• 대한수학회보
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• 제41권3호
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• pp.573-587
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• 2004

Disentangling is the essential operation of Feynman's operational calculus for noncommuting operators. Thus formulas which simplify this operation are central to the subject. In a recent paper the procedure for 'extracting a linear factor' has been established in the setting of Feynman's operational calculus for time independent operators $A_1, ... , A_n$ and associated probability measures ${\mu}_1,..., {\mu}_n$. While the setting just described is natural in many circumstances, it is not natural for evolution problems. There the measures should not be restricted to probability measures and it is worthwhile to allow the operators to depend on time. The main purpose for this paper is to extend the procedure for extracting a linear factor to this latter setting. We should mention that Feynman's primary motivation for developing an operational calculus for noncommuting operators came from a desire to describe the evolution of certain quantum systems.m systems.

• 시스템엔지니어링학술지
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• 제6권1호
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• pp.47-52
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• 2010

Human Factors Engineering (HFE) for Main Control Room (MCR) of Nuclear Power Plant (NPP) has been applied to optimize the design and operation of Man-Machine Interface (MMI) between operators and their equipment in consideration of physical, psychological and cognitive aspects. However, it has been observed that operators complain about environmental discomfort in the MCR since the operators in the MCR experience excessive stress due to the environmental factors such as inappropriate interior and lighting system. Since the HFE is an essential factor for the high fidelity performance of operators in the MCR, the adequate MCR environment design with HFE rules and guidelines is as much important to enhance the operability and reliability of the MCRs. Therefore, there has been a strong need to design a pleasant environment for the MCR to improve human performance of the operators.

• 대한수학회논문집
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• 제33권4호
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• pp.1125-1140
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• 2018

Let A be a normed space, ${\mathcal{B}}(A)$ the algebra of all bounded operators on A, and V a family of strongly upper semicontinuous functions from a Hausdorff completely regular space X into ${\mathcal{B}}(A)$. In this paper, we investigate some properties of the weighted spaces CV (X, A) of all A-valued continuous functions f on X such that the mapping $x{\mapsto}v(x)(f(x))$ is bounded on X, for every $v{\in}V$, endowed with the topology generated by the seminorms ${\parallel}f{\parallel}v={\sup}\{{\parallel}v(x)(f(x)){\parallel},\;x{\in}X\}$. Our main purpose is to characterize continuous, bounded, and locally equicontinuous weighted composition operators between such spaces.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.931-938
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• 2010

The disentangling map from the commutative algebra to the noncommutative algebra of operators is the essential operation of Feynman's operational calculus for noncommuting operators. Thus formulas which simplify this operation are meaningful to the subject. In a recent paper the procedure for "methods for iterative disentangling" has been established in the setting of Feynman's operational calculus for time independent operators $A_1$, $\cdots$, $A_n$ and associated probability measures${\mu}_1$, $\cdots$, ${\mu}_n$. The main purpose for this paper is to extend the procedure for methods for iterative disentangling to time dependent operators.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.345-353
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• 2015

Subnormality of bounded weighted composition operators on $L^2({\Sigma})$ of the form $Wf=uf{\circ}T$, where T is a nonsingular measurable transformation on the underlying space X of a ${\sigma}$-finite measure space (X, ${\Sigma}$, ${\mu}$) and u is a weight function on X; is studied. The standard moment sequence characterizations of subnormality of weighted composition operators are given. It is shown that weighted composition operators are subnormal if and only if $\{J_n(x)\}^{+{\infty}}_{n=0}$ is a moment sequence for almost every $x{{\in}}X$, where $J_n=h_nE_n({\mid}u{\mid}^2){\circ}T^{-n}$, $h_n=d{\mu}{\circ}T^{-n}/d{\mu}$ and $E_n$ is the conditional expectation operator with respect to $T^{-n}{\Sigma}$.

• 한국항해항만학회지
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• 제29권2호
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• pp.141-146
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• 2005

For a long time, genetic algorithms have been recognized as a new method to solve difficult and complex problems and the performance of genetic algorithms depends on genetic operators, especially crossover operator. Various problems like the traveling salesman problem, the transportation problem or the job shop problem, in logistics engineering can be modeled as a sequencing problem This paper proposes modified genetic crossover operators to be used at various sequencing problems and uses the traveling salesman problem to be applied to a real world problem like the delivery problem and the vehicle routing problem as a benchmark problem Because the proposed operators use parental information as well as network information, they could show better efficiency in performance and computation time than conventional operators.

• East Asian mathematical journal
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• 제18권1호
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• pp.111-125
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• 2002

Many different families of infinite series were recently observed to be summable in closed forms by means of certain operators of fractional calculus(that is, calculus of integrals and derivatives of any arbitrary real or complex order). In this sequel to some of these recent investigations, the authors present yet another instance of applications of certain fractional calculus operators. Alternative derivations without using these fractional calculus operators are shown to lead naturally a family of analogous infinite sums involving hypergeometric functions.

• Journal of Electrical Engineering and Technology
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• 제9권2호
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• pp.749-754
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• 2014

In this paper, we suggest tree-structure-aware GP (Genetic Programming) operators that heed tree distributions in structure space and their possible structural difficulties. The main idea of the proposed GP operators is to place the generated offspring of crossover and/or mutation in a specified region of tree structure space insofar as possible by biasing the tree structures of the altered subtrees, taking into account the observation that most solutions are found in that region. To demonstrate the effectiveness of the proposed approach, experiments on the binomial-3 regression, multiplexor and even parity problems are performed. The results show that the results using the proposed tree-structure-aware operators are superior to the results of standard GP for all three test problems in both success rate and number of evaluations.

• 대한수학회지
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• 제58권4호
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• pp.799-817
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• 2021

In this paper, we investigate the normal and complex symmetric weighted composition operators W_𝜓,𝜑 on the Hardy space H²(𝔻). Firstly, we give the explicit conditions of weighted composition operators to be normal and complex symmetric with respect to conjugations 𝒞₁ and 𝒞₂ on H²(𝔻), respectively. Moreover, we particularly investigate the weighted composition operators W_𝜓,𝜑 on H²(𝔻) which are normal and complex symmetric with respect to conjugations 𝓙, 𝒞₁ and 𝒞₂, respectively, when 𝜑 has an interior fixed point, 𝜑 is of hyperbolic type or parabolic type.

• Korean Journal of Mathematics
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• 제29권1호
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• pp.137-167
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• 2021

Spherical fuzzy set (SFS) is also one of the fundamental concepts for address more uncertainties in decision problems than the existing structures of fuzzy sets, and thus its implementation was more substantial. The well-known sine trigonometric function maintains the periodicity and symmetry of the origin in nature and thus satisfies the expectations of the experts over the multi parameters. Taking this feature and the significance of the SFSs into the consideration, the main objective of the article is to describe some reliable sine trigonometric laws (ST L) for SFSs. Associated with these laws, we develop new average and geometric aggregation operators to aggregate the Spherical fuzzy numbers (SFNs). Then, we presented a group decision- making (DM) strategy to address the multi-attribute group decision making (MAGDM) problem using the developed aggregation operators. In order to verify the value of the defined operators, a MAGDM strategy is provided along with an application for the selection of laptop. Moreover, a comparative study is also performed to present the effectiveness of the developed approach.