• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1297-1314
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• 2019

In this work, we investigate the following fractional boundary value problems $$\{_tD^{\alpha}_T({\mid}_0D^{\alpha}_t(u(t)){\mid}^{p-2}_0D^{\alpha}_tu(t))\\={\nabla}W(t,u(t))+{\lambda}g(t){\mid}u(t){\mid}^{q-2}u(t),\;t{\in}(0,T),\\u(0)=u(T)=0,$$ where ${\nabla}W(t,u)$ is the gradient of W(t, u) at u and $W{\in}C([0,T]{\times}{\mathbb{R}}^n,{\mathbb{R}})$ is homogeneous of degree r, ${\lambda}$ is a positive parameter, $g{\in}C([0,T])$, 1 < r < p < q and ${\frac{1}{p}}<{\alpha}<1$. Using the Fibering map and Nehari manifold, for some positive constant ${\lambda}_0$ such that $0<{\lambda}<{\lambda}_0$, we prove the existence of at least two non-trivial solutions

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.151-184
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• 2022

In the article, we handle with the existence and controllability results for fractional impulsive neutral functional integro-differential equation in Banach spaces. We have used advanced phase space definition for infinite delay. State dependent infinite delay is the main motivation using advanced version of phase space. The results are acquired using Schaefer's fixed point theorem. Examples are given to illustrate the theory.

• JSTS:Journal of Semiconductor Technology and Science
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• v.16 no.1
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• pp.143-146
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• 2016

A new area-efficient multi-phase clock frequency multiplier is presented. The proposed fractional-ratio frequency multiplying DLL (FFMDLL) is implemented in a 65 nm CMOS process and occupies an active area of just $0.01mm^2$. The proposed FFMDLL provides 8-phase output clocks and achieves a frequency range of 0.6-1.0 GHz with programmable multiplication ratios of N/M, where N = 4, 5, 8, 10 and M = 1, 2, 3. It achieves an effective peak-to-peak jitter of 5 ps and dissipates 3.4 mW from a 1.0 V supply at 1 GHz.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.5
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• pp.889-895
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• 2008

In this paper a Fractional-N frequency synthesizer is designed for UHF RFID readers. It satisfies the ISO/IEC frequency band($860{\sim}960MHz$) and is also applicable to mobile RFID readers. A VCO is designed to operate at 1.8GHz band such that the LO pulling effect is minimized. The 900MHz differential I/Q LO signals are obtained by dividing the differential signal from an integrated 1.8GHz VCO. It is designed using a $0.18{\mu}m$ RF CMOS process. The measured results show that the designed circuit has a phase noise of -103dBc/Hz at 100KHz offset and consumes 9mA from a 1.8V supply. The channel switching time of $10{\mu}s$ over 5MHz transition have been achieved, and the chip size including PADs is $1.8{\times}0.99mm^2$.

• Journal of the military operations research society of Korea
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• v.3 no.1
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• pp.97-107
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• 1977

This report examines several models, such as random or area bombardment, salvo fire and pattern fire, for the computation of target coverage when multiple rounds are fired at a target. Fractional kill of a fragment sensitive target by a fragmenting projectile as a function of the number of rounds fired is compared for two salvo fire models. The first is a standard salvo fire model in which N rounds are fired at the same aim point, in the second model single kill probability is computed for a fragment sensitive target and then fractional kill from the firing of N rounds is computed according to the assumption that the effects of each round are independent. Because the method of solution becomes very laborious for large patterns, this report gives a method only for the case of evaluating the effectiveness of stick and trianglar pattern fire. The need for the sophisticated and complicated target coverage models is demonstrated by the results of computations performed in this report.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.2
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• pp.526-533
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• 1996

In this paper, the 800 MHz band N fractional frquency synthesizer having 677 channel with 30 kHz channel bandwidth is designed on the based on the theory which is dervied in terms of the relation between reference freqiency and the number of channels, loop bandwidth and acquistion time. The experimental resuls show 10 Hz deviation from the bandwidth and acquisition time. The experimental results show 10 Hz deviation from the bandwidth, the spurious suppression of aroud -45 dBc and the acqusition time of 1.44 ms. The results satisfy the given specification, but don't achieve thebesired spurious -60 dBc suppression. It is found that 500 hop per second will be possible over the range from 800 to 820 MHz.

• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.303-309
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• 2024

An imaginary bicyclic biquadratic number field K is a field of the form ${\mathbb{Q}}({\sqrt{-m}},{\sqrt{-n}})$ where m and n are squarefree positive integers. The ideal class number h_K of K is the order of the abelian group I_K/P_K, where I_K and P_K are the groups of fractional and principal fractional ideals in the ring of integers 𝒪_K of K, respectively. This provides a measure on how far is 𝒪_K from being a PID. We determine all imaginary bicyclic biquadratic number fields with class number 5. We show there are exactly 243 such fields.

• Proceedings of the IEEK Conference
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• 2000.06b
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• pp.5-8
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• 2000

This paper proposes GaN film as a piezoelectric material for SAW(surface acoustic wave) filters. The fabricated GaN SAW filter exhibited a very high velocity of 5800 ㎧and relatively low insertion loss of -9.9 dB without matching circuit. From Smith's equivalent circuit model, the calculated electromechanical coupling factor (K$^2$) was about 4.$\pm$03％. which is larger than those obtained from other thin film piezoelectric materials and allows the realization of wider filter fractional bandwidths.

• The KIPS Transactions:PartC
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• v.11C no.5
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• pp.621-632
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• 2004

Recent measurement studies of real teletraffic data in modern telecommunication networks have shown that self-similar (or fractal) processes may provide better models of teletraffic in modern telecommunication networks than Poisson processes. If this is not taken into account, it can lead to inaccurate conclusions about performance of telecommunication networks. Thus, an important requirement for conducting simulation studies of telecommunication networks is the ability to generate long synthetic stochastic self-similar sequences. A new generator of pseu-do-random self-similar sequences, based on the fractional Gaussian nois and a wavelet transform, is proposed and analysed in this paper. Specifically, this generator uses Daubechies wavelets. The motivation behind this selection of wavelets is that Daubechies wavelets lead to more accurate results by better matching the self-similar structure of long range dependent processes, than other types of wavelets. The statistical accuracy and time required to produce sequences of a given (long) length are experimentally studied. This generator shows a high level of accuracy of the output data (in the sense of the Hurst parameter) and is fast. Its theoretical algorithmic complexity is 0(n).

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.747-775
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• 2020

In this work we investigate the nonlocal elliptic equation with critical Hardy-Sobolev exponents as follows, $$(P)\;\{(-{\Delta}_p)^su={\lambda}{\mid}u{\mid}^{q-2}u+{\frac{{\mid}u{\mid}^{p{^*_s}(t)-2}u}{{\mid}x{\mid}^t}}{\hspace{10}}in\;{\Omega},\\u=0{\hspace{217}}in\;{\mathbb{R}}^N{\backslash}{\Omega},$$ where Ω ⊂ ℝ^N is an open bounded domain with Lipschitz boundary, 0 < s < 1, λ > 0 is a parameter, 0 < t < sp < N, 1 < q < p < p^∗_s where $p^*_s={\frac{N_p}{N-sp}}$, $p^*_s(t)={\frac{p(N-t)}{N-sp}}$, are the fractional critical Sobolev and Hardy-Sobolev exponents respectively. The fractional p-laplacian (-∆_p)^su with s ∈ (0, 1) is the nonlinear nonlocal operator defined on smooth functions by $\displaystyle(-{\Delta}_p)^su(x)=2{\lim_{{\epsilon}{\searrow}0}}\int{_{{\mathbb{R}}^N{\backslash}{B_{\epsilon}}}}\;\frac{{\mid}u(x)-u(y){\mid}^{p-2}(u(x)-u(y))}{{\mid}x-y{\mid}^{N+ps}}dy$, x ∈ ℝ^N. The main goal of this work is to show how the usual variational methods and some analysis techniques can be extended to deal with nonlocal problems involving Sobolev and Hardy nonlinearities. We also prove that for some α ∈ (0, 1), the weak solution to the problem (P) is in C^1,α(${\bar{\Omega}}$).