• Title/Summary/Keyword: Linear operator

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CHARACTERIZATIONS OF CENTRALIZERS AND DERIVATIONS ON SOME ALGEBRAS

  • He, Jun;Li, Jiankui;Qian, Wenhua
    • Journal of the Korean Mathematical Society
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    • v.54 no.2
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    • pp.685-696
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    • 2017
  • A linear mapping ${\phi}$ on an algebra $\mathcal{A}$ is called a centralizable mapping at $G{\in}{\mathcal{A}}$ if ${\phi}(AB)={\phi}(A)B= A{\phi}(B)$ for each A and B in $\mathcal{A}$ with AB = G, and ${\phi}$ is called a derivable mapping at $G{\in}{\mathcal{A}}$ if ${\phi}(AB)={\phi}(A)B+A{\phi}(B)$ for each A and B in $\mathcal{A}$ with AB = G. A point G in A is called a full-centralizable point (resp. full-derivable point) if every centralizable (resp. derivable) mapping at G is a centralizer (resp. derivation). We prove that every point in a von Neumann algebra or a triangular algebra is a full-centralizable point. We also prove that a point in a von Neumann algebra is a full-derivable point if and only if its central carrier is the unit.

Natural frequencies and response amplitude operators of scale model of spar-type floating offshore wind turbine

  • Hong, Sin-Pyo;Cho, Jin-Rae
    • Structural Engineering and Mechanics
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    • v.61 no.6
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    • pp.785-794
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    • 2017
  • This paper is concerned with the comparative numerical and experimental study on the natural behavior and the motion responses of a 1/75 moored scale model of a 2.5 MW spar-type floating offshore wind turbine subject to 1-D regular wave. Heave, pitch and surge motions and the mooring tensions are investigated and compared by numerical and experimental methods. The upper part of wind turbine which is composed of three rotor blades, hub and nacelle is modeled as a lumped mass and three mooring lines are pre-tensioned by means of linear springs. The numerical simulations are carried out by a coupled FEM-cable dynamics code, while the experiments are performed in a wave tank equipped with the specially-designed vision and data acquisition system. Using the both methods, the natural behavior and the motion responses in RAOs are compared and parametrically investigated to the fairlead position, the spring constant and the location of mass center of platform. It is confirmed, from the comparison, that both methods show a good agreement for all the test cases. And, it is observed that the mooring tension is influenced by all three parameters but the platform motion is dominated by the location of mass center. In addition, from the sensitivity analysis of RAOs, the coupling characteristic of platform motions and the sensitivities to the mooring parameters are investigated.

A GENERAL VISCOSITY APPROXIMATION METHOD OF FIXED POINT SOLUTIONS OF VARIATIONAL INEQUALITIES FOR NONEXPANSIVE SEMIGROUPS IN HILBERT SPACES

  • Plubtieng, Somyot;Wangkeeree, Rattanaporn
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.4
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    • pp.717-728
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    • 2008
  • Let H be a real Hilbert space and S = {T(s) : $0\;{\leq}\;s\;<\;{\infty}$} be a nonexpansive semigroup on H such that $F(S)\;{\neq}\;{\emptyset}$ For a contraction f with coefficient 0 < $\alpha$ < 1, a strongly positive bounded linear operator A with coefficient $\bar{\gamma}$ > 0. Let 0 < $\gamma$ < $\frac{\bar{\gamma}}{\alpha}$. It is proved that the sequences {$x_t$} and {$x_n$} generated by the iterative method $$x_t\;=\;t{\gamma}f(x_t)\;+\;(I\;-\;tA){\frac{1}{{\lambda}_t}}\;{\int_0}^{{\lambda}_t}\;T(s){x_t}ds,$$ and $$x_{n+1}\;=\;{\alpha}_n{\gamma}f(x_n)\;+\;(I\;-\;{\alpha}_nA)\frac{1}{t_n}\;{\int_0}^{t_n}\;T(s){x_n}ds,$$ where {t}, {${\alpha}_n$} $\subset$ (0, 1) and {${\lambda}_t$}, {$t_n$} are positive real divergent sequences, converges strongly to a common fixed point $\tilde{x}\;{\in}\;F(S)$ which solves the variational inequality $\langle({\gamma}f\;-\;A)\tilde{x},\;x\;-\;\tilde{x}{\rangle}\;{\leq}\;0$ for $x\;{\in}\;F(S)$.

