• Korean Journal of Mathematics
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• v.30 no.2
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• pp.239-247
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• 2022

Let C₀[0, T] denote the Wiener space, the space of continuous functions x(t) on [0, T] such that x(0) = 0. Define a random vector $Z_{\vec{e},k}:C_0[0,\;T] {\rightarrow}{\mathbb{R}}^k$ by $$Z_{\vec{e},k}(x)=({\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^T}\;e_1(t)dx(t),\;{\ldots},\;{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^T}\;ek(t)dx(t))$$ where e_j ∈ L₂[0, T] with e_j ≠ 0 a.e., j = 1, …, k. In this paper we study the conditional Fourier-Feynman transform and a conditional convolution product for a cylinder type functionals defined on C0[0, T] with a general vector valued conditioning functions $Z_{\vec{e},k}$ above which need not depend upon the values of x at only finitely many points in (0, T] rather than a conditioning function X(x) = (x(t₁), …, x(t_n)) where 0 < t₁ < … < t_n = T. In particular we show that the conditional Fourier-Feynman transform of the conditional convolution product is the product of conditional Fourier-Feynman transforms.

• Honam Mathematical Journal
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• v.34 no.4
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• pp.505-512
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• 2012

In this paper, we give some properties on submodule transforms.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.49-61
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• 2011

Let D be an integral domain with quotient field K, X be a nonempty set of indeterminates over D, * be a star operation on D, $N_*$={f $\in$ D[X]|c(f)$^*$= D}, $*_w$ be the star operation on D defined by $I^{*_w}$ = ID[X]${_N}_*$ $\cap$ K, and [*] be the star operation on D[X] canonically associated to * as in Theorem 2.1. Let $A^g$ (resp., $A^{[*]g}$, $A^{[*]g}$) be the global (resp.,*-global, [*]-global) transform of a ring A. We show that D is a $*_w$-Noetherian domain if and only if D[X] is a [*]-Noetherian domain. We prove that $D^{*g}$[X]${_N}_*$ = (D[X]${_N}_*$)$^g$ = (D[X])$^{[*]g}$; hence if D is a $*_w$-Noetherian domain, then each ring between D[X]${_N}_*$ and $D^{*g}$[X]${_N}_*$ is a Noetherian domain. Let $\tilde{D}$ = $\cap${$D_P$|P $\in$ $*_w$-Max(D) and htP $\geq$2}. We show that $D\;\subseteq\;\tilde{D}\;\subseteq\;D^{*g}$ and study some properties of $\tilde{D}$ and $D^{*g}$.

• Bulletin of the Korean Chemical Society
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• v.35 no.1
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• pp.165-172
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• 2014

The distribution of basic nitrogen-containing compounds in three vacuum gas oils (VGOs) with different boiling ranges and their dewaxed oils from the lube base oil refining unit of a refinery were characterized by positive-ion electrospray ionization (ESI) Fourier transform-ion cyclotron resonance mass spectrometry (FT-ICR MS). It turned out that the composition of basic nitrogen compounds in the samples varied significantly in DBE and carbon number, and the dominant basic N-containing compounds in these oil samples were N1 class species. $N_1O_1$, $N_1O_2$, and $N_2$ class species with much lower relative abundance were also identified. The composition of basic nitrogen compounds in VGOs and dewaxed VGOs were correlated with increased boiling point and varied in DBE and carbon numbers. The comparison of the analytical results between VGOs and dewaxed VGOs indicated that more basic N-containing compounds in VGO with low carbon number and small molecular weight tend to be removed by solvent refining in lube base oil processing.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.427-430
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• 2002

Recently the subject of "wavelet analysis" has be drawn by both mathematical and engineering application fields such as Signal Processing, Compression/Decomposition, Wavelet-Neural Network, Statistics and etc. Even though its similar to Fourier analysis, wavelet is a versatile tool with much mathematical content and great potential for applications. Especially, wavelet transform uses localizable various mother wavelet functions in time-frequency domain. Therefore, wavelet transform has good time-analysis ability for high frequency component, and has good frequency-analysis ability for low frequency component. Using the discriminative ability is more easy method than other conventional techniques. In this paper, Morlet wavelet transform was applied to discriminate the kind of line fault by acquired data from real power transformation network. The experimental result presented that Morlet wavelet transform is easier,and more useful method than the FFT (Fast Fourier Transform).

