• 제어로봇시스템학회논문지
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• 제17권4호
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• pp.289-294
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• 2011

Digital redesign is yet another efficient tool to convert a pre-designed analog controller into a sampled-data one to maintain the analog closed-loop performance in the sense of state matching. A rising difficulty in developing a digital redesign technique for trackers with time-varying references is the unavailability of a closed-form discrete-time model of a system, even if it is linear time-invariant. A way to resolve this is to approximate the time-varying reference as a piecewise constant one, which deteriorates the state matching performance. Another remedy may be to decrease a sampling period, which however could numerically destabilize the optimization-based digital redesign condition. In this paper, we develop a digital redesign condition for time-varying trackers by approximating the time-varying reference through a triangular hold and by introducing delta-operated discrete-time models. It is shown that the digitally redesigned sampled-data tracker recovers the performance of the pre-designed analog tracker under a fast sampling limit. Simulation results on the formation flying of satellites convincingly show the effectiveness of the development.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.137-152
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• 2014

In this paper, we prove, in the spirit of [3, 12, 20, 22, 23], the existence of infinitely many small solutions to the following quasilinear elliptic equation $-{\Delta}_{p(x)}u+{\mid}u{\mid}^{p(x)-2}u={\mid}u{\mid}^{q(x)-2}u+{\lambda}f(x,u)$ in a smooth bounded domain ${\Omega}$ of ${\mathbb{R}}^N$. We also assume that $\{q(x)=p^*(x)\}{\neq}{\emptyset}$, where $p^*(x)$ = Np(x)/(N - p(x)) is the critical Sobolev exponent for variable exponents. The proof is based on a new version of the symmetric mountainpass lemma due to Kajikiya [22], and property of these solutions are also obtained.

• 대한수학회지
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• 제47권4호
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• pp.831-843
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• 2010

Let $\cal{H}$ and $\cal{K}$ be Hilbert spaces and let T, $\tilde{T}$ = T + ${\delta}T$ be bounded operators from $\cal{H}$ into $\cal{K}$. In this article, two facts related to the perturbation bounds are studied. The first one is to find the upper bound of $\parallel\tilde{T}^+\;-\;T^+\parallel$ which extends the results obtained by the second author and enriches the perturbation theory for the Moore-Penrose inverse. The other one is to develop explicit representations of projectors $\parallel\tilde{T}\tilde{T}^+\;-\;TT^+\parallel$ and $\parallel\tilde{T}^+\tilde{T}\;-\;T^+T\parallel$. In addition, some spectral cases related to these results are analyzed.

• 대한수학회지
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• 제57권6호
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• pp.1451-1470
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• 2020

We are concerned with the following elliptic equations: $$\{(-{\Delta})^s_pu={\lambda}f(x,u)\;{\text{in {\Omega}}},\\u=0\;{\text{on {\mathbb{R}}^N{\backslash}{\Omega}},$$ where λ are real parameters, (-∆)^s_p is the fractional p-Laplacian operator, 0 < s < 1 < p < + ∞, sp < N, and f : Ω × ℝ → ℝ satisfies a Carathéodory condition. By applying abstract critical point results, we establish an estimate of the positive interval of the parameters λ for which our problem admits at least one or two nontrivial weak solutions when the nonlinearity f has the subcritical growth condition. In addition, under adequate conditions, we establish an apriori estimate in L^∞(Ω) of any possible weak solution by applying the bootstrap argument.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권1호
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• pp.61-74
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• 2014

This paper presents accurate and efficient numerical methods for calculating the sensitivities of two-asset European options, the Greeks. The Greeks are important financial instruments in management of economic value at risk due to changing market conditions. The option pricing model is based on the Black-Scholes partial differential equation. The model is discretized by using a finite difference method and resulting discrete equations are solved by means of an operator splitting method. For Delta, Gamma, and Theta, we investigate the effect of high-order discretizations. For Rho and Vega, we develop an accurate and robust automatic algorithm for finding an optimal value. A cash-or-nothing option is taken to demonstrate the performance of the proposed algorithm for calculating the Greeks. The results show that the new treatment gives automatic and robust calculations for the Greeks.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.459-468
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• 2011

