• Korean Journal of Mathematics
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• v.23 no.1
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• pp.129-151
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• 2015

In this paper, we prove an $L^p$ version of Donoho-Stark's uncertainty principle for the inverse of the hypergeometric Fourier transform on $\mathbb{R}^d$. Next, using the ultracontractive properties of the semigroups generated by the Heckman-Opdam Laplacian operator, we obtain an $L^p$ Heisenberg-Pauli-Weyl uncertainty principle for the inverse of the hypergeometric Fourier transform on $\mathbb{R}^d$.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.71-84
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• 2017

We discuss the qualitative uncertainty principle for Gabor transform on certain classes of the locally compact groups, like abelian groups, ${\mathbb{R}}^n{\times}K$, K ⋉ ${\mathbb{R}}^n$ where K is compact group. We shall also prove a weaker version of qualitative uncertainty principle for Gabor transform in case of compact groups.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.875-883
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• 2017

In this work, we establish Heisenberg-type uncertainty principle for the Bessel-Struve Fock space ${\mathbb{F}}_{\nu}$ associated to the Airy operator $L_{\nu}$. Next, we give an application of the theory of extremal function and reproducing kernel of Hilbert space, to establish the extremal function associated to a bounded linear operator $T:{\mathbb{F}}_{\nu}{\rightarrow}H$, where H be a Hilbert space. Furthermore, we come up with some results regarding the extremal functions, when T are difference operators.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.283-296
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• 2001

The Heisenberg inequality associated with the uncertainty principle is extended to an infinite dimensional abstract Wiener space (H, B) with an abstract Wiener measure p$_1$. For $\phi$ $\in$ L$^2$(p$_1$) and T$\in$L(B, H), it is shown that (※Equations, See Full-text), where F(sub)$\phi$ is the Fourier-Wiener transform of $\phi$. The conditions when the equality holds also discussed.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.521-535
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• 2022

In this paper, we introduce the k-Hankel-Wigner transform on R in some problems of time-frequency analysis. As a first point, we present some harmonic analysis results such as Plancherel's, Parseval's and an inversion formulas for this transform. Next, we prove a Heisenberg's uncertainty principle and a Calderón's reproducing formula for this transform. We conclude this paper by studying an extremal function for this transform.

• Journal of Science and Technology Studies
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• v.10 no.2
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• pp.143-174
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• 2010

How can a regulatory policy to address potential hazards be made legitimate in the face of scientific uncertainty? The precautionary principle has been gradually regarded as the most persuasive answer to this intricate question in Europe since the 1970s and generally recognized as a guiding principle in international environmental law. This principle, however, has often been subject to diverse concerns and criticisms due to its vague definition. This article tries to elaborate the precautionary principle while reviewing both the validity and unreasonableness of these criticisms over this principle. Then, this article explores the policy relevance of this principle by applying this elaborated definition to the concrete case of risk governance such as the risk assesment of food safety. In the end, this paper emphasizes the fact that the precautionary principle can be applied in the field of risk governance, refuting the argument that the precautionary principle is only a moral attitude or a political position.

• Journal of Environmental Science International
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• v.20 no.3
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• pp.321-327
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• 2011

Bootstrap methods is the computer-based resampling method that estimates the standard errors and confidence intervals of summary statistics using the plug-in principle for assessing the accuracy or uncertainty of statistical estimates, and the BCa method among the Bootstrap methods is known much superior to other Bootstrap methods in respect of the standards of statistical validation. Therefore this study suggests the method of the representation and treatment of uncertainty in flood risk assessment and water resources planning from the construction and application of rainfall frequency analysis model considersing the uncertainty based on the nonparametric BCa method among the Bootstrap methods for the assessement of the estimation of probability rainfall and the effect of uncertainty considering the uncertainty of the parameter estimation of probability in the rainfall frequency analysis that is the most fundamental in flood risk assessement and water resources planning.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.8
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• pp.1071-1080
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• 2003

A national standard system was developed in order to calibrate and test the oil flowmeters for the petroleum field. A stop valve and a gyroscopic weighing scale were employed for the primary standard of the flow quantity. It is operated by the standing start and finish mode and the static weighing method. The model equation for uncertainty evaluation was based on the calibration principle of standard system. The sources of the uncertainties were quantified and combined according to the GUM(Guide to the Expression of Uncertainty in Measurement). It was found that the standard system had the relative expanded uncertainty of 0.04 % in the range of 18 - 350 ㎥/ｈ. According to the uncertainty budget, the uncertainties of the fluid density and the volume of pipeline, which were temperature dependent, contributed 92% of final uncertainty in the oil flow standard system.

• Journal of electromagnetic engineering and science
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• v.15 no.3
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• pp.181-184
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• 2015

Evaluation of radiating radiofrequency fields from hand-held and body-mounted wireless communication devices to human bodies are conducted by measuring the specific absorption rate (SAR). The uncertainty of system validation and probe calibration in SAR measurement depend on the variation of RF power used for the validation and calibration. RF input power for system validation or probe calibration is controlled manually during the test process of the existing systems in the laboratories. Consequently, a long time is required to reach the stable power needed for testing that will cause less uncertainty. The standard uncertainty due to this power drift is typically 2.89%, which can be obtained by applying IEC 62209 in a normal operating condition. The principle of the Automatic Input Power Level Control System (AIPLC), which controls the equipment by a program that maintains a stable input power level, is suggested in this paper. The power drift is reduced to less than ${\pm}1.16dB$ by AIPLC, which reduces the standard uncertainty of power drift to 0.67%.

• The Korean Journal of Air & Space Law and Policy
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• v.26 no.1
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• pp.241-269
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• 2011

Solar flare and storm may give an adverse effect upon electromagnetic environment around the Earth, so that various kinds of satellite cease to normally function. This kind of space storm disaster is characterized by the uncertainty about when and what size. Recently the UN has been paying attention to this plausible disaster. Particularly the COPUOS has taken the view that this disaster would threaten the sustainable space environment. The precautionary principle, rooted and excercised in the environment protection filed, has been adopted in the case of disaster with uncertainty. The reports and opinions given by the expert and representatives of the member States have stated that the precautionary principle should be adopted for the purpose of dealing with this disaster. On the other hand, it is advanced that the principle has been already included in the space law principle enshrined in the 1967 Space Treaty. The Treaty has adopted the freedom of navigation and use of the outer space for the interest of all States as the basic principles. Sustainable environment is necessary for implementing the principle. Therefore, the rules for the protection of sustainable space environment should be based upon the space law principle.