• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.185-190
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• 1989

In [4], J. Leray introduced the notion of partial hyperbolicity to characterize the operators for which the non-characteristic Cauchy problem is solvable in the Geverey class for any data which are holomorphic in a part of variables x"=(x$_{2}$,..,x$_{l}$ ) in the initial hyperplane x$_{1}$=0. A linear partial differential operator is called partially hyperbolic modulo the linear subvarieties S:x"=constant if the equation P$_{m}$(x, .zeta.$_{1}$, .xi.')=0 for .zeta.$_{1}$ has only real roots when .xi.'is real and .xi."=0, where P$_{m}$ is the principal symbol of pp. Limiting to the case of operators with constant coefficients, A. Kaneko proposed a new sharper condition when S is a hyperplane [3]. In this paper, we generalize this condition to the case of general linear subvariety S and show that it is sufficient for the solvability of Cauchy problem for the hyperfunction Cauchy data which contains variables parallel to S as holomorphic parameters.blem for the hyperfunction Cauchy data which contains variables parallel to S as holomorphic parameters.

• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.543-564
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• 1999

Consider a symmetric bilinear form defined on $\prod\times\prod$ by $_{\lambda\mu}$ = $<\sigma,fg>\;+\;\lambdaL[f](a)L[g](a)\;+\;\muM[f](b)m[g](b)$ ,where $\sigma$ is a quasi-definite moment functional, L and M are linear operators on $\prod$, the space of all real polynomials and a,b,$\lambda$ , and $\mu$ are real constants. We find a necessary and sufficient condition for the above bilinear form to be quasi-definite and study various properties of corresponding orthogonal polynomials. This unifies many previous works which treated cases when both L and M are differential or difference operators. finally, infinite order operator equations having such orthogonal polynomials as eigenfunctions are given when $\mu$=0.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.223-240
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• 2020

The paper is concerned with periodic linear evolution equations of the form x"(t) = A(t)x(t)+f(t), where A(t) is a family of (unbounded) linear operators in a Banach space X, strongly and periodically depending on t, f is an almost (or asymptotic) almost periodic function. We study conditions for this equation to have almost periodic solutions on ℝ as well as to have asymptotic almost periodic solutions on ℝ⁺. We convert the second order equation under consideration into a first order equation to use the spectral theory of functions as well as recent methods of study. We obtain new conditions that are stated in terms of the spectrum of the monodromy operator associated with the first order equation and the frequencies of the forcing term f.

• Journal of the Korean Institute of Telematics and Electronics
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• v.19 no.2
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• pp.1-6
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• 1982

This paper reviews and describes some applications of perturbation theory in the practical analysis of linear systems which involve random parameters. Statistical measures of the system outputs are derived in terms of statistical measures of the system parameters and inputs (i.e., in the way of perturbed linear operator equations). Perturbed state transition matrix is also derived. With simple first-order and second-order linear system models, we compare the accuracy of perturbation results with the exact ones. And the convergence of perturbation series is also investigated.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.67.5-67
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• 2001

A closed loop system with a linear plant and nonlinearity in the feedback connection is analyzed for its quasi-static orbital stability by a state-space approach. First a periodic orbit is assumed to exist in the loop which is determined by describing function method for the given nonlinearity. This is possible by selecting a proper nonlinearity and a rigorous justification of the describing function method.[1-3, 18, 20]. Then by introducing residual operator, a linear perturbed model can be formulated. Using various transformations like a modified eigenstructure decomposition, periodic-averaging, charge of variables and coordinate transformation, the stability of the periodic orbit, as a solution of harmonic balance, can be shown by investigating a simple scalar function and result of linear algebra. This is ...

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.243-243
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• 2000

This paper introduces a visual inspecting and monitoring system based on an image processing technique. We propose an image processing method for analyzing landslide movement in real time. The method adopts Laplacian of Gaussian operator to extract linear features for the captured images and uses a linear matching algorithm to distinguish the matching error for those features. When the algorithm is processed, motion parameters such as displacement area and its direction are computed. Once movement is recognized, displacements are estimated graphically with statistical amount in the image plane. The simulation results are shown us to verify the effectiveness of the developed method.

• International Journal of Precision Engineering and Manufacturing
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• v.5 no.4
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• pp.21-27
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• 2004

In this paper, data acquisition and analysis of a measuring machine for marine engine's cams are discussed. A rotary encoder and linear scale of the machine to measure angular and linear displacement, respectively, are interfaced to the PC via an encoder board with 2 channels. The design and measuring data are interpolated by cubic spline curves to compute the precision error which is defined by the maximum and minimum distances between two curves. The minimum zone fit of ISO is employed to evaluate the geometric deviation. The developed system takes only 5 minutes to measure and analyze the precision error while the CMM takes over I hours even with a skilled operator.

• Communications for Statistical Applications and Methods
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• v.27 no.4
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• pp.445-458
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• 2020

The least absolute shrinkage and selection operator (LASSO) is a popular method for a high-dimensional regression model. LASSO has high prediction accuracy; however, it also selects many irrelevant variables. In this paper, we consider the moderately clipped LASSO (MCL) for the high-dimensional generalized linear model which is a hybrid method of the LASSO and minimax concave penalty (MCP). The MCL preserves advantages of the LASSO and MCP since it shows high prediction accuracy and successfully selects relevant variables. We prove that the MCL achieves the oracle property under some regularity conditions, even when the number of parameters is larger than the sample size. An efficient algorithm is also provided. Various numerical studies confirm that the MCL can be a better alternative to other competitors.

• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.21-37
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• 2021

There is a direct connection between linear discriminant analysis (LDA) and linear regression since the direction vector of the LDA can be obtained by the least square estimation. The connection motivates the penalized LDA when the model is high-dimensional where the number of predictive variables is larger than the sample size. In this paper, we study the penalized LDA for a class of penalties, called the moderately clipped LASSO (MCL), which interpolates between the least absolute shrinkage and selection operator (LASSO) and minimax concave penalty. We prove that the MCL penalized LDA correctly identifies the sparsity of the Bayes direction vector with probability tending to one, which is supported by better finite sample performance than LASSO based on concrete numerical studies.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.205-209
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• 2011

Let $\mathcal{QA}$ denote the class of bounded linear Hilbert space operators T which satisfy the operator inequality $T^*|T^2|T{\geq}T^*|T|^2T$. Let $f$ be an analytic function defined on an open neighbourhood $\mathcal{U}$ of ${\sigma}(T)$ such that $f$ is non-constant on the connected components of $\mathcal{U}$. We generalize a theorem of Sheth [10] to $f(T){\in}\mathcal{QA}$.