• Communications for Statistical Applications and Methods
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• v.16 no.1
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• pp.185-193
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• 2009

Machine learning methods such as support vector machines and random forests yield nonparametric prediction functions of the form y = $f(x_1,{\ldots},x_p)$. As a sequel to the previous article (Huh and Lee, 2008) for visualizing nonparametric functions, I propose more sensible graphs for visualizing y = $f(x_1,{\ldots},x_p)$ herein which has two clear advantages over the previous simple graphs. New graphs will show a small number of prototype curves of $f(x_1,{\ldots},x_{j-1},x_j,x_{j+1}{\ldots},x_p)$, revealing statistically plausible portion over the interval of $x_j$ which changes with ($x_1,{\ldots},x_{j-1},x_{j+1},{\ldots},x_p$). To complement the visual display, matching importance measures for each of p predictor variables are produced. The proposed graphs and importance measures are validated in simulated settings and demonstrated for an environmental study.

• Honam Mathematical Journal
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• v.27 no.3
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• pp.399-404
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• 2005

Let M be a finite commutative nilpotent algebra over a perfect field k of prime characteristic p and let $M^p$ be the sub-algebra of M generated by $x^p$, $x{\in}M$. Eggert[3] conjectures that $dim_kM{\geq}pdim_kM^p$. In this paper, we show that the conjecture holds for $M=R^+/I$, where $R=k[X_1,\;X_2,\;{\cdots},\;X_t]$ is a polynomial ring with indeterminates $X_1,\;X_2,\;{\cdots},\;X_t$ over k and $R^+$ is the maximal ideal of R generated by $X_1,\;X_2,{\cdots},\;X_t$ and I is a monomial ideal of R containing $X_1^{n_1+1},\;X_2^{n_2+1},\;{\cdots},\;X_t^{n_t+1}$ ($n_i{\geq}0$ for all i).

• Korean Journal of Mathematics
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• v.18 no.1
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• pp.63-77
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• 2010

Infinite finite range inequalities relate the norm of a weighted polynomial over ${\mathbb{R}}$ to its norm over a finite interval. In this paper we extend such inequalities to generalized polynomials with the weight $W(x)={\prod}^{m}_{k=1}{\mid}x-x_k{\mid}^{{\gamma}_k}{\cdot}{\exp}(-{\mid}x{\mid}^{\alpha})$.

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.1-5
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• 1985

The differential polynomial ring A[X, D] has been studied by many authors J. Cozzens, C. Faith, R.E. Johnson and D. Mathis and others. The main purpose of the present paper is to study some properties of .phi.-differential polynomial ring A[X, D, .phi.] and modules over the .phi.-differential polynomial ring X[X, D, .phi.].

• Journal of the Chungcheong Mathematical Society
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• v.1 no.1
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• pp.43-53
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• 1988

The main result of this paper is a characterization of almost projective modules over art in algebras by means of irreducible maps and almost split sequences. A module X is an almost projective module if and only if it has a presentation $0{\longrightarrow}L{\longrightarrow^{\alpha}}P{\longrightarrow}X{\longrightarrow}0$ with projective module P and irreducible maps ${\alpha}$. Let X be an injective almost projective non simple module and $0{\rightarrow}Dtr(x){\rightarrow}E{\rightarrow}X{\rightarrow}0$ be an almost split sequence. If $E=E_1{\oplus}E_2$ is a direct decomposition of indecomposable modules then ${\ell}(X)=3$.

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.11-15
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• 1985

Manddelberg [9] has shown that a Clifford algebra of a free quadratic space over an arbitrary semi-local ring R in Brawer-Wall group BW(R) is determined by its rank, determinant, and Hasse invariant. In this paper, we prove a corresponding result when R is a full ring.Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is non-degenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$(V,R) induced by B is an isomorphism), and with a quadratic mapping .phi.: V.rarw.R such that B(x,y)=1/2(.phi.(x+y)-.phi.(x)-.phi.(y)) and .phi.(rx) = $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U9R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$,.., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2 we reserve the notation [a $a_{11}$, $a_{22}$] for the space. A commutative ring R having 2 a unit is called full [10] if for every triple $a_{1}$, $a_{2}$, $a_{3}$ of elements in R with ( $a_{1}$, $a_{2}$, $a_{3}$)=R, there is an element w in R such that $a_{1}$+ $a_{2}$w+ $a_{3}$ $w^{2}$=unit.TEX>=unit.t.t.t.

