• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.123-135
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• 2023

The goal of this article is to introduce the concept of pseudo-weighted Browder spectrum when the underlying Hilbert space is not necessarily separable. To attain this goal, the notion of α-pseudo-Browder operator has been introduced. The properties and the relation of the weighted spectrum, pseudo-weighted spectrum, weighted Browder spectrum, and pseudo-weighted Browder spectrum have been investigated by extending analogous properties of their corresponding essential pseudo-spectrum and essential pseudo-weighted spectrum. The weighted spectrum, pseudo-weighted spectrum, weighted Browder, and pseudo-weighted Browder spectrum of the sum of two bounded linear operators have been characterized in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces. This exploration ends with a characterization of the pseudo-weighted Browder spectrum of the sum of two bounded linear operators defined over the arbitrary Hilbert spaces under certain conditions.

• Atmosphere
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• v.24 no.2
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• pp.197-206
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• 2014

The effects of different averaging operators and atmospheric stability on the turbulent fluxes are investigated using the vertical velocity, air temperature, carbon dioxide concentration, and absolute humidity data measured at 10 Hz by a 3-dimensional sonic anemometer and an open-path $CO_2/H_2O$ infrared gas analyzer installed at a height of 18.5 m on the rooftop of the Jungnang KT building located at a typical residential area in Seoul, Korea. For this purpose, 7 different averaging operators including block average, linear regression, and moving averages during 100 s, 300 s, 600 s, 900 s, and 1800 s are considered and the data quality control procedure such as physical limit check and spike removal is also applied. It is found that as the averaging interval becomes shorter, turbulent fluxes computed by the moving average become smaller and the ratios of turbulent fluxes computed by the 100 s moving average to the fluxes by the 1800 s moving average under unstable stability are smaller than those under neutral stability. The turbulent fluxes computed by the linear regression are 85~92% of those computed by the 1800 s moving average and nearly the same as those computed by 900 s moving average, implying that the adequate selection of an averaging operator and its interval will be very important to estimate more accurate turbulent fluxes at urban area.

• Progress in Medical Physics
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• v.34 no.3
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• pp.23-32
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• 2023

Purpose: In radiomics analysis, to evaluate features, and predict genetic characteristics and survival time, the pixel values of lesions depicted in computed tomography (CT) and magnetic resonance imaging (MRI) images are used. CT and MRI offer three-dimensional images, thus producing three-dimensional features (Features_3d) as output. However, in reports, the superiority between Features_3d and two-dimensional features (Features_2d) is distinct. In this study, we aimed to investigate whether a difference exists in the prediction accuracy of radiomics analysis of lung cancer using Features_2d and Features_3d. Methods: A total of 38 cases of large cell carcinoma (LCC) and 40 cases of squamous cell carcinoma (SCC) were selected for this study. Two- and three-dimensional lesion segmentations were performed. A total of 774 features were obtained. Using least absolute shrinkage and selection operator regression, seven Features_2d and six Features_3d were obtained. Results: Linear discriminant analysis revealed that the sensitivities of Features_2d and Features_3d to LCC were 86.8% and 89.5%, respectively. The coefficients of determination through multiple regression analysis and the areas under the receiver operating characteristic curve (AUC) were 0.68 and 0.70 and 0.93 and 0.94, respectively. The P-value of the estimated AUC was 0.87. Conclusions: No difference was found in the prediction accuracy for LCC and SCC between Features_2d and Features_3d.

• Journal of Sensor Science and Technology
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• v.7 no.5
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• pp.334-341
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• 1998

In this paper, we present a new interpolation scheme for image enhancement using nonlinear operator. In general, interpolation techniques are based on linear operators which are essentially lowpass filters, hence, they tend to blur fine details in the original image. In our approach, the operator itself balances the strength of its sharpening and noise suppressing components according to the properties of the input image data.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.661-676
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• 2017

Let T be a bounded linear operator acting on a complex Hilbert space ${\mathfrak{H}}$. In this paper we introduce the class, denoted ${\mathcal{Q}}(A(k),m)$, of operators satisfying $T^{m{\ast}}(T^{\ast}{\mid}T{\mid}^{2k}T)^{1/(k+1)}T^m{\geq}T^{{\ast}m}{\mid}T{\mid}^2T^m$, where m is a positive integer and k is a positive real number and we prove basic structural properties of these operators. Using these results, we prove that if P is the Riesz idempotent for isolated point ${\lambda}$ of the spectrum of $T{\in}{\mathcal{Q}}(A(k),m)$, then P is self-adjoint, and we give a necessary and sufficient condition for $T{\otimes}S$ to be in ${\mathcal{Q}}(A(k),m)$ when T and S are both non-zero operators. Moreover, we characterize the quasinilpotent part $H_0(T-{\lambda})$ of class A(k) operator.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.5
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• pp.525-532
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• 2004