Let T ${\in}$ L(X), S ${\in}$ L(Y), A ${\in}$ L(X, Y) and B ${\in}$ L(Y, X) such that SA = AT, TB = BS, AB = S and BA = T. Then S and T shares the same local spectral properties SVEP, Bishop's property (${\beta}$), property $({\beta})_{\epsilon}$, property (${\delta}$) and and subscalarity. Moreover, the operators ${\lambda}I$ - T and ${\lambda}I$ - S have many basic operator properties in common.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권3호
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• pp.149-158
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• 2013

In this article, we study the Gauss map of generalized slant cylindrical surfaces (GSCS's) in the 3-dimensional Euclidean space $\mathbb{E}^3$. Surfaces of revolution, cylindrical surfaces and tubes along a plane curve are special cases of GSCS's. Our main results state that the only GSCS's with Gauss map G satisfying ${\Delta}G=AG$ for some $3{\times}3$ matrix A are the planes, the spheres and the circular cylinders.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2006년도 춘계종합학술대회
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• pp.461-465
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• 2006

최근 다수의 외부 장치를 제어하는 운전원 모듈에서는 빈번하게 변하는 신호를 자동적으로 관리하는 시스템을 이용하고 있다. 이러한 모듈들은 높은 신뢰성과 실시간 처리를 필요로 한다. 데이터 들은 매우 용량이 크며, 짧은 보고 주기, 비동기적인 보고 시간을 가진다. 시스템에 가장 일반적으로 사용되는 질의는 최신의 값을 검색하는 현재질의, 과거 특정시점의 값을 검색하는 스냅샷 질의, 과거부터 현재까지의 값들을 검색하는 이력 질의 등이 있다. 이 논문에서는 QNX 운영체제에서 파일 구조화된 데이터베이스를 이용하여 위와 같은 신호들을 효율적으로 관리하는 기법을 제안하고자한다. 장치들 간의 데이터 통신은 Profibus-FMS 프로토콜을 이용하며, 모니터 주기를 자유롭게 설정하거나 데이터를 저장하기 위해 파일 데이터베이스를 이용한다. 파일 데이터베이스는 QNX COM의 적은 저장장치, 낮은 계산 능력을 감안하여 델타버젼과 주기적 백업 등의 방법을 도입한다.

• The Journal of Advanced Prosthodontics
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• 제10권3호
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• pp.252-258
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• 2018

PURPOSE. The purpose of this study was to evaluate the repeatability and matching accuracy between two identical intraoral spectrophotometers. MATERIALS AND METHODS. The maxillary right central incisor, canine, and mandibular left central incisor of each of 30 patients were measured using 2 identical intraoral spectrophotometers with different serial numbers (EasyShade V). The color of each shade tab from 3 shade guides (VITA 3D-Master) was also determined with both devices. All measurements were performed by a single operator. Statistical analyses were performed to verify the repeatability, accuracy, and the differences between the devices with paired t-tests, one-way ANOVA, and intra-class correlation coefficients (ICCs) (${\alpha}=.05$). RESULTS. A high level of measurement repeatability (ICC>0.90) among $L^*$, $a^*$, and $b^*$ color components was observed within and between devices (P<.001). Intra-device matching agreement rates were 80.00% and 81.11%, respectively, while inter-device matching agreement rate was 51.85%. ANOVA revealed no significant different color values within each device, while paired t-test provided significant different color values between both devices. The CIEDE2000 color differences between both devices were $2.28{\pm}1.61$ ${\Delta}E_{00}$ for in-vivo readings. Regarding the clinical matching accuracy of both devices, ${\Delta}E_{00}$ values between teeth and matching shade tabs were $3.05{\pm}1.19$ and $2.86{\pm}1.02$, respectively. CONCLUSION. Although two EasyShade V devices with different serial numbers show high repeatability of CIE $L^*$, $a^*$, and $b^*$ measurements, they could provide different color values and shade for the same tooth.

• 대한수학회지
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• 제57권3호
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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(${\bar{\Omega}}$).