• The Mathematical Education
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• v.26 no.2
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• pp.55-61
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• 1988

이 논문에서는 CS-Semistratifiable 공간보다 더 일반화된 공간 Cn-Semistratifiable을 정의 하며 그에 따른 여러가지 성질들을 조사하였다. 위상 공간(X, $\tau$)에 대하여 $\alpha$$\times$$\tau$에서 X의 폐집합족으로의 함수 S가 존재하여 다음 조건들을 만족할 때 공간X는 Cn-Semistratifiable over $\alpha$라 정의한다. a) 임의의 개집합 U에 대하여 U=U{S($\beta$, U) : $\beta$<$\alpha$} b) U, V가 X의 개집합이고 U⊂CV이면 모든 $\beta$<$\alpha$에 대하여 S($\beta$, V)⊂S($\beta$, V)이다. c) 만약 ${\gamma}$<$\beta$<$\alpha$ 이라면 임의의 개집합 U에 대하여 S(${\gamma}$, U)⊂S($\beta$, U)이다. d) X의 수렴하는 net $X_{\beta}$$\longrightarrow$X와 X를 품는 임의의 개집합 U에 대하여 적당한 $\beta$<$\alpha$가 존재하여 X$\in$S($\beta$. U)이고 { $X_{\beta}$}는 S($\beta$, U)안에 eventual하게 들어간다. 위의 정의에 의하여 다음과 같은 성질들이 증명되었다. 1 . Strstifiable over $\alpha$$\longrightarrow$cn-semistratifiable over$\longrightarrow$semistratifiable over $\alpha$ 2, 어떤 공간이 cn-Semistratifiable over $\alpha$이기 위한 필요충분 조건은 그것이 linearly cushioned cn-pairnet를 갖는 것이다. 3. cn-semistratifiable over $\alpha$의 부분공간 역시 cn-semistratifiabie over $\alpha$ 하다. 4. on-semistratifiable over $\alpha$의 유한개의 적공간 역시 cn-semistratifiabie over $\alpha$한다. 5. 폐 cn-semistratifiable over $\alpha$ 부분공간들의 합공간 역시 on-semistrbtifiable over $\alpha$ 하다. 6. 폐연속 net-cevering 함수에 의하여 cn-semistratifiable over $\alpha$ 성질이 보존된다.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.54 no.8
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• pp.510-516
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• 2005

Rapid advances in telecommunication make emergency telemedicine possible that specialist offers medical care to an emergency case in moving vehicle. Although there were many telemedicine projects delivering the image or video of patient over several wireless networks, none of them considered effective solutions for optimizing video transmission over error-prone environments, such like wireless links. To alleviate the effect of channel errors on compressed video bit-stream, this paper analyzed the error resilient features of MPEG-4 standard and measured the quality of transmitted MPEG-4 encoded video over commercially available CDMA2000 1xEV-DO networks, transmitting different IP packet sizes and RM positions. we propose an error resilient transmission methods for emergency telemedicine over real 3G network.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.55 no.6
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• pp.296-301
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• 2006

Even though the emergency telecommunication make possible that specialist offers medical care over emergency cases in moving vehicle, we still have many problems in transmitting the image or video of patient over several wireless networks. To alleviate the effect of channel errors on compressed video bit-stream, this paper analyzed the error resilient features of JPEG2000 standard and measured the quality of transmission over noisy wireless channel, CDMA2000 1xEV-DO networks, compared to the features of error resilient tool of MPEG-4. We also proposed the optimum solution of transmitting images over real 3G network using JPEG2000 error resilient tool.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.697-706
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• 2007

In [8], we showed that any ideal of $\mathbb{Z}_4[X]/(X^{2^n}-1)$ is generated by at most two polynomials of the standard forms. The purpose of this paper is to find a description of the cyclic codes of even length over $\mathbb{Z}_4$ namely the ideals of $\mathbb{Z}_4[X]/(X^l\;-\;1)$, where $l$ is an even integer.