• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.411-420
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• 2013

We consider fractional Gussian noise and FARIMA sequence with Gaussian innovations and show that the suitably scaled distributions of the FARIMA sequences converge to fractional Gaussian noise in the sense of finite dimensional distributions. Finally, we figure out ACF function and estimate the self-similarity parameter H of FARIMA(0, $d$, 0) by using R/S method.

• JSTS:Journal of Semiconductor Technology and Science
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• v.2 no.1
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• pp.41-48
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• 2002

This paper presents a 18-mW, 2.5-㎓ fractional-N frequency synthesizer with l-bit $4^{th}$-order interpolative delta-sigma ($\Delta{\;}$\sum$)modulator to suppress fractional spurious tones while reducing in-band phase noise. A fractional-N frequency synthesizer with a quadruple prescaler has been designed and implemented in a $0.5-\mu\textrm{m}$ 15-GHz $f_t$ BiCMOS. Synthesizing 2.1 GHzwith less than 200 Hz resolution, it exhibits an in-band phase noise of less than -85 dBc/Hz at 1 KHz offset frequency with a reference spur of -85 dBc and no fractional spurs. The synthesizer also shows phase noise of -139 dBc/Hz at an offset frequency of 1.2 MHz from a 2.1GHz center frequency.

• Journal of IKEEE
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• v.3 no.1 s.4
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• pp.39-49
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• 1999

This paper describes a 1 GHz, low-phase-noise CMOS fractional-N frequency synthesizer with an integrated LC VCO. The proposed frequency synthesizer, which uses a high-order delta-sigma modulator to suppress the fractional spurious tones at all multiples of the fractional frequency resolution offset, has 64 programmable frequency channels with frequency resolution of $f_ref/64$. The measured phase noise is as low as -110 dBc/Hz at a 200 KHz offset frequency from a carrier frequency of 980 MHz. The reference sideband spurs are -73.5 dBc. The prototype is implemented in a $0.5{\mu}m$ CMOS process with triple metal layers. The active chip area is about $4mm^2$ and the prototype consumes 43 mW, including the VCO buffer power consumption, from a 3.3 V supply voltage.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.365-382
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• 2023

In this paper we prove the existence and uniqueness of solution of stochastic fractional neutral differential equations with Gaussian noise or Lévy noise by using the Picard-Lindelöf successive approximation scheme. Further stability results of nonlinear stochastic fractional dynamical system with Gaussian and Lévy noises are established. Examples are provided to illustrate the theoretical results.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.631-648
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• 2019

In this paper, we consider a semilinear stochastic heat equation driven by an additive fractional white noise. Under the pathwise uniqueness property, we establish various strong stability results. As a consequence, we give an application to the convergence of the Picard successive approximation.

• Communications for Statistical Applications and Methods
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• v.17 no.1
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• pp.47-54
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• 2010

By using the white noise theory for fractional Brownian sheet, we give new representations of the Wick integrals of various types with respect to fractional Brownian sheet with Hurst parameters $H_1,H_2{\in}$(0, 1).

• Current Optics and Photonics
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• v.7 no.5
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• pp.557-561
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• 2023

Ultralow-noise soliton pulse generation over a wider Fourier frequency range is highly desirable for many high-precision applications. Here, we realize a low-phase-noise soliton pulse generation by transferring the low phase noise of a mode-locked laser to a silica microcomb. A 21.956-GHz and a 9.9167-GHz Kerr soliton combs are synchronized to a 2-GHz and a 2.5-GHz mode-locked laser through a fractional optoelectronic phase-locked loop, respectively. The phase noise of the microcomb was suppressed by up to ~40 dB at 1-Hz Fourier frequency. This result provides a simple method for low-phase-noise soliton pulse generation, thereby facilitating extensive applications.

• JSTS:Journal of Semiconductor Technology and Science
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• v.8 no.3
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• pp.179-192
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• 2008

A multiphase compensation method with mismatch linearization technique, is presented and demonstrated in a $\Sigma-\Delta$ fractional-N frequency synthesizer. An on-chip delay-locked loop (DLL) and a proposed delay line structure are constructed to provide multiphase compensation on $\Sigma-\Delta$ quantizetion noise. In the delay line structure, dynamic element matching (DEM) techniques are employed for mismatch linearization. The proposed $\Sigma-\Delta$ fractional-N frequency synthesizer is fabricated in a $0.18-{\mu}m$ CMOS technology with 2.14-GHz output frequency and 4-Hz resolution. The die size is 0.92 mm$\times$1.15 mm, and it consumes 27.2 mW. In-band phase noise of -82 dBc/Hz at 10 kHz offset and out-of-band phase noise of -103 dBc/Hz at 1 MHz offset are measured with a loop bandwidth of 200 kHz. The settling time is shorter than $25{\mu}s$.

• Journal of Mechanical Science and Technology
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• v.14 no.9
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• pp.947-955
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• 2000

This paper proposes an optimal design scheme to improve the muffler's capacity of noise reduction of the exhaust system by combining the Taguchi method and a fractional factorial design. As a measuring tool for the performance of a muffler, the performance prediction software which is developed by Oh, Lee and Lee (1996) is used. In the first stage of a design, the length and radius of each component of the current muffler system are selected as control factors. Then, the $L_{18}$ table of orthogonal arrays is adopted to extract the effective main factors. In the second stage, the fractional factorial design is adopted to take interactions into consideration, which the $L_{18}$ table of orthogonal arrays can not consider. For an optimal design, the $L_{27}$ table of orthogonal arrays with main and interaction effects is proposed and the noise factors such as temperature, background noise and humidity are analyzed for more efficient design simultaneously.

• Transactions of the Korean Society of Automotive Engineers
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• v.7 no.5
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• pp.121-129
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• 1999

Recently, the regulations from the govemment and the concems of the people give rise to the interest in exhaust noise of passenger car as much as other vehicles. The exact analysis of various mufflers is needed to reduce the level of exhaust noise. In this paper, we propose a design to improve the mufflers capacity by reducing noise of exhaust system combining Taguchi method and fractional factorial design. In order to measure the performance of a muffler, the performance prediction software which is developed by the Dept. of Automotive Engineering at Hanyang University is used. From the current muffler system we select control factors such as lenght and radius of each component that are thought to be effective on capacity of muffler. Factors are arranged using L18, L27 table of orthogonal array and the fractional factorial design for analysis. We find some significant interaction effects using 1/3 fractional factorial design and accomplish the reduction of noise from the muffler.