• Structural Engineering and Mechanics
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• v.34 no.1
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• pp.85-95
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• 2010

In this paper, numerical solution of the singular integral equation for the multiple curved branch-cracks is investigated. If some quadrature rule is used, one difficult point in the problem is to balance the number of unknowns and equations in the solution. This difficult point was overcome by taking the following steps: (a) to place a point dislocation at the intersecting point of branches, (b) to use the curve length method to covert the integral on the curve to an integral on the real axis, (c) to use the semi-open quadrature rule in the integration. After taking these steps, the number of the unknowns is equal to the number of the resulting algebraic equations. This is a particular advantage of the suggested method. In addition, accurate results for the stress intensity factors (SIFs) at crack tips have been found in a numerical example. Finally, several numerical examples are given to illustrate the efficiency of the method presented.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.2
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• pp.883-900
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• 2017

In this paper block based blind secure gray image watermarking scheme based on discrete wavelet transform and singular value decomposition is proposed. In devising the proposed scheme, security is given high importance along with other two requirements: robustness and imperceptibility. The use of discrete wavelet transform not only improves robustness but the selection of bands with high tolerance towards noise caused an improvement in terms of imperceptibility. The robustness further improved due to the involvement of singular vectors along with singular values in watermark embedding and extraction process. Finally, to achieve security, the selected DWT band is decomposed into smaller blocks and random blocks are chosen for modification. Furthermore, the elements of left and right singular vectors of selected blocks are chosen based on their dependence upon each other for watermark embedding. Various experiments using different images as host and watermark were conducted to examine and validate the proposed technique. Additionally, the proposed technique is tested against various attacks like compression, affine transformation, cropping, translation, X shearing, scaling, Y shearing, filtering, blurring, different kinds of noises, histogram equalization, rotation, etc. Lastly, the proposed technique is compared with state-of-the-art watermarking techniques and their comparison shows significant improvement of proposed scheme over existing techniques.

• The Journal of the Acoustical Society of Korea
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• v.20 no.8
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• pp.3-11
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• 2001

This paper describes an implementation of inverse filter using SVD in order to recover the input in multi-channel system. The matrix formulation in SISO system is extended to MIMO system. In time and frequency domain we investigates the inversion of minimum phase system and non-minimum phase system. To execute an effective inversion of non-minimum phase system, SVD is introduced. First of all we computes singular values of system matrix and then investigates the phase property of system. In case of overall system is non-minimum phase, system matrix has one (or more) very small singular value (s). The very small singular value (s) carries information about phase properties of system. Using this property, approximate inverse filter of overall system is founded. The numerical simulation shows potentials in use of the inverse filter.

• East Asian mathematical journal
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• v.36 no.5
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• pp.583-591
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• 2020

In [8, 9] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with corner singularities, compute the finite element solutions using standard Finite Element Methods and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. The error analysis was given in [5]. In their approaches, the singular functions and the extraction formula which give the stress intensity factor are the basic elements. In this paper we consider the biharmonic problems with the cramped and/or simply supported boundary conditions and get the singular functions and its duals and find properties of them, which are the cornerstones of the approaches of [8, 9, 10].

• Honam Mathematical Journal
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• v.40 no.4
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• pp.785-794
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• 2018

In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous Dirichlet boundary condition with one corner singularity at the origin, and compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. This approach uses the polar coordinate and the cut-off function to control the singularity and the boundary condition. In this paper we consider Poisson equations with multiple singular points, which involves different cut-off functions which might overlaps together and shows the way of cording in FreeFEM++ to control the singular functions and cut-off functions with numerical experiments.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.335-341
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• 2008

In this paper, we use the convexity of distance function between geodesics in a singular Hadamard space to generalize Hadamard-Cartan theorem for 2-dimensional metric spaces. We also determine a neighborhood of a closed geodesic where no other closed geodesic exists in a complete space of nonpositive curvature.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.17-28
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• 1999

A new procedure of the boundary element method(BEM),say, singular BEM for the potential problems with singularities is presented. To obtain the numerical solution of which asymptotic behavior near the singularities is close to that of the analytic solution, we use particular elements on the boundary segments containing singularities. The Motz problem and the crack problem are taken as the typical examples, and numerical results of these cases show the efficiency of the present method.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.1028-1033
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• 1992

Loop shaping techniques are developed for the LQG/LTR controller design of singular multivariable sytems. One approach is to use the mode form of plant and the other is to replace the eigenvalues at 0 by ones at .epsilon.(.rarw.0). These two concepts for the target filter loop design are applied to a flight autopilot. And it is shown that these techniques are effective ones for the desired loop-shaping of singular multivariable systems.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.875-888
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• 1998

The use of the zeros of Chebyshev polynomial of the first kind $T_{4n＋4(x}$ ) and second kind $U_{2n＋1}$ (x) for Gauss-Chebyshev quad-rature and collocation of singular integral equations of Cauchy type yields computationally accurate solutions over other combinations of $T_{n}$ /(x) and $U_{m}$(x) as in [8]. We show that the coefficient matrix of the overdetermined system has the generalized inverse. We estimate the residual error using the norm of the generalized inverse.e.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1762-1765
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• 1997

Some ill-conditioned processes are very sensitive to small element-wise uncertainties arising in classical element-by-element model identifications. For such processes, accurate identification of simgular values and right singular vectors are more important than theose of the elements themselves. Singular values and right singular vectors can be found by iteraive identification methods which implement the input and output transformations iteratively. Methods based on SVD decomposition, QR decomposition and LU decomposition are proposed and compared with the Kuong and Mac Gregor's method. Convergence proofs are given. These SVD and QR mehtods use normal matrices for the transformations which cannot be calculated analytically in general and so they are hoard to apply to dynamic processes, whereas the LU method used simple analyitc transformations and can be directly applied to dynamic processes.