• Journal of the Korean Statistical Society
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• v.1 no.1
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• pp.18-24
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• 1973

Study on convexity has been improved in many statistical fields, such as linear programming, stochastic inverntory problems and decision theory. In proof of main theorem in Section 3, M. Loeve already proved this theorem with the $r$-th absolute moments on page 160 in [1]. Main consideration is given to prove this theorem using convex theorems with the generalized $t$-th mean when some convex properties hold on a real linear vector space $R_N$, which satisfies all properties of finite dimensional Hilbert space. Throughout this paper $\b{x}_j, \b{y}_j$ where $j = 1,2,......,k,.....,N$, denotes the vectors on $R_N$, and $C_N$ also denotes a subspace of $R_N$.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.677-685
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• 2003

Let M be the vector space of all real S-measurable functions defined on a measure space (X, S, $\mu$). In this paper, we investigate some topological structure of T on M. Indeed, (M, T) becomes a topological vector space. Moreover, if $\mu$, is ${\sigma}-finite$, we can define a complete invariant metric on M which is compatible with the topology T on M, and hence (M, T) becomes a F-space.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.655-672
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• 2011

Let $C^r$[0,t] be the function space of the vector-valued continuous paths x : [0,t] ${\rightarrow}$ $R^r$ and define $X_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{(n+1)r}$ and $Y_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{nr}$ by $X_t(x)$ = (x($t_0$), x($t_1$), ..., x($t_{n-1}$), x($t_n$)) and $Y_t$(x) = (x($t_0$), x($t_1$), ..., x($t_{n-1}$)), respectively, where 0 = $t_0$ < $t_1$ < ... < $t_n$ = t. In the present paper, with the conditioning functions $X_t$ and $Y_t$, we introduce two simple formulas for the conditional expectations over $C^r$[0,t], an analogue of the r-dimensional Wiener space. We establish evaluation formulas for the analogues of the analytic Wiener and Feynman integrals for the function $G(x)=\exp{{\int}_0^t{\theta}(s,x(s))d{\eta}(s)}{\psi}(x(t))$, where ${\theta}(s,{\cdot})$ and are the Fourier-Stieltjes transforms of the complex Borel measures on ${\mathbb{R}}^r$. Using the simple formulas, we evaluate the analogues of the conditional analytic Wiener and Feynman integrals of the functional G.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.413-431
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• 2012

Let $C^r[0,t]$ be the function space of the vector-valued continuous paths $x:[0,t]{\rightarrow}\mathbb{R}^r$ and define $X_t:C^r[0,t]{\rightarrow}\mathbb{R}^{(n+1)r}$ and $Y_t:C^r[0,t]{\rightarrow}\mathbb{R}^{nr}$ by $X_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}),\;x(t_n))$ and $Y_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}))$, respectively, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n=t$. In the present paper, using two simple formulas for the conditional expectations over $C^r[0,t]$ with the conditioning functions $X_t$ and $Y_t$, we establish evaluation formulas for the analogue of the conditional analytic Fourier-Feynman transform for the function of the form $${\exp}\{{\int_o}^t{\theta}(s,\;x(s))\;d{\eta}(s)\}{\psi}(x(t)),\;x{\in}C^r[0,t]$$ where ${\eta}$ is a complex Borel measure on [0, t] and both ${\theta}(s,{\cdot})$ and ${\psi}$ are the Fourier-Stieltjes transforms of the complex Borel measures on $\mathbb{R}^r$.

• Korean Journal of Remote Sensing
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• v.25 no.1
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• pp.21-30
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• 2009

The purposes of this paper are to present a selection method of neighboring pixels whose local statistics are similar to the center pixel and combine the selection result with mean curvature diffusion filter to reduce noises in remote sensed imagery. The order of selection of neighboring pixels is critical, especially for finding a pixel belonging to the homogeneous region, since the statistics of the homogeneous region vary according to the selection order. An effective strategy for selecting neighboring pixels, which uses rank-order differences vector obtained by computing the intensity differences between the center pixel and neighboring pixels and arranging them in ascending order, is proposed in this paper. By using region growing method, we divide the elements of the rank-ordered differences vector into two groups, homogeneous rank-ordered differences vector and outlier rank-ordered differences vector. The mean curvature diffusion filter is combined with a line process, which chooses selectively diffusion coefficient of the neighboring pixels belonging into homogeneous rank-ordered differences vector. Experimental results using an aerial image and a TerraSAR-X satellite image showed that the proposed method reduced more efficiently noises than some conventional adaptive filters using all neighboring pixels in updating the center pixel.

