• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.441-453
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• 1998

We use the heat kernel method to prove newly the Paley-Wiener theorem for the distributions with compact support.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.91-111
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• 2019

We give a direct proof of the sharp two-sided estimates, recently established in [4, 9], for the Dirichlet heat kernel of the fractional Laplacian with gradient perturbation in $C^{1,1}$ open sets by using Duhamel's formula. We also obtain a gradient estimate for the Dirichlet heat kernel. Our assumption on the open set is slightly weaker in that we only require D to be $C^{1,{\theta}}$ for some ${\theta}{\in}({\alpha}/2,1]$.

• Korean Journal of Remote Sensing
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• v.26 no.6
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• pp.693-703
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• 2010

High spectral resolution of hyperspectral data enables analysis of complex natural phenomena that is reflected on the data nonlinearly. Although many manifold learning methods have been developed for such problems, most methods do not consider the spatial correlation between samples that is inherent and useful in remote sensing data. We propose a manifold learning method which directly combines the spatial proximity and the spectral similarity through kernel PCA framework. A gain factor caused by spatial proximity is first modelled with a heat kernel, and is added to the original similarity computed from the spectral values of a pair of samples. Parameters are tuned with intelligent grid search (IGS) method for the derived manifold coordinates to achieve optimal classification accuracies. Of particular interest is its performance with small training size, because labelled samples are usually scarce due to its high acquisition cost. The proposed spatial kernel PCA (KPCA) is compared with PCA in terms of classification accuracy with the nearest-neighbourhood classification method.

• Journal of Mechanical Science and Technology
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• v.16 no.6
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• pp.829-838
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• 2002

A constant volume combustion chamber is used to investigate the flame kernel development of gasoline air mixtures under various ignition systems, ignition energies and spark plugs. Three kinds of ignition systems are designed and assembled, and the ignition energy is controlled by the variation of the dwell time. Several kinds of spark plugs are also tested. The velocity of flame propagation is measured by a laser deflection method, and the combustion pressure is analyzed by the heat release rate and the mass fraction burnt. The results represent that as the ignition energy is increased by enlarging either dwell time or spark plug gap, the heat release rate and the mass fraction burnt are increased. The electrodes materials and shapes influence the flame kernel development by changing he transfer efficiency of electrical energy to chemical energy. The diameter of electrodes also influences the heat release rate and the burnt mass fraction.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.939-947
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• 2012

In this paper, we give a generalization of the embeddings of Riemannian manifolds via their heat kernel and via a finite number of eigenfunctions. More precisely, we embed a family of Riemannian manifolds endowed with a time-dependent metric analytic in time into a Hilbert space via a finite number of eigenfunctions of the corresponding Laplacian. If furthermore the volume form on the manifold is constant with time, then we can construct an embedding with a complete eigenfunctions basis.

• Transactions of the Korean Society of Automotive Engineers
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• v.7 no.8
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• pp.24-33
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• 1999

This paper investigate the effects of the variations of engine operation condition in the flame kernel formation and developmnet . A model for calculating the initial kernel development in spark ignition engines is formualted. It considered input of electrical energy, combustion energy release and heat transfer to the spark plyg, cylinder head, and unburned mixture. The model also takes into accounts strain rate of initial kernel and residual gas fraction. The breakdown process and the subsequent electrical power input initially control the kernel growth while intermediate growth is mainly dominated by diffusion or conduction. Then, the flame propagates by the chemical energy and turbulent flame expansion. Flame kernel development also influenced by engine operating conditions, for example, EGR rate, air-fuel ration and intake manifold pressure.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.555-565
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• 2008

We will derive the asymptotic expansions of solutions of the heat equation with hyperfunctions initial data.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.2
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• pp.288-298
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• 1999

In spark ignited engines, the electrical spark not only sets the time for the onset of combustion but also is able to greatly influence the character of the initial flame growth and the subsequent combustion, and thereby can influence engine performance. The relative importance of the ignition energy is particularly high under lean or high residual gas or exhaust gas recirculation (EGR). In this study, a modeling of flame Initiation and its development is proposed. Submodels consist in representing of cylinder pressure and temperature, heat transfer to cylinder wall, and flame kernel heat transfer to ambient air and to spark plug electrodes. The breakdown process and the subsequent electrical power input initially control the kernel growth while intermediate growth is mainly dominated by diffusion or conduction. Then, the flame propagates by the chemical energy, and laminar and turbulent flame velocity.

• Nuclear Engineering and Technology
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• v.55 no.11
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• pp.4102-4111
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• 2023

In order to better perform thermal hydraulic calculation and analysis of supercritical water reactor, based on the experimental data of supercritical water, the model training and predictive analysis of the heat transfer coefficient of supercritical water were carried out by using the support vector machine (SVM) algorithm. The changes in the prediction accuracy of the supercritical water heat transfer coefficient are analyzed by the changes of the regularization penalty parameter C, the slack variable epsilon and the Gaussian kernel function parameter gamma. The predicted value of the SVM model obtained after parameter optimization and the actual experimental test data are analyzed for data verification. The research results show that: the normalization of the data has a great influence on the prediction results. The slack variable has a relatively small influence on the accuracy change range of the predicted heat transfer coefficient. The change of gamma has the greatest impact on the accuracy of the heat transfer coefficient. Compared with the calculation results of traditional empirical formula methods, the trained algorithm model using SVM has smaller average error and standard deviations. Using the SVM trained algorithm model, the heat transfer coefficient of supercritical water can be effectively predicted and analyzed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.11
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• pp.1486-1496
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• 2000

The initial flame kernel development and flame propagation in a constant volume combustion chamber is analyzed by the heat release rate and the mass fraction burnt. The combustion pressure is measured with a piezoelectric type pressure sensor. In order to evaluate the effects of ignition system and ignition energy on the flame propagation, four different ignition systems are designed and tested, and the ignition energy is varied by the dwell time. Several different spark plugs are also tested and examined to analysis the effects of electrodes on flame kernel development. The results show that the when the dwell time is increased, and when the spark plug gap is extended, heat release rate and the mass burnt fraction are increased. The materials and shapes of electrodes affect the flame development, because they change the energy transfer efficiency from electrical energy to chemical energy. The diameter of electrodes influences not only the heat release rate but also the mass burnt fraction as well.