• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.207-213
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• 2003

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx=y. An interpolating operator for n-vectors satisfies the equation Ax$_{i}$=y$_{i}$. for i=1,2, …, n. In this article, we investigate unitary interpolation problems in CSL-Algebra AlgL : Let L be a commutative subspace lattice on a Hilbert space H. Let x and y be vectors in H. When does there exist a unitary operator A in AlgL such that Ax=y?

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.359-365
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• 2003

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. In this article, we investigate invertible interpolation problems in CSL-Algebra AlgL : Let L be a commutative subspace lattice on a Hilbert space H and x and y be vectors in H. When does there exist an invertible operator A in AlgL suth that An = ㅛ?

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.7
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• pp.1255-1265
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• 1992

Under uniform heat flow, the thermal stress intensity factors for the interfacial crack on a rigid cusp-type inclusion are determined by Hilbert problem expressed with complex variable. The thermal stress intensity factors are expressed in terms of the periodic function of heat flow angle. When the tip of the interfacial crack meets that of the cusp crack, the thermal stress intensity factors have singularities. The thermal stress intensity factors at the interfacial crack tip located in the distance from the cusp crack tip vary with the location of the interfacial crack tip. From the results of the analysis, the complex potential functions and the thermal stress intensity factors for the cusp-type inclusion without the interfacial crack are derived under the cusp surface boundary conditions insulated or fixed to zero relative temperature.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.421-438
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• 2015

In this paper, we study the existence of classical and generalized solutions for nonlinear differential inclusions $x^{\prime}(t){\in}F(t,x(t))$ in Hilbert spaces in which the multifunction F on the right-hand side is hemicontinuous and satisfies the semimonotone condition or is condensing. Our existence results are obtained via the selection and fixed point methods by reducing the problem to an ordinary differential equation. We first prove the existence theorem in finite dimensional spaces and then we generalize the results to the infinite dimensional separable Hilbert spaces. Then we apply the results to prove the existence of the mild solution for semilinear evolution inclusions. At last, we give an example to illustrate the results obtained in the paper.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.7
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• pp.1705-1712
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• 1994

Hilbert problems are derived to evaluate thermal stress intensity factors for a partially insulated crack subjected to vertically uniform heat flow in infinite bonded dissimilar materials. In case of fully insulated crack surface, the present solutions of thermal stress intensity factors are reduced into the same as the previous results. For the homogeneous material, mode II thermal stress intensity factor only exists. However, in the bonded dissimilar materials, both mode I and II thermal stress intensity factors are obtained. Specially, in this case, mode II thermal stress intensity factor is dominent. Also, thermal stress intensity factors are strongly influenced by the material properties. Thermal stress intensity factors decrease when the degree of insulation decreases.

• Structural Engineering and Mechanics
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• v.36 no.6
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• pp.697-714
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• 2010

This paper presents an improved version of the Hilbert-Huang transform (HHT) for the modal evaluation of structural systems or signals. In this improved HHT, a well-designed bandpass filter is used as preprocessing to separate and determine each mode of the signal for solving the inherent modemixing problem in HHT (i.e., empirical mode decomposition, EMD, associated with the Hilbert transform). A screening process is then applied to remove undesired intrinsic mode functions (IMFs) derived from the EMD of the signal's mode. A "best" IMF is selected in each screening process that utilizes the orthogonalization coefficient between the signal's mode and its IMFs. Through mode-by-mode signal filtering, parameters such as the modal frequency can be evaluated accurately when compared to the theoretical value. Time history of the identified modal frequency is available. Numerical results prove the efficiency of the proposed approach, showing relative errors 1.40%, 2.06%, and 1.46%, respectively, for the test cases of a benchmark structure in the lab, a simulated time-varying structural system, and of a linear superimposed cosine waves.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.4
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• pp.700-705
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• 2008

In this paper, we propose object classification algorithm for real-time surveillance system. We have approached this problem using silhouette-based template matching. The silhouette of the object is extracted, and then it is compared with representative template models. Template models are previously stored in the database. Our algorithm is similar to previous pixel-based template matching scheme like Hausdorff Distance, but we use 1D image array rather than 2D regions inspired by Hilbert Path. Transformation of images could reduce computational burden to compute similarity between the detected image and the template images. Experimental results show robustness and real-time performance in object classification, even in low resolution images.

• Korean Journal of Logic
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• v.14 no.2
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• pp.1-38
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• 2011

Bernays has not drawn scholarly attention that he deserves. Only quite recently, the reevaluation of his philosophy, including the projects of editing, translating, and reissuing his writings, has just started. As a part of this renaissance of Bernays studies, this article tries to distinguish carefully between Hilbert's and Bernays' views regarding the axiomatic method. We shall highlight the fact that Hilbert was so proud of his own axiomatic method on textual evidence. Bernays' estimation of the place of Hilbert's achievements in the history of the axiomatic method will be scrutinized. Encouraged by the fact that there are big differences between the early middle Bernays and the later Bernays in this matter, we shall contrast them vividly. The most salient difference between Hilbert and Bernays will shown to be found in the problem of the uniformity of the axiomatic method. In the same vein, we will discuss the later Bernays' criticism of Carnap, for Carnap's project of philosophy of science in the late 1950's seems to be a continuation and an extension of Hilbert's faith in the uniformity of the axiomatic method.

• Smart Structures and Systems
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• v.17 no.5
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• pp.753-771
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• 2016

This paper addresses the free and transient responses of a SDOF linear complex stiffness system by making use of the Hilbert transform and the convolution integral. Because the second-order differential equation of motion having the complex stiffness give rise to the conjugate complex eigen values, its time-domain analysis using the standard time integration scheme suffers from the numerical instability and divergence. In order to overcome this problem, the transient response of the linear complex stiffness system is obtained by the convolution integral of a green function which corresponds to the unit-impulse free vibration response of the complex system. The damped free vibration of the complex system is theoretically derived by making use of the state-space formulation and the Hilbert transform. The convolution integral is implemented by piecewise-linearly interpolating the external force and by superimposing the transient responses of discretized piecewise impulse forces. The numerical experiments are carried out to verify the proposed time-domain analysis method, and the correlation between the real and imaginary parts in the free and transient responses is also investigated.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.545-551
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• 2008

We investigate the multiple solutions for a parabolic boundary value problem with jumping nonlinearity crossing no eigenvalues. We show the existence of the unique solution of the parabolic problem with Dirichlet boundary condition and periodic condition when jumping nonlinearity does not cross eigenvalues of the Laplace operator $-{\Delta}$. We prove this result by investigating the Lipschitz constant of the inverse compact operator of $D_t-{\Delta}$ and applying the contraction mapping principle.