• Journal of Astronomy and Space Sciences
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• v.40 no.3
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• pp.123-129
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• 2023

This paper presents an analysis of the trans-lunar trajectory insertion performance of the Korea Pathfinder Lunar Orbiter (KPLO), the first lunar exploration spacecraft of the Republic of Korea. The successful launch conducted on August 4, 2022 (UTC), utilized the SpaceX Falcon 9 rocket from Cape Canaveral Space Force Station. The trans-lunar trajectory insertion performance plays a crucial role in ensuring the overall mission success by directly influencing the spacecraft's onboard fuel consumption. Following separation from the launch vehicle (LV), a comprehensive analysis of the trajectory insertion performance was performed by the KPLO flight dynamics (FD) team. Both orbit parameter message (OPM) and orbit determination (OD) solutions were employed using deep space network (DSN) tracking measurements. As a result, the KPLO was accurately inserted into the ballistic lunar transfer (BLT) trajectory, satisfying all separation requirements at the target interface point (TIP), including launch injection energy per unit mass (C3), right ascension of the injection orbit apoapsis vector (RAV), and declination of the injection orbit apoapsis vector (DAV). The precise BLT trajectory insertion facilitated the smoother operation of the KPLO's remainder mission phase and enabled the utilization of reserved fuel, consequently significantly enhancing the possibilities of an extended mission.

• Journal of Korean Society of Forest Science
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• v.105 no.2
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• pp.177-185
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• 2016

Fertilization is required to keep the balance of tissue nutrients and to produce high quality seedlings at the permanent nursery. This study was conducted to verify the optimum fertilization method for Fraxinus rhynchophylla, F. mandshurica, Pinus koraiensis, and Abies holophylla seedlings with vector diagnosis method. Seven treatments include nitrogen (N, $13.8g{\cdot}m^{-2}$), phosphorus (P, $6.1g{\cdot}m^{-2}$), potassium ($7.5g{\cdot}m^{-2}$) fertilization and 1x (N $6.9g{\cdot}m^{-2}$, P $3.05g{\cdot}m^{-2}$, K $3.65g{\cdot}m^{-2}$), 2x (twice of 1x), 4x (four times of 1x) fertilization and no fertilization. Soil pH decreased as fertilization increased. Nitrogen and NPK fertilization decreased exchangeable $Ca^{2+}$ and $Mg^{2+}$ concentrations. Height and root collar diameter of F. rhynchophylla and F. mandshurica significantly increased with N and NPK fertilization, but those of P. koraiensis and A. holophylla did not. The biomass of F. rhynchophylla and F. mandshurica was about twice higher at NPK fertilization compared to the control. The responses of vector diagnosis were different by tree species and fertilization treatment: F. rhynchophylla was in the status of N "dilution", which means the N concentration decreases with N content. Phosphorus and K were "sufficiency" state with 4x fertilization. F. mandshurica showed "retranslocation" as N content decreased without change of dry weight at N, P, K fertilization, but "dilution" state at NPK fertilization. This result suggested that optimal fertilization was required for F. rhynchophylla and F. mandshurica in seedling production stage, but was not essential for P. koraiensis and A. holophylla.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.413-424
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• 2008

In [21], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\parallel}\frac{1}{n}\sum\limits_{i=1}^{n}x_i{\parallel}^2+\sum\limits_{i=1}^{n}{\parallel}x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j{\parallel}^2=\sum\limits_{i=1}^{n}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\dots},x_n{\in}V$. We consider the functional equation $$nf(\frac{1}{n}\sum\limits^n_{i=1}x_i)+\sum\limits_{i=1}^{n}f(x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j)=\sum\limits_{i=1}^nf(x_i)$$ Using fixed point methods, we prove the generalized Hyers-Ulam stability of the functional equation $$(1)\;2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})=f(x)+f(y)$$.

• Journal of The Korean Astronomical Society
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• v.45 no.2
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• pp.31-38
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• 2012

In this study we apply Support Vector Machine (SVM) to the prediction of geo-effective halo coronal mass ejections (CMEs). The SVM, which is one of machine learning algorithms, is used for the purpose of classification and regression analysis. We use halo and partial halo CMEs from January 1996 to April 2010 in the SOHO/LASCO CME Catalog for training and prediction. And we also use their associated X-ray flare classes to identify front-side halo CMEs (stronger than B1 class), and the Dst index to determine geo-effective halo CMEs (stronger than -50 nT). The combinations of the speed and the angular width of CMEs, and their associated X-ray classes are used for input features of the SVM. We make an attempt to find the best model by using cross-validation which is processed by changing kernel functions of the SVM and their parameters. As a result we obtain statistical parameters for the best model by using the speed of CME and its associated X-ray flare class as input features of the SVM: Accuracy=0.66, PODy=0.76, PODn=0.49, FAR=0.72, Bias=1.06, CSI=0.59, TSS=0.25. The performance of the statistical parameters by applying the SVM is much better than those from the simple classifications based on constant classifiers.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1879-1903
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• 2017

In this paper we study the closure property and probability tail asymptotics for randomly weighted sums $S^{\Theta}_n={\Theta}_1X_1+{\cdots}+{\Theta}_nX_n$ for long-tailed random variables $X_1,{\ldots},X_n$ and positive bounded random weights ${\Theta}_1,{\ldots},{\Theta}_n$ under similar dependence structure as in [26]. In particular, we study the case where the distribution of random vector ($X_1,{\ldots},X_n$) is generated by an absolutely continuous copula.