• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.1-22
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• 1997

In the linear regression model $y_{i}$ = .alpha. $x_{i}$ $^{T}$ .beta. + .epsilon.$_{i}$ , i = 1,2,...,n, the weighted pairwise absolute deviation (WPAD) estimator was defined by minimizing the dispersion function D (.beta.) = .sum..sum.$_{{i $w_{{ij}}$$\mid$ $r_{j}$ (.beta.) $r_{i}$ (.beta.)$\mid$, where $r_{i}$ (.beta.)'s are residuals and $w_{{ij}}$'s are weights. This estimator can achive bounded total influence with positive breakdown by choice of weights $w_{{ij}}$. In this paper, we consider a more general type of dispersion function than that of D(.beta.) and propose a pairwise GM-estimator based on the dispersion function. Under some regularity conditions, the proposed estimator has a bounded influence function, a high breakdown point, and asymptotically a normal distribution. Results of a small-sample Monte Carlo study are also presented. presented.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.687-695
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• 2014

In this article we introduce the zweier double sequence spaces $_2Z^I$(M), $_2Z_0^I$(M) and $_2Z_{\infty}^I$(M) using the Orlicz function M. We study the algebraic properties and inclusion relations on these spaces.

• Journal of Korean Society for Quality Management
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• v.48 no.4
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• pp.535-552
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• 2020

Purpose: The main theme of this study is to derive a specific quality loss function with multiple characteristics according to the same analytical structure as the single characteristic quality loss function of Taguchi. In other words, it presents an analytical framework for measuring quality costs that can be controlled in practice. Methods: This study followed the analytical methodology through geometric, linear algebraic, and statistical approaches Results: The function suggested by this study is as follows; $$L(x_1,x_2,{\cdots},x_t)={\sum\limits_{i=1}^{t}}k_i\{x_i+{\sum\limits_{j=1}^{t}}\({\rho}_{ij}{\frac{d_i}{d_j}}\)x_j\}x_i$$ Conclusion: This paper derived the quality loss function with multiple quality characteristics to expand the usefulness of the Taguchi quality loss function. The function derived in this paper would be more meaningful to estimate quality costs under the practical situation and general structure with multiple quality characteristics than the function by linear algebraic approach in response surface analysis.

• The Korean Journal of Physiology and Pharmacology
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• v.8 no.5
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• pp.253-257
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• 2004

Schwann cells play an important role in peripheral nerve regeneration. Upon neuronal injury, activated Schwann cells clean up the myelin debris by phagocytosis, and promote neuronal survival and axon outgrowth by secreting various neurotrophic factors. However, it is unclear how the nerve injury induces Schwann cell activation. Recently, it was reported that certain cytoplasmic molecules, which are secreted by cells undergoing necrotic cell death, induce immune cell activation via the toll-like receptors (TLRs). This suggests that the TLRs expressed on Schwann cells may recognize nerve damage by binding to the endogenous ligands secreted by the damaged nerve, thereby inducing Schwann cell activation. Accordingly, this study was undertaken to examine the expression and the function of the TLRs on primary Schwann cells and iSC, a rat Schwann cell line. The transcripts of TLR2, 3, 4, and 9 were detected on the primary Schwann cells as well as on iSC. The stimulation of iSC with poly (I : C), a synthetic ligand for the TLR3, induced the expression of $TNF-{\alpha}$ and RANTES. In addition, poly (I : C) stimulation induced the iNOS expression and nitric oxide secretion in iSC. These results suggest that the TLRs may be involved in the inflammatory activation of Schwann cells, which is observed during Wallerian degeneration after a peripheral nerve injury.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.375-384
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• 2008

