• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.35 no.6
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• pp.573-580
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• 2017

Precise stochastic modeling for GPS measurements is one of key factors in adjustment computations for GPS positioning. To analyze the GPS measurement errors, Minimum Norm Quadratic Unbiased Estimators(MINQUE) approach is used in this study to estimate the variance components for measurement types with short-baseline GPS positioning model. The results showed the magnitudes of measurement errors for C1, P2, L1, L2 are 22.3cm, 27.6cm, 2.5mm, 2.2mm, respectively. To reduce the memory usage and computational burden, variance components are also estimated on epoch-by-epoch basis. The results showed that there exists slight differences between the solutions. However, epoch-by-epoch analysis may also be used for most of GPS applications considering the magnitudes of the differences.

• The Korean Journal of Applied Statistics
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• v.4 no.2
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• pp.157-170
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• 1991

This article is concerned with the goodness - of - fit test for exponentiality when both the scale and location parameters are unknown. A test procedure based on the $L_1$-norm of discrepancy between the cumulative distribution function and the empirical distribution function is proposed, and the critical values of the test statistic are obtained by Monte Carlo simulations. Also the null distributions of the proposed test statistic are presented for small sample sizes. The power of tests under certain alternative distributions is investigated to compare the proposed test statistic with the well-known EDF test statistics. Our Monte Carlo power studies reveal that the proposed test statistic has good power properties, for moderate-to-large sample sizes, in comparison to other statistics although it is a conservative test.

• Journal of Computing Science and Engineering
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• v.11 no.4
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• pp.121-129
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• 2017

Feature selection has been widely established as an efficient technique for microarray data analysis. Feature selection aims to search for the most important feature/gene subset of a given dataset according to its relevance to the current target. Unsupervised feature selection is considered to be challenging due to the lack of label information. In this paper, we propose a novel method for unsupervised feature selection, which incorporates embedded learning and $l_{2,1}-norm$ sparse regression into a framework to select genes in microarray data analysis. Local tangent space alignment is applied during embedded learning to preserve the local data structure. The $l_{2,1}-norm$ sparse regression acts as a constraint to aid in learning the gene weights correlatively, by which the proposed method optimizes for selecting the informative genes which better capture the interesting natural classes of samples. We provide an effective algorithm to solve the optimization problem in our method. Finally, to validate the efficacy of the proposed method, we evaluate the proposed method on real microarray gene expression datasets. The experimental results demonstrate that the proposed method obtains quite promising performance.

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.183-205
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• 2024

In this paper, for an m-dimensional (m ≥ 5) complete non-compact submanifold M immersed in an n-dimensional (n ≥ 6) simply connected Riemannian manifold N with negative sectional curvature, under suitable constraints on the squared norm of the second fundamental form of M, the norm of its weighted mean curvature vector |H_f| and the weighted real-valued function f, we can obtain: • several one-end theorems for M; • two Liouville theorems for harmonic maps from M to complete Riemannian manifolds with nonpositive sectional curvature.

• East Asian mathematical journal
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• v.21 no.1
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• pp.41-48
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• 2005

In this paper we first introduce a space of homogeneous type X, and then consider a kind of generalized upper half-space $X{\times}(0,\;\infty)$. We are mainly considered with inequalities for the $L^p$ norms of area functions associated with approach regions in $X{\times}(0,\;\infty)$.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.295-300
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• 1992

In [5] it was shown that if T .mem. L(X) is regular on a Banach space X, with finite dimensional intersection T$^{-1}$ (0).cap.T(X) and if S .mem. L(X) is invertible, commute with T and has sufficiently small norm then T - S in upper semi-Fredholm, and hence essentially one-one, in the sense that the null space of T - S is finite dimensional ([4] Theorem 2; [5] Theorem 2). In this note we extend this result to incomplete normed space.

• Honam Mathematical Journal
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• v.27 no.1
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• pp.69-76
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• 2005

The aim of this work is to generalize $L_1$-approximation in order to apply them to a discrete approximation. In $L_1$-approximation, we use the norm given by $${\parallel}f{\parallel}_1={\int}{\mid}f{\mid}d{\mu}$$ where ${\mu}$ a non-atomic positive measure. In this paper, we go to the other extreme and consider measure ${\mu}$ which is purely atomic. In fact we shall assume that ${\mu}$ has exactly m atoms. For any ${\ell}$-tuple $b^1,\;{\cdots},\;b^{\ell}{\in}{\mathbb{R}}^m$, we defined the ${\ell}^m_1{w}$-norn, and consider $s^*{\in}S$ such that, for any $b^1,\;{\cdots},\;b^{\ell}{\in}{\mathbb{R}}^m$, $$\array{min&max\\{s{\in}S}&{1{\leq}i{\leq}{\ell}}}\;{\parallel}b^i-s{\parallel}_w$$, where S is a n-dimensional subspace of ${\mathbb{R}}^m$. The $s^*$ is called the Chebyshev center or a discrete simultaneous ${\ell}^m_1$-approximation from the finite dimensional subspace.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1029-1036
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• 1997

Let ${A_t)}_{t>0}$ be a dilation group given by $A_t = exp(-P log t)$, where P is a real $n \times n$ matrix whose eigenvalues has strictly positive real part. Let $\nu$ be the trace of P and $P^*$ denote the adjoint of pp. Suppose that $K$ is a function defined on $R^n$ such that $$\mid$K(x)$\mid$ \leq k($\mid$x$\mid$_Q)$ for a bounded and decreasing function $k(t) on R_+$ satisfying $k \diamond $\mid$\cdot$\mid$_Q \in \cup_{\varepsilon >0}L^1((1 + $\mid$x$\mid$)^\varepsilon dx)$ where $Q = \int_{0}^{\infty} exp(-tP^*) exp(-tP)$ dt and the norm $$\mid$\cdot$\mid$_Q$ stands for $$\mid$x$\mid$_Q = \sqrt{}, x \in R^n$. For $f \in L^1(R^n)$, define $mf(x) = sup_{t>0}$\mid$K_t * f(x)$\mid$$ where $K_t(X) = t^{-\nu}K(A_{1/t}^* x)$. Then we show that $m$ is a bounded operator of $L^1(R^n) into L^{1, \infty}(R^n)$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.173-182
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• 2015

In this paper, the blow-up rate of $L^2$-norm for the semi-linear wave equation with a power nonlinearity is obtained in the bounded domain for any p > 1. We also get the blow-up rate of the derivative under the condition 1 < p < $1+\frac{4}{N-1}$ for $N{\geq}2$ or 1 < p < 5 for N = 1.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.377-383
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• 1996

We consider in this paper the following nonlinear regression model $$ (1.1) y_t = f(x_t, \theta_o) + \in_t, t = 1, \ldots, n, $$ where $y_t$ is the tth response, $x_t$ is m-vector imput variable, $\theta_o$ is a p-vector of unknown parameter belong to a parameter space $\Theta, f:R^m \times \Theta \ to R^1$ is a nonlinear known function, and $\in_t$ are independent unobservable random errors with finite second moment.