• Korean Journal of Mathematics
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• v.24 no.2
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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.

• Journal of the Ergonomics Society of Korea
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• v.32 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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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 ${\mathbf{Z}}_p$.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.467-474
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• 2022

In this article, we consider the integral operator 𝓒^b,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 𝓒^b,c operators on Bloch spaces.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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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).

• Proceedings of the KIEE Conference
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• 2005.10b
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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).

• Honam Mathematical Journal
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• v.26 no.3
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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 $H^2({\beta})$.

• Nuclear Engineering and Technology
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• v.50 no.4
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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.

• Journal of Korean Society for Quality Management
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• v.32 no.4
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.7
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• pp.881-886
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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 tile 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 tile digitally controlled system are formulated in terms of linear matrix inequalities (LMIs). Finally, a TS fuzzy model for the chaotic Lorentz system is used as an example to guarantee the stability and effectiveness of the proposed method.