Effect of outliers on the variable selection by the regularized regression

  • Jeong, Junho;Kim, Choongrak
    • Communications for Statistical Applications and Methods
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    • v.25 no.2
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    • pp.235-243
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    • 2018
  • Many studies exist on the influence of one or few observations on estimators in a variety of statistical models under the "large n, small p" setup; however, diagnostic issues in the regression models have been rarely studied in a high dimensional setup. In the high dimensional data, the influence of observations is more serious because the sample size n is significantly less than the number variables p. Here, we investigate the influence of observations on the least absolute shrinkage and selection operator (LASSO) estimates, suggested by Tibshirani (Journal of the Royal Statistical Society, Series B, 73, 273-282, 1996), and the influence of observations on selected variables by the LASSO in the high dimensional setup. We also derived an analytic expression for the influence of the k observation on LASSO estimates in simple linear regression. Numerical studies based on artificial data and real data are done for illustration. Numerical results showed that the influence of observations on the LASSO estimates and the selected variables by the LASSO in the high dimensional setup is more severe than that in the usual "large n, small p" setup.

Parametric pitch instability investigation of Deep Draft Semi-submersible platform in irregular waves

  • Mao, Huan;Yang, Hezhen
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.8 no.1
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    • pp.13-21
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    • 2016
  • Parametric pitch instability of a Deep Draft Semi-submersible platform (DDS) is investigated in irregular waves. Parametric pitch is a form of parametric instability, which occurs when parameters of a system vary with time and the variation satisfies a certain condition. In previous studies, analyzing of parametric instability is mainly limited to regular waves, whereas the realistic sea conditions are irregular waves. Besides, parametric instability also occurs in irregular waves in some experiments. This study predicts parametric pitch of a Deep Draft Semi-submersible platform in irregular waves. Heave motion of DDS is simulated by wave spectrum and response amplitude operator (RAO). Then Hill equation for DDS pitch motion in irregular waves is derived based on linear-wave theory. By using Bubnov-Galerkin approach to solve Hill equation, the corresponding stability chart is obtained. The differences between regular-waves stability chart and irregular-waves stability chart are compared. Then the sensitivity of wave parameters on DDS parametric pitch in irregular waves is discussed. Based on the discussion, some suggestions for the DDS design are proposed to avoid parametric pitch by choosing appropriate parameters. The results indicate that it's important and necessary to predict DDS parametric pitch in irregular waves during design process.

Factors Affecting Business Performance of Rural Tourism Operators (농촌관광 사업자의 경영성과에 영향을 미치는 요인)

  • Kim, Kyung-Hee;Hwang, Dae Yong
    • Journal of Agricultural Extension & Community Development
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    • v.27 no.2
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    • pp.65-74
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    • 2020
  • The study aims to identify the factors affecting business performance of rural tourism operators. For this study, 1,004 questionnaires were collected by field survey of rural tourism operators. The linear multiple regression analysis were used to identify factors affecting performance of rural tourism business. The result indicate that the factors influencing the sales of rural tourism business were in order of owning sales facilities, perception of multi-functional value of agriculture and rural, group promotion, number of rooms, and gender. In the case of gender, it was found that females had a high probability of positively affecting sales. The factors influencing the satisfaction of the rural tourism business were in the order of management strategy, number of days of operation, perception of multi-functional value of agriculture and rural, and business career. In the case of management strategy, it was found that the differentiation strategy have a positively affecting the satisfaction of the rural tourism business. As for the business career, the shorter the career, the higher the probability of positively affecting the satisfaction of the rural tourism business. The results of this study would be useful for establishing strategies to improve the management performance of the rural tourism business.

