• JSTS:Journal of Semiconductor Technology and Science
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• 제8권3호
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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 $25{\mu}s$.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.435-450
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• 2024

This study depends on the modified conformable fractional derivative definition to generalize and proves some theorems of the classical power series into the fractional power series. Furthermore, a comprehensive formulation of the generalized Taylor's series is derived within this context. As a result, a new technique is introduced for the fractional power series. The efficacy of this new technique has been substantiated in solving some fractional differential equations.

• 응용통계연구
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• 제11권2호
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• pp.303-315
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• 1998

요인실험에서 어떤 처리조합은 조작상 또는 경제적인 이유로 실험할 수 없는 경우가 있다. 이러한 실험불가능한 처리조합을 포함하고 있는 일부실시법은 불균형적인 처리조합을 구성하게 되어 어떤 요인효과에 대해 추론할 수 없게 된다. 본 논문은 실험불가능한 처리조합을 포함하지 않는 3$^{n-p}$ 일부실시법을 실행하기 위한 정의 대비의 선택 방법을 논한다한다

• 대한수학회지
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• 제58권6호
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• pp.1449-1460
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• 2021

In this paper, we consider the following nonlocal fractional Laplacian equation with a singular nonlinearity (-∆)^su(x) = λu^β (x) + a₀u^-γ (x), x ∈ ℝⁿ, where 0 < s < 1, γ > 0, $1<{\beta}{\leq}\frac{n+2s}{n-2s}$, λ > 0 are constants and a₀ ≥ 0. We use a direct method of moving planes which introduced by Chen-Li-Li to prove that positive solutions u(x) must be radially symmetric and monotone increasing about some point in ℝⁿ.

• Journal of the Korean Statistical Society
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• 제25권2호
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• pp.277-288
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• 1996

The minimum aberration criterion is commonly used for selecting good fractional factorial designs. In this paper we give same necessary conditions for $3^{n-k}$ fractional factorial designs. We obtain minimum aberration $3^{n-k}$ designs for k = 2 and any n. For k > 2, minimum aberration designs have not found yet. As an alternative, we select a design with minimum aberration among minimum-variance designs.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.181-191
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• 2006

In this paper, multiobjective generalized fractional programming problems with set functions are considered, in which objective functions are maximum of finite fractional set functions. At first, optimality conditions are established. Then, saddle existence theorem is proved.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.281-292
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• 2007

A pair of symmetric fractional variational programming problems is formulated over cones. Weak, strong, converse and self duality theorems are discussed under pseudoinvexity. Static symmetric dual fractional programs are included as special case and corresponding symmetric duality results are merely stated.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.793-809
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• 2021

This paper gives sufficient conditions to ensure the existence and stability of solutions for generalized nonlinear fractional integrodifferential equations of order α (1 < α < 2). The main theorem asserts the stability results in a weighted Banach space, employing the Krasnoselskii's fixed point technique and the existence of at least one mild solution satisfying the asymptotic stability condition. Two examples are provided to illustrate the theory.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.1035-1044
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• 2021

Existence and uniqueness results for solutions of system of Riemann-Liouville (R-L) fractional differential equations with initial time difference are obtained. Monotone technique is developed to obtain existence and uniqueness of solutions of system of R-L fractional differential equations with initial time difference.

• 한국전자파학회논문지
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• 제28권12호
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• pp.941-947
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• 2017

본 논문에서는 $0.35{\mu}m$ CMOS 공정으로 FRS 대역 무전기용 반송파 신호를 쿼드러쳐(Quadrature) 형식으로 출력하는 Fractional-N 위상 고정루프(PLL) 주파수 합성기를 설계 및 제작하였다. 설계한 주파수 합성기의 주요 블록은 전압 제어 발진기(VCO), 전하 펌프(CP), 루프 필터(LF), 위상 주파수 검출기(PFD) 그리고 주파수 분주기이다. VCO는 우수한 위상잡음과 전력 특성을 얻을 수 있는 LC 공진 방식으로 설계했고, CP는 참조 주파수에 따라 펌핑 전류를 조절할 수 있도록 설계하였다. 주파수 분주기는 16분주의 전치 분주기와 3차 델타-시그마 모듈레이터($3^{rd}$ DSM) 방식의 Fractional-N 분주기로 설계하였다. LF는 외부의 3차 RC 루프 필터로 구성하였다. 측정결과, 주파수 합성기의 동작 주파수 영역은 최소 460 MHz에서 최대 510 MHz이고, 출력전력으로는 약 -3.86 dBm을 얻었다. 출력의 위상잡음은 100 Hz offset 주파수에서 -94.8 dBc/Hz이며 위상 루프 고착 시간은 약 $300{\mu}s$이다.