• 대한수학회보
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• 제30권1호
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• pp.125-134
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• 1993

Let X be a compact Hausdorff space, and let C(X) (resp. $C_{R}$(X)) be the complex (resp. real) Banach algebra of all continuous complex-valued(resp. real-valued) functions on X with the pointwise operations and the supremum norm x. A Banach function algebra on X is a Banach algebra lying in C(X) which separates the points of X and contains the constants. A Banach function algebra on X equipped with the supremum norm is called a uniform algebra on X, that is, a uniformly closed subalgebra of C(X) which separates the points of X and contains the constants.s.

• 전기학회논문지
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• 제62권8호
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• pp.1144-1150
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• 2013

The stabilizing controller design problem of time-delay singularly perturbed systems is considered. The proposed approach is based on the $H_{\infty}$ norm and the composite control method. A sufficient condition for the stability of the time-delay slow subsystem is presented. Using this condition, we can construct the composite control law for the time-delay singularly perturbed system and analysis the system by the matrix Lambert W function. Illustrated examples are presented to demonstrate the validity and applicability of the proposed method.

• 대한수학회보
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• 제52권5호
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• pp.1729-1735
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• 2015

It is known that the partial sum of the Taylor series of an holomorphic function of one complex variable converges in norm on $H^p(\mathbb{D})$ for 1 < p < ${\infty}$. In this paper, we consider various type of partial sums of a holomorphic function of several variables which also converge in norm on $H^p(\mathbb{B}_n)$ for 1 < p < ${\infty}$. For the partial sums in several variable cases, some variables could be chosen slowly (fastly) relative to other variables. We prove that in any cases the partial sum converges to the original function, regardlessly how slowly (fastly) some variables are taken.

• 전자공학회논문지B
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• 제32B권3호
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• pp.503-511
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• 1995

A batch-mode algorithm is proposed to increase the speed of learning in the error backpropagation algorithm with variable learning rate and variable momentum parameters in classification problems. The objective function is normalized with respect to the number of patterns and output nodes. Also the gradient of the objective function is normalized in updating the connection weights to increase the effect of its backpropagated error. The learning rate and momentum parameters are determined from a function of the gradient norm and the number of weights. The learning rate depends on the square rott of the gradient norm while the momentum parameters depend on the gradient norm. In the two typical classification problems, simulation results demonstrate the effectiveness of the proposed algorithm.

• 한국지구물리탐사학회:학술대회논문집
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• 한국지구물리탐사학회 2007년도 공동학술대회 논문집
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• pp.118-123
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• 2007

A robust objective function in the frequency domain is applied to the acoustic full waveform inversion. The proposed objective function is defined as $l_1$-norm of residual wavefields in the frequency domain. Generally, the full waveform inversion is extremely sensitive to a number of factors such as parameterization, initial model, noise and so on. The numerical tests were performed for checking the sensitivity to attenuation and several noises. For the comparison with other objective functions, the conventional least-squares method and the logarithmic method were tested under the same condition. The synthetic data examples show that the proposed algorithm is more robust than the well-known methods.

• Structural Engineering and Mechanics
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• 제55권1호
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• pp.229-244
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• 2015

H-infinity norm relates to the maximum in the frequency response function and H-infinity control method focuses on the case that the vibration is excited at the fundamental frequency, while 2-norm relates to the output energy of systems with the input of pulses or white noises and 2-norm control method weighs the overall vibration performance of systems. The trade-off between the performance in frequency-domain and that in time-domain may be achieved by integrating two indices in the mixed vibration control method. Based on the linear fractional state space representation in the modal space for a piezoelectric flexible structure with uncertain modal parameters and un-modeled residual high-frequency modes, a mixed dynamic output feedback control design method is proposed to suppress the structural vibration. Using the linear matrix inequality (LMI) technique, the initial populations are generated by the designing of robust control laws with different H-infinity performance indices before the robust 2-norm performance index of the closed-loop system is included in the fitness function of optimization. A flexible beam structure with a piezoelectric sensor and a piezoelectric actuator are used as the subject for numerical studies. Compared with the velocity feedback control method, the numerical simulation results show the effectiveness of the proposed method.

• 로봇학회논문지
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• 제18권3호
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• pp.330-336
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• 2023

In this paper, a novel line-based simultaneous localization and mapping (SLAM) using a loss function of vanishing point measurements is proposed. In general, the Huber norm is used as a loss function for point and line features in feature-based SLAM. The proposed loss function of vanishing point measurements is based on the unit sphere model. Because the point and line feature measurements define the reprojection error in the image plane as a residual, linear loss functions such as the Huber norm is used. However, the typical loss functions are not suitable for vanishing point measurements with unbounded problems. To tackle this problem, we propose a loss function for vanishing point measurements. The proposed loss function is based on unit sphere model. Finally, we prove the validity of the loss function for vanishing point through experiments on a public dataset.

• 대한수학회보
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• 제44권2호
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• pp.309-313
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• 2007

By applying ideas from [M. S. Moslehian, et al., Norms of operators in $X_{\lambda}$ spaces, Appl. Math. Lett. (2007), doi:10.1016/j.aml.2006. 11.009], we investigate the norm of the cubic operator on the function space $X_{\lambda}$.

• The Journal of the Acoustical Society of Korea
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• 제16권3E호
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• pp.62-68
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• 1997

In this paper, a modified adaptive sign (MAS) algorithm based on a mixed norm error criterion is proposed. The mixed norm error criterion of be minimized is constructed as a combined convex function of the mean-absolute error and the mean-absolute error to the third power. A convergence analysis of the MAS algorithm is also presented. Under a set of mild assumptions, a set of nonlinear evolution equations that characterizes the statistical mean and mean-squared behavior of the algorithm is derived. Computed simulations are carried out to verify the validity of our derivations.

• Journal of Applied and Pure Mathematics
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• 제6권1_2호
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• pp.71-96
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• 2024

In this paper we present many interesting results such as completeness and composition theorems in the 𝛼 norm. Moreover, under some conditions, we establish the existence and uniqueness of Cⁿ-(𝜇, 𝜈) pseudo-almost automorphic solutions of class r in the 𝛼-norm for some partial functional differential equations in Banach space when the delay is distributed. An example is given to illustrate our results.