An Imprevement of the Approximate-Factorization Scheme and Its Application to the Analysis of Incompressible Viscous Flows (근사인자화법의 개량과 비압축성 유동해석에의 응용)

  • 신병록
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.19 no.8
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    • pp.1950-1963
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    • 1995
  • A modification of the approximate-factorization method is made to accelerate the convergency rate and to take sufficiently large Courant number without loss of accuracy. And a stable implicit finite-difference scheme for solving the incompressible Navier-Stokes equations employed above modified method is developed. In the present implicit scheme, the volume fluxes with contravariant velocity components and the pressure formulation in curvilinear coordinates is adopted. In order to satisfy the continuity condition completely and to remove spurious errors for the pressure, the Navier-Stokes equations are solved by a modified SMAC scheme using a staggered gird. The upstream-difference scheme such as the QUICK scheme is also employed to the right hand side. The implicit scheme is unconditionally stable and satisfies a diagonally dominant condition for scalar diagonal linear systems of implicit operator on the left hand side. Numerical results for some test calculations of the two-dimensional flow in a square cavity and over a backward-facing step are obtained using both usual approximate-factorization method and the modified one, and compared with each other. It is shown that the present scheme allows a sufficiently large Courant number of O(10$^{2}$) and reduces the computing time.

The Effects of Welding Process Parameters on Weld bead Width in GMAW Processes (GMAW 공정 중 용접 변수들이 용접 폭에 미치는 영향에 관한 연구)

  • 김일수;권욱현;박창언
    • Journal of Welding and Joining
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    • v.14 no.4
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    • pp.33-42
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    • 1996
  • In recent years there has been a significant growth in the use of the automated and/or robotic welding system, carried out as a means of improving productivity and quality, reducing product costs and removing the operator from tedious and potentially hazardous environments. One of the major difficulties with the automated and/or robotic welding process is the inherent lack of mathematical models for determination of suitable welding process parameters. Partial-penetration, single-pass bead-on-plate welds were fabricated in 12mm AS 1204 mild steel flats employing five different welding process parameters. The experimental results were used to develop three empirical equations: curvilinear; polynomial; and linear equations. The results were also employed to find the best mathematical equation under weld bend width to assist in the process control algorithms for the Gas Metal Arc Welding(GMAW) process and to correlate welding process parameters with weld bead width of bead-on-plates deposited. With the help of a standard statistical package program. SAS, multipe regression analysis was undertaken for investigating and modeling the GMAW process, and significance test techniques were applied for the interpretation of the experimental data.

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Improving a Digital Redesign for Time-Varying Trackers (시변 추종제어기를 위한 디지털 재설계의 개선)

  • Song, Hyun-Seok;Lee, Ho-Jae;Kim, Do-Wan
    • Journal of Institute of Control, Robotics and Systems
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    • v.17 no.4
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    • pp.289-294
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    • 2011
  • Digital redesign is yet another efficient tool to convert a pre-designed analog controller into a sampled-data one to maintain the analog closed-loop performance in the sense of state matching. A rising difficulty in developing a digital redesign technique for trackers with time-varying references is the unavailability of a closed-form discrete-time model of a system, even if it is linear time-invariant. A way to resolve this is to approximate the time-varying reference as a piecewise constant one, which deteriorates the state matching performance. Another remedy may be to decrease a sampling period, which however could numerically destabilize the optimization-based digital redesign condition. In this paper, we develop a digital redesign condition for time-varying trackers by approximating the time-varying reference through a triangular hold and by introducing delta-operated discrete-time models. It is shown that the digitally redesigned sampled-data tracker recovers the performance of the pre-designed analog tracker under a fast sampling limit. Simulation results on the formation flying of satellites convincingly show the effectiveness of the development.

An Edge Detection Algorithm for Impulse Noise Images (임펄스 잡음 영상을 위한 에지 검출 알고리즘)

  • Lee, Chang-Young;Kim, Nam-Ho
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 2013.10a
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    • pp.770-772
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    • 2013
  • Edges on the images are widely used in preprocessing in various areas including recognition and detection of the object. As generally known edge detection methods, there is a method using mask and these methods are Sobel, Prewitt, Roberts, Laplacian operator and etc. Implementation of these existing edge detection methods is simple. However, when processing the impulse noise added images, the properties of edge detection is not sufficient. Accordingly, in order to compensate for the weakness of existing edge detection methods and to detect strong edges on the images which were damaged by impulse noise, the edge detection algorithm using transformed mask was proposed in this paper.

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