• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.177-183
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• 1997

A data-adaptive order selection procedure is proposed for local polynomial nonparametric regression. For each given polynomial order, bias and variance are estimated and the adaptive polynomial order that has the smallest estimated mean squared error is selected locally at each location point. To estimate mean squared error, empirical bias estimate of Ruppert (1995) and local polynomial variance estimate of Ruppert, Wand, Wand, Holst and Hossjer (1995) are used. Since the proposed method does not require fitting polynomial model of order higher than the model order, it is simpler than the order selection method proposed by Fan and Gijbels (1995b).

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.119-126
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• 2016

In this paper, we study both the numerical index and the polynomial numerical index. First, we give a sufficient condition for a Banach space X to have lushness. Second, we study the relation between the renormings of a Banach space and the k-order polynomial numerical index. This shows that every real Banach spaces of dimension greater that 1 can be renormed to have 2-order polynomial numerical index ${\alpha}$ for any ${\alpha}{\in}[0,1/18)$.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.445-456
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• 2008

We characterize the helical polynomial space curves and solve the first-order Hermite interpolation problem for helical polynomial space quintics.

• Proceedings of the Korea Water Resources Association Conference
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• 2020.06a
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• pp.268-268
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• 2020

토양수분량은 수문연구에 있어 중요한 인자 중의 하나이며, 그 필요성이 점차 강조되고 있다. 국내에서도 최근 새로운 관측기기의 도입이나 수자원위성의 개발 등에 관한 연구가 점차 활발하게 이뤄지고 있으나, 토양수분량 자료의 생산, 품질관리 및 배포 시스템에 관한 연구 및 개발이 부족한 실정이다. 반면에 해외에서는 International Soil Moisture Network(ISMN)을 통해 토양수분량 자료의 품질관리 및 배포가 활발하게 이루어지고 있는데, ISMN에서는 토양특성, 강우에 대한 반응, 토양온도, 시계열특성을 이용해 토양수분량 관측 자료를 품질관리 하고 있다. 본 연구에서는 ISMN의 spike 검출 알고리즘에서 그래프 평활화(smoothing)를 위해 이용되는 Savitzky-Golay 필터의 window size와 polynomial order(filter order)를 다양하게 변화시키고, 이를 설마천 관측소에서 측정한 토양수분량 원시자료에 적용하여 window size와 polynomial order별로 편의(bias), 변동(variation), 평균 제곱근 오차(Root Mean Square Error, RMSE)를 산정하였다. 통계산정 결과 원시자료와의 bias는 window size가 3이고 polynomial order가 2인 필터를 적용했을 때 가장 작은 것으로 나타났으며, variance는 window size가 3이고 polynomial order가 2인 필터를 이용했을 때가 원시자료와 가장 유사한 것으로 나타났다. 또한, RMSE는 window size가 5이고 polynomial order가 3일 때 가장 작은 것으로 나타났다. 이는 추후 토양수분량 품질관리를 수행하기 위해 적절한 필터 계수 값을 제시할 수 있는 논문으로 사료된다.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.183-198
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• 2009

In this paper, we derive a characterization of orthonormal balanced multiwavelets of order p in terms of the continuous moments of the multiscaling function $\phi$. As a result, the continuous moments satisfy the discrete polynomial preserving properties of order p (or degree p - 1) for orthonormal balanced multiwavelets. We derive polynomial reproduction formula of degree p - 1 in terms of continuous moments for orthonormal balanced multiwavelets of order p. Balancing of order p implies that the series of scaling functions with the discrete-time monomials as expansion coefficients is a polynomial of degree p - 1. We derive an algorithm for computing the polynomial of degree p - 1.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.641-651
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• 2014

Because of difficulty of using Schauder's fixed point theorem to the polynomial-like iterative equation, a lots of work are contributed to the existence of solutions for the polynomial-like iterative equation on compact set. In this paper, by applying the Schauder-Tychonoff fixed point theorem we discuss monotone solutions and convex solutions of the polynomial-like iterative equation on an open set (possibly unbounded) in $\mathbb{R}^N$. More concretely, by considering a partial order in $\mathbb{R}^N$ defined by an order cone, we prove the existence of increasing and decreasing solutions of the polynomial-like iterative equation on an open set and further obtain the conditions under which the solutions are convex in the order.

• Structural Engineering and Mechanics
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• v.76 no.6
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• pp.675-685
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• 2020

As the classical response surface method (RSM), the polynomial RSM is so easy-to-apply that it is widely used in reliability analysis. However, the trade-off of accuracy and efficiency is still a challenge and the "curse of dimension" usually confines RSM to low dimension systems. In this paper, based on the univariate decomposition, the polynomial RSM is executed in a new mode, called as DPRSM. The general form of DPRSM is given and its implementation is designed referring to the classical RSM firstly. Then, in order to balance the accuracy and efficiency of DPRSM, its adaptive order revision around the most probable point (MPP) is proposed by introducing the univariate polynomial order analysis, noted as RDPRSM, which can analyze the exact nonlinearity of the limit state surface in the region around MPP. For testing the proposed techniques, several numerical examples are studied in detail, and the results indicate that DPRSM with low order can obtain similar results to the classical RSM, DPRSM with high order can obtain more precision with a large efficiency loss; RDPRSM can perform a good balance between accuracy and efficiency and preserve the good robustness property meanwhile, especially for those problems with high nonlinearity and complex problems; the proposed methods can also give a good performance in the high-dimensional cases.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.899-927
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• 2019

In this paper we establish some results depending on the comparative growth properties of composite entire and meromorphic functions using relative (p, q)-th order and relative (p, q)-th lower order where p, q are any two positive integers and that of a special type of differential polynomial generated by one of the factors.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2004.04a
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• pp.279-284
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• 2004

This paper presents on adjustment methods of the vendor-provided RPC(Rational Polynomial Coefficient) of GEO-level stereo images for the IKONOS satellite. RPC are adjusted with control points by the first-order polynomial and the block adjustment method in this study. As results, the maximum error of 3D ground coordinates by the adjusted RPC model did not exceed 4m. The block adjustment method is more stability than the first-order polynomial method.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.103-111
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• 1986

In [2] and [3], the Shinwon polynomial S$_{n}$(x) of order n is defined and studied in some details. In this paper we will define the general Shinwon polynomial S$_{n}$(a,x) and the Dickson polynomial D$_{n}$(a,x) of the second kind of order n which is a slightly changed form of the Dickson polynomial g$_{n}$(a,x), and show that D$_{n}$(a,x) is closely related to S$_{n}$(a,x).EX> n/(a,x).