• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.689-695
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• 2014

Let M be an N-function satisfies the ${\Delta}_2$-condition and let $O_M$ be the Orlicz space associated with M. Let $C(O_M)$ be the space of all continuous functions defined on the interval [0, T] with values in $O_M$. In this note, we define the analogue of Wiener measure $m^M_{\phi}$ on $C(O_M)$, establish the Wiener integration formulae for the cylinder functions on $C(O_M)$ and give some examples related to our formulae.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.609-631
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• 2021

Let C[0, T] denote a generalized analogue of Wiener space, the space of real-valued continuous functions on the interval [0, T]. Define $Z_{\vec{e},n}$ : C[0, T] → ℝⁿ⁺¹ by $$Z_{\vec{e},n}(x)=\(x(0),\;{\int}_0^T\;e_1(t)dx(t),{\cdots},\;{\int}_0^T\;e_n(t)dx(t)\)$$, where e₁,…, e_n are of bounded variations on [0, T]. In this paper we derive a simple evaluation formula for Radon-Nikodym derivatives similar to the conditional expectations of functions on C[0, T] with the conditioning function $Z_{\vec{e},n}$ which has an initial weight and a kind of drift. As applications of the formula, we evaluate the Radon-Nikodym derivatives of various functions on C[0, T] which are of interested in Feynman integration theory and quantum mechanics. This work generalizes and simplifies the existing results, that is, the simple formulas with the conditioning functions related to the partitions of time interval [0, T].

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.703-715
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• 2006

Recently, we proved the existence theorem of measure-valued Feynman-Kac formula and showed that it satisfied Volterra's integral equation. In this paper, we establish the operational calculus for a measure-valued Dyson series and give some examples related to the measure-valued Dyson series.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.465-475
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• 1996

Fix t > 0. Denote by $C^t$ the space of $R$-valued continuous functions x on [0,t]. Let $C_0^t$ be the Wiener space - $C_0^t = {x \in C^t : x(0) = 0}$ - equipped with Wiener measure m. Let F be a function from $C^t to C$.

• The Journal of the Korea institute of electronic communication sciences
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• v.8 no.9
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• pp.1293-1298
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• 2013

This paper proposes a noise reduction algorithm using Wiener filter to remove the noise components from the noisy speech in order to improve the speech signal. The proposed algorithm first removes the noise spectrums of white noise from the noisy signal based on the noise reshaping and reduction method at each frame. And this algorithm enhances the speech signal using Wiener filter based on linear predictive coding analysis. In this experiment, experimental results of the proposed algorithm demonstrate using the speech and noise data by Japanese male speaker. Based on measuring the spectral distortion (SD) measure, experiments confirm that the proposed algorithm is effective for the speech by contaminated white noise. From the experiments, the maximum improvement in the output SD values was 4.94 dB better for white noise compared with former Wiener filter.

• Journal of Broadcast Engineering
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• v.16 no.5
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• pp.883-893
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• 2011

In this paper, we propose a novel focus measure that determines in-focus and out-of-focus region in an image. In addition, we achieved extended depth of field by blending the acquired image and Wiener filtered image using a decision map based on the designed focus measure. Since conventional focus measures are based on the amount of high frequency components in an acquired image, the measures may not be accurate if there exist high frequency components in out-of-focused region. To overcome the problem, we designed the novel focus measure based on effective band pass filtering. In simulations and experiments, the proposed method showed better performance than existing methods.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.413-431
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• 2012

Let $C^r[0,t]$ be the function space of the vector-valued continuous paths $x:[0,t]{\rightarrow}\mathbb{R}^r$ and define $X_t:C^r[0,t]{\rightarrow}\mathbb{R}^{(n+1)r}$ and $Y_t:C^r[0,t]{\rightarrow}\mathbb{R}^{nr}$ by $X_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}),\;x(t_n))$ and $Y_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}))$, respectively, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n=t$. In the present paper, using two simple formulas for the conditional expectations over $C^r[0,t]$ with the conditioning functions $X_t$ and $Y_t$, we establish evaluation formulas for the analogue of the conditional analytic Fourier-Feynman transform for the function of the form $${\exp}\{{\int_o}^t{\theta}(s,\;x(s))\;d{\eta}(s)\}{\psi}(x(t)),\;x{\in}C^r[0,t]$$ where ${\eta}$ is a complex Borel measure on [0, t] and both ${\theta}(s,{\cdot})$ and ${\psi}$ are the Fourier-Stieltjes transforms of the complex Borel measures on $\mathbb{R}^r$.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.505-512
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• 2015

In this note we find the upper bound for ${\rho}(u^n,M)=\int_{0}^{T}\int_{0}^{{\mid}u(t){\mid}^n}p(s)dsdt$ and show that $F(y)=y^n$ is $m_{\phi}^M$-Bochner integrable on $C(\mathcal{O} _M)$ for $0{\leq}t{\leq}T$ when $\int_{\mathcal{O}_M}{\parallel}u_0{\parallel}_M^nd{\phi}(u_0)$ is finite.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.461-489
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• 2006

In this article, we establish the existence theorem for measure-valued Dyson series and show that it satisfies the Volterra-type integral equation. Furthermore, we prove the stability theorems for measure-valued Dyson series.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.615-622
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• 2005

In this paper, we discuss the average case errors of some numerical quadratures, namely Trapezoidal and Simpson's, in the numerical integration problem. Our integrands are r-fold Wiener functions from the interval [0,1] and only at finite number of points the function values are evaluated. We study average case errors of these quadratures theoretically and then compare it with our practical (a posteriori) researches. Monte-Carlo simulation is used to perform these empirical researches. Finally we empirically compute the error bounds of studied quadratures for the higher degrees of Wiener functions.