• Communications of the Korean Mathematical Society
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• v.4 no.2
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• pp.349-358
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• 1989

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1996.06a
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• pp.209-212
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• 1996

In this paper, we propose to re-size images using an oblique projection operator instead of the orthogonal one in order to obtain faster, simpler, and more general algorithms. The main advantage is that it becomes perfectly feasible to use higher order models(e.g., splines of degree n 3). We develop the theoretical background and present a simple and practical implementation procedure that uses B-splines. Experiments show that the proposed algorithm consistently outperforms the standard interpolation method and that it essentially provides the same performance as the optimal procedure (least squares solution) with considerably less computations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.1
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• pp.55-66
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• 2004

First the notion of the A-monotonicity is applied to the approximation - solvability of a class of nonlinear variational inclusion problems, and then the convergence analysis is given based on a projection-like method. Results generalize nonlinear variational inclusions involving H-monotone mappings in the Hilbert space setting.

• East Asian mathematical journal
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• v.28 no.5
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• pp.561-567
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• 2012

The approximate solvability of a generalized system for relaxed cocoercive extended general variational inequalities is studied by using the project operator technique. The results presented in this paper are more general and include many previously known results as special cases.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.89-98
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• 1999

We propose some new iterative methods for solving the generalized variational inequalities where the underlying operator T is monotone. These methods may be viewed as projection-type meth-ods. Convergence of these methods requires that the operator T is only monotone. The methods and the proof of the convergence are very simple. The results proved in this paper also represent a signif-icant improvement and refinement of the known results.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.547-556
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• 2010

In this paper, we present the reprentation of all operators B which are Drazin invertible and sharing the spectral projections at 0 with a given Drazin invertible operator A. Meanwhile, some related results for EP operators with closed range are obtained.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.9-23
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• 2002

For a closed densely defined linear operator T on a Hilbert space H, let ${\prod}$ denote the function which corresponds to T, the orthogonal projection from $H{\oplus}H$ onto the graph of T. We extend some ordinary norm ineqralites comparing ${\parallel}{\Pi}(A)-{\Pi}(B){\parallel}$ and ${\parallel}A-B{\parallel}$ to the Schatten p-norm where A and B are bounded operators on H.

• Bulletin of the Korean Chemical Society
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• v.6 no.5
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• pp.309-311
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• 1985

When a molecule is perturbed by an external field, the perturbed moecue can be described as a doubly perturbed system. Hartree-Fock operator in the absence of the field is the zeroth order Hamiltonian, and a correlation operator and the external field operator are perturbations. The effective Hamiltonian, which is a projection of the total Hamiltonian onto a small finite subspace (usually a valence space), has been formally derived. The influence of the external field to the molecular Hamiltonian itself has been examined within an effective Hamiltonian framework. The first order effective expectation values, for instance electromagnetic transition amplitudes, between valence states are found to be easily calculated - by simply taking matrix elements of the effective external field operator. Implications of the terms in perturbation expansion are discussed.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.6C
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• pp.815-823
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• 2004

A hue-based attention operator and a combinational integral projection function(CIPF) are proposed to extract the normalized regions of face and facial features robustly against illumination variation. The face candidate regions are efficiently detected by using skin color filter, and the eyes are located accurately nil robustly against illumination variation by applying the proposed hue- and symmetry-based attention operator to the face candidate regions. And the faces are confirmed by verifying the eyes with the color-based eye variance filter. The proposed CIPF, which combines the weighted hue and intensity, is applied to detect the accurate vertical locations of the eyebrows and the mouth under illumination variations and the existence of mustache. The global face and its local feature regions are exactly located and normalized based on these accurate geometrical information. Experimental results on the AR face database［8］ show that the proposed eye detection method yields better detection rate by about 39.3% than the conventional gray GST-based method. As a result, the normalized facial features can be extracted robustly and consistently based on the exact eye location under illumination variations.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.513-525
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• 1996

Let the operator A be self-adjoint with domain, Dom(A), dense in $(H)$ which is a separable Hilbert space with norm $\left\$\mid$ \cdot \right\$\mid$$ and inner product $<\cdot, \cdot>$.