• 제목/요약/키워드: Power series of operators

검색결과 19건 처리시간 0.024초

SOME TRACE INEQUALITIES FOR CONVEX FUNCTIONS OF SELFADJOINT OPERATORS IN HILBERT SPACES

  • Dragomir, Silvestru Sever
    • Korean Journal of Mathematics
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    • 제24권2호
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    • pp.273-296
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    • 2016
  • Some new trace inequalities for convex functions of self-adjoint operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated. Some trace inequalities for matrices are also derived. Examples for the operator power and logarithm are presented as well.

A Study on a Trend of Human Error Types Observed in a Simulated Computerized Nuclear Power Plant Control Room

  • Lee, Dhong Ha
    • 대한인간공학회지
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    • 제32권1호
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    • pp.9-16
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    • 2013
  • Objective: The aim of this study is to investigate a trend of human error types observed in a series of verification and validation experiments for an Advanced Control Room(ACR) equipped with Lager Display Panel(LDP), Work Station Flat Panel Display(WS FPD), list type Alarm System(AS), Soft Control(SC) and Computerized Procedure System(CPS). Background: Operator behaviors in a fully computerized control room are quite different from those in a traditional hard-wired control room. Operators in an ACR all together monitor plant status and variables through their own interface system such as LDP and WS FPD, are notified of abnormal plant status through their own list type AS, control the plant through their own SC, and follow the structured procedure through their own CPS whereas operators in a traditional control room only separately do their duty directed by their supervisor. Especially the secondary task such as manipulating the user interface of ACR can be an extra burden to all the operators including the supervisor. Method: The Reason's human error classification method was applied to operators' behavioral data collected from a series of verification and validation experiments where operators showed their plant operational behaviors under a couple of harsh scenarios using the ACR simulator. Results: As operators accustomed to the new ACR system, knowledge or rule based mistakes appearing frequently in the early series of experiments decreased drastically in the latest stage of the series. Slip and lapse types of errors were observed throughout the series of experiments. Conclusion: Education and training can be one of the most important factors for the operators accustomed to the traditional control room to be adapted to the new system and to run the ACR successfully. Application: The results of this study implied that knowledge or rule based mistakes can be reduced by training and education but that lapse type errors might be reduced only through innovative improvement in human-system interface design or teamwork culture design including a new leadership style suitable for ACR.

CARTIER OPERATORS ON COMPACT DISCRETE VALUATION RINGS AND APPLICATIONS

  • Jeong, Sangtae
    • 대한수학회지
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    • 제55권1호
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    • pp.101-129
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    • 2018
  • From an analytical perspective, we introduce a sequence of Cartier operators that act on the field of formal Laurent series in one variable with coefficients in a field of positive characteristic p. In this work, we discover the binomial inversion formula between Hasse derivatives and Cartier operators, implying that Cartier operators can play a prominent role in various objects of study in function field arithmetic, as a suitable substitute for higher derivatives. For an applicable object, the Wronskian criteria associated with Cartier operators are introduced. These results stem from a careful study of two types of Cartier operators on the power series ring ${\mathbf{F}}_q$[[T]] in one variable T over a finite field ${\mathbf{F}}_q$ of q elements. Accordingly, we show that two sequences of Cartier operators are an orthonormal basis of the space of continuous ${\mathbf{F}}_q$-linear functions on ${\mathbf{F}}_q$[[T]]. According to the digit principle, every continuous function on ${\mathbf{F}}_q$[[T]] is uniquely written in terms of a q-adic extension of Cartier operators, with a closed-form of expansion coefficients for each of the two cases. Moreover, the p-adic analogues of Cartier operators are discussed as orthonormal bases for the space of continuous functions on ${\mathbf{Z}}_p$.

BOUNDEDNESS OF 𝓒b,c OPERATORS ON BLOCH SPACES

  • Nath, Pankaj Kumar;Naik, Sunanda
    • Korean Journal of Mathematics
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    • 제30권3호
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    • pp.467-474
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    • 2022
  • In this article, we consider the integral operator 𝓒b,c, which is defined as follows: $${\mathcal{C}}^{b,c}(f)(z)={\displaystyle\smashmargin{2}{\int\nolimits_{0}}^z}{\frac{f(w)*F(1,1;c;w)}{w(1-w)^{b+1-c}}}dw,$$ where * denotes the Hadamard/ convolution product of power series, F(a, b; c; z) is the classical hypergeometric function with b, c > 0, b + 1 > c and f(0) = 0. We investigate the boundedness of the 𝓒b,c operators on Bloch spaces.

Julia operators and linear systems

  • Yang, Mee-Hyea
    • 대한수학회논문집
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    • 제12권4호
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    • pp.895-904
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    • 1997
  • Let B(z) be a power series with operator coefficients where multiplication by B(z), T, is a contractive and everywhere defined transforamtion in the square summable power series. Then there is a Julia operator U for T such that $$ U = (T D)(\tilde{D}^* L) \in B(H \oplus D, K \oplus \tilde{D}), $$ where D is the state space of a conjugate canonical linear system with transfer function B(z).

