• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.27-32
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• 2000

To overcome boundary problems with wavelet regression, we propose a simple method that reduces bias at the boundaries. It is based on a combination of wavelet functions and low-order polynomials. The utility of the method is illustrated with simulation studies and a real example. Asymptotic results show that the estimators are competitive with other nonparametric procedures.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.717-725
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• 2009

We show that to every real polynomial of degree n, there corresponds a certain basis for the space of polynomials of degree less than or equal to (n-1). As an application, we give a new proof for the existence and uniqueness of the partial fraction decomposition of a rational function.

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.341-371
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• 2003

This article discusses in detail how the study of proper holomorphic rational mappings between balls in different dimensions relates to positivity conditions and to isometric imbedding of holomorphic bundles. The first chapter discusses rational proper mappings between balls; the second chapter discusses seven distinct positivity conditions for real-valued polynomials in several complex variables; the third chapter reveals how these issues relate to an isometric imbedding theorem for holomorphic vector bundles proved by the author and Catlin.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.41-49
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• 2009

Let $\zeta$ be a fixed complex number. In this paper, we study the quantity $S(\zeta,\;n):=mas_{f{\in}{\Lambda}_n}\;|f(\zeta)|$, where ${\Lambda}_n$ is the set of all real polynomials of degree at most n-1 with coefficients in the interval [0, 1]. We first show how, in principle, for any given ${\zeta}\;{\in}\;{\mathbb{C}}$ and $n\;{\in}\;{\mathbb{N}}$, the quantity S($\zeta$, n) can be calculated. Then we compute the limit $lim_{n{\rightarrow}{\infty}}\;S(\zeta,\;n)/n$ for every ${\zeta}\;{\in}\;{\mathbb{C}}$ of modulus 1. It is equal to 1/$\pi$ if $\zeta$ is not a root of unity. If $\zeta\;=\;\exp(2{\pi}ik/d)$, where $d\;{\in}\;{\mathbb{N}}$ and k $\in$ [1, d-1] is an integer satisfying gcd(k, d) = 1, then the answer depends on the parity of d. More precisely, the limit is 1, 1/(d sin($\pi$/d)) and 1/(2d sin($\pi$/2d)) for d = 1, d even and d > 1 odd, respectively.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.17 no.9
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• pp.2483-2504
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• 2023

Most existing low-light enhancement algorithms either use a large number of training parameters or lack generalization to real-world scenarios. This paper presents a novel lightweight and robust pixel-wise polynomial approximation-based deep network for low-light image enhancement. For mapping the low-light image to the enhanced image, pixel-wise higher-order polynomials are employed. A deep convolution network is used to estimate the coefficients of these higher-order polynomials. The proposed network uses multiple branches to estimate pixel values based on different receptive fields. With a smaller receptive field, the first branch enhanced local features, the second and third branches focused on medium-level features, and the last branch enhanced global features. The low-light image is downsampled by the factor of 2b-1 (b is the branch number) and fed as input to each branch. After combining the outputs of each branch, the final enhanced image is obtained. A comprehensive evaluation of our proposed network on six publicly available no-reference test datasets shows that it outperforms state-of-the-art methods on both quantitative and qualitative measures.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.67 no.3
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• pp.427-432
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• 2018

This paper uses a recursive least squares method to estimate the projectile motion trajectory of an object in real time. The equations of motion of the object are obtained considering the air resistance which occurs in the actual experiment environment. Because these equations consider air resistance, parameter estimation of nonlinear terms is required. However, nonlinear recursive least squares estimation is not suitable for estimating trajectory of projectile in that it requires a lot of computation time. Therefore, parameter estimation for real-time trajectory prediction is performed by recursive least square estimation after using Taylor series expansion to approximate nonlinear terms to polynomials. The proposed method is verified through experiments by using VICON Bonita motion capture system which can get three dimensional coordinates of projectile. The results indicate that proposed method is more accurate than linear Kalman filter method based on the equations of motion of projectile that does not consider air resistance.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.263-273
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• 2013

A mean-value result, saying that the difference quotient of a differentiable function in a real interval is a mean value of its derivatives at the endpoints of the interval, leads to the functional equation $$\frac{f(x)-F(y)}{x-y}=M(g(x),\;G(y)),\;x{\neq}y$$, where M is a given mean and $f$, F, $g$, G are the unknown functions. Solving this equation for the arithmetic, geometric and harmonic means, we obtain, respectively, characterizations of square polynomials, homographic and square-root functions. A new criterion of the monotonicity of a real function is presented.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1998.03a
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• pp.148-153
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• 1998

In order to control thermal deformation of machine origin of machine tools due to internal and external heat sources, the real-time compensation system has been developed. First, GMDH models were constructed to estimate thermal deformation of machine origin for a vertical machining center through the measurement of deformation data and temperature data of specific points on the machine tool. Thermocouples and gap sensors are used respectively for measurement. These models are nonlinear equations with high-order polynomials and implemented in a multilayered perceptron type network structure. Secondly, work origin shift method were developed by implementing digital I/O interface board between CNC controller and IBM-PC. The work origin shift method is to shift the work origin by the compensation amounts which is calculated by pre-established GMDH model. From the experimental result, thermal deformation of machine origin was reduced to below $\pm$5${\mu}{\textrm}{m}$.

• Journal of IKEEE
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• v.24 no.4
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• pp.1039-1049
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• 2020

Neural decoding is important to recognize the user's intention for controlling a neuro-prosthetic hand. This paper proposes a real-time decoding method for multi-channel peripheral neural activity. Peripheral nerve signals were measured from the median and radial nerves, and motion artifacts were removed based on locally fitted polynomials. Action potentials were then classified using a k-means algorithm. The firing rate of action potentials was extracted as a feature vector and its dimensionality was reduced by a self-organizing feature map. Finally, a multi-layer perceptron was used to classify hand motions. In monkey experiments, all processes were completed within a real-time constrain, and the hand motions were recognized with a high success rate.

• Proceedings of the IEEK Conference
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• 2000.06a
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• pp.244-247
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• 2000

This paper deals with methods for partial response maximum-likelihood (PRML) detection and crosstalk cancellation. In accrodance with the demand for increased recording density, 20 gigabyte (Gbyte) digital versatile disk (DVD) ROM channel is considered. Channel is modelled to be close to real optical channel using DIFFRACT$\^$TM/. After comparing the spectral characteristics of various PR polynomials, P(D)=1＋D＋D$^2$＋D$^3$is proposed as a target PR. The performance of the system is illustrated under the condition that the readout signal is degraded by crosstalk, radial tilt and nonlinear distortions in optics. The experimental results show that crosstalk and nonlinear distortions degrade performance by about 2dB, respectively. We also show that when radial tilt is added to the crosstalk, the performance degradation assumes quite significant proprotions.