• Structural Engineering and Mechanics
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• v.4 no.6
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• pp.703-715
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• 1996

In stochastic analysis, the randomness of the structural parameters is taken into consideration and the response variability is obtained in addition to the conventional (mean) response. In the present paper the structural response variability of plate structure is calculated using the weighted integral method and is compared with the results obtained by different methods. The stochastic field is assumed to be normally distributed and to have the homogeneity. The decomposition of strain-displacement matrix enabled us to extend the formulation to the stochastic analysis with the quadratic elements in the weighted integral method. A new auto-correlation function is derived considering the uncertainty of plate thickness. The results obtained in the numerical examples by two different methods, i.e., weighted integral method and Monte Carlo simulation, are in a close agreement. In the case of the variable plate thickness, the obtained results are in good agreement with those of Lawrence and Monte Carlo simulation.

• Proceedings of the Acoustical Society of Korea Conference
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• 1994.06c
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• pp.133-137
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• 1994

In this paper, a method for designing an optimal weight function for the weighted cepstral distance measure is proposed. A conventional weight function or cepstral lifter is obtained eperimentally depending on the spectral components to be emphasized. The proposed method minimizes the error between word reference patterns and the traning data. To compare the proposed optimal weight function with conventional function, speech recognition systems based on Dpynamic Time Warping and Hidden Markov Models were constructed to conduct speaker independent isolated word necogination eperiment. Results show that the proposed method gives better performance than conventional weight functions.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1923-1936
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• 2013

We prove that the intrinsic square functions including Lusin area integral and Littlewood-Paley $g^*_{\lambda}$-function as defined by Wilson, are bounded in a class of function spaces include weighted Morrey spaces. The corresponding commutators generated by BMO functions are also considered.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.1873-1882
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• 2017

We give a generating function for the number of graphs with given numerical properties and prescribed weighted number of connected components. As an application, we give a generating function for the number of q-partite graphs of given order, size and number of connected components.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.135-145
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• 1995

A new algorithm was given to successively fit the multiexponential function/nonlinear function to data by a weighted least squares method, using Gauss-Newton, Marquardt, gradient and DUD methods for convergence. This study also considers the problem of linear-nonlimear weighted least squares estimation which is based upon the usual Taylor's formula process.

• International Journal of Contents
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• v.10 no.1
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• pp.18-22
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• 2014

Hidden nodes have a key role in the information processing of feed-forward neural networks in which inputs are processed through a series of weighted sums and nonlinear activation functions. In order to understand the role of hidden nodes, we must analyze the effect of the nonlinear activation functions on the weighted sums to hidden nodes. In this paper, we focus on the effect of nonlinear functions in a viewpoint of information theory. Under the assumption that the nonlinear activation function can be approximated piece-wise linearly, we prove that the entropy of weighted sums to hidden nodes decreases after piece-wise linear functions. Therefore, we argue that the nonlinear activation function decreases the uncertainty among hidden nodes. Furthermore, the more the hidden nodes are saturated, the more the entropy of hidden nodes decreases. Based on this result, we can say that, after successful training of feed-forward neural networks, hidden nodes tend not to be in linear regions but to be in saturated regions of activation function with the effect of uncertainty reduction.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.9 no.2
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• pp.1-6
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• 2009

One of the most important problems in bioinformatics is how to extract the useful information from a huge amount of data, and make a decision in diagnosis, prognosis, and medical treatment applications. This paper proposes a weighted kernel function for support vector machine and its learning method with a fast convergence and a good classification performance. We defined the weighted kernel function as the weighted sum of a set of different types of basis kernel functions such as neural, radial, and polynomial kernels, which are trained by a learning method based on genetic algorithm. The weights of basis kernel functions in proposed kernel are determined in learning phase and used as the parameters in the decision model in classification phase. The experiments on several clinical datasets such as colon cancer indicate that our weighted kernel function results in higher and more stable classification performance than other kernel functions.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.366-370
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• 2003

This paper is on weighted model reduction using structurally balanced truncation. For a given weighted(single or double-sided) transfer function, a state space realization with the linear fractional transformation form is obtained. Then we prove that two block diagonal LMI(linear matrix inequality) solutions always exist, and it is possible to get a reduced order model with guaranteed stability and a priori error bound. Finally, two examples are used to show the validity of proposed weighted reduction method, and the method is compared with other existing methods.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.527-534
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• 2002

The weighted shifts have been made a central role in the study of κ-hyponormality for hyponormal and subnormal operators in discrete notion. In this note we discuss the κ-hyponormality of weighted translation semigroups with a symbol function in continuous notion.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1233-1241
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• 2007

We derive a kind of weighted norm inequalities which relate the commutators of potential type operators to the corresponding maximal operators.