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Power Series를 이용한 불확실성을 포함된 비선형 시스템의 지능형 디지털 재설계 (Intelligent Digital Redesign of Uncertain Nonlinear Systems Using Power Series)

  • 성화창;주영훈;박진배;김도완
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 2005년도 학술대회 논문집 정보 및 제어부문
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    • pp.496-498
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    • 2005
  • This paper presents intelligent digital redesign method of global approach for hybrid state space fuzzy-model-based controllers. For effectiveness and stabilization of continuous-time uncertain nonlinear systems under discrete-time controller, Takagi-Sugeno(TS) fuzzy model is used to represent the complex system. And global approach design problems viewed as a convex optimization problem that we minimize the error of the norm bounds between nonlinearly interpolated linear operators to be matched. Also by using the power series, we analyzed nonlinear system's uncertain parts more precisely. When a sampling period is sufficiently small, the conversion of a continuous-time structured uncertain nonlinear system to an equivalent discrete-time system have proper reason. Sufficiently conditions for the global state-matching of the digitally controlled system are formulated in terms of linear matrix inequalities (LMIs).

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ON THE HILBERT SPACE OF FORMAL POWER SERIES

  • YOUSEFI, Bahman;SOLTANI, Rahmat
    • 호남수학학술지
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    • 제26권3호
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    • pp.299-308
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    • 2004
  • Let $\{{\beta}(n)\}^{\infty}_{n=0}$ be a sequence of positive numbers such that ${\beta}(0)=1$. We consider the space $H^2({\beta})$ of all power series $f(z)=^{Po}_{n=0}{\hat{f}}(n)z^n$ such that $^{Po}_{n=0}{\mid}{\hat{f}}(n){\mid}^2{\beta}(n)^2<{\infty}$. We link the ideas of subspaces of $H^2({\beta})$ and zero sets. We give some sufficient conditions for a vector in $H^2({\beta})$ to be cyclic for the multiplication operator $M_z$. Also we characterize the commutant of some multiplication operators acting on $H^2({\beta})$.

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Application of ecological interface design in nuclear power plant (NPP) operator support system

  • Anokhin, Alexey;Ivkin, Alexey;Dorokhovich, Sergey
    • Nuclear Engineering and Technology
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    • 제50권4호
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    • pp.619-626
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    • 2018
  • Most publications confirm that an ecological interface is a very efficient tool to supporting operators in recognition of complex and unusual situations and in decision-making. The present article describes the experience of implementation of an ecological interface concept for visualization of material balance in a drum separator of RBMK-type NPPs. Functional analysis of the domain area was carried out and revealed main factors and contributors to the balance. The proposed ecological display was designed to facilitate execution of the most complicated cognitive operations, such as comparison, summarizing, prediction, etc. The experimental series carried out at NPPs demonstrated considerable reduction of operators' mental load, time of reaction, and error rate.

최대 시스템 신뢰도를 위한 최적 중복 설계: 유전알고리즘에 의한 접근 (Optimum redundancy design for maximum system reliability: A genetic algorithm approach)

  • 김재윤;신경석
    • 품질경영학회지
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    • 제32권4호
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    • pp.125-139
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    • 2004
  • Generally, parallel redundancy is used to improve reliability in many systems. However, redundancy increases system cost, weight, volume, power, etc. Due to limited availability of these resources, the system designer has to maximize reliability subject to various constraints or minimize resources while satisfying the minimum requirement of system reliability. This paper presents GAs (Genetic Algorithms) to solve redundancy allocation in series-parallel systems. To apply the GAs to this problem, we propose a genetic representation, the method for initial population construction, evaluation and genetic operators. Especially, to improve the performance of GAs, we develop heuristic operators (heuristic crossover, heuristic mutation) using the reliability-resource information of the chromosome. Experiments are carried out to evaluate the performance of the proposed algorithm. The performance comparison between the proposed algorithm and a pervious method shows that our approach is more efficient.

Powrer Series를 이용한 불확실성을 갖는 비선형 시스템의 지능형 디지털 재설계 (Intelligent Digital Redesign for Uncertain Nonlinear Systems Using Power Series)

  • 성화창;박진배;고성현;주영훈
    • 한국지능시스템학회논문지
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    • 제15권7호
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    • pp.881-886
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    • 2005
  • 본 논문은 복합 상태 공간에서의 피지 기반 제어기를 이용한 지능형 디지털 재설계의 전 역적 접근 방안에 대해 제안하고자 한다. 이산화를 통한 제어기 설계에 있어서 불확실성이 포함된 실시간 비선형 시스템에 대해 보다 효율적이고 안정적인 접근을 위해 TS 퍼지 모델이 사용되었다. 그리고 전 역적 접근을 위한 방안으로서 문제를 볼록 최적화 관점으로 변환 후, 에러가 가질 수 있는 놈의 영역을 최소화하여 상태 접합을 이루고자 하였다. 또한 power series를 사용함으로써 불확실성이 조합된 비선형 시스템을 보다 더 정확하게 분석하였다. 샘플링 기간이 충분히 작다면, 불확실 비선형 시스템의 실시간 시스템으로의 전환이 충분한 이유를 가지게 된다. 전 역적 접근을 통한 디지털로 제어된 시스템은 선형 행렬 부등식 형태로 바꾸어 시스템의 안정성을 보장하고자 하였다. 마지막으로 TS 퍼지 모델로 분석된 혼돈 Lorenz System에 적용함으로써 제안된 방법의 안정성과 효율성을 보장받게 된다.