Telemanipulator is distingushed from industrial robot by iterating same specified work. Manipulator operator is included in control loop for controlling the telemanipulator because he decide directly during the work and order controllabily. We implement fuzzy controller for reducing the modelling error of telemanipulator which depend on the PID controller. But position-force control method of bidirectional control impose unsafety of vibiration and Analytic Hierchy method can stabilize for reducing nonlinear modelling error by expert operator because of transformation empirical control rule to linear model.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.10
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• pp.60-67
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• 1990

This paper proposes a model-based fault detection method for linear/nonlinear system having modelling errors, nonlinearities and measurement noise. The system model is represented by the unified operator [5] in order to apply to both the continuous-time and discrete-time problems. The fault detection method suggested here accounts for the effects of noise, model mismatch and nonlinearities. Modelling errors are depicted by additive forms and the nominal model denominator is fixed via prior experiments in order to quantify the nucertainty bound on the parameter estima-tion. The least square method is used to estimate the numerator parameters of the nominal model. performance than traditional methods.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2004.11a
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• pp.179-182
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• 2004

This paper deals with a new mathematical formulation of nonlinear wave profile based on Banach fixed point theorem. As application of the formulation and its solution procedure, some numerical solutions was presented in this paper and nonlinear equation was derived. Also we introduce a new operator for iteration and getting solution. A numerical study was accomplished with Stokes' first-order solution and iteration scheme, and then we can know the nonlinear characteristic of Stokes' high-order solution. That is, using only Stokes' first-oder(linear) velocity potential and an initial guess of wave profile, it is possible to realize the corresponding high-oder Stokian wave profile with tile new numerical scheme which is the method of iteration. We proved the mathematical convergence of tile proposed scheme. The nonlinear strategy of iterations has very fast convergence rate, that is, only about 6-10 iterations arc required to obtain a numerically converged solution.

• Journal of Institute of Convergence Technology
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• v.3 no.2
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• pp.23-29
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• 2013

When a human operator interacts with a virtual wall that is modeled as a virtual spring model, the lager the stiffness of the virtual spring is, the more realistic the operator feels that the virtual wall is. In the previous studies, it is shown that the maximum available stiffness of a virtual spring to guarantee the stability can be increased when the first-order-hold method is applied, however the effects of a human impedance on the stability are not considered. This paper presents the effects of a human impedance on stability of haptic system with a virtual spring and a first-order-hold (FOH) method. The human impedance model is modeled as a linear second-order system model. The relations between the maximum available stiffness of a virtual spring and the human impedance such as a mass, a damping and a stiffness are analyzed through the MATLAB simulation. It is shown that the maximum available stiffness is proportional to the square root of the human mass or damping respectively.

• Bulletin of the Korean Chemical Society
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• v.14 no.1
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• pp.21-29
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• 1993

For the study of relaxation processes in complex spin system, a general master equation, which can be used to simulate a vast range of pulse experiments, has been formulated using the Liouville representation of quantum mechanics. The state of a nonequilibrium spin system in magnetic field is described by a density vector in Liouville space and the time evolution of the system is followed by the application of a linear master operator to the density vector in this Liouville space. In this master equation the nuclear spin relaxation due to intramolecular dipolar interaction or randomly fluctuating field interaction is explicitly implemented as a relaxation supermatrix for a strong coupled two-spin (1/2) system. The whole dynamic information inherent in the spin system is thus contained in the density vector and the master operator. The radiofrequency pulses are applied in the same space by corresponding unitary rotational supertransformations of the density vector. If the resulting FID is analytically Fourier transformed, it is possible to represent the final nonstationary spectrum using a frequency dependent spectral vector and intensity determining shape vector. The overall algorithm including relaxation interactions is then translated into an ANSIFORTRAN computer program, which can simulate a variety of two dimensional spectra. Furthermore a new strategy is tested by simulation of multiple quantum signals to differentiate the two relaxation interaction types.