• 대한수학회지
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• 제45권6호
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• pp.1705-1723
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• 2008

Let n be a 2-step nilpotent Lie algebra which has an inner product <, > and has an orthogonal decomposition $n\;=z\;{\oplus}v$ for its center z and the orthogonal complement v of z. Then Each element z of z defines a skew symmetric linear map $J_z\;:\;v\;{\longrightarrow}\;v$ given by <$J_zx$, y> = for all x, $y\;{\in}\;v$. In this paper we characterize Jacobi fields and calculate all conjugate points of a simply connected 2-step nilpotent Lie group N with its Lie algebra n satisfying $J^2_z$ = A for all $z\;{\in}\;z$, where S is a positive definite symmetric operator on z and A is a negative definite symmetric operator on v.

• Kyungpook Mathematical Journal
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• 제62권2호
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• pp.229-242
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• 2022

In this paper, we introduce a new subclass of k-uniformly close-to-convex functions with respect to conjugate points. We study characterization, coefficient estimates, distortion bounds, extreme points and radii problems for this class. We also discuss integral means inequality with the extremal functions. Our findings may be related with the previously known results.

• 대한원격탐사학회:학술대회논문집
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• 대한원격탐사학회 2003년도 Proceedings of ACRS 2003 ISRS
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• pp.1467-1469
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• 2003

Image matching is fundamental process to identify conjugate points on the stereo images. However, standard methods or general solutions for matching problem have not been found yet, in spite of long history. Quality of the matching basically depends on uniqueness of the matching entity and robustness of the algorithm. In this study, conjugate points were extracted by implementing interest operator, then area based matching method was applied to the topographical characteristics of the gray value as the matching entities. The matching entities were utilized based on the concept of the intrinsic image.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.173-190
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• 2011

In this paper, we construct a new approach of affine scaling interior algorithm using the affine scaling conjugate gradient and Lanczos methods for bound constrained nonlinear optimization. We get the iterative direction by solving quadratic model via affine scaling conjugate gradient and Lanczos methods. By using the line search backtracking technique, we will find an acceptable trial step length along this direction which makes the iterate point strictly feasible and the objective function nonmonotonically decreasing. Global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions. Finally, we present some numerical results to illustrate the effectiveness of the proposed algorithm.

• East Asian mathematical journal
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• 제22권2호
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• pp.249-257
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• 2006

Let n be a 2-step nilpotent Lie algebra which has an inner product <,> and has an orthogonal decomposition $n=\delta{\oplus}\varsigma$ for its center $\delta$ and the orthogonal complement $\varsigma\;of\;\delta$. Then Each element Z of $\delta$ defines a skew symmetric linear map $J_Z:\varsigma{\rightarrow}\varsigma$ given by $=$ for all $X,\;Y{\in}\varsigma$. Let $\gamma$ be a unit speed geodesic in a 2-step nilpotent Lie group H(2, 1) with its Lie algebra n(2, 1) and let its initial velocity ${\gamma}$(0) be given by ${\gamma}(0)=Z_0+X_0{\in}\delta{\oplus}\varsigma=n(2,\;1)$ with its center component $Z_0$ nonzero. Then we showed that $\gamma(0)$ is conjugate to $\gamma(\frac{2n{\pi}}{\theta})$, where n is a nonzero intger and $-{\theta}^2$ is a nonzero eigenvalue of $J^2_{Z_0}$, along $\gamma$ if and only if either $X_0$ is an eigenvector of $J^2_{Z_0}$ or $adX_0:\varsigma{\rightarrow}\delta$ is not surjective.

• 한국측량학회지
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• 제37권2호
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• pp.55-62
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• 2019

The stereo geometry establishment based on the precise sensor modeling is prerequisite for accurate stereo data processing. Ground control points are generally required for the accurate sensor modeling though it is not possible over the area where the accessibility is limited or reference data is not available. For the areas, the relative orientation should be carried out to improve the geometric consistency between the stereo data though it does not improve the absolute positional accuracy. The relative orientation requires conjugate points that are well distributed over the entire image region. Therefore the automatic conjugate point extraction is required because the manual operation is labor-intensive. In this study, we applied the method consisting of the key point extraction, the search space minimization based on the epipolar line, and the rigorous outlier detection based on the RPCs (Rational Polynomial Coefficients) bias compensation modeling. We tested different parameters of window sizes for Kompsat-2 across track stereo data and analyzed the RPCs precision after the bias compensation for the cases whether the epipolar line information is used or not. The experimental results showed that matching outliers were inevitable for the different matching parameterization but they were successfully detected and removed with the rigorous method for sub-pixel level of stereo RPCs precision.

• 대한원격탐사학회:학술대회논문집
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• 대한원격탐사학회 2005년도 Proceedings of ISRS 2005
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• pp.683-686
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• 2005

This study addresses a photogrammetric approach to generate Mars topographic products from mapping data of Mars Global Surveyor (MGS). High-resolution stereo images and laser altimetry data collected from the MGS mission are combined and processed to produce Digital Elevation Models (DEM) and orthoimages. First, altimeter data is registered to high resolution images and considerable registration offset (around 325 m) is discovered on high resolution stereo images. Altimetry data, exterior orientation elements of the camera and conjugate points are used for bundle adjustment to solve this mis-registration and detennine the ground coordinates. The mis-registration of altimetry data are effectively eliminated after the bundle adjustment. Using the adjusted exterior orientation the ground coordinates of conjugate points are detennined. A sufficient number of corresponding points collected through image matching and their precise 3-D ground coordinates are used to generate DEM and orthoimages. A posteriori standard deviations of ground points after bundle adjustment indicate the accuracy of OEM generated in this study. This paper addresses the photogrammetric procedure: the registration of altimetry data to stereo pair images, the bundle adjustment and the evaluation, and the generation of OEM and orthoimages.

• 대한수학회논문집
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• 제10권2호
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• pp.365-374
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• 1995

On a compact manifold without conjugate points, the volume entropy can be obtained as the average mean curvature of the horospheres in the universal covering space. In the case when the volume entropy is zero, we prove that the universal covering space is diffeomorphic to a product space with a line factor. This fact can be considered as a surporting evidence for the Mane's conjecture, which claims the flatness of the mainfold.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권4호
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• pp.309-321
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• 2004

For a complete open Riemannian manifold, the ideal boundary consists of points at infinity. The so-called Busemann-functions play the role of distance functions for points at infinity. We study the similarity and difference between Busemann-functions and ordinary distance functions.

• 한국인쇄학회지
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• 제20권1호
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• pp.113-122
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• 2002

We designed the illumination optical system to use Fresnel lens which is the most general type of large aperture system. The normal construction of Fresnel lens is a thin molded piece of material, usually some kind of plastic, with one side flat and the other comprising a series of concentric segments each angled in a way to provide for optimum focusing for a pair of conjugate points. The 155 mm Marine Signal Lantern is the approved for use on buoys and a maximum omnidirectional range of 8 nmi, can be obtained with standard 12V equipment, respectively. Finally, Fresnel lens with 155 mm diameter was designed and evaluated. Also, we re-designed groove "out" of Fresnel lens and compared results of groove "in" type with groove "out" type. According to the results, Fresnel lens is obtained best optical results when grooved side faces the longer conjugate.de faces the longer conjugate.