g) in a complex space form M_n+1(c), c ≠ 0. We denote by R_ξ and R'_X be the structure Jacobi operator with respect to the structure vector ξ and be R'_X = (∇_XR)(·, X)X for any unit vector field X on M, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a scalar 𝜃(≠ 2c) and any vector fields X and Y on M. In this paper, we prove that if it satisfies R_ξ𝜙 = 𝜙R_ξ and at the same time R'_ξ = 0, then M is a Hopf real hypersurfaces of type (A), provided that the scalar curvature ${\bar{r}}$ of M holds ${\bar{r}}-2(n-1)c{\leq}0$.

• 대한수학회보
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• 제44권3호
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• pp.483-492
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• 2007

In this paper, we study the map projections from pseudo-sphere $S_1^2$ onto the non-lightlike surfaces in the 3-dimensional Lorentzian space, $L^3$, with curvature zero. We show geometrical means and properties of $\mathbb{R}{\times}S_1^1-cylindrical$, $S^1{\times}L-cylindrical$ and $\mathbb{R}{\times}H_0^1-cylindrical$ projections defined on $S_1^2$ to cylinders $\mathbb{R}{\times}S_1^1,\;S^1{\times}L$ and $\mathbb{R}{\times}H_0^1$, respectively, and orthographic and stereographic projections on $S_1^2$ to Lorentzian plane, $L^2$.

• 대한수학회보
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• 제47권3호
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• pp.623-632
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• 2010

A holomorphic function F defined on the unit disc belongs to $A^{p,{\alpha}}$ (0 < p < $\infty$, 1 < ${\alpha}$ < $\infty$) if $\int\limits_U|F(z)|^p \frac{1}{1-|z|}(1+log)\frac{1}{1-|z|})^{-\alpha}$ dxdy < $\infty$. For boundedness of the composition operator defined by $C_{fg}=g{\circ}f$ mapping Blochs into $A^{p,{\alpha}$ the following (1) is a sufficient condition while (2) is a necessary condition. (1) $\int\limits_o^1\frac{1}{1-r}(1+log\frac{1}{1-r})^{-\alpha}M_p(r,\lambda{\circ}f)^p\;dr$ < $\infty$ (2) $\int\limits_o^1\frac{1}{1-r}(1+log\frac{1}{1-r})^{-\alpha+p}(1-r)^pM_p(r,f^#)^p\;dr$ < $\infty$.

• 대한수학회지
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• 제50권4호
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• pp.771-795
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• 2013

In this paper we consider the Navier-Stokes equations in the half space. Our aim is to construct a mild solution for initial data in $B^{-\alpha}_{{\infty},{\infty}}(\mathbb{R}^n_+)$, 0 < ${\alpha}$ < 1. To do this, we derive the estimate of the Stokes flow with singular initial data in $B^{-\alpha}_{{\infty},q}(\mathbb{R}^n_+)$, 0 < ${\alpha}$ < 1, 1 < $q{\leq}{\infty}$.

• 충청수학회지
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• 제28권3호
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• pp.397-408
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• 2015

In this paper, we solve the Hyers-Ulam stability problem for the following cubic type functional equation $$f(rx+sy)+f(rx-sy)=rs^2f(x+y)+rs^2f(x-y)+2r(r^2-s^2)f(x)$$in quasi-Banach space and non-Archimedean space, where $r={\neq}{\pm}1,0$ and s are real numbers.

• Journal of Positioning, Navigation, and Timing
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• 제1권1호
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• pp.59-64
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• 2012

Precise Point Positioning (PPP) has been widely used in navigation and orbit determination applications as we can obtain precise Global Positioning System (GPS) satellite orbit and clock products. Kinematic PPP, which is based on the GPS measurements only from the spaceborne GPS receiver, has some advantages for a simple precise orbit determination (POD). In this study, we developed kinematic PPP technique to estimate the orbits of GRACE-A satellite. The comparison of the mean position between the JPL's orbit product and our results showed the orbit differences 0.18 cm, 0.54 cm, and 0.98 cm in the Radial, in Along-track, and Cross-track direction respectively. In addition, we obtained the root mean square (rms) values of 4.06 cm, 3.90 cm, and 3.23 cm in the satellite coordinate components relative to the known coordinates.