• Proceedings of the KIPE Conference
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• 2014.07a
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• pp.150-151
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• 2014

높은 SOC(state-of-charge) 추정알고리즘의 성능을 위해서는 측정된 배터리 단자전압의 정확도가 요구된다. 그렇지만, 예기치 않은 에러로 인해 단자전압에 노이즈 성분이 추가될 경우 SOC 추정성능의 저하를 피할 수 없다. 그러므로, 본 논문에서는 이산 웨이블릿 변환(DWT;discrete wavelet transform)의 다해상도 분석(MRA;multi resolution analysis)의 디노이징(denoising)기법을 적용한 이차전지의 SOC 추정방법을 소개한다. MRA의 시간-주파수 분석을 통해 분해(decomposition)된 저주파 성분(approximation;$A_n$)과 고주파 성분(detail;$D_n$)중 노이즈에 관계된 $D_n$의 고주파 상세 계수(detail coefficient) $d_{j,k}$를 새로이 조정하고 이를 합성(synthesis)하여 디노이징을 마무리 한다. 확장 칼만필터(EKF;extended Kalman filter)의 비교 분석을 통해 제안된 방법의 타당성을 검증한다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38A no.4
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• pp.295-302
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• 2013

In the network coding, throughput can be increased by allowing the transformation of the received data at the intermediate nodes. However, the adversary can obtain more information at the intermediate nodes and make troubles for decoding of transmitted data at the sink nodes by modifying transmitted data at the compromised nodes. In order to resist the adversary activities, various information theoretic or cryptographic secure network coding schemes are proposed. Recently, a secure network coding based on the cryptographic hash function can be used at the random network coding. However, because of the computational resource requirement for cryptographic hash functions, networks with limited computational resources such as sensor nodes have difficulties to use the cryptographic solution. In this paper, we propose a new secure network coding scheme which uses linear transformations and table lookup and safely transmits n-1 packets at the random network coding under the assumption that the adversary can eavesdrop at most n-1 nodes. It is shown that the proposed scheme is an all-or-nothing transform (AONT) and weakly secure network coding in the information theory.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.322-325
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• 2003

In this paper, we propose n new fuzzy model identification of time series system using wavelet transform and genetic DNA code. Generally, it is well known that the DNA coding method is more diverse in the knowledge expression and better in the optimization performance than the genetic algorithm (GA) because it can encode more plentiful genetic information based on the biological DNA. The proposed method can construct a fuzzy model using the wavelet transform, in which the coefficients are identified by the DNA coding method. Thus, we can effectively get the fuzzy model of the nonlinear system by using the advantages of both wavelet transform and DNA coding method. In order to demonstrate the superiority of the proposed method, it is compared with modeling method using the conventional GA.

• Journal of Korean Academy of Oral and Maxillofacial Radiology
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• v.28 no.2
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• pp.339-353
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• 1998

The purpose of this study was to investigate whether a radiographic estimate of osseous fractal dimension and power spectrum of 2D discrete Fourier transform is useful in the characterization of structural changes in bone. Ten specimens of bone were decalcified in fresh 50 ml solutions of 0.1 N hydrochloric acid solution at cummulative timed periods of 0 and 90 minutes. and radiographed from 0 degree projection angle controlled by intraoral parelleling device. I performed one-dimensional variance. fractal analysis of bony profiles and 2D discrete Fourier transform. The results of this study indicate that variance and fractal dimension of scan line pixel intensities decreased significantly in decalcified groups but Fourier spectral analysis didn't discriminate well between control and decalcified specimens.

• Proceedings of the KIEE Conference
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• 2006.04a
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• pp.114-116
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• 2006

This paper is to propose the palm print recognition system using wavelet transform. The palm print is frequently used as the material for the biometric recognition system such as the finger print, iris, face, etc. Since the palm print has lots of properties which include principle line, wrinkles, ridge and so forth, the ways of the implementation of the system are various. In this paper, at first, the palm print image is acquired and then some level of wavelet transform is performed. The coefficients become to be some blocks size of M by N after divided into the horizontal, vertical, diagonal components each level. The mean values, which are calculated with values of each block, are used as the feature vector. To compare between the stored template and the acquired vectors, we adopt the PNN (Probability Neural Network) method.