• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.183-200
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• 2015

In this paper, we define the directional associated curve and the self-associated curve of a null curve in Minkowski 3-space. We study the properties and relations between the null curve, its directional associated curve and its self-associated curve. At the same time, by solving certain differential equations, we get the explicit representations of some null curves.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.885-899
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• 2013

In this paper, we study null helices, null slant helices and Cartan slant helices in $\mathb{E}^3_1$. Using some associated curves, we characterize the null helices and the Cartan slant helices and construct them. Also, we study a space-like curve with the principal normal vector field which is a degenerate plane curve.

• Communications of the Korean Mathematical Society
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• v.15 no.3
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• pp.533-540
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• 2000

In the present paper, we study a non-degenrate ruled surface along a null curve in a 3-dimensional Minkowski space E31, which is called a null scroll, an investigate some characterizations of null scrolls satisfying the condition H=AH, A Mat(3, ), where denotes the Laplacian of the surface with respect to the induced metric, H the mean curvature vector and Mat(3, ) the set of 3$\times$3-real matrices.

• Korean Journal of Optics and Photonics
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• v.11 no.4
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• pp.246-249
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• 2000

The null lens is designed for testing the elliptical (conic constant>O) mirror which is the third mirror of the off-axis Three Mirror Anastigmat (TMA) designed as a high resolution camera for remote sensing. The mixed type design is proposed as a new design type which has a small annular flat mirror, but has as twice sensitivity as the autostigmatic type design. It is also shown that the null lens of the Mixed type is better than that of the autostigmatic type in terms of the sensitivity of the wavefront distortion which is given as the magnitude of optical path difference with respect to the change of each surface parameters such as the radius of curvature, thickness of lenses and tested mirror.

• Korean Journal of Optics and Photonics
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• v.15 no.3
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• pp.254-257
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• 2004

A null optical system for monitoring the alignment of the optical beam director is proposed instead of the conventional autocollimator alignment system. A null optical system for the optical beam director of aperture 30 cm is designed and its performance is analysed.

• Korean Journal of Optics and Photonics
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• v.12 no.5
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• pp.352-355
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• 2001

A null lens is designed for testing the hyperbolic mirror which is the first mirror of the off-axis three mirror anastigmat(TMA) designed as a high resolution camera for remote sensing. To choose a better null lens system for the hyperbolic surface under test, both autostigmatic and mixed type null lenses are designed and analysed for sensitivity with respect to change of each surface parameter such as the radius of curvature and the thickness.

• The Journal of the Acoustical Society of Korea
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• v.25 no.4E
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• pp.142-147
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• 2006

Blind signal separation is known as a powerful tool for enhancing noisy speech in many real world environments. In this paper, it is demonstrated that the performance of blind signal separation can be further improved by combining with a null beamformer (NBF). Cascading the blind source separation with null beamforming is equivalent to the decomposition of the received signals into the direct parts and reverberant parts. Investigation of beam patterns of the null beamformer and blind signal separation reveals that directional null of NBF reduces mainly direct parts of the unwanted signals whereas blind signal separation reduces reverberant parts. Further, it is shown that the decomposition of received signals can be exploited to solve the local stability problem. Therefore, faster and improved separation can be obtained by removing the direct parts first by null beamforming. Simulation results using real office recordings confirm the expectation.

• Korean Journal of Optics and Photonics
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• v.17 no.2
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• pp.186-190
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• 2006

The use of null optics is proposed as a new concept for the precise alignment of a confocal unstable resonator. The characteristics of the proposed null optics are investigated and analysed with the designed null lens for a real confocal unstable resonator of which the length is 3.5 m. As a result of the analysis, the pupil map data are shown about the despace error of 1.0 mm and tilt error of 1.0 mrad.

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.15-21
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• 2005

Null designs on the poset of dual polar spaces are considered. A poset of dual polar spaces is the set of isotropic subspaces of a finite vector space equipped with a nondegenerate bilinear form, ordered by inclusion. We show that the minimum number of isotropic subspaces to construct a nonzero null t-design is ${\prod}^{t}_{i=0}(1+q^{i})$ for the types $B_N,\;D_N$, whereas for the case of type $C_N$, more isotropic subspaces are needed.

• Honam Mathematical Journal
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• v.26 no.3
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• pp.341-353
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• 2004

We denote by ${{\mathcal{Q}}(A)}$ the set of all matrices with the same sign pattern as A. A matrix A has signed null-space provided there exists a set ${\mathcal{S}}$ of sign patterns such that the set of sign patterns of vectors in the null-space of ${\tilde{A}}$ is ${\mathcal{S}}$, for each ${\tilde{A}}{\in}{{\mathcal{Q}}(A)}$. Some properties of matrices with signed null-spaces are investigated.