Let $k={\mathbb{F}}_q(T)$ and ${\mathbb{A}}={\mathbb{F}}_q[T]$. Fix a prime divisor ${\ell}$ q-1. In this paper, we consider a ${\ell}$-cyclic real function field $k(\sqrt[{\ell}]P)$ as a subfield of the imaginary bicyclic function field K = $k(\sqrt[{\ell}]P,\;(\sqrt[{\ell}]{-Q})$, which is a composite field of $k(\sqrt[{\ell}]P)$ wit a ${\ell}$-cyclic totally imaginary function field $k(\sqrt[{\ell}]{-Q})$ of class number one. und give various conditions for the class number of $k(\sqrt[{\ell}]{P})$ to be one by using invariants of the relatively cyclic unramified extensions $K/F_i$ over ${\ell}$-cyclic totally imaginary function field $F_i=k(\sqrt[{\ell}]{-P^iQ})$ for $1{\leq}i{\leq}{\ell}-1$.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.229-247
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• 2000

This paper is concerned with the impulsive Cauchy problem where the control function u is a possibly discontinuous vector-valued function with finite total variation. We assume that the vector fields f, $g_i$(i=1,…, m) are dependent on the time variable. The impulsive Cauchy problem is of the form x(t)=f(t,x) +$\SUMg_i(t,x)u_i(t)$, $t\in$[0,T], x(0)=$\in\; R^n$, where the vector fields f, $g_i$ : $\mathbb{R}\; \times\; \mathbb{R}\; \longrightarrow\; \mathbb(R)^n$ are measurable in t and Lipschitz continuous in x, If $g_i's$ satisfy a condition that $\SUM{\mid}g_i(t_2,x){\mid}{\leq}{\phi}$ $\forallt_1\; <\; t-2,x\; {\epsilon}\;\mathbb{R}^n$ for some increasing function $\phi$, then the imput-output function can be continuously extended to measurable functions of bounded variation.

• Bulletin of the Korean Chemical Society
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• v.34 no.12
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• pp.3743-3748
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• 2013

A tetradentate ligand of 2-phenyl-4,6-di(pyridin-2-yl)pyrimidine (L) has been synthesized and its complexes with $ZnI_2$ and CuI have been obtained by hydrothermal method. single crystal X-ray diffraction analysis indicates that ligand L coordinates with Zn(II) ions to form a simple four-coordinate di-nuclear complex, while the complexation of L with Cu(I) constructs a one-dimensional chain polymer. The existence of $I^-$ ion hampers the L to assemble grid-type complexes with Zn(II) and Cu(I). Fluorescence spectra show that the L emits blue fluorescence while its Cu(I) polymer decrease the fluorescence intensity and Zn(II) complex quenches the fluorescence.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.257-264
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• 2012

Exton introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ${\ldots}$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function ${\Psi}_1$, and a Humbert function ${\Phi}_2$. The object of this paper is to present 18 new integral representations of Euler type for the Exton hypergeometric function $X_8$, whose kernels include the Exton functions ($X_2$, $X_8$) itself, the Horn's function $H_4$, the Gauss hypergeometric function $F$, and Lauricella hypergeometric function $F_C$. We also provide a system of partial differential equations satisfied by $X_8$.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.207-212
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• 2022

In this paper, an interesting integral involving the Ī-function of one variable introduced by Rathie has been derived. Since Ī-function is a very generalized function of one variable and includes as special cases many of the known functions appearing in the literature, a number of integrals can be obtained by reducing the Ī function of one variable to simpler special functions by suitably specializing the parameters. A few special cases of our main results are also discussed.

• Journal of Korean Society of Transportation
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• v.8 no.2
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• pp.77-97
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• 1990

Compared to modal split, the methods of forecasting traffic volumes diverted in various types of I.C.s have not been sufficiently studied. The purpose of this study is to derive a new diversion function that can represent the directional traffic volume in accordance with various geometrics of I.C.s. In general, knowing various traffic impedances and the amount of traffic production and attraction, one can estimate proper traffic volumes associated with directions by using a well-defined diversion function. This function is usually made by a series of process such as surveying directional traffic volumes on several I.C.s, analyzing with a regression method and verifying those results by statistical approaches. The function has been developed by rigorous statistical testings, mainly a regression analysis. This paper presents an effective method in planning and designing new roads, I.C.s and route choice of subway. Finally, some comparisons and improvements and suggested when one uses different types of